\section{Introduction}





In the $\Lambda$CDM model of structure formation, dark matter halos form from the gravitational collapse of primordial density fluctuations. Within these halos, baryons collapse into a rotating disc with the same angular momentum as the dark matter halo.  With sufficient radiative cooling, the gas is able to collapse and form stars, resulting in a co-rotating disc of gas and stars within a dark matter halo with a density profile which can be approximated by a simple formula (Navarro, Frenk \& White 1996, 1997).  On large scales, the $\Lambda$CDM model of structure formation agrees well with observations of massive galaxies and clusters.  

However, large discrepancies in the low-mass regime raise doubts about $\Lambda$CDM.  For example, there is a large disagreement between the number of small dark matter halos and observed dwarfs \citep[missing satellite problem,][]{Moore1999,Klypin1999}.  There is also a conspicuous absence of observed large satellites compared to predictions \citep[too big to fail problem,][]{Read2006,Boylan-Kolchin2011}.  Finally, rotation profiles of dwarfs show a variety of inner slopes, indicating a diversity of dark matter halo profiles, many of which are in disagreement with the predicted NFW dark matter density profile \citep[cusp vs. core problem,][]{Flores1994,Simon2005,Oh2011}.  These departures from the $\Lambda$CDM model have prompted some to look into warm \citep[e.g.][]{Lovell2014} or self-interacting dark matter \citep[e.g.][] {Rocha2013}.  A promising alternative to re-thinking the nature of dark matter is to investigate the effects of baryonic feedback on star formation.  
        
High resolution simulations conclude that baryonic processes can be used to reconcile the observed properties of dwarf galaxies with $\Lambda$CDM \citep{Wetzel2016ApJ...827L..23W}.  Theoretical work commonly attributes star formation suppression in dwarf galaxies to heating from the UV background during reionization  \citep[e.g.][]{Katz2020}, stellar radiation \citep[e.g.][]{Emerick2018}, and supernovae feedback \citep[e.g.][]{Hu2019}.  Indeed, powerful star-formation driven outflows are observed in starbursting dwarf galaxies \citep[][]{Martin1998,Strickland_Stevens_2000}, and some observational evidence suggests that stellar feedback may dominate in dwarf galaxies \citet{Navarro2018}. 


Stellar feedback is only part of the picture, as the role of AGN feedback in dwarfs becomes harder to ignore.  Evidence of AGN via optical and infrared (IR) indicators has been detected in hundreds of nearby dwarf galaxies \citep[][]{Reines2013,Moran2014,Sartori2015,Baldassare2020,Birchall2020}.  \citet{Kaviraj2019} report the IR-selected AGN occupation fraction in high mass galaxies to be $1-3\%$, while the same criteria yield a $10-30\%$ fraction in dwarf galaxies ($M_* \sim 10^{8-10} M_\odot$).  Given that there are several factors that hinder the detection of AGN in dwarfs \citep{Satyapal2018, Cann2019}, this large AGN fraction can be regarded as a lower limit.  These studies suggest that AGN are common and potentially important phenomena in the low mass regime.  

Additionally, observational evidence of AGN-driven outflows in dwarf galaxies has begun to surface \citep{Penny2018,Bradford2018,Dickey2019,Manzano2019}.  Each of these studies present observations of AGN coexisting with kinematically disturbed gas.  Such disturbances are distinguished by broadened components in their emission line profiles and velocity measurements indicating gas that is disconnected or even counter-rotating with respect to their stars. For example, \citet{Starkenburg2019} (henceforth S19) use data from Illustris \citep{Vogelsberger2014a,Genel2014} to investigate the origin of star-gas counter-rotation in dwarf galaxies.  By examining the evolutionary history of simulated galaxies with counter-rotating gas, they found that such counter-rotating components require removal of the original gas reservoir and re-accretion of new gas, with misaligned angular momentum.  S19 identify two plausible mechanisms for gas removal: stripping from an encounter with a neighbouring galaxy, or AGN outflow events.

The role of AGN feedback in galaxy formation and evolution is not well understood in general.  The shallow potential wells of dwarf galaxies leave them particularly susceptible to feedback, making them ideal laboratories to study how the energy output of an AGN couples to the gas in the host galaxy.  The discovery of AGN-driven outflows in the dwarf regime challenges current conceptions of feedback in dwarf galaxies and raises the question of whether the gas in these outflows permanently escapes the halo.  In this paper, we explore the connection between AGN and kinematically disturbed gas and present further evidence of AGN feedback in dwarf galaxies.

Throughout the paper we assume the cosmological model $H_0 = 71\,\rm{km}\,\rm{s}^{-1}\,\rm{Mpc}^{-1}$, $\Omega_m = 0.27$, and $\Omega_\Lambda = 0.73$.


\section{Data}\label{sec:Data}

\begin{figure
\includegraphics[width=0.49\textwidth]{./figures/bpt_hist.pdf}
\caption{Top: BPT diagnostic for all 50 galaxies in this sample. The dotted line denotes the \citet{kauffmann2003} classification cutoff, and the solid line is the \citet{kewley2001} maximum starburst line. Blue circles indicate isolated galaxies with disturbed gas and with no neighbours of comparable mass (i.e. the neighbouring galaxy is at least 0.75 times the stellar mass of the dwarf) within 1.5 Mpc (see Section \ref{sec:environment}).  Galaxies with counter-rotating stellar and gas components are marked as orange triangles.
Bottom:Stacked histograms of redshift and stellar mass of the galaxies presented in this paper. Dark gray represents AGN hosts and light gray represents star forming galaxies.
}
\label{fig:bpthist}
\end{figure}

\begin{center}
\begin{figure}
\includegraphics[width=\linewidth,clip]{figures/all__thumb.pdf}
\caption{colour images of all 50 dwarf galaxies in our sample.  All images were generated using the SDSS DR12 finding chart tool, with the exception of NGC 1569, which is outside of the SDSS footprint.  The NGC 1569 thumbnail (second row, second column) is a PanSTARS z,g band colour image rendered in the Aladin Lite Viewer with a 3' field of view ($\sim 1\,$kpc on a side).  Each SDSS image is scaled to 10 kpc on a side and the placement of the 1 arcsecond-wide slit is shown in light gray.  
}
\label{fig:thumbs}
\end{figure}
\end{center}

Our complete sample contains 50 nearby ($z=0.05$) dwarf galaxies (roughly $M_\star < 10^{10} M_\odot$) drawn from the Sloan Digital Sky Survey (SDSS).  SDSS is 95\% complete to $r$ band magnitude of 22.2, which is well below the magnitude range covered in this sample ($r\approx 12-17)$.  Twenty-nine of the galaxies in our sample are classified as AGN based on emission line flux ratios that fall above the \citet{kauffmann2003} star forming sequence on the Baldwin, Phillips \& Terlevich (BPT) diagnostic \citep{baldwin1981} or the presence of detectable \ion{He}{II} emission \citep{shirazi2012}.  This sample of 29 dwarf galaxies hosting AGN was selected from the parent samples of \citet{Reines2013,Moran2014,Sartori2015,Oh2015} based on right ascensions that could be observed during our allotted Keck time.   In order to facilitate spatially resolved kinematic measurements, we prioritized spatially extended galaxies and excluded face-on galaxies whenever possible.  

To enable comparison between galaxies with and without AGN, we selected a control sample of 21 star forming galaxies from SDSS Data Release 8, based on their absence of optical and infrared (IR) signatures of AGN.  The control sample was selected by applying the same stellar mass and redshift cuts used to build the AGN sample, then excluding objects with emission line flux ratios falling above the star forming sequence on the BPT diagram.  We also excluded all potential AGN using the WISE mid-IR colour criteria \citep{Jarrett2011, stern2012} and further excluded all galaxies with detectable \ion{He}{II} emission.  The BPT diagnostic diagram and distributions of the redshifts and stellar masses of our full sample are shown in Figure \ref{fig:bpthist}.  


We collected long-slit spectroscopy of 50 galaxies using the Low Resolution Imaging Spectrometer on the Keck I telescope \citep[LRIS][]{Oke_1995,Rockosi2010}. 
Observation dates, conditions, and spectrograph setups for each object are listed in Table \ref{tab:obs_setups}.  The DIMM seeing (Full Width at Half Maximum value of a star observed at zenith, at 5000\AA) is listed for each night. The slit position angles (PA) were determined by fitting $r-$band SDSS photometry using the IRAF ellipse task.  By placing the slit along the semi-major axes determined by these ellipse fits, as shown in Figure \ref{fig:thumbs}, we obtained spatially resolved spectra, presumably perpendicular to the rotation axis of each galaxy.








\newpage
\begin{table*}
\centering
\begin{tabular}{| l c c c c c c c c c c c|}
\hline
Name in SDSS & Observation Date  & Seeing  & slit PA& red setup & exposure time \\ 
& & $\arcsec$ & CCW N&&  s \\ 
\hline
J002145.80+003327.3   & 2015-12-05 &  0.59  &  42.4   & B & 1200 \\
J004214.99$-$104415.0 & 2015-12-04 &  0.55  &  26.9   & B & 1200 \\
J010005.94$-$011059.0 & 2015-12-04 &  0.55  &  51.2   & B & 1200 \\
J015645.30-003737.8   & 2015-12-04 &  0.55  &  126    & B & 1200 \\
J024656.39-003304.8*  & 2015-12-04 &  0.55  &  131.9  & B & 1200 \\
J030040.20+000113.3   & 2015-12-04 &  0.55  &  28.3   & B & 2400 \\
NGC 1569*             & 2015-12-04 &  0.55  &  122.5  & B & 2400 \\
J075538.19+240103.5   & 2015-12-04 &  0.55  &  0      & B & 2400 \\
J080212.06+103234.1   & 2015-12-05 &  0.59  &  100.7  & B & 2400 \\
J080228.83+203050.2   & 2015-12-04 &  0.55  &  73.3   & B & 2400 \\
J081145.29+232825.7   & 2015-12-04 &  0.55  &  0      & B & 2400 \\
J081256.37+545808.4   & 2015-12-05 &  0.59  &  32.77  & B & 1200 \\
J084025.54+181858.9   & 2015-12-04 &  0.55  &  101    & B & 2400 \\
J084234.51+031930.7   & 2015-12-05 &  0.59  &  0      & B & 1200 \\
J085125.81+393541.7   & 2015-03-24 &  0.70  & -43.96  & C & 1200 \\
J090613.75+561015.5   & 2015-12-04 &  0.55  &  0      & B & 2400 \\
J091122.24+615245.2   & 2015-03-24 &  0.70  &  -13    & C & 2400 \\
J092149.44+233438.7   & 2015-12-05 &  0.59  &  156.3  & B & 1200 \\
J093251.11+314145.0   & 2015-03-25 &  0.58  &  -94.6  & B & 1200 \\
J094800.79+095815.4   & 2015-12-05 &  0.59  &  117.8  & B & 1200 \\
J094941.20+321315.9   & 2015-12-04 &  0.55  &  64     & B & 1200 \\
J095418.16+471725.1   & 2015-12-05 &  0.59  &  0      & B & 2400 \\
J100200.96+591508.3   & 2015-12-04 &  0.55  &  148.5  & B & 1200 \\
J100551.19+125740.6   & 2015-12-04 &  0.55  &  60.1   & B & 1200 \\
J100935.66+265648.9   & 2015-12-05 &  0.59  &  45.5   & B & 1200 \\
J101440.21+192448.9   & 2015-03-25 &  0.58  & -57.58  & B & 1200 \\
J114343.76+550019.2   & 2015-03-25 &  0.58  & -117.58 & B & 1200 \\
J122342.82+581446.2*  & 2015-03-24 &  0.70  & -106.86 & C & 1200 \\
J130724.63+523715.2   & 2015-03-25 &  0.58  &  74.09  & B & 2400 \\
J131503.77+223522.7*  & 2015-03-24 &  0.70  &  -144.8 & C & 1200 \\
J134332.09+253157.7   & 2015-03-24 &  0.70  &  -21.33 & C & 2400 \\
J140116.03+542507.4   & 2015-03-25 &  0.58  &  81.76  & B & 1200 \\
J140228.72+091856.4   & 2017-06-24 &  1.17  &  120    & B & 1200 \\
J140510.39+114616.9   & 2017-06-25 &  0.85  &  12     & A & 1200 \\
J140735.47+503242.7   & 2017-06-25 &  0.85  &  163    & A & 2400 \\
J141208.47+102953.8   & 2017-06-24 &  1.17  &  0.0    & B & 1200 \\
J144252.78+205451.6   & 2017-06-24 &  1.17  &  101    & B & 1200 \\
J145843.39+113745.4   & 2017-06-25 &  0.85  &  19     & A & 1200 \\
J151116.53+233421.6   & 2017-06-25 &  0.85  &  165    & A & 1200 \\
J154603.78+031339.4   & 2017-06-24 &  1.17  &  31     & B & 1200 \\
J160839.57+120038.5   & 2017-06-25 &  0.85  &  174    & A & 1200 \\
J162307.88+391847.5   & 2017-06-24 &  1.17  &  80     & B & 1200 \\
J162335.06+454443.6   & 2017-06-25 &  0.85  &  40     & A & 1200 \\
J164428.48+435904.2   & 2017-06-24 &  1.17  &  82     & B & 1200 \\
J170639.14+334103.4   & 2017-06-25 &  0.85  &  156    & A & 1200 \\
J171759.66+332003.8   & 2017-06-24 &  1.17  &  68     & B & 1200 \\
J172125.92+281134.9   & 2017-06-24 &  1.17  &  168    & B & 1200 \\
J172208.82+280155.8   & 2017-06-24 &  1.17  &  130    & B & 1200 \\
J232028.21+150420.9*  & 2015-12-04 &  0.55  &  122.2  & B & 1200 \\
\hline
\end{tabular}
\caption{LRIS configuration for each object, using the 1$\arcsec$ slit placed along the semimajor axis of each galaxy.  For  the  blue  side  (LRIS-B),  we  used  the  600 groove mm$^{-1}$ grism blazed at 4000\AA, yielding a dispersion  of  0.63\AA\, pixel$^{-1}$.  We used three setups on the red side (LRIS-R):\newline
A: 600 groove mm$^{-1}$ grating blazed at 5000\AA, 5600\AA\, dichroic, yielding a dispersion of 0.80\AA\,pixel$^{-1}$\newline
B: 900 groove mm$^{-1}$ grating blazed at 5500\AA, 5600\AA\, dichroic, yielding a dispersion of 0.53\AA\,pixel$^{-1}$\newline
C: 1200 groove mm$^{-1}$ grating blazed at 7500\AA, 5000\AA\, dichroic, yielding a dispersion of 0.40\AA\,pixel$^{-1}$}
\label{tab:obs_setups}
\end{table*}
\newpage



The LRIS data were reduced using a Python pipeline to automate the standard IRAF reduction tasks.  Flexure on the red camera was corrected using the average shift in sky lines.  Sky lines are sparse in the wavelength range covered by the blue CCD, so each galaxy spectrum on the blue side was redshift-corrected using the redshift measured from the flexure-corrected red spectrum.  Flexure on the blue CCD was then calculated by comparing redshift-corrected galaxy emission lines with their expected rest frame values.  The longslit spectra were rectified along both the wavelength and spatial axes, yielding 2-dimensional spectra where each pixel row along the spatial axis is a fully reduced 1-dimensional spectrum. 




\section{Analysis}
\label{sec:analysis}


\subsection{Spatially Resolved Spectra}
\label{sec:binning}
The longslit spectra have been rectified along both the wavelength and spatial axes, creating a 2D spectrum where each pixel row is a fully reduced 1D spectrum.  Much of our analysis depends on fitting subtle spectral features, and thus require high signal to noise (S/N), especially in the dim outskirts of each galaxy.  To achieve the required S/N, we spatially bin the spectra, using larger bins on the outskirts of the galaxy, as shown in Figure \ref{fig:bin_example}.

Spectra were extracted along the slit by summing pixel rows until the target S/N ratio (typically 15$-$20) or maximum bin size was reached. In order to prevent summing the entire image and losing spatial data, the maximum bin size is set to be 20\% of the spatial axis.  The signal to noise was measured using the mean and standard deviation of a relatively featureless portion of the stellar spectrum, just red-ward of [\ion{O}{III}]$\lambda5007$.  The next bin would begin at the central pixel of the last bin.  Figure \ref{fig:bin_example} shows the signal to noise of each pixel row along the spatial axis (black). Vertical gray lines mark the divisions between bins, and the green line indicates the signal to noise when all pixel rows within each bin is summed.

\begin{center}
\begin{figure}
\includegraphics[width=\linewidth,clip]{figures/bin_example.pdf}
\caption{Pixel number along the spatial axis is shown on the x axis.  The y axis shows the signal to noise ratio of a featureless portion of the spectrum red-ward of [\ion{O}{III}]$\lambda$5007.  Moving along the slit, we summed pixel rows (black) until the integrated spectrum's signal to noise ratio (green) reached the target S/N (red) or the maximum bin size was reached. The minimum bin size is 3 pixel rows, which sometimes results in even higher S/N.  Exposure times for each object were chosen with the intention of obtaining sufficient S/N in the outskirts, so the bin size is dependent on the observational setup used.
}
\label{fig:bin_example}
\end{figure}
\end{center}



\subsection{Emission Line Fluxes}
\label{sec:emission}
In order to measure accurate emission line fluxes, it is necessary to account for stellar absorption, which primarily affects the Balmer emission lines. The Penalized Pixel-Fitting software (\textsc{ppxf}) \citep{Cappellari2017} is used to fit and subtract the stellar continuum following the method described in \citet{Manzano2019} (henceforth Paper I), Section 3.1.  

After subtracting the best-fitting stellar population model of the galaxy, the residual emission lines were fit using a custom Bayesian MCMC maximum likelihood sampling algorithm, implemented using the Python package {\it emcee} \citep{emcee}.  A single-Gaussian model was used to fit emission lines for each galaxy in this sample, except in 13 cases when a second Gaussian component was needed (Paper I).  In these 13 cases the BPT flux ratios of the narrow component of the emission lines are shown in Figure \ref{fig:bpthist} and used when classifying these galaxies as AGN or star forming.



\subsection{Multi-Component Velocity Measurements}
\label{sec:ppxf}

In the \textsc{ppxf} software, emission lines are modeled as Gaussians and fit simultaneously with stellar templates.  Each stellar and gas template can be matched to a unique kinematic component, enabling the decomposition of multiple distinct line of sight velocities for stars and various species of emission lines.  Each spatially resolved velocity measurement presented in this work consists of three components: stellar, ionized hydrogen, and forbidden gas emission.

To avoid systematic errors introduced by wavelength calibration on the blue CCD, we fit $\sim 1000$\AA\, sections of the spectrum using \textsc{ppxf}.  Due to the strength of the H$\beta$ and [\ion{O}{III}] emission lines, and their proximity to the stellar feature MgIb, we measured line of sight velocities using the spectral region at rest wavelength $4500 - 5560$\AA\, whenever favorable.  Five galaxies were observed using the 5000\AA\, dichroic, which disrupts the H$\beta$, [\ion{O}{III}] region of the spectrum.  In these cases, stellar and gas kinematics were measured by fitting the portion of the spectrum containing [\ion{O}{II}] and  Balmer break ($3650 - 4550$\AA).  In cases where the [\ion{O}{III}] lines were faint, the fitting area containing H$\alpha$, [\ion{N}{II}], and [\ion{S}{II}] ($6400-6800$\AA) enabled gas velocity measurements to extend to a larger radius than fitting the $4500 - 5560$\AA\, region.  An example of fits to these three regions is shown in Figure \ref{fig:fit_example}.  

Thirteen galaxies in our sample have gas profiles that cannot be accurately modeled by a single Gaussian.  In these cases, two Gaussian components were used for each emission line: a narrow and a broad.  The velocity measurements presented in this work were obtained from the narrow Gaussian components.

\begin{center}
\begin{figure}
\includegraphics[width=\linewidth,clip]{figures/ppxf_example.pdf}
\caption{Example \textsc{ppxf} fits to each of the three spectral sections used to determine velocity curves.  Each velocity curve consists of three components: stellar (red), hydrogen (orange), and forbidden (purple, green, and blue).}
\label{fig:fit_example}
\end{figure}
\end{center}


\subsection{Circular Velocity Curves}
\label{sec:vcurves}
We extracted spatially resolved spectra along the semimajor axis of each galaxy by summing pixel rows, as described in Section \ref{sec:binning}.  Multicomponent line of sight velocity measurements were then taken from each spectrum following the method outlined in Section \ref{sec:ppxf}.  To convert line of sight velocity measured in \textsc{ppxf} into rotational velocity, we correct for the disc inclination angle (see Appendix \ref{app:incl}).  Zero velocity is measured at the galaxy's kinematic center, which is determined by the point of symmetry in the stellar velocity curve.  

Figure \ref{fig:rotation_example1} shows the resulting rotational velocity curve for J170639.14+334103.4  as an example.  Stellar velocity measurements are plotted as gray stars and the ionized gas velocities for H$\beta$ and [\ion{O}{III}] are shown as orange and teal circles, respectively.  $r_{50}$ refers to the 50\% SDSS r-band Petrosian radius. The gray shaded region shows the analytic prediction of the rotation curve assuming the dark matter halo follows an NFW density profile (see Section \ref{subsec:nfw}). 


\section{Results}
\label{sec:Results}
\begin{figure}
	\includegraphics[width=\columnwidth]{./figures/rotation_example_single.pdf}
    \caption{The object J170639.14+334103.4 was chosen randomly from our sample to provide an example of an orderly rotation curve, with a co-rotating disc of gas and stars.  The stellar (gray stars), H$\beta$ (orange circles) and [\ion{O}{III}] (teal circles) velocities are shown as a function of normalized radius, where $r_{50}$ is the r-band Petrosian 50\% radius.  The dotted black line indicates the expected velocity curve for an NFW profile with concentration parameter $c=10$.  The shaded gray region represents the NFW curve expected from halos with concentration parameter $c=8-15$.}
    \label{fig:rotation_example1}
\end{figure}
We obtained circular velocity curves for the stellar and ionized gas components of all 50 galaxies.  Five galaxies are excluded from the rest of this analysis based on the limited spatial extent of their stellar velocity curves.  For three galaxies (J024656.39-003304.8, J131503.77+223522.7, and J232028.21+150420.9), the spatial extent of their velocity curves were comparable (within 0.3\arcsec) with the seeing.  NGC 1569 was excluded because the slit only covered the central 0.25 kpc of the galaxy.  J122342.82+581446.2 was excluded because we were unable to achieve a sufficient S/N ratio to obtain more than two stellar velocity measurements.
Rotation curves for the remaining 45 galaxies (26 AGN and 19 star forming) included in this analysis are shown in Appendix \ref{app:curves}.  



\subsection{Comparison with NFW}
\label{subsec:nfw}

\begin{figure}
	\includegraphics[width=\columnwidth]{./figures/cusp-core.pdf}
    \caption{Four stellar absolute circular velocity curves are shown to demonstrate the variety of inner slopes found in our sample. Two examples of AGN are displayed in the left panels and two star forming galaxies are shown on the right.  Dashed black lines and shaded gray regions represent NFW velocity curves corresponding to a halo mass determined by abundance matching, with the MPA-JHU stellar mass as input.  Stellar velocity curves showing agreement with the expected NFW profile are shown on the top two panels. The velocity profiles in the bottom panels rise slowly, indicating cored dark matter density profiles.  }
    \label{fig:cusp-core}
\end{figure}

The $\Lambda$CDM model predicts that dark matter halos will follow an NFW profile, where the density steepens quickly in the inner regions and more slowly in the outer regions, forming a `cusp' profile.  However, observed dwarf galaxy rotation curves show a variety of slopes in their velocity profiles, some of which rise linearly with radius \citep{Oman2015}, implying underdense dark matter, or `cores,' in some galactic centres. This diversity in inferred dark matter profiles reported in a large number of observational studies and is yet to be explained by baryonic feedback models \citep[e.g.][]{Santos-Santos2020}.  
Since both AGN and stellar feedback have been shown to move large quantities of gas, and thus would be capable of altering the dark matter distribution of their host galaxies \citep[e.g.][]{Governato2010,Martizzi2013}, the process of forming cores might be a complex interplay between multiple feedback modes.  Any observed association between velocity curve shapes and AGN activity could help disentangle role of AGN in shaping dwarf galaxy dark matter halos. 

To aid in visual identification of cores in our sample,  we plot the NFW velocity curve of a $\Lambda$CDM halo corresponding to the predicted halo mass of each galaxy as gray shaded regions in Figures \ref{fig:rotation_example1}, \ref{fig:cusp-core}, and all other velocity curve plots in Appendix \ref{app:curves}. 


It is difficult to observationally constrain the halo mass of a galaxy, so one popular approach is to use abundance matching \citep[e.g.][]{Moster2013}.  Abundance matching assumes a monotonic relation between stellar and halo mass and matches the cumulative abundance of galaxies on that relation.  We used abundance matching to estimate the halo mass corresponding to each galaxy's stellar mass reported in the MPA-JHU catalogue \citep{Brinchmann2004, kauffmann2003, tremonti2004}.  The only observational input is the stellar mass $M_\star$, so the halo mass $M_h$ can be estimated using abundance matching (\citet{Moster2013}, Equation 2):

\begin{equation}
M_* = M_h \left[2N\left(\frac{M_*}{M_1}\right)^{-\beta} + \left(\frac{M_h}{M_1}\right)^\gamma \right]^{-1}
\end{equation}
with four free parameters: N, the normalization parameter, a characteristic mass $M_1$ and low and high mass slopes $\beta$ and $\gamma$.

From these estimated halo masses, we estimate a virial radius 
\begin{equation}
r_v = \left(\frac{3}{4}\frac{M_h}{\pi v \rho_c^0}\right)^{1/3}
\end{equation} 

where $v = 200$ km/s, and $\rho_c^0 = 277.5 M_\odot/$kpc.  Assuming an NFW dark matter density profile, we construct a radial mass distribution (\citet{Lokas2001}, Equation 8):

\begin{equation}
M(r) = g(c) \left[ \ln(1+cs) - \frac{cs}{1+cs}   \right] M_h
\end{equation}

where $c$ is the concentration parameter, $s=r/r_v$, and $g(c) = [\ln(1+c)-c/(1+c)]^{-1}$.  We estimate the circular velocity curve from the radial mass distribution using $v(r) = \sqrt{G M(r)/r}$.  The dotted black line in Figure \ref{fig:rotation_example1} represents the rotation curve expected with an NFW profile with concentration parameter $c=10$, and the shaded gray region was calculated assuming a concentration parameter between $c=8,15$.  

There is no clear correlation between rotational velocity slopes and AGN activity in our sample.  Figure \ref{fig:cusp-core} shows examples of two AGN and two star forming stellar absolute velocity curves in varying levels of agreement with their predicted NFW profiles. The lack of any association between current AGN activity and central mass deficits could be attributed to a difference in time scales for AGN activity and core formation, or a number of other proposed factors not related to AGN \citep[e.g.][]{deBlok2010}.  A solution to the cusp-core dilemma appears to be beyond the scope of this work, and it remains to be seen whether AGN play a role in carving out cores in dwarf galaxies.




\subsection{Peculiar Gas}
\label{sec:peculiar}
\begin{figure}
	\includegraphics[width=\columnwidth]{./figures/disturbed_hist_iso.pdf}
    \caption{We define $\Delta_{\text{off}}$ to be the weighted absolute average of the velocity offset between stars and gas, divided by the average absolute stellar velocity.  This metric is used to quantify the degree of separation between the stellar and forbidden gas component.  Based on the bimodal distribution of  $\Delta_{\text{off}}$  in our sample, we consider galaxies $\Delta_{\text{off}} >= 0.75$ to have kinematically disturbed gas.}  
   \label{fig:del_off}
\end{figure}

\begin{figure*}
	\includegraphics[width=\textwidth]{./figures/rotation_examples.pdf}
    \caption{Examples of rotation curves where the gas is disturbed in different ways.
    In some instances, gas is offset from the stars without showing any clear sign of rotation (left).  Some AGN have stratified narrow line components, where the Balmer and forbidden lines are kinematically distinct from one another (centre).  Five galaxies in our sample have gas and stellar discs rotating separately, and sometimes in opposite directions (right).}
    \label{fig:rotation_example}
\end{figure*}


The gas in these dwarfs show several distinct indications of non-rotational motion, which could be interpreted as inflows, outflows, or recently accreted gas.  To identify disturbed gas kinematics, we designed a metric to quantify the relative offset between the gas and stellar rotation curves.  $\Delta_{\text{off}}$ is the weighted average of the absolute velocity offset between the stellar and gas component, divided by the average absolute stellar velocity.

\begin{equation}
    \Delta_{\text{off}} = \dfrac{|\bar{\Delta}_{v}|}{|\bar{v}_*|}
\end{equation}

where the weighted average of the absolute velocity offset is 

\begin{equation}
   |\bar{\Delta}_{v}| = \dfrac{\sum_i |v_{*,i}-v_{\text{gas},i}|\,w_i}{\sum_i w_i}
\end{equation}

and the weights are the inverse of the combined errors of each velocity measurement, $w_i = (\Delta v_{*,i}^2 + \Delta v_{\text{gas},i}^2)^{-\frac{1}{2}}$

This calculation considers the offset between the stellar and forbidden gas component because the [\ion{O}{II}], [\ion{O}{III}], and [\ion{S}{II}] doublets are less affected by the subtraction of the stellar continuum and absorption than Balmer lines.  Faint broad lines associated with the AGN may also contribute to the line profiles, adding further uncertainty in velocities measured using Balmer emission lines. The forbidden [\ion{O}{II}], [\ion{O}{III}], and [\ion{S}{II}] doublets are not affected by such absorption or broad line region features and therefore give more accurate velocity measurements.

Histograms of $\Delta_{\text{off}}$ are shown in Figure \ref{fig:del_off} and individual $\Delta_\text{off}$ values are reported in the figures for each galaxy in Appendix \ref{app:curves}.  The top panel shows $\Delta_{\text{off}}$ for all 45 galaxies with rotation curves, the middle panel shows the distribution for all isolated galaxies, and the bottom shows the distribution for all galaxies that have at least one neighbour of comparable (or greater) mass (see Section \ref{sec:environment} for a discussion on galaxy environment).  The histograms show a bimodal distribution, which is most pronounced in the middle panel.  Based on this bimodality, we classify a galaxy as `disturbed' when $\Delta_{\text{off}} \geq 0.75$ (dotted gray line).  

Two galaxies (J010005.94-011059.0 and J090613.75+561015.5) have $\Delta_{\text{off}} < 0.75$ between the stars and forbidden emission lines, but the Balmer and forbidden gas components are offset from one another.  Following the same approach, we determine the threshold for offset Balmer and forbidden emission components to be (H$\beta$ - [\ion{O}{III}] $\Delta_{\text{off}} > 0.5$). Distinct kinematics associated with higher ionization emission lines is known as line stratification (see Section \ref{subsec:stratification}), and we count galaxies with stratified emission lines among the galaxies with disturbed gas.   By this criteria, 25 of the 45 galaxies with rotation curves are disturbed.   All rotation curves are plotted in Appendix \ref{app:curves}. The rotation curves showing orderly, co-rotating discs are shown in Figure \ref{fig:wellbehaved} and 25 disturbed rotation curves are shown in Figure \ref{fig:disturbed}.  

Of the 25 galaxies with disturbed gas, 19 host AGN and 6 do not. The majority (73\%) the AGN in our sample have disturbed gas, while only 32\% of star forming galaxies have $\Delta_\text{off} > 0.75$.  We noticed distinct properties in the non-rotational motion exhibited in the disturbed gas, and we show examples of rotation curves exhibiting different types of disturbances.  We observe gas that is generally offset from the stellar component, stratified emission lines, and counter-rotating gas. Examples of each type of disturbance are shown in Figure \ref{fig:rotation_example}. 



\subsubsection{Line Stratification}
\label{subsec:stratification}
In the stratified model of the narrow line region (NLR), lower ionization gas resides on the outer parts of the NLR while higher ionization lines are generated closer to the AGN \citep[e.g.][]{Croom2002,Andika2020}.  Distinct kinematics associated with emission lines of different ionization potentials imply a complex narrow line region that is  stratified in ionization and wind speed. We observe stratified gas components in seven AGN in our sample, with higher ionization lines showing higher velocities than lower ionization lines.  This implies a decelerating outflow: where a high velocity, high ionization wind is generated near the AGN, and while the low ionization gas in the outer region of the NLR flows more slowly.

We observe no correlation between wind speed and AGN luminosity, though the line stratification we observe in these seven galaxies preferentially occurs in galaxies that have outflows indicated by broad [\ion{O}{III}] components.  Plots of the stratified gas kinematics in these seven galaxies can be found in the Appendix, Figure \ref{fig:strat_curves}.



\subsubsection{Counter-Rotating
\label{subsec:counter-rotating}
\begin{figure*}
	\includegraphics[width=\textwidth]{./figures/Crot_vel.pdf}
    \caption{The rotation curves for five galaxies with counter-rotating gas are shown here.  The colours are as in Figure \ref{fig:rotation_example}, and the blue dots in the middle panel indicate gas velocities measured from the [SII] doublet.}
    \label{fig:cr_curves}
\end{figure*}

Of the 45 galaxies with rotation curves, five have counter-rotating gas and stellar components, shown in Figure \ref{fig:cr_curves}.  Counter rotating gas and stars have long been explained as the effect of the accretion of gas clouds or small satellites after the formation of the stellar disc \citep[e.g.][]{Thakar1996,Thomas2006,Katkov2014}.  As mentioned in the introduction, S19 found that counter-rotating gas in dwarf galaxies requires substantial gas removal, either via black hole feedback or environmental effects from fly-by interactions with more massive systems.  Interestingly, all five counter-rotating dwarfs in our sample host AGN.

S19 also make several predictions about the present-day properties of counter-rotating dwarfs.  In cases where re-accretion of gas is gradual, they find that counter-rotation can be very long lived (up to $\sim 2$ Gyr).  As a result, S19 predict no significant correlation with environment.  Three counter-rotating galaxies are isolated (J004214.99-104415.0, J080228.83+203050.2, J093251.11+314145.0) and two (J094941.20+321315.9, J130434.92+075505.0) have at least one neighbour with comparable mass.

An event that removes most of the original gas reservoir would quench star formation, making it likely that counter-rotating dwarfs will have older stellar populations and appear redder in colour.  All five counter-rotating galaxies discussed here have colours  $u-r > 2$, which is redder than the average for our sample ($u-r = 1.83$). S19 also find a 30\% gas deficit in counter-rotating dwarfs at $z=0$, relative to control galaxies at fixed stellar mass.  Though most of the galaxies in our sample lack gas mass estimates, we can turn our attention to the six galaxies with HI masses measured in the ALFALFA survey \citep{Bradford2018}.   Of these six, five are not disturbed and one is counter-rotating (J094941.20+321315.9).  The five co-rotating galaxies with HI measurements have a wide range of gas fractions ($\frac{M_{HI}}{M_*} \sim 0.23 - 7.3$), and the one counter-rotating has the smallest gas fraction ($\frac{M_{HI}}{M_*}* = 0.16$).  The gas component of J094941.20+321315.9 reaches velocities that exceed the predicted NFW curve, suggesting that this galaxy inhabits a more massive halo than predicted from its stellar mass.







\subsection{Star Formation Suppression}
\label{subsec:suppression}
\begin{figure}
	\includegraphics[width=\columnwidth]{./figures/sf_suppression.pdf}
    \caption{Absolute line of sight velocity $(v_\text{los})$ measurements that far exceed the expected NFW velocity curves based on their stellar masses indicate overmassive dark matter haloes relative to the measured stellar mass, implying ongoing star formation suppression.  Stellar (left), Balmer emission (centre) and forbidden emission (right) components are shown for the three galaxies in our sample where this is most apparent. Green curves mark expected NFW velocity curves for galaxies with stellar mass $\log(M_\star)=10.5, 11,\text{and } 12$ and concentration parameter $c=10$. Black dotted lines denote the expected NFW velocity curves based on each galaxy's MPA-JHU stellar mass.  All three of these galaxies host AGN, and two have counter-rotating gas components, which lends additional evidence potentially associating AGN with gas depletion and star formation suppression in dwarf galaxies.
    }  
   \label{fig:sf_supp}
\end{figure}



While abundance matching enables us to infer halo masses based on stellar masses, maximum line of sight velocity measurements can be used to place lower limits on the true halo mass of each galaxy.  If the measured lower limit of the halo mass of a galaxy exceeds the halo mass inferred from abundance matching to stellar mass, the galaxy can be said to have a lower star formation rate than expected.  Figure \ref{fig:sf_supp} shows absolute line of sight velocity curves for the three galaxies in our sample where this is most apparent.  As in previous figures, black dotted lines indicate the NFW curve predicted based on each galaxy's stellar mass. Green curves mark the NFW curves associated with stellar masses $\log(M_\star/M_\odot) = 10.5, 11, \text{and } 12$ and concentration parameter $c=10$.  The absolute line of sight velocity curves for the stellar (left), hydrogen Balmer emission (middle), and forbidden emission (right) components are shown. Line of sight velocities are plotted here in place of circular velocities to avoid errors introduced when correcting for disc inclination (Appendix \ref{app:incl}).  

The three galaxies shown in Figure \ref{fig:sf_supp} were selected from our sample using a similar approach to the one used to identify disturbed gas in Section \ref{sec:peculiar}.  We calculated the  offset between each kinematic component ($v_\text{los})$ and the predicted NFW curve $v_\text{NFW}$:
\begin{equation}
\Delta_{v_{\text{los}}\text{, NFW}} = \frac{\Sigma_i (v_{\text{los},i} - v_\text{NFW}) w_{\text{los},i}}{\Sigma_i w_{\text{los},i}}
\end{equation}
The distribution of $\Delta_{v_{\text{los}}\text{, NFW}}$ values for each component revealed three outlying galaxies that consistently fell above the threshold $\Delta_{v_{\text{los}}\text{, NFW}} > 0.5$: J093251.11+314145.0, J094941.20+321315.9, and J140116.03+542507.4.  

These galaxies have measured velocity curves that far exceed the expected NFW profile, indicating that they inhabit much larger halos than expected based on their stellar masses.  Their small stellar masses and red colours $(u-r \geq 2.23)$ suggest ongoing or recent star formation suppression.  It is interesting to note that all three galaxies host AGN, and two have counter-rotating gas, consistent with the scenario where AGN clear a substantial amount of gas from their hosts, limiting star formation.






\subsection{Environment}
\label{sec:environment}


To distinguish between the effects of environmental and secular processes on gas kinematics, we searched for luminous galaxies in the regions surrounding each dwarf.  Following the method and  criteria employed by \citet{Janz2017}, we queried the SDSS DR12 and 2MASS Redshift survey catalogues for luminous neighbours with $M_{K_S} < -21.5$ mag and SDSS $r < -16$ mag.  The completeness limit of this search is $M_{K_S} = -21.5$ mag at $z=0.02$; corresponding to $M_*\sim8\times10^9 M_\odot$ \citep{geha2012}. 
This limit is well below the magnitudes expected for galaxies in the mass range explored in this work, so extending the search to the redshift limit of our sample ($z=0.05$) has no effect on completeness.
The 2MASS Redshift Survey search revealed matches overlooked in the SDSS search due to missing redshifts, but SDSS optical counterparts existed for all 2MASS matches. We use SDSS DR12 g- and r-band photometry and the mass-magnitude relation of \citet{Bernardi2010} to estimate the masses of neighbouring galaxies. 

We identify galaxies within 1.5 Mpc and $\pm 1000\text{ km s}^{-1}$ of each dwarf in this sample as neighbours.  Using the g- and r-band mass-magnitude relation, we estimate the mass of each neighbour. In order to identify isolated galaxies, we count the number of neighbours with comparable mass (i.e. stellar mass $M_{\star,\text{neighbour}} \geq 0.75 \times M_{\odot,\text{dwarf}}$) within 1.5 Mpc and $\pm 1000\,\text{km}\,\text{s}^{-1}$.  The number of neighbours for each dwarf can be found in Table \ref{tab:sample}.  

A recent study of 62,258 dwarf ($M_\star < 5\times10^9 M_\odot$) galaxies finds no discernible difference between the environments of AGN and non-AGN dwarf galaxies, suggesting that environmental factors may not play a dominant role in triggering AGN \citep{Kristensen2020}.  Similarly, we find no statistically significant link between AGN and environment.  However, \citet{Kristensen2020} suggest that remnants of past interactions may be reflected in gas kinematics.

The importance of environment in disturbing gas kinematics can be explored by considering the bottom panel of Figure \ref{fig:del_off}, which shows the distribution of $\Delta_{\text{off}}$ for galaxies with at least one neighbour of comparable (or greater) mass within 1.5 Mpc.  Star forming and AGN-hosting galaxies with neighbours show varying degrees of gas disturbance, further supporting the notion that environment may not play a dominant role in triggering AGN activity.  The most extreme values of $\Delta_{\text{off}}$ are associated with AGN, suggesting that AGN are capable of generating large scale disturbances in their host galaxies' ISM, though the presence of AGN-hosting galaxies with undisturbed gas implies this is not always the case.  

On the other hand, isolated galaxies show a distinct bimodal distribution, where star forming galaxies tend to have orderly rotating discs, and disturbed gas is almost always associated with AGN.  Table \ref{tab:isolated} lists the seven disturbed, isolated galaxies, six of which host AGN.  Two of these six isolated AGN have counter rotating gas, and three have outflows indicated by distinct broadened components in [\ion{O}{III}]$\lambda$5007, as in Paper I.  To clarify, the outflows in these four galaxies are identified with multicomponent Gaussian fits to the [\ion{O}{III}] line profile; disturbed gas is determined here by a velocity offset between the narrow component of the emission lines from the stellar component.

The single isolated and disturbed star forming galaxy, J101440.21+192448.9, was originally included in our sample based on broad lines in H$\alpha$ \citep{Reines2013}, which later faded, likely due to transient stellar activity \citep{baldassare2016}.  This object is classified as an outflow galaxy in Paper I based on broadened wings in its [\ion{O}{III}] emission line profile.  Follow-up Integral Field Unit (IFU) observations with KCWI revealed that the rotation axis of J101440.21+192448.9 is in fact parallel to the slit position in our LRIS observations (Liu et al., in prep).  Since the slit is not aligned with the stellar disc, these velocity measurements do not reflect the true rotational velocity of this galaxy.  

Follow-up KCWI observations were obtained for eight objects in this sample (Liu et al., in prep). These IFU observations produce line of sight velocities that agree with our longslit measurements and confirm that in all other cases, the LRIS slit was oriented perpendicular to the rotational axes, as intended.  Proper slit orientation for the remainder of the sample should be verified with similar follow-up IFU observations, though the confirmation of correct slit placement in all but one galaxy is encouraging. Since J101440.21+192448.9 is an active star forming galaxy with supernova-driven outflows, it is reasonable to surmise that bright star forming regions could outshine the rest of the disc, confusing the photometric fit used to determine slit placement. This calls into question the slit placement for other galaxies with non-rotational kinematics and signs of active star formation, such as J171759.66+332003.8.



\begin{table*}
\centering
\begin{tabular}{| l c c c c c c c c c c c c|}
\hline
Abbreviated & Redshift  & $\log(M_*)$  & $\log(M_{\text{BH}})$& $r_{50}$  & BPT & HeII & neigh- & dist-   & counter- & outflow & strat- \\ 
Name        &           &              &                      & (kpc)     &     &      & bors   & urbed   & rotating &         & ified \\ 
(1)         & (2)       & (3)          & (4)                  & (5)       & (6) & (7)  & (8)    & (9)     & (10)     & (11) & (12) \\ \hline
J0021+00    & 0.0180 &  9.15        & ---                  & 0.89      &  AGN       & AGN    &   7  & -- & -- & -- & -- \\
J0042-10    & 0.0359 &  9.44        & ---                  & 1.34      &  AGN       & AGN    &   5  & \checkmark & \checkmark & -- & -- \\
J0100-01    & 0.0515 &  9.44        & ---                  & 0.99      &  Comp.     & Comp.  &   5  & \checkmark & -- & \checkmark & -- \\
J0156-00    & 0.0450 &  9.39        & ---                  & 1.91      &  SF        & SF     &  13  & \checkmark & -- & -- & -- \\
J0246-00    & 0.0464 &  9.35        & 5.7$^c$              & 1.34      &  AGN       & AGN    &  37  & -- & -- & -- & -- \\
J0300+00    & 0.0095 &  8.72        & ---                  & 2.11      &  SF        & SF     &   0  & -- & -- & -- & -- \\
NGC 1569    & $-80\text{ km s}^{-1}$ &  8.56 & ---         & 7.09      &  SF        & SF     &  --  & -- & -- & \checkmark & -- \\
J0755+24    & 0.0290 &  8.85        & ---                  & 1.78      &  SF        & SF     &   3  & -- & -- & -- & -- \\
J0802+10    & 0.0145 &  9.60        & 3.6$^b$              & 1.29      &  AGN       & AGN    &   3  & -- & -- & -- & -- \\
J0802+20    & 0.0286 &  10.6        & ---                  & 1.97      &  Comp.     & AGN    &   0  & \checkmark & \checkmark & -- & -- \\
J0811+23    & 0.0157 &  9.06        & 4.4$^c$              & 0.58      &  AGN       & AGN    &   2  & \checkmark & -- & \checkmark & \checkmark \\
J0812+54    & 0.0086 &  9.29        & ---                  & 1.49      &  SF        & SF     &   0  & -- & -- & -- & -- \\
J0840+18    & 0.0149 &  9.13        & 4.3$^c$              & 0.94      &  AGN       & AGN    &   2  & \checkmark & -- & \checkmark & -- \\
J0842+03    & 0.0289 &  9.33        & ---                  & 0.75      &  Comp.     & AGN    &   2  & \checkmark & -- & \checkmark & \checkmark \\
J0851+39    & 0.0407 &  9.28        & 5.4$^c$              & 1.70      &  AGN       & AGN    &   2  & -- & -- & -- & -- \\ 
J0906+56    & 0.0465 &  9.37        & 5.4$^c$              & 1.51      &  AGN       & AGN    &   5  & \checkmark & -- & \checkmark & -- \\
J0911+61    & 0.0263 &  8.95        & ---                  & 2.03      &  SF        & SF     &   7  & \checkmark & -- & -- & -- \\      
J0921+23    & 0.0281 &  9.27        & ---                  & 1.27      &  SF        & SF     &   0  & -- & -- & -- & -- \\
J0932+31    & 0.0153 &  9.62        & 3.5$^b$              & 0.58      &  AGN       & AGN    &   0  & \checkmark & \checkmark & -- & -- \\          
J0948+09    & 0.0103 &  8.73        & 4.2$^b$              & 0.73      &  Comp.     & AGN    &   5  & \checkmark & -- & -- & \checkmark \\
J0949+32    & 0.0051 &  9.22        & 4.1$^b$              & 0.58      &  Comp.     & AGN    &   6  & \checkmark & \checkmark & -- & -- \\
J0954+47    & 0.0326 &  9.47        & 4.9$^c$              & 1.75      &  AGN       & AGN    &   0  & \checkmark & -- & \checkmark & -- \\
J1002+59    & 0.0093 &  9.60        & 4.1$^b$              & 1.12      &  AGN       & Comp.  &   1  & \checkmark & -- & -- & \checkmark \\
J1005+12    & 0.0093 &  9.64        & 4.8$^b$              & 0.97      &  AGN       & AGN    &   0  & \checkmark & -- & \checkmark & -- \\
J1009+26    & 0.0143 &  8.75        & 5.1$^c$              & 0.62      &  AGN       & AGN    &   0  & \checkmark & -- & \checkmark & -- \\
J1014+19    & 0.0284 &  8.56        & ---                  & 0.88      &  SF        & SF     &   0  & \checkmark & -- & \checkmark & -- \\           
J1143+55    & 0.0269 &  8.92        & ---                  & 1.03      &  SF        & SF     &   1  & -- & -- & -- & -- \\         
J1223+58    & 0.0146 &  9.39        & 6.1$^b$              & 1.01      &  AGN       & AGN    &   6  & -- & -- & -- & -- \\         
J1304+07    & 0.0479 &  9.41        & ---                  & 1.13      &  AGN       & AGN    &  16  & \checkmark & \checkmark & -- & -- \\  
J1307+52    & 0.0259 &  9.10        & ---                  & 1.18      &  SF        & SF     &   2  & -- & -- & -- & -- \\      
J1315+22    & 0.0226 &  9.20        & ---                  & 1.58      &  SF        & SF     &   1  & -- & -- & -- & -- \\        
J1343+25    & 0.0280 &  9.19        & ---                  & 3.09      &  SF        & SF     &   3  & -- & -- & -- & -- \\        
J1401+54    & 0.0059 &  9.57        & 3.2$^b$              & 0.59      &  AGN       & AGN    &   5  & -- & -- & -- & -- \\      
J1402+09    & 0.0195 &  8.83        & ---                  & 0.79      &  AGN       & AGN    &  26  & \checkmark & -- & -- & -- \\     
J1405+11    & 0.0178 &  9.23        & ---                  & 1.15      &  AGN       & AGN    &   4  & -- & -- & -- & -- \\
J1407+50    & 0.0070 &  8.72        & ---                  & 0.77      &  Comp.     & AGN    &   8  & -- & -- & -- & -- \\ 
J1412+10    & 0.0324 &  8.99        & ---                  & 0.56      &  AGN       & AGN    &   3  & \checkmark & -- & -- & -- \\
J1442+20    & 0.0426 &  8.89        & ---                  & 0.89      &  AGN       & AGN    &   1  & \checkmark & -- & \checkmark & \checkmark \\
J1458+11    & 0.0198 &  9.91        & ---                  & 2.40      &  SF        & SF     &   0  & -- & -- & -- & -- \\
J1511+23    & 0.0143 &  9.68        & ---                  & 1.01      &  SF        & SF     &   0  & -- & -- & -- & -- \\
J1546+03    & 0.0132 &  9.49        & ---                  & 2.05      &  SF        & AGN    &   3  & -- & -- & -- & -- \\
J1608+12    & 0.0166 &  9.75        & ---                  & 2.65      &  SF        & SF     &   0  & -- & -- & -- & -- \\
J1623+39    & 0.0172 &  9.22        & ---                  & 2.68      &  SF        & SF     &   2  & \checkmark & -- & -- & -- \\
J1623+45    & 0.0064 &  9.41        & ---                  & 0.82      &  AGN       & AGN    &   0  & \checkmark & -- & -- & -- \\
J1644+43    & 0.0178 &  9.53        & ---                  & 0.86      &  SF        & SF     &   0  & -- & -- & -- & -- \\
J1706+33    & 0.0301 &  9.41        & ---                  & 1.95      &  SF        & SF     &   7  & -- & -- & -- & -- \\
J1717+33    & 0.0151 &  9.85        & ---                  & 1.03      &  SF        & SF     &   1  & \checkmark & -- & \checkmark & -- \\
J1721+28    & 0.0280 &  10.0        & ---                  & 3.49      &  SF        & SF     &   0  & -- & -- & -- & -- \\
J1722+28    & 0.0281 &  9.23        & ---                  & 1.71      &  SF        & SF     &   3  & \checkmark & -- & -- & -- \\
J2320+15    & 0.0130 &  9.57        & 3.7$^b$              & 0.59      &  AGN       & AGN    &   6  & -- & -- & -- & -- \\
\hline
\end{tabular}
\caption{
(1) * indicates objects excluded from this study.
(2) Redshift is calculated by fits to stellar absorption lines in LRIS spectra using \textsc{ppxf}.
(3) Stellar mass reported in the MPA-JHU catalogue.
(4) $^b$ Black hole mass lower limits derived using Eddington Luminosity arguments (M14) $^c$ Black hole mass estimated using as $M_{BH}\propto R\Delta V^2/G$, where $\Delta V$ is measured from broad H$\alpha$, extrapolating the BLR radius -- luminosity relation extends into the low mass regime (R13)
(5) SDSS Petrosian radius containing 50\% of r-band flux, in kiloparsecs.
(6) Classification of dominant ionization source based on Gaussian fits to emission lines using the process described in Section \ref{sec:emission}.  The spectra were extracted from the central 1kpc of each galaxy.
(7) Same as (6) but for HeII classification (S15)
(8) Number of galaxies with comparable mass within 1.5 Mpc. 
(9) Classified as disturbed (see Section \ref{sec:peculiar})
(10) Gas is clearly rotating and offset from stellar component. 
(11) Has an outflow identified by an additional broad component in as defined in Paper I.
(12) Narrow emission lines are stratified (see Section \ref{subsec:stratification})}
\label{tab:sample}
\end{table*}




\begin{center}
\begin{table}
\begin{tabular}{|c|c|c|c|c|c|}
    name &  $\log(M_\star)$ & AGN & counter-  & outflow & u$-$r \\ 
    &&& rotating & (Paper I) &colour  \\\hline
J0802+20   & 10.6 & \checkmark & \checkmark &    &  2.39 \\
J0932+31   &  9.6 & \checkmark & \checkmark &    &  2.23 \\
J0954+47   &  9.5 & \checkmark &    & \checkmark &  2.20 \\
J1005+12   &  9.6 & \checkmark &    & \checkmark &  2.16 \\
J1009+26   &  8.7 & \checkmark &    & \checkmark &  1.91 \\
J1014+19   &  8.6 &    &    & \checkmark &  1.25 \\ 
J1623+45   &  9.4 & \checkmark &    &    &  2.13 \\\hline

\end{tabular}
\caption{Seven galaxies in our sample have disturbed gas kinematics and no neighbours of comparable mass within 1.5 Mpc and $\pm 1000$ km s$^{-1}$.  Six of them host AGN, two have counter-rotating gas, and four have outflows indicated by broad wings in their [OIII]5007 emission line profiles.  $u-r$ colour is based on SDSS cModelMag photometry.}
\label{tab:isolated}
\end{table}
\end{center}








\section{Summary}
\label{sec:Summary}
From Keck LRIS longslit spectroscopy, we measured rotational velocity curves of 45 dwarf galaxies.  Our sample consists of  26 galaxies with AGN and a control sample of 19 star forming galaxies with no optical or IR evidence of AGN.  The rotation curves are decomposed into stellar, Balmer emission, and forbidden emission components.  In order to investigate the potential effects of AGN on gas kinematics in this sample, we quantified velocity offsets between stellar and gas components.  We summarize our conclusions below.


\begin{enumerate}




\item We detect counter-rotating gas in five of 45 galaxies, and AGN are present in all five cases. A study of the occurrence, properties, and evolutionary history of counter-rotating galaxies in Illustris \citep{Starkenburg2019} finds that removal and re-accretion of gas is necessary for counter-rotating gas discs to form, and that periods of AGN activity are sometimes associated with large drops in gas mass.  We find that the properties of the counter-rotating dwarfs in our sample agree with present-day properties of counter-rotating dwarf galaxies predicted from Illustris.

\item We use the weighted average of velocity offsets between stellar spectra and emission lines to identify disturbed gas kinematics. We find disturbed gas in 25 out of 45 galaxies in our sample.  Of the 26 AGN in our sample, 19 (or 73\%) have disturbed gas.  Star forming galaxies tend to have orderly, co-rotating gas discs, with only 32\% showing disturbed gas.  

\item At least three galaxies in our sample have line of sight velocities far exceeding those expected based on their stellar masses.  These line of sight velocities constitute a lower limit estimate of true halo mass, indicating that these galaxies inhabit much more massive dark matter haloes than expected based on their small stellar masses. This potential evidence of ongoing star formation suppression is most apparent in three AGN-hosting galaxies within our sample, two of which have counter-rotating gas.  This suggests that AGN could be associated with gas removal and star formation suppression in dwarf galaxies.  A detailed study of the star formation histories of these galaxies is warranted.

\item In the absence of environmental influence, kinematically disturbed gas is expected to be caused by secular processes.  Fifteen dwarfs in our sample are isolated, with no neighbouring galaxies of comparable mass within 1.5 Mpc and $\pm1000$ km s$^{-1}$.  Of these, seven galaxies have disturbed gas.  We find that six out of seven isolated galaxies with disturbed gas host AGN. 

\end{enumerate}

Our findings imply that AGN play an important, and perhaps dominant, role in disturbing gas and limiting star formation in dwarf galaxies.  This represents additional evidence of the importance of AGN-driven winds in dwarf galaxy evolution and further highlights the importance of including AGN feedback in galaxy formation models.  A detailed follow-up IFU study of ionized gas kinematics in a subset of these galaxies is in progress (Liu et. al., in prep). Multiphase gas kinematic measurements, gas mass measurements, and comparison with simulations run with detailed AGN feedback models are necessary for a full understanding of AGN feedback in dwarf galaxies.

\vspace{1cm}
{\bf Acknowledgements}
We would like to thank the anonymous referee,
whose careful reading and thoughtful feedback 
has helped to improve and clarify this manuscript. 
Support for this program was provided
by the National Science Foundation, under
grant number AST 1817233.  Additional support
was provided by NASA through a grant from the
Space Telescope Science Institute (Program AR-
14582.001-A), which is operated by the Association of
Universities for Research in Astronomy, Incorporated,
under NASA contract NAS5-26555.  
The data presented herein were obtained at the W. M.
Keck Observatory, which is operated as a scientific partnership 
among the California Institute of Technology,
the University of California and the National Aeronautics 
and Space Administration. The Observatory was made 
possible by the generous financial support of the
W. M. Keck Foundation.
The authors wish to recognize and acknowledge the
very significant cultural role and reverence that the 
summit of Mauna Kea has always had within the Indigenous
Hawaiian community. We are most fortunate to have the
opportunity to conduct observations from this mountain.
Some of the data presented herein were obtained using the UCI
Remote Observing Facility, made possible by a generous gift 
from John and Ruth Ann Evans. 
This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

{\bf Data Availability}\\
The data underlying this article will be shared on reasonable request to the corresponding author.
\bibliographystyle{mnras}

\section{Introduction}

The journal \textit{Monthly Notices of the Royal Astronomical Society} (MNRAS) encourages authors to prepare their papers using \LaTeX.
The style file \verb'mnras.cls' can be used to approximate the final appearance of the journal, and provides numerous features to simplify the preparation of papers.
This document, \verb'mnras_guide.tex', provides guidance on using that style file and the features it enables.

This is not a general guide on how to use \LaTeX, of which many excellent examples already exist.
We particularly recommend \textit{Wikibooks \LaTeX}\footnote{\url{https://en.wikibooks.org/wiki/LaTeX}}, a collaborative online textbook which is of use to both beginners and experts.
Alternatively there are several other online resources, and most academic libraries also hold suitable beginner's guides.

For guidance on the contents of papers, journal style, and how to submit a paper, see the MNRAS Instructions to Authors\footnote{\label{foot:itas}\url{http://www.oxfordjournals.org/our_journals/mnras/for_authors/}}.
Only technical issues with the \LaTeX\ class are considered here.


\section{Obtaining and installing the MNRAS package}
Some \LaTeX\ distributions come with the MNRAS package by default.
If yours does not, you can either install it using your distribution's package manager, or download it from the Comprehensive \TeX\ Archive Network\footnote{\url{http://www.ctan.org/tex-archive/macros/latex/contrib/mnras}} (CTAN).

The files can either be installed permanently by placing them in the appropriate directory (consult the documentation for your \LaTeX\ distribution), or used temporarily by placing them in the working directory for your paper.

To use the MNRAS package, simply specify \verb'mnras' as the document class at the start of a \verb'.tex' file:

\begin{verbatim}
\documentclass{mnras}
\end{verbatim}
Then compile \LaTeX\ (and if necessary \bibtex) in the usual way.

\section{Preparing and submitting a paper}
We recommend that you start with a copy of the \texttt{mnras\_template.tex} file.
Rename the file, update the information on the title page, and then work on the text of your paper.
Guidelines for content, style etc. are given in the instructions to authors on the journal's website$^{\ref{foot:itas}}$.
Note that this document does not follow all the aspects of MNRAS journal style (e.g. it has a table of contents).

If a paper is accepted, it is professionally typeset and copyedited by the publishers.
It is therefore likely that minor changes to presentation will occur.
For this reason, we ask authors to ignore minor details such as slightly long lines, extra blank spaces, or misplaced figures, because these details will be dealt with during the production process.

Papers must be submitted electronically via the online submission system; paper submissions are not permitted.
For full guidance on how to submit a paper, see the instructions to authors.

\section{Class options}
\label{sec:options}
There are several options which can be added to the document class line like this:

\begin{verbatim}
\documentclass[option1,option2]{mnras}
\end{verbatim}
The available options are:
\begin{itemize}
\item \verb'letters' -- used for papers in the journal's Letters section.
\item \verb'onecolumn' -- single column, instead of the default two columns. This should be used {\it only} if necessary for the display of numerous very long equations.
\item \verb'doublespacing' -- text has double line spacing. Please don't submit papers in this format.
\item \verb'referee' -- \textit{(deprecated)} single column, double spaced, larger text, bigger margins. Please don't submit papers in this format.
\item \verb'galley' -- \textit{(deprecated)} no running headers, no attempt to align the bottom of columns.
\item \verb'landscape' -- \textit{(deprecated)} sets the whole document on landscape paper.
\item \verb"usenatbib" -- \textit{(all papers should use this)} this uses Patrick Daly's \verb"natbib.sty" package for citations.
\item \verb"usegraphicx" -- \textit{(most papers will need this)} includes the \verb'graphicx' package, for inclusion of figures and images.
\item \verb'useAMS' -- adds support for upright Greek characters \verb'\upi', \verb'\umu' and \verb'\upartial' ($\upi$, $\umu$ and $\upartial$). Only these three are included, if you require other symbols you will need to include the \verb'amsmath' or \verb'amsymb' packages (see section~\ref{sec:packages}).
\item \verb"usedcolumn" -- includes the package \verb"dcolumn", which includes two new types of column alignment for use in tables.
\end{itemize}

Some of these options are deprecated and retained for backwards compatibility only.
Others are used in almost all papers, but again are retained as options to ensure that papers written decades ago will continue to compile without problems.
If you want to include any other packages, see section~\ref{sec:packages}.

\section{Title page}

If you are using \texttt{mnras\_template.tex} the necessary code for generating the title page, headers and footers is already present.
Simply edit the title, author list, institutions, abstract and keywords as described below.

\subsection{Title}
There are two forms of the title: the full version used on the first page, and a short version which is used in the header of other odd-numbered pages (the `running head').
Enter them with \verb'\title[]{}' like this:
\begin{verbatim}
\title[Running head]{Full title of the paper}
\end{verbatim}
The full title can be multiple lines (use \verb'\\' to start a new line) and may be as long as necessary, although we encourage authors to use concise titles. The running head must be $\le~45$ characters on a single line.

See appendix~\ref{sec:advanced} for more complicated examples.

\subsection{Authors and institutions}

Like the title, there are two forms of author list: the full version which appears on the title page, and a short form which appears in the header of the even-numbered pages. Enter them using the \verb'\author[]{}' command.

If the author list is more than one line long, start a new line using \verb'\newauthor'. Use \verb'\\' to start the institution list. Affiliations for each author should be indicated with a superscript number, and correspond to the list of institutions below the author list.

For example, if I were to write a paper with two coauthors at another institution, one of whom also works at a third location:
\begin{verbatim}
\author[K. T. Smith et al.]{
Keith T. Smith,$^{1}$
A. N. Other,$^{2}$
and Third Author$^{2,3}$
\\
$^{1}$Affiliation 1\\
$^{2}$Affiliation 2\\
$^{3}$Affiliation 3}
\end{verbatim}
Affiliations should be in the format `Department, Institution, Street Address, City and Postal Code, Country'.

Email addresses can be inserted with the \verb'\thanks{}' command which adds a title page footnote.
If you want to list more than one email, put them all in the same \verb'\thanks' and use \verb'\footnotemark[]' to refer to the same footnote multiple times.
Present addresses (if different to those where the work was performed) can also be added with a \verb'\thanks' command.

\subsection{Abstract and keywords}

The abstract is entered in an \verb'abstract' environment:
\begin{verbatim}
\begin{abstract}
The abstract of the paper.
\end{abstract}
\end{verbatim}
\noindent Note that there is a word limit on the length of abstracts.
For the current word limit, see the journal instructions to authors$^{\ref{foot:itas}}$.

Immediately following the abstract, a set of keywords is entered in a \verb'keywords' environment:
\begin{verbatim}
\begin{keywords}
keyword 1 -- keyword 2 -- keyword 3
\end{keywords}
\end{verbatim}
\noindent There is a list of permitted keywords, which is agreed between all the major astronomy journals and revised every few years.
Do \emph{not} make up new keywords!
For the current list of allowed keywords, see the journal's instructions to authors$^{\ref{foot:itas}}$.

\section{Sections and lists}

Sections and lists are generally the same as in the standard \LaTeX\ classes.

\subsection{Sections}
\label{sec:sections}
Sections are entered in the usual way, using \verb'\section{}' and its variants. It is possible to nest up to four section levels:
\begin{verbatim}
\section{Main section}
 \subsection{Subsection}
  \subsubsection{Subsubsection}
   \paragraph{Lowest level section}
\end{verbatim}
\noindent The other \LaTeX\ sectioning commands \verb'\part', \verb'\chapter' and \verb'\subparagraph{}' are deprecated and should not be used.

Some sections are not numbered as part of journal style (e.g. the Acknowledgements).
To insert an unnumbered section use the `starred' version of the command: \verb'\section*{}'.

See appendix~\ref{sec:advanced} for more complicated examples.

\subsection{Lists}

Two forms of lists can be used in MNRAS -- numbered and unnumbered.

For a numbered list, use the \verb'enumerate' environment:
\begin{verbatim}
\begin{enumerate}
 \item First item
 \item Second item
 \item etc.
\end{enumerate}
\end{verbatim}
\noindent which produces
\begin{enumerate}
 \item First item
 \item Second item
 \item etc.
\end{enumerate}
Note that the list uses lowercase Roman numerals, rather than the \LaTeX\ default Arabic numerals.

For an unnumbered list, use the \verb'description' environment without the optional argument:
\begin{verbatim}
\begin{description}
 \item First item
 \item Second item
 \item etc.
\end{description}
\end{verbatim}
\noindent which produces
\begin{description}
 \item First item
 \item Second item
 \item etc.
\end{description}

Bulleted lists using the \verb'itemize' environment should not be used in MNRAS; it is retained for backwards compatibility only.

\section{Mathematics and symbols}

The MNRAS class mostly adopts standard \LaTeX\ handling of mathematics, which is briefly summarised here.
See also section~\ref{sec:packages} for packages that support more advanced mathematics.

Mathematics can be inserted into the running text using the syntax \verb'$1+1=2$', which produces $1+1=2$.
Use this only for short expressions or when referring to mathematical quantities; equations should be entered as described below.

\subsection{Equations}
Equations should be entered using the \verb'equation' environment, which automatically numbers them:

\begin{verbatim}
\begin{equation}
 a^2=b^2+c^2
\end{equation}
\end{verbatim}
\noindent which produces
\begin{equation}
 a^2=b^2+c^2
\end{equation}

By default, the equations are numbered sequentially throughout the whole paper. If a paper has a large number of equations, it may be better to number them by section (2.1, 2.2 etc.). To do this, add the command \verb'\numberwithin{equation}{section}' to the preamble.

It is also possible to produce un-numbered equations by using the \LaTeX\ built-in \verb'\['\textellipsis\verb'\]' and \verb'$$'\textellipsis\verb'$$' commands; however MNRAS requires that all equations are numbered, so these commands should be avoided.

\subsection{Special symbols}


\begin{table}
 \caption{Additional commands for special symbols commonly used in astronomy. These can be used anywhere.}
 \label{tab:anysymbols}
 \begin{tabular}{lll}
  \hline
  Command & Output & Meaning\\
  \hline
  \verb'\sun' & \sun & Sun, solar\\[2pt]
  \verb'\earth' & \earth & Earth, terrestrial\\[2pt]
  \verb'\micron' & \micron & microns\\[2pt]
  \verb'\degr' & \degr & degrees\\[2pt]
  \verb'\arcmin' & \arcmin & arcminutes\\[2pt]
  \verb'\arcsec' & \arcsec & arcseconds\\[2pt]
  \verb'\fdg' & \fdg & fraction of a degree\\[2pt]
  \verb'\farcm' & \farcm & fraction of an arcminute\\[2pt]
  \verb'\farcs' & \farcs & fraction of an arcsecond\\[2pt]
  \verb'\fd' & \fd & fraction of a day\\[2pt]
  \verb'\fh' & \fh & fraction of an hour\\[2pt]
  \verb'\fm' & \fm & fraction of a minute\\[2pt]
  \verb'\fs' & \fs & fraction of a second\\[2pt]
  \verb'\fp' & \fp & fraction of a period\\[2pt]
  \verb'\diameter' & \diameter & diameter\\[2pt]
  \verb'\sq' & \sq & square, Q.E.D.\\[2pt]
  \hline
 \end{tabular}
\end{table}

\begin{table}
 \caption{Additional commands for mathematical symbols. These can only be used in maths mode.}
 \label{tab:mathssymbols}
 \begin{tabular}{lll}
  \hline
  Command & Output & Meaning\\
  \hline
  \verb'\upi' & $\upi$ & upright pi\\[2pt]
  \verb'\umu' & $\umu$ & upright mu\\[2pt]
  \verb'\upartial' & $\upartial$ & upright partial derivative\\[2pt]
  \verb'\lid' & $\lid$ & less than or equal to\\[2pt]
  \verb'\gid' & $\gid$ & greater than or equal to\\[2pt]
  \verb'\la' & $\la$ & less than of order\\[2pt]
  \verb'\ga' & $\ga$ & greater than of order\\[2pt]
  \verb'\loa' & $\loa$ & less than approximately\\[2pt]
  \verb'\goa' & $\goa$ & greater than approximately\\[2pt]
  \verb'\cor' & $\cor$ & corresponds to\\[2pt]
  \verb'\sol' & $\sol$ & similar to or less than\\[2pt]
  \verb'\sog' & $\sog$ & similar to or greater than\\[2pt]
  \verb'\lse' & $\lse$ & less than or homotopic to \\[2pt]
  \verb'\gse' & $\gse$ & greater than or homotopic to\\[2pt]
  \verb'\getsto' & $\getsto$ & from over to\\[2pt]
  \verb'\grole' & $\grole$ & greater over less\\[2pt]
  \verb'\leogr' & $\leogr$ & less over greater\\
  \hline
 \end{tabular}
\end{table}

Some additional symbols of common use in astronomy have been added in the MNRAS class. These are shown in tables~\ref{tab:anysymbols}--\ref{tab:mathssymbols}. The command names are -- as far as possible -- the same as those used in other major astronomy journals.

Many other mathematical symbols are also available, either built into \LaTeX\ or via additional packages. If you want to insert a specific symbol but don't know the \LaTeX\ command, we recommend using the Detexify website\footnote{\url{http://detexify.kirelabs.org}}.

Sometimes font or coding limitations mean a symbol may not get smaller when used in sub- or superscripts, and will therefore be displayed at the wrong size. There is no need to worry about this as it will be corrected by the typesetter during production.

To produce bold symbols in mathematics, use \verb'\bmath' for simple variables, and the \verb'bm' package for more complex symbols (see section~\ref{sec:packages}). Vectors are set in bold italic, using \verb'\mathbfit{}'.

For matrices, use \verb'\mathbfss{}' to produce a bold sans-serif font e.g. \mathbfss{H}; this works even outside maths mode, but not all symbols are available (e.g. Greek). For $\nabla$ (del, used in gradients, divergence etc.) use \verb'$\nabla$'.

\subsection{Ions}

A new \verb'\ion{}{}' command has been added to the class file, for the correct typesetting of ionisation states.
For example, to typeset singly ionised calcium use \verb'\ion{Ca}{ii}', which produces \ion{Ca}{ii}.

\section{Figures and tables}
\label{sec:fig_table}
Figures and tables (collectively called `floats') are mostly the same as built into \LaTeX.

\subsection{Basic examples}
\begin{figure}
 \includegraphics[width=\columnwidth]{example}
 \caption{An example figure.}
 \label{fig:example}
\end{figure}
Figures are inserted in the usual way using a \verb'figure' environment and \verb'\includegraphics'. The example Figure~\ref{fig:example} was generated using the code:
\begin{verbatim}
\begin{figure}
 \includegraphics[width=\columnwidth]{example}
 \caption{An example figure.}
 \label{fig:example}
\end{figure}
\end{verbatim}

\begin{table}
 \caption{An example table.}
 \label{tab:example}
 \begin{tabular}{lcc}
  \hline
  Star & Mass & Luminosity\\
   & $M_{\sun}$ & $L_{\sun}$\\
  \hline
  Sun & 1.00 & 1.00\\
  $\alpha$~Cen~A & 1.10 & 1.52\\
  $\epsilon$~Eri & 0.82 & 0.34\\
  \hline
 \end{tabular}
\end{table}
The example Table~\ref{tab:example} was generated using the code:
\begin{verbatim}
\begin{table}
 \caption{An example table.}
 \label{tab:example}
 \begin{tabular}{lcc}
  \hline
  Star & Mass & Luminosity\\
   & $M_{\sun}$ & $L_{\sun}$\\
  \hline
  Sun & 1.00 & 1.00\\
  $\alpha$~Cen~A & 1.10 & 1.52\\
  $\epsilon$~Eri & 0.82 & 0.34\\
  \hline
 \end{tabular}
\end{table}
\end{verbatim}

\subsection{Captions and placement}
Captions go \emph{above} tables but \emph{below} figures, as in the examples above.

The \LaTeX\ float placement commands \verb'[htbp]' are intentionally disabled.
Layout of figures and tables will be adjusted by the publisher during the production process, so authors should not concern themselves with placement to avoid disappointment and wasted effort.
Simply place the \LaTeX\ code close to where the figure or table is first mentioned in the text and leave exact placement to the publishers.

By default a figure or table will occupy one column of the page.
To produce a wider version which covers both columns, use the \verb'figure*' or \verb'table*'  environment.

If a figure or table is too long to fit on a single page it can be split it into several parts.
Create an additional figure or table which uses \verb'\contcaption{}' instead of \verb'\caption{}'.
This will automatically correct the numbering and add `\emph{continued}' at the start of the caption.
\begin{table}
 \contcaption{A table continued from the previous one.}
 \label{tab:continued}
 \begin{tabular}{lcc}
  \hline
  Star & Mass & Luminosity\\
   & $M_{\sun}$ & $L_{\sun}$\\
  \hline
  $\tau$~Cet & 0.78 & 0.52\\
  $\delta$~Pav & 0.99 & 1.22\\
  $\sigma$~Dra & 0.87 & 0.43\\
  \hline
 \end{tabular}
\end{table}
Table~\ref{tab:continued} was generated using the code:

\begin{verbatim}
\begin{table}
 \contcaption{A table continued from the previous one.}
 \label{tab:continued}
 \begin{tabular}{lcc}
  \hline
  Star & Mass & Luminosity\\
   & $M_{\sun}$ & $L_{\sun}$\\
  \hline
  $\tau$~Cet & 0.78 & 0.52\\
  $\delta$~Pav & 0.99 & 1.22\\
  $\sigma$~Dra & 0.87 & 0.43\\
  \hline
 \end{tabular}
\end{table}
\end{verbatim}

To produce a landscape figure or table, use the \verb'pdflscape' package and the \verb'landscape' environment.
The landscape Table~\ref{tab:landscape} was produced using the code:
\begin{verbatim}
\begin{landscape}
 \begin{table}
  \caption{An example landscape table.}
  \label{tab:landscape}
  \begin{tabular}{cccccccccc}
    \hline
    Header & Header & ...\\
    Unit & Unit & ...\\
    \hline
    Data & Data & ...\\
    Data & Data & ...\\
    ...\\
    \hline
  \end{tabular}
 \end{table}
\end{landscape}
\end{verbatim}
Unfortunately this method will force a page break before the table appears.
More complicated solutions are possible, but authors shouldn't worry about this.

\begin{landscape}
 \begin{table}
  \caption{An example landscape table.}
  \label{tab:landscape}
  \begin{tabular}{cccccccccc}
    \hline
    Header & Header & Header & Header & Header & Header & Header & Header & Header & Header\\
    Unit & Unit & Unit & Unit & Unit & Unit & Unit & Unit & Unit & Unit \\
    \hline
    Data & Data & Data & Data & Data & Data & Data & Data & Data & Data\\
    Data & Data & Data & Data & Data & Data & Data & Data & Data & Data\\
    Data & Data & Data & Data & Data & Data & Data & Data & Data & Data\\
    Data & Data & Data & Data & Data & Data & Data & Data & Data & Data\\
    Data & Data & Data & Data & Data & Data & Data & Data & Data & Data\\
    Data & Data & Data & Data & Data & Data & Data & Data & Data & Data\\
    Data & Data & Data & Data & Data & Data & Data & Data & Data & Data\\
    Data & Data & Data & Data & Data & Data & Data & Data & Data & Data\\
    \hline
  \end{tabular}
 \end{table}
\end{landscape}

\section{References and citations}

\subsection{Cross-referencing}

The usual \LaTeX\ commands \verb'\label{}' and \verb'\ref{}' can be used for cross-referencing within the same paper.
We recommend that you use these whenever relevant, rather than writing out the section or figure numbers explicitly.
This ensures that cross-references are updated whenever the numbering changes (e.g. during revision) and provides clickable links (if available in your compiler).

It is best to give each section, figure and table a logical label.
For example, Table~\ref{tab:mathssymbols} has the label \verb'tab:mathssymbols', whilst section~\ref{sec:packages} has the label \verb'sec:packages'.
Add the label \emph{after} the section or caption command, as in the examples in sections~\ref{sec:sections} and \ref{sec:fig_table}.
Enter the cross-reference with a non-breaking space between the type of object and the number, like this: \verb'see Figure~\ref{fig:example}'.

The \verb'\autoref{}' command can be used to automatically fill out the type of object, saving on typing.
It also causes the link to cover the whole phrase rather than just the number, but for that reason is only suitable for single cross-references rather than ranges.
For example, \verb'\autoref{tab:journal_abbr}' produces \autoref{tab:journal_abbr}.

\subsection{Citations}
\label{sec:cite}

MNRAS uses the Harvard -- author (year) -- citation style, e.g. \citet{author2013}.
This is implemented in \LaTeX\ via the \verb'natbib' package, which in turn is included via the \verb'usenatbib' package option (see section~\ref{sec:options}), which should be used in all papers.

Each entry in the reference list has a `key' (see section~\ref{sec:ref_list}) which is used to generate citations.
There are two basic \verb'natbib' commands:
\begin{description}
 \item \verb'\citet{key}' produces an in-text citation: \citet{author2013}
 \item \verb'\citep{key}' produces a bracketed (parenthetical) citation: \citep{author2013}
\end{description}
Citations will include clickable links to the relevant entry in the reference list, if supported by your \LaTeX\ compiler.

\defcitealias{smith2014}{Paper~I}
\begin{table*}
 \caption{Common citation commands, provided by the \texttt{natbib} package.}
 \label{tab:natbib}
 \begin{tabular}{lll}
  \hline
  Command & Ouput & Note\\
  \hline
  \verb'\citet{key}' & \citet{smith2014} & \\
  \verb'\citep{key}' & \citep{smith2014} & \\
  \verb'\citep{key,key2}' & \citep{smith2014,jones2015} & Multiple papers\\
  \verb'\citet[table 4]{key}' & \citet[table 4]{smith2014} & \\
  \verb'\citep[see][figure 7]{key}' & \citep[see][figure 7]{smith2014} & \\
  \verb'\citealt{key}' & \citealt{smith2014} & For use with manual brackets\\
  \verb'\citeauthor{key}' & \citeauthor{smith2014} & If already cited in close proximity\\
  \verb'\defcitealias{key}{Paper~I}' &  & Define an alias (doesn't work in floats)\\
  \verb'\citetalias{key}' & \citetalias{smith2014} & \\
  \verb'\citepalias{key}' & \citepalias{smith2014} & \\
  \hline
 \end{tabular}
\end{table*}

There are a number of other \verb'natbib' commands which can be used for more complicated citations.
The most commonly used ones are listed in Table~\ref{tab:natbib}.
For full guidance on their use, consult the \verb'natbib' documentation\footnote{\url{http://www.ctan.org/pkg/natbib}}.

If a reference has several authors, \verb'natbib' will automatically use `et al.' if there are more than two authors. However, if a paper has exactly three authors, MNRAS style is to list all three on the first citation and use `et al.' thereafter. If you are using \bibtex\ (see section~\ref{sec:ref_list}) then this is handled automatically. If not, the \verb'\citet*{}' and \verb'\citep*{}' commands can be used at the first citation to include all of the authors.

\subsection{The list of references}
\label{sec:ref_list}

It is possible to enter references manually using the usual \LaTeX\ commands, but we strongly encourage authors to use \bibtex\ instead.
\bibtex\ ensures that the reference list is updated automatically as references are added or removed from the paper, puts them in the correct format, saves on typing, and the same reference file can be used for many different papers -- saving time hunting down reference details.
An MNRAS \bibtex\ style file, \verb'mnras.bst', is distributed as part of this package.
The rest of this section will assume you are using \bibtex.

References are entered into a separate \verb'.bib' file in standard \bibtex\ formatting.
This can be done manually, or there are several software packages which make editing the \verb'.bib' file much easier.
We particularly recommend \textsc{JabRef}\footnote{\url{http://jabref.sourceforge.net/}}, which works on all major operating systems.
\bibtex\ entries can be obtained from the NASA Astrophysics Data System\footnote{\label{foot:ads}\url{http://adsabs.harvard.edu}} (ADS) by clicking on `Bibtex entry for this abstract' on any entry.
Simply copy this into your \verb'.bib' file or into the `BibTeX source' tab in \textsc{JabRef}.

Each entry in the \verb'.bib' file must specify a unique `key' to identify the paper, the format of which is up to the author.
Simply cite it in the usual way, as described in section~\ref{sec:cite}, using the specified key.
Compile the paper as usual, but add an extra step to run the \texttt{bibtex} command.
Consult the documentation for your compiler or latex distribution.

Correct formatting of the reference list will be handled by \bibtex\ in almost all cases, provided that the correct information was entered into the \verb'.bib' file.
Note that ADS entries are not always correct, particularly for older papers and conference proceedings, so may need to be edited.
If in doubt, or if you are producing the reference list manually, see the MNRAS instructions to authors$^{\ref{foot:itas}}$ for the current guidelines on how to format the list of references.

\section{Appendices and online material}

To start an appendix, simply place the \verb'
\section{Introduction}





In the $\Lambda$CDM model of structure formation, dark matter halos form from the gravitational collapse of primordial density fluctuations. Within these halos, baryons collapse into a rotating disc with the same angular momentum as the dark matter halo.  With sufficient radiative cooling, the gas is able to collapse and form stars, resulting in a co-rotating disc of gas and stars within a dark matter halo with a density profile which can be approximated by a simple formula (Navarro, Frenk \& White 1996, 1997).  On large scales, the $\Lambda$CDM model of structure formation agrees well with observations of massive galaxies and clusters.  

However, large discrepancies in the low-mass regime raise doubts about $\Lambda$CDM.  For example, there is a large disagreement between the number of small dark matter halos and observed dwarfs \citep[missing satellite problem,][]{Moore1999,Klypin1999}.  There is also a conspicuous absence of observed large satellites compared to predictions \citep[too big to fail problem,][]{Read2006,Boylan-Kolchin2011}.  Finally, rotation profiles of dwarfs show a variety of inner slopes, indicating a diversity of dark matter halo profiles, many of which are in disagreement with the predicted NFW dark matter density profile \citep[cusp vs. core problem,][]{Flores1994,Simon2005,Oh2011}.  These departures from the $\Lambda$CDM model have prompted some to look into warm \citep[e.g.][]{Lovell2014} or self-interacting dark matter \citep[e.g.][] {Rocha2013}.  A promising alternative to re-thinking the nature of dark matter is to investigate the effects of baryonic feedback on star formation.  
        
High resolution simulations conclude that baryonic processes can be used to reconcile the observed properties of dwarf galaxies with $\Lambda$CDM \citep{Wetzel2016ApJ...827L..23W}.  Theoretical work commonly attributes star formation suppression in dwarf galaxies to heating from the UV background during reionization  \citep[e.g.][]{Katz2020}, stellar radiation \citep[e.g.][]{Emerick2018}, and supernovae feedback \citep[e.g.][]{Hu2019}.  Indeed, powerful star-formation driven outflows are observed in starbursting dwarf galaxies \citep[][]{Martin1998,Strickland_Stevens_2000}, and some observational evidence suggests that stellar feedback may dominate in dwarf galaxies \citet{Navarro2018}. 


Stellar feedback is only part of the picture, as the role of AGN feedback in dwarfs becomes harder to ignore.  Evidence of AGN via optical and infrared (IR) indicators has been detected in hundreds of nearby dwarf galaxies \citep[][]{Reines2013,Moran2014,Sartori2015,Baldassare2020,Birchall2020}.  \citet{Kaviraj2019} report the IR-selected AGN occupation fraction in high mass galaxies to be $1-3\%$, while the same criteria yield a $10-30\%$ fraction in dwarf galaxies ($M_* \sim 10^{8-10} M_\odot$).  Given that there are several factors that hinder the detection of AGN in dwarfs \citep{Satyapal2018, Cann2019}, this large AGN fraction can be regarded as a lower limit.  These studies suggest that AGN are common and potentially important phenomena in the low mass regime.  

Additionally, observational evidence of AGN-driven outflows in dwarf galaxies has begun to surface \citep{Penny2018,Bradford2018,Dickey2019,Manzano2019}.  Each of these studies present observations of AGN coexisting with kinematically disturbed gas.  Such disturbances are distinguished by broadened components in their emission line profiles and velocity measurements indicating gas that is disconnected or even counter-rotating with respect to their stars. For example, \citet{Starkenburg2019} (henceforth S19) use data from Illustris \citep{Vogelsberger2014a,Genel2014} to investigate the origin of star-gas counter-rotation in dwarf galaxies.  By examining the evolutionary history of simulated galaxies with counter-rotating gas, they found that such counter-rotating components require removal of the original gas reservoir and re-accretion of new gas, with misaligned angular momentum.  S19 identify two plausible mechanisms for gas removal: stripping from an encounter with a neighbouring galaxy, or AGN outflow events.

The role of AGN feedback in galaxy formation and evolution is not well understood in general.  The shallow potential wells of dwarf galaxies leave them particularly susceptible to feedback, making them ideal laboratories to study how the energy output of an AGN couples to the gas in the host galaxy.  The discovery of AGN-driven outflows in the dwarf regime challenges current conceptions of feedback in dwarf galaxies and raises the question of whether the gas in these outflows permanently escapes the halo.  In this paper, we explore the connection between AGN and kinematically disturbed gas and present further evidence of AGN feedback in dwarf galaxies.

Throughout the paper we assume the cosmological model $H_0 = 71\,\rm{km}\,\rm{s}^{-1}\,\rm{Mpc}^{-1}$, $\Omega_m = 0.27$, and $\Omega_\Lambda = 0.73$.


\section{Data}\label{sec:Data}

\begin{figure
\includegraphics[width=0.49\textwidth]{./figures/bpt_hist.pdf}
\caption{Top: BPT diagnostic for all 50 galaxies in this sample. The dotted line denotes the \citet{kauffmann2003} classification cutoff, and the solid line is the \citet{kewley2001} maximum starburst line. Blue circles indicate isolated galaxies with disturbed gas and with no neighbours of comparable mass (i.e. the neighbouring galaxy is at least 0.75 times the stellar mass of the dwarf) within 1.5 Mpc (see Section \ref{sec:environment}).  Galaxies with counter-rotating stellar and gas components are marked as orange triangles.
Bottom:Stacked histograms of redshift and stellar mass of the galaxies presented in this paper. Dark gray represents AGN hosts and light gray represents star forming galaxies.
}
\label{fig:bpthist}
\end{figure}

\begin{center}
\begin{figure}
\includegraphics[width=\linewidth,clip]{figures/all__thumb.pdf}
\caption{colour images of all 50 dwarf galaxies in our sample.  All images were generated using the SDSS DR12 finding chart tool, with the exception of NGC 1569, which is outside of the SDSS footprint.  The NGC 1569 thumbnail (second row, second column) is a PanSTARS z,g band colour image rendered in the Aladin Lite Viewer with a 3' field of view ($\sim 1\,$kpc on a side).  Each SDSS image is scaled to 10 kpc on a side and the placement of the 1 arcsecond-wide slit is shown in light gray.  
}
\label{fig:thumbs}
\end{figure}
\end{center}

Our complete sample contains 50 nearby ($z=0.05$) dwarf galaxies (roughly $M_\star < 10^{10} M_\odot$) drawn from the Sloan Digital Sky Survey (SDSS).  SDSS is 95\% complete to $r$ band magnitude of 22.2, which is well below the magnitude range covered in this sample ($r\approx 12-17)$.  Twenty-nine of the galaxies in our sample are classified as AGN based on emission line flux ratios that fall above the \citet{kauffmann2003} star forming sequence on the Baldwin, Phillips \& Terlevich (BPT) diagnostic \citep{baldwin1981} or the presence of detectable \ion{He}{II} emission \citep{shirazi2012}.  This sample of 29 dwarf galaxies hosting AGN was selected from the parent samples of \citet{Reines2013,Moran2014,Sartori2015,Oh2015} based on right ascensions that could be observed during our allotted Keck time.   In order to facilitate spatially resolved kinematic measurements, we prioritized spatially extended galaxies and excluded face-on galaxies whenever possible.  

To enable comparison between galaxies with and without AGN, we selected a control sample of 21 star forming galaxies from SDSS Data Release 8, based on their absence of optical and infrared (IR) signatures of AGN.  The control sample was selected by applying the same stellar mass and redshift cuts used to build the AGN sample, then excluding objects with emission line flux ratios falling above the star forming sequence on the BPT diagram.  We also excluded all potential AGN using the WISE mid-IR colour criteria \citep{Jarrett2011, stern2012} and further excluded all galaxies with detectable \ion{He}{II} emission.  The BPT diagnostic diagram and distributions of the redshifts and stellar masses of our full sample are shown in Figure \ref{fig:bpthist}.  


We collected long-slit spectroscopy of 50 galaxies using the Low Resolution Imaging Spectrometer on the Keck I telescope \citep[LRIS][]{Oke_1995,Rockosi2010}. 
Observation dates, conditions, and spectrograph setups for each object are listed in Table \ref{tab:obs_setups}.  The DIMM seeing (Full Width at Half Maximum value of a star observed at zenith, at 5000\AA) is listed for each night. The slit position angles (PA) were determined by fitting $r-$band SDSS photometry using the IRAF ellipse task.  By placing the slit along the semi-major axes determined by these ellipse fits, as shown in Figure \ref{fig:thumbs}, we obtained spatially resolved spectra, presumably perpendicular to the rotation axis of each galaxy.








\newpage
\begin{table*}
\centering
\begin{tabular}{| l c c c c c c c c c c c|}
\hline
Name in SDSS & Observation Date  & Seeing  & slit PA& red setup & exposure time \\ 
& & $\arcsec$ & CCW N&&  s \\ 
\hline
J002145.80+003327.3   & 2015-12-05 &  0.59  &  42.4   & B & 1200 \\
J004214.99$-$104415.0 & 2015-12-04 &  0.55  &  26.9   & B & 1200 \\
J010005.94$-$011059.0 & 2015-12-04 &  0.55  &  51.2   & B & 1200 \\
J015645.30-003737.8   & 2015-12-04 &  0.55  &  126    & B & 1200 \\
J024656.39-003304.8*  & 2015-12-04 &  0.55  &  131.9  & B & 1200 \\
J030040.20+000113.3   & 2015-12-04 &  0.55  &  28.3   & B & 2400 \\
NGC 1569*             & 2015-12-04 &  0.55  &  122.5  & B & 2400 \\
J075538.19+240103.5   & 2015-12-04 &  0.55  &  0      & B & 2400 \\
J080212.06+103234.1   & 2015-12-05 &  0.59  &  100.7  & B & 2400 \\
J080228.83+203050.2   & 2015-12-04 &  0.55  &  73.3   & B & 2400 \\
J081145.29+232825.7   & 2015-12-04 &  0.55  &  0      & B & 2400 \\
J081256.37+545808.4   & 2015-12-05 &  0.59  &  32.77  & B & 1200 \\
J084025.54+181858.9   & 2015-12-04 &  0.55  &  101    & B & 2400 \\
J084234.51+031930.7   & 2015-12-05 &  0.59  &  0      & B & 1200 \\
J085125.81+393541.7   & 2015-03-24 &  0.70  & -43.96  & C & 1200 \\
J090613.75+561015.5   & 2015-12-04 &  0.55  &  0      & B & 2400 \\
J091122.24+615245.2   & 2015-03-24 &  0.70  &  -13    & C & 2400 \\
J092149.44+233438.7   & 2015-12-05 &  0.59  &  156.3  & B & 1200 \\
J093251.11+314145.0   & 2015-03-25 &  0.58  &  -94.6  & B & 1200 \\
J094800.79+095815.4   & 2015-12-05 &  0.59  &  117.8  & B & 1200 \\
J094941.20+321315.9   & 2015-12-04 &  0.55  &  64     & B & 1200 \\
J095418.16+471725.1   & 2015-12-05 &  0.59  &  0      & B & 2400 \\
J100200.96+591508.3   & 2015-12-04 &  0.55  &  148.5  & B & 1200 \\
J100551.19+125740.6   & 2015-12-04 &  0.55  &  60.1   & B & 1200 \\
J100935.66+265648.9   & 2015-12-05 &  0.59  &  45.5   & B & 1200 \\
J101440.21+192448.9   & 2015-03-25 &  0.58  & -57.58  & B & 1200 \\
J114343.76+550019.2   & 2015-03-25 &  0.58  & -117.58 & B & 1200 \\
J122342.82+581446.2*  & 2015-03-24 &  0.70  & -106.86 & C & 1200 \\
J130724.63+523715.2   & 2015-03-25 &  0.58  &  74.09  & B & 2400 \\
J131503.77+223522.7*  & 2015-03-24 &  0.70  &  -144.8 & C & 1200 \\
J134332.09+253157.7   & 2015-03-24 &  0.70  &  -21.33 & C & 2400 \\
J140116.03+542507.4   & 2015-03-25 &  0.58  &  81.76  & B & 1200 \\
J140228.72+091856.4   & 2017-06-24 &  1.17  &  120    & B & 1200 \\
J140510.39+114616.9   & 2017-06-25 &  0.85  &  12     & A & 1200 \\
J140735.47+503242.7   & 2017-06-25 &  0.85  &  163    & A & 2400 \\
J141208.47+102953.8   & 2017-06-24 &  1.17  &  0.0    & B & 1200 \\
J144252.78+205451.6   & 2017-06-24 &  1.17  &  101    & B & 1200 \\
J145843.39+113745.4   & 2017-06-25 &  0.85  &  19     & A & 1200 \\
J151116.53+233421.6   & 2017-06-25 &  0.85  &  165    & A & 1200 \\
J154603.78+031339.4   & 2017-06-24 &  1.17  &  31     & B & 1200 \\
J160839.57+120038.5   & 2017-06-25 &  0.85  &  174    & A & 1200 \\
J162307.88+391847.5   & 2017-06-24 &  1.17  &  80     & B & 1200 \\
J162335.06+454443.6   & 2017-06-25 &  0.85  &  40     & A & 1200 \\
J164428.48+435904.2   & 2017-06-24 &  1.17  &  82     & B & 1200 \\
J170639.14+334103.4   & 2017-06-25 &  0.85  &  156    & A & 1200 \\
J171759.66+332003.8   & 2017-06-24 &  1.17  &  68     & B & 1200 \\
J172125.92+281134.9   & 2017-06-24 &  1.17  &  168    & B & 1200 \\
J172208.82+280155.8   & 2017-06-24 &  1.17  &  130    & B & 1200 \\
J232028.21+150420.9*  & 2015-12-04 &  0.55  &  122.2  & B & 1200 \\
\hline
\end{tabular}
\caption{LRIS configuration for each object, using the 1$\arcsec$ slit placed along the semimajor axis of each galaxy.  For  the  blue  side  (LRIS-B),  we  used  the  600 groove mm$^{-1}$ grism blazed at 4000\AA, yielding a dispersion  of  0.63\AA\, pixel$^{-1}$.  We used three setups on the red side (LRIS-R):\newline
A: 600 groove mm$^{-1}$ grating blazed at 5000\AA, 5600\AA\, dichroic, yielding a dispersion of 0.80\AA\,pixel$^{-1}$\newline
B: 900 groove mm$^{-1}$ grating blazed at 5500\AA, 5600\AA\, dichroic, yielding a dispersion of 0.53\AA\,pixel$^{-1}$\newline
C: 1200 groove mm$^{-1}$ grating blazed at 7500\AA, 5000\AA\, dichroic, yielding a dispersion of 0.40\AA\,pixel$^{-1}$}
\label{tab:obs_setups}
\end{table*}
\newpage



The LRIS data were reduced using a Python pipeline to automate the standard IRAF reduction tasks.  Flexure on the red camera was corrected using the average shift in sky lines.  Sky lines are sparse in the wavelength range covered by the blue CCD, so each galaxy spectrum on the blue side was redshift-corrected using the redshift measured from the flexure-corrected red spectrum.  Flexure on the blue CCD was then calculated by comparing redshift-corrected galaxy emission lines with their expected rest frame values.  The longslit spectra were rectified along both the wavelength and spatial axes, yielding 2-dimensional spectra where each pixel row along the spatial axis is a fully reduced 1-dimensional spectrum. 




\section{Analysis}
\label{sec:analysis}


\subsection{Spatially Resolved Spectra}
\label{sec:binning}
The longslit spectra have been rectified along both the wavelength and spatial axes, creating a 2D spectrum where each pixel row is a fully reduced 1D spectrum.  Much of our analysis depends on fitting subtle spectral features, and thus require high signal to noise (S/N), especially in the dim outskirts of each galaxy.  To achieve the required S/N, we spatially bin the spectra, using larger bins on the outskirts of the galaxy, as shown in Figure \ref{fig:bin_example}.

Spectra were extracted along the slit by summing pixel rows until the target S/N ratio (typically 15$-$20) or maximum bin size was reached. In order to prevent summing the entire image and losing spatial data, the maximum bin size is set to be 20\% of the spatial axis.  The signal to noise was measured using the mean and standard deviation of a relatively featureless portion of the stellar spectrum, just red-ward of [\ion{O}{III}]$\lambda5007$.  The next bin would begin at the central pixel of the last bin.  Figure \ref{fig:bin_example} shows the signal to noise of each pixel row along the spatial axis (black). Vertical gray lines mark the divisions between bins, and the green line indicates the signal to noise when all pixel rows within each bin is summed.

\begin{center}
\begin{figure}
\includegraphics[width=\linewidth,clip]{figures/bin_example.pdf}
\caption{Pixel number along the spatial axis is shown on the x axis.  The y axis shows the signal to noise ratio of a featureless portion of the spectrum red-ward of [\ion{O}{III}]$\lambda$5007.  Moving along the slit, we summed pixel rows (black) until the integrated spectrum's signal to noise ratio (green) reached the target S/N (red) or the maximum bin size was reached. The minimum bin size is 3 pixel rows, which sometimes results in even higher S/N.  Exposure times for each object were chosen with the intention of obtaining sufficient S/N in the outskirts, so the bin size is dependent on the observational setup used.
}
\label{fig:bin_example}
\end{figure}
\end{center}



\subsection{Emission Line Fluxes}
\label{sec:emission}
In order to measure accurate emission line fluxes, it is necessary to account for stellar absorption, which primarily affects the Balmer emission lines. The Penalized Pixel-Fitting software (\textsc{ppxf}) \citep{Cappellari2017} is used to fit and subtract the stellar continuum following the method described in \citet{Manzano2019} (henceforth Paper I), Section 3.1.  

After subtracting the best-fitting stellar population model of the galaxy, the residual emission lines were fit using a custom Bayesian MCMC maximum likelihood sampling algorithm, implemented using the Python package {\it emcee} \citep{emcee}.  A single-Gaussian model was used to fit emission lines for each galaxy in this sample, except in 13 cases when a second Gaussian component was needed (Paper I).  In these 13 cases the BPT flux ratios of the narrow component of the emission lines are shown in Figure \ref{fig:bpthist} and used when classifying these galaxies as AGN or star forming.



\subsection{Multi-Component Velocity Measurements}
\label{sec:ppxf}

In the \textsc{ppxf} software, emission lines are modeled as Gaussians and fit simultaneously with stellar templates.  Each stellar and gas template can be matched to a unique kinematic component, enabling the decomposition of multiple distinct line of sight velocities for stars and various species of emission lines.  Each spatially resolved velocity measurement presented in this work consists of three components: stellar, ionized hydrogen, and forbidden gas emission.

To avoid systematic errors introduced by wavelength calibration on the blue CCD, we fit $\sim 1000$\AA\, sections of the spectrum using \textsc{ppxf}.  Due to the strength of the H$\beta$ and [\ion{O}{III}] emission lines, and their proximity to the stellar feature MgIb, we measured line of sight velocities using the spectral region at rest wavelength $4500 - 5560$\AA\, whenever favorable.  Five galaxies were observed using the 5000\AA\, dichroic, which disrupts the H$\beta$, [\ion{O}{III}] region of the spectrum.  In these cases, stellar and gas kinematics were measured by fitting the portion of the spectrum containing [\ion{O}{II}] and  Balmer break ($3650 - 4550$\AA).  In cases where the [\ion{O}{III}] lines were faint, the fitting area containing H$\alpha$, [\ion{N}{II}], and [\ion{S}{II}] ($6400-6800$\AA) enabled gas velocity measurements to extend to a larger radius than fitting the $4500 - 5560$\AA\, region.  An example of fits to these three regions is shown in Figure \ref{fig:fit_example}.  

Thirteen galaxies in our sample have gas profiles that cannot be accurately modeled by a single Gaussian.  In these cases, two Gaussian components were used for each emission line: a narrow and a broad.  The velocity measurements presented in this work were obtained from the narrow Gaussian components.

\begin{center}
\begin{figure}
\includegraphics[width=\linewidth,clip]{figures/ppxf_example.pdf}
\caption{Example \textsc{ppxf} fits to each of the three spectral sections used to determine velocity curves.  Each velocity curve consists of three components: stellar (red), hydrogen (orange), and forbidden (purple, green, and blue).}
\label{fig:fit_example}
\end{figure}
\end{center}


\subsection{Circular Velocity Curves}
\label{sec:vcurves}
We extracted spatially resolved spectra along the semimajor axis of each galaxy by summing pixel rows, as described in Section \ref{sec:binning}.  Multicomponent line of sight velocity measurements were then taken from each spectrum following the method outlined in Section \ref{sec:ppxf}.  To convert line of sight velocity measured in \textsc{ppxf} into rotational velocity, we correct for the disc inclination angle (see Appendix \ref{app:incl}).  Zero velocity is measured at the galaxy's kinematic center, which is determined by the point of symmetry in the stellar velocity curve.  

Figure \ref{fig:rotation_example1} shows the resulting rotational velocity curve for J170639.14+334103.4  as an example.  Stellar velocity measurements are plotted as gray stars and the ionized gas velocities for H$\beta$ and [\ion{O}{III}] are shown as orange and teal circles, respectively.  $r_{50}$ refers to the 50\% SDSS r-band Petrosian radius. The gray shaded region shows the analytic prediction of the rotation curve assuming the dark matter halo follows an NFW density profile (see Section \ref{subsec:nfw}). 


\section{Results}
\label{sec:Results}
\begin{figure}
	\includegraphics[width=\columnwidth]{./figures/rotation_example_single.pdf}
    \caption{The object J170639.14+334103.4 was chosen randomly from our sample to provide an example of an orderly rotation curve, with a co-rotating disc of gas and stars.  The stellar (gray stars), H$\beta$ (orange circles) and [\ion{O}{III}] (teal circles) velocities are shown as a function of normalized radius, where $r_{50}$ is the r-band Petrosian 50\% radius.  The dotted black line indicates the expected velocity curve for an NFW profile with concentration parameter $c=10$.  The shaded gray region represents the NFW curve expected from halos with concentration parameter $c=8-15$.}
    \label{fig:rotation_example1}
\end{figure}
We obtained circular velocity curves for the stellar and ionized gas components of all 50 galaxies.  Five galaxies are excluded from the rest of this analysis based on the limited spatial extent of their stellar velocity curves.  For three galaxies (J024656.39-003304.8, J131503.77+223522.7, and J232028.21+150420.9), the spatial extent of their velocity curves were comparable (within 0.3\arcsec) with the seeing.  NGC 1569 was excluded because the slit only covered the central 0.25 kpc of the galaxy.  J122342.82+581446.2 was excluded because we were unable to achieve a sufficient S/N ratio to obtain more than two stellar velocity measurements.
Rotation curves for the remaining 45 galaxies (26 AGN and 19 star forming) included in this analysis are shown in Appendix \ref{app:curves}.  



\subsection{Comparison with NFW}
\label{subsec:nfw}

\begin{figure}
	\includegraphics[width=\columnwidth]{./figures/cusp-core.pdf}
    \caption{Four stellar absolute circular velocity curves are shown to demonstrate the variety of inner slopes found in our sample. Two examples of AGN are displayed in the left panels and two star forming galaxies are shown on the right.  Dashed black lines and shaded gray regions represent NFW velocity curves corresponding to a halo mass determined by abundance matching, with the MPA-JHU stellar mass as input.  Stellar velocity curves showing agreement with the expected NFW profile are shown on the top two panels. The velocity profiles in the bottom panels rise slowly, indicating cored dark matter density profiles.  }
    \label{fig:cusp-core}
\end{figure}

The $\Lambda$CDM model predicts that dark matter halos will follow an NFW profile, where the density steepens quickly in the inner regions and more slowly in the outer regions, forming a `cusp' profile.  However, observed dwarf galaxy rotation curves show a variety of slopes in their velocity profiles, some of which rise linearly with radius \citep{Oman2015}, implying underdense dark matter, or `cores,' in some galactic centres. This diversity in inferred dark matter profiles reported in a large number of observational studies and is yet to be explained by baryonic feedback models \citep[e.g.][]{Santos-Santos2020}.  
Since both AGN and stellar feedback have been shown to move large quantities of gas, and thus would be capable of altering the dark matter distribution of their host galaxies \citep[e.g.][]{Governato2010,Martizzi2013}, the process of forming cores might be a complex interplay between multiple feedback modes.  Any observed association between velocity curve shapes and AGN activity could help disentangle role of AGN in shaping dwarf galaxy dark matter halos. 

To aid in visual identification of cores in our sample,  we plot the NFW velocity curve of a $\Lambda$CDM halo corresponding to the predicted halo mass of each galaxy as gray shaded regions in Figures \ref{fig:rotation_example1}, \ref{fig:cusp-core}, and all other velocity curve plots in Appendix \ref{app:curves}. 


It is difficult to observationally constrain the halo mass of a galaxy, so one popular approach is to use abundance matching \citep[e.g.][]{Moster2013}.  Abundance matching assumes a monotonic relation between stellar and halo mass and matches the cumulative abundance of galaxies on that relation.  We used abundance matching to estimate the halo mass corresponding to each galaxy's stellar mass reported in the MPA-JHU catalogue \citep{Brinchmann2004, kauffmann2003, tremonti2004}.  The only observational input is the stellar mass $M_\star$, so the halo mass $M_h$ can be estimated using abundance matching (\citet{Moster2013}, Equation 2):

\begin{equation}
M_* = M_h \left[2N\left(\frac{M_*}{M_1}\right)^{-\beta} + \left(\frac{M_h}{M_1}\right)^\gamma \right]^{-1}
\end{equation}
with four free parameters: N, the normalization parameter, a characteristic mass $M_1$ and low and high mass slopes $\beta$ and $\gamma$.

From these estimated halo masses, we estimate a virial radius 
\begin{equation}
r_v = \left(\frac{3}{4}\frac{M_h}{\pi v \rho_c^0}\right)^{1/3}
\end{equation} 

where $v = 200$ km/s, and $\rho_c^0 = 277.5 M_\odot/$kpc.  Assuming an NFW dark matter density profile, we construct a radial mass distribution (\citet{Lokas2001}, Equation 8):

\begin{equation}
M(r) = g(c) \left[ \ln(1+cs) - \frac{cs}{1+cs}   \right] M_h
\end{equation}

where $c$ is the concentration parameter, $s=r/r_v$, and $g(c) = [\ln(1+c)-c/(1+c)]^{-1}$.  We estimate the circular velocity curve from the radial mass distribution using $v(r) = \sqrt{G M(r)/r}$.  The dotted black line in Figure \ref{fig:rotation_example1} represents the rotation curve expected with an NFW profile with concentration parameter $c=10$, and the shaded gray region was calculated assuming a concentration parameter between $c=8,15$.  

There is no clear correlation between rotational velocity slopes and AGN activity in our sample.  Figure \ref{fig:cusp-core} shows examples of two AGN and two star forming stellar absolute velocity curves in varying levels of agreement with their predicted NFW profiles. The lack of any association between current AGN activity and central mass deficits could be attributed to a difference in time scales for AGN activity and core formation, or a number of other proposed factors not related to AGN \citep[e.g.][]{deBlok2010}.  A solution to the cusp-core dilemma appears to be beyond the scope of this work, and it remains to be seen whether AGN play a role in carving out cores in dwarf galaxies.




\subsection{Peculiar Gas}
\label{sec:peculiar}
\begin{figure}
	\includegraphics[width=\columnwidth]{./figures/disturbed_hist_iso.pdf}
    \caption{We define $\Delta_{\text{off}}$ to be the weighted absolute average of the velocity offset between stars and gas, divided by the average absolute stellar velocity.  This metric is used to quantify the degree of separation between the stellar and forbidden gas component.  Based on the bimodal distribution of  $\Delta_{\text{off}}$  in our sample, we consider galaxies $\Delta_{\text{off}} >= 0.75$ to have kinematically disturbed gas.}  
   \label{fig:del_off}
\end{figure}

\begin{figure*}
	\includegraphics[width=\textwidth]{./figures/rotation_examples.pdf}
    \caption{Examples of rotation curves where the gas is disturbed in different ways.
    In some instances, gas is offset from the stars without showing any clear sign of rotation (left).  Some AGN have stratified narrow line components, where the Balmer and forbidden lines are kinematically distinct from one another (centre).  Five galaxies in our sample have gas and stellar discs rotating separately, and sometimes in opposite directions (right).}
    \label{fig:rotation_example}
\end{figure*}


The gas in these dwarfs show several distinct indications of non-rotational motion, which could be interpreted as inflows, outflows, or recently accreted gas.  To identify disturbed gas kinematics, we designed a metric to quantify the relative offset between the gas and stellar rotation curves.  $\Delta_{\text{off}}$ is the weighted average of the absolute velocity offset between the stellar and gas component, divided by the average absolute stellar velocity.

\begin{equation}
    \Delta_{\text{off}} = \dfrac{|\bar{\Delta}_{v}|}{|\bar{v}_*|}
\end{equation}

where the weighted average of the absolute velocity offset is 

\begin{equation}
   |\bar{\Delta}_{v}| = \dfrac{\sum_i |v_{*,i}-v_{\text{gas},i}|\,w_i}{\sum_i w_i}
\end{equation}

and the weights are the inverse of the combined errors of each velocity measurement, $w_i = (\Delta v_{*,i}^2 + \Delta v_{\text{gas},i}^2)^{-\frac{1}{2}}$

This calculation considers the offset between the stellar and forbidden gas component because the [\ion{O}{II}], [\ion{O}{III}], and [\ion{S}{II}] doublets are less affected by the subtraction of the stellar continuum and absorption than Balmer lines.  Faint broad lines associated with the AGN may also contribute to the line profiles, adding further uncertainty in velocities measured using Balmer emission lines. The forbidden [\ion{O}{II}], [\ion{O}{III}], and [\ion{S}{II}] doublets are not affected by such absorption or broad line region features and therefore give more accurate velocity measurements.

Histograms of $\Delta_{\text{off}}$ are shown in Figure \ref{fig:del_off} and individual $\Delta_\text{off}$ values are reported in the figures for each galaxy in Appendix \ref{app:curves}.  The top panel shows $\Delta_{\text{off}}$ for all 45 galaxies with rotation curves, the middle panel shows the distribution for all isolated galaxies, and the bottom shows the distribution for all galaxies that have at least one neighbour of comparable (or greater) mass (see Section \ref{sec:environment} for a discussion on galaxy environment).  The histograms show a bimodal distribution, which is most pronounced in the middle panel.  Based on this bimodality, we classify a galaxy as `disturbed' when $\Delta_{\text{off}} \geq 0.75$ (dotted gray line).  

Two galaxies (J010005.94-011059.0 and J090613.75+561015.5) have $\Delta_{\text{off}} < 0.75$ between the stars and forbidden emission lines, but the Balmer and forbidden gas components are offset from one another.  Following the same approach, we determine the threshold for offset Balmer and forbidden emission components to be (H$\beta$ - [\ion{O}{III}] $\Delta_{\text{off}} > 0.5$). Distinct kinematics associated with higher ionization emission lines is known as line stratification (see Section \ref{subsec:stratification}), and we count galaxies with stratified emission lines among the galaxies with disturbed gas.   By this criteria, 25 of the 45 galaxies with rotation curves are disturbed.   All rotation curves are plotted in Appendix \ref{app:curves}. The rotation curves showing orderly, co-rotating discs are shown in Figure \ref{fig:wellbehaved} and 25 disturbed rotation curves are shown in Figure \ref{fig:disturbed}.  

Of the 25 galaxies with disturbed gas, 19 host AGN and 6 do not. The majority (73\%) the AGN in our sample have disturbed gas, while only 32\% of star forming galaxies have $\Delta_\text{off} > 0.75$.  We noticed distinct properties in the non-rotational motion exhibited in the disturbed gas, and we show examples of rotation curves exhibiting different types of disturbances.  We observe gas that is generally offset from the stellar component, stratified emission lines, and counter-rotating gas. Examples of each type of disturbance are shown in Figure \ref{fig:rotation_example}. 



\subsubsection{Line Stratification}
\label{subsec:stratification}
In the stratified model of the narrow line region (NLR), lower ionization gas resides on the outer parts of the NLR while higher ionization lines are generated closer to the AGN \citep[e.g.][]{Croom2002,Andika2020}.  Distinct kinematics associated with emission lines of different ionization potentials imply a complex narrow line region that is  stratified in ionization and wind speed. We observe stratified gas components in seven AGN in our sample, with higher ionization lines showing higher velocities than lower ionization lines.  This implies a decelerating outflow: where a high velocity, high ionization wind is generated near the AGN, and while the low ionization gas in the outer region of the NLR flows more slowly.

We observe no correlation between wind speed and AGN luminosity, though the line stratification we observe in these seven galaxies preferentially occurs in galaxies that have outflows indicated by broad [\ion{O}{III}] components.  Plots of the stratified gas kinematics in these seven galaxies can be found in the Appendix, Figure \ref{fig:strat_curves}.



\subsubsection{Counter-Rotating
\label{subsec:counter-rotating}
\begin{figure*}
	\includegraphics[width=\textwidth]{./figures/Crot_vel.pdf}
    \caption{The rotation curves for five galaxies with counter-rotating gas are shown here.  The colours are as in Figure \ref{fig:rotation_example}, and the blue dots in the middle panel indicate gas velocities measured from the [SII] doublet.}
    \label{fig:cr_curves}
\end{figure*}

Of the 45 galaxies with rotation curves, five have counter-rotating gas and stellar components, shown in Figure \ref{fig:cr_curves}.  Counter rotating gas and stars have long been explained as the effect of the accretion of gas clouds or small satellites after the formation of the stellar disc \citep[e.g.][]{Thakar1996,Thomas2006,Katkov2014}.  As mentioned in the introduction, S19 found that counter-rotating gas in dwarf galaxies requires substantial gas removal, either via black hole feedback or environmental effects from fly-by interactions with more massive systems.  Interestingly, all five counter-rotating dwarfs in our sample host AGN.

S19 also make several predictions about the present-day properties of counter-rotating dwarfs.  In cases where re-accretion of gas is gradual, they find that counter-rotation can be very long lived (up to $\sim 2$ Gyr).  As a result, S19 predict no significant correlation with environment.  Three counter-rotating galaxies are isolated (J004214.99-104415.0, J080228.83+203050.2, J093251.11+314145.0) and two (J094941.20+321315.9, J130434.92+075505.0) have at least one neighbour with comparable mass.

An event that removes most of the original gas reservoir would quench star formation, making it likely that counter-rotating dwarfs will have older stellar populations and appear redder in colour.  All five counter-rotating galaxies discussed here have colours  $u-r > 2$, which is redder than the average for our sample ($u-r = 1.83$). S19 also find a 30\% gas deficit in counter-rotating dwarfs at $z=0$, relative to control galaxies at fixed stellar mass.  Though most of the galaxies in our sample lack gas mass estimates, we can turn our attention to the six galaxies with HI masses measured in the ALFALFA survey \citep{Bradford2018}.   Of these six, five are not disturbed and one is counter-rotating (J094941.20+321315.9).  The five co-rotating galaxies with HI measurements have a wide range of gas fractions ($\frac{M_{HI}}{M_*} \sim 0.23 - 7.3$), and the one counter-rotating has the smallest gas fraction ($\frac{M_{HI}}{M_*}* = 0.16$).  The gas component of J094941.20+321315.9 reaches velocities that exceed the predicted NFW curve, suggesting that this galaxy inhabits a more massive halo than predicted from its stellar mass.







\subsection{Star Formation Suppression}
\label{subsec:suppression}
\begin{figure}
	\includegraphics[width=\columnwidth]{./figures/sf_suppression.pdf}
    \caption{Absolute line of sight velocity $(v_\text{los})$ measurements that far exceed the expected NFW velocity curves based on their stellar masses indicate overmassive dark matter haloes relative to the measured stellar mass, implying ongoing star formation suppression.  Stellar (left), Balmer emission (centre) and forbidden emission (right) components are shown for the three galaxies in our sample where this is most apparent. Green curves mark expected NFW velocity curves for galaxies with stellar mass $\log(M_\star)=10.5, 11,\text{and } 12$ and concentration parameter $c=10$. Black dotted lines denote the expected NFW velocity curves based on each galaxy's MPA-JHU stellar mass.  All three of these galaxies host AGN, and two have counter-rotating gas components, which lends additional evidence potentially associating AGN with gas depletion and star formation suppression in dwarf galaxies.
    }  
   \label{fig:sf_supp}
\end{figure}



While abundance matching enables us to infer halo masses based on stellar masses, maximum line of sight velocity measurements can be used to place lower limits on the true halo mass of each galaxy.  If the measured lower limit of the halo mass of a galaxy exceeds the halo mass inferred from abundance matching to stellar mass, the galaxy can be said to have a lower star formation rate than expected.  Figure \ref{fig:sf_supp} shows absolute line of sight velocity curves for the three galaxies in our sample where this is most apparent.  As in previous figures, black dotted lines indicate the NFW curve predicted based on each galaxy's stellar mass. Green curves mark the NFW curves associated with stellar masses $\log(M_\star/M_\odot) = 10.5, 11, \text{and } 12$ and concentration parameter $c=10$.  The absolute line of sight velocity curves for the stellar (left), hydrogen Balmer emission (middle), and forbidden emission (right) components are shown. Line of sight velocities are plotted here in place of circular velocities to avoid errors introduced when correcting for disc inclination (Appendix \ref{app:incl}).  

The three galaxies shown in Figure \ref{fig:sf_supp} were selected from our sample using a similar approach to the one used to identify disturbed gas in Section \ref{sec:peculiar}.  We calculated the  offset between each kinematic component ($v_\text{los})$ and the predicted NFW curve $v_\text{NFW}$:
\begin{equation}
\Delta_{v_{\text{los}}\text{, NFW}} = \frac{\Sigma_i (v_{\text{los},i} - v_\text{NFW}) w_{\text{los},i}}{\Sigma_i w_{\text{los},i}}
\end{equation}
The distribution of $\Delta_{v_{\text{los}}\text{, NFW}}$ values for each component revealed three outlying galaxies that consistently fell above the threshold $\Delta_{v_{\text{los}}\text{, NFW}} > 0.5$: J093251.11+314145.0, J094941.20+321315.9, and J140116.03+542507.4.  

These galaxies have measured velocity curves that far exceed the expected NFW profile, indicating that they inhabit much larger halos than expected based on their stellar masses.  Their small stellar masses and red colours $(u-r \geq 2.23)$ suggest ongoing or recent star formation suppression.  It is interesting to note that all three galaxies host AGN, and two have counter-rotating gas, consistent with the scenario where AGN clear a substantial amount of gas from their hosts, limiting star formation.






\subsection{Environment}
\label{sec:environment}


To distinguish between the effects of environmental and secular processes on gas kinematics, we searched for luminous galaxies in the regions surrounding each dwarf.  Following the method and  criteria employed by \citet{Janz2017}, we queried the SDSS DR12 and 2MASS Redshift survey catalogues for luminous neighbours with $M_{K_S} < -21.5$ mag and SDSS $r < -16$ mag.  The completeness limit of this search is $M_{K_S} = -21.5$ mag at $z=0.02$; corresponding to $M_*\sim8\times10^9 M_\odot$ \citep{geha2012}. 
This limit is well below the magnitudes expected for galaxies in the mass range explored in this work, so extending the search to the redshift limit of our sample ($z=0.05$) has no effect on completeness.
The 2MASS Redshift Survey search revealed matches overlooked in the SDSS search due to missing redshifts, but SDSS optical counterparts existed for all 2MASS matches. We use SDSS DR12 g- and r-band photometry and the mass-magnitude relation of \citet{Bernardi2010} to estimate the masses of neighbouring galaxies. 

We identify galaxies within 1.5 Mpc and $\pm 1000\text{ km s}^{-1}$ of each dwarf in this sample as neighbours.  Using the g- and r-band mass-magnitude relation, we estimate the mass of each neighbour. In order to identify isolated galaxies, we count the number of neighbours with comparable mass (i.e. stellar mass $M_{\star,\text{neighbour}} \geq 0.75 \times M_{\odot,\text{dwarf}}$) within 1.5 Mpc and $\pm 1000\,\text{km}\,\text{s}^{-1}$.  The number of neighbours for each dwarf can be found in Table \ref{tab:sample}.  

A recent study of 62,258 dwarf ($M_\star < 5\times10^9 M_\odot$) galaxies finds no discernible difference between the environments of AGN and non-AGN dwarf galaxies, suggesting that environmental factors may not play a dominant role in triggering AGN \citep{Kristensen2020}.  Similarly, we find no statistically significant link between AGN and environment.  However, \citet{Kristensen2020} suggest that remnants of past interactions may be reflected in gas kinematics.

The importance of environment in disturbing gas kinematics can be explored by considering the bottom panel of Figure \ref{fig:del_off}, which shows the distribution of $\Delta_{\text{off}}$ for galaxies with at least one neighbour of comparable (or greater) mass within 1.5 Mpc.  Star forming and AGN-hosting galaxies with neighbours show varying degrees of gas disturbance, further supporting the notion that environment may not play a dominant role in triggering AGN activity.  The most extreme values of $\Delta_{\text{off}}$ are associated with AGN, suggesting that AGN are capable of generating large scale disturbances in their host galaxies' ISM, though the presence of AGN-hosting galaxies with undisturbed gas implies this is not always the case.  

On the other hand, isolated galaxies show a distinct bimodal distribution, where star forming galaxies tend to have orderly rotating discs, and disturbed gas is almost always associated with AGN.  Table \ref{tab:isolated} lists the seven disturbed, isolated galaxies, six of which host AGN.  Two of these six isolated AGN have counter rotating gas, and three have outflows indicated by distinct broadened components in [\ion{O}{III}]$\lambda$5007, as in Paper I.  To clarify, the outflows in these four galaxies are identified with multicomponent Gaussian fits to the [\ion{O}{III}] line profile; disturbed gas is determined here by a velocity offset between the narrow component of the emission lines from the stellar component.

The single isolated and disturbed star forming galaxy, J101440.21+192448.9, was originally included in our sample based on broad lines in H$\alpha$ \citep{Reines2013}, which later faded, likely due to transient stellar activity \citep{baldassare2016}.  This object is classified as an outflow galaxy in Paper I based on broadened wings in its [\ion{O}{III}] emission line profile.  Follow-up Integral Field Unit (IFU) observations with KCWI revealed that the rotation axis of J101440.21+192448.9 is in fact parallel to the slit position in our LRIS observations (Liu et al., in prep).  Since the slit is not aligned with the stellar disc, these velocity measurements do not reflect the true rotational velocity of this galaxy.  

Follow-up KCWI observations were obtained for eight objects in this sample (Liu et al., in prep). These IFU observations produce line of sight velocities that agree with our longslit measurements and confirm that in all other cases, the LRIS slit was oriented perpendicular to the rotational axes, as intended.  Proper slit orientation for the remainder of the sample should be verified with similar follow-up IFU observations, though the confirmation of correct slit placement in all but one galaxy is encouraging. Since J101440.21+192448.9 is an active star forming galaxy with supernova-driven outflows, it is reasonable to surmise that bright star forming regions could outshine the rest of the disc, confusing the photometric fit used to determine slit placement. This calls into question the slit placement for other galaxies with non-rotational kinematics and signs of active star formation, such as J171759.66+332003.8.



\begin{table*}
\centering
\begin{tabular}{| l c c c c c c c c c c c c|}
\hline
Abbreviated & Redshift  & $\log(M_*)$  & $\log(M_{\text{BH}})$& $r_{50}$  & BPT & HeII & neigh- & dist-   & counter- & outflow & strat- \\ 
Name        &           &              &                      & (kpc)     &     &      & bors   & urbed   & rotating &         & ified \\ 
(1)         & (2)       & (3)          & (4)                  & (5)       & (6) & (7)  & (8)    & (9)     & (10)     & (11) & (12) \\ \hline
J0021+00    & 0.0180 &  9.15        & ---                  & 0.89      &  AGN       & AGN    &   7  & -- & -- & -- & -- \\
J0042-10    & 0.0359 &  9.44        & ---                  & 1.34      &  AGN       & AGN    &   5  & \checkmark & \checkmark & -- & -- \\
J0100-01    & 0.0515 &  9.44        & ---                  & 0.99      &  Comp.     & Comp.  &   5  & \checkmark & -- & \checkmark & -- \\
J0156-00    & 0.0450 &  9.39        & ---                  & 1.91      &  SF        & SF     &  13  & \checkmark & -- & -- & -- \\
J0246-00    & 0.0464 &  9.35        & 5.7$^c$              & 1.34      &  AGN       & AGN    &  37  & -- & -- & -- & -- \\
J0300+00    & 0.0095 &  8.72        & ---                  & 2.11      &  SF        & SF     &   0  & -- & -- & -- & -- \\
NGC 1569    & $-80\text{ km s}^{-1}$ &  8.56 & ---         & 7.09      &  SF        & SF     &  --  & -- & -- & \checkmark & -- \\
J0755+24    & 0.0290 &  8.85        & ---                  & 1.78      &  SF        & SF     &   3  & -- & -- & -- & -- \\
J0802+10    & 0.0145 &  9.60        & 3.6$^b$              & 1.29      &  AGN       & AGN    &   3  & -- & -- & -- & -- \\
J0802+20    & 0.0286 &  10.6        & ---                  & 1.97      &  Comp.     & AGN    &   0  & \checkmark & \checkmark & -- & -- \\
J0811+23    & 0.0157 &  9.06        & 4.4$^c$              & 0.58      &  AGN       & AGN    &   2  & \checkmark & -- & \checkmark & \checkmark \\
J0812+54    & 0.0086 &  9.29        & ---                  & 1.49      &  SF        & SF     &   0  & -- & -- & -- & -- \\
J0840+18    & 0.0149 &  9.13        & 4.3$^c$              & 0.94      &  AGN       & AGN    &   2  & \checkmark & -- & \checkmark & -- \\
J0842+03    & 0.0289 &  9.33        & ---                  & 0.75      &  Comp.     & AGN    &   2  & \checkmark & -- & \checkmark & \checkmark \\
J0851+39    & 0.0407 &  9.28        & 5.4$^c$              & 1.70      &  AGN       & AGN    &   2  & -- & -- & -- & -- \\ 
J0906+56    & 0.0465 &  9.37        & 5.4$^c$              & 1.51      &  AGN       & AGN    &   5  & \checkmark & -- & \checkmark & -- \\
J0911+61    & 0.0263 &  8.95        & ---                  & 2.03      &  SF        & SF     &   7  & \checkmark & -- & -- & -- \\      
J0921+23    & 0.0281 &  9.27        & ---                  & 1.27      &  SF        & SF     &   0  & -- & -- & -- & -- \\
J0932+31    & 0.0153 &  9.62        & 3.5$^b$              & 0.58      &  AGN       & AGN    &   0  & \checkmark & \checkmark & -- & -- \\          
J0948+09    & 0.0103 &  8.73        & 4.2$^b$              & 0.73      &  Comp.     & AGN    &   5  & \checkmark & -- & -- & \checkmark \\
J0949+32    & 0.0051 &  9.22        & 4.1$^b$              & 0.58      &  Comp.     & AGN    &   6  & \checkmark & \checkmark & -- & -- \\
J0954+47    & 0.0326 &  9.47        & 4.9$^c$              & 1.75      &  AGN       & AGN    &   0  & \checkmark & -- & \checkmark & -- \\
J1002+59    & 0.0093 &  9.60        & 4.1$^b$              & 1.12      &  AGN       & Comp.  &   1  & \checkmark & -- & -- & \checkmark \\
J1005+12    & 0.0093 &  9.64        & 4.8$^b$              & 0.97      &  AGN       & AGN    &   0  & \checkmark & -- & \checkmark & -- \\
J1009+26    & 0.0143 &  8.75        & 5.1$^c$              & 0.62      &  AGN       & AGN    &   0  & \checkmark & -- & \checkmark & -- \\
J1014+19    & 0.0284 &  8.56        & ---                  & 0.88      &  SF        & SF     &   0  & \checkmark & -- & \checkmark & -- \\           
J1143+55    & 0.0269 &  8.92        & ---                  & 1.03      &  SF        & SF     &   1  & -- & -- & -- & -- \\         
J1223+58    & 0.0146 &  9.39        & 6.1$^b$              & 1.01      &  AGN       & AGN    &   6  & -- & -- & -- & -- \\         
J1304+07    & 0.0479 &  9.41        & ---                  & 1.13      &  AGN       & AGN    &  16  & \checkmark & \checkmark & -- & -- \\  
J1307+52    & 0.0259 &  9.10        & ---                  & 1.18      &  SF        & SF     &   2  & -- & -- & -- & -- \\      
J1315+22    & 0.0226 &  9.20        & ---                  & 1.58      &  SF        & SF     &   1  & -- & -- & -- & -- \\        
J1343+25    & 0.0280 &  9.19        & ---                  & 3.09      &  SF        & SF     &   3  & -- & -- & -- & -- \\        
J1401+54    & 0.0059 &  9.57        & 3.2$^b$              & 0.59      &  AGN       & AGN    &   5  & -- & -- & -- & -- \\      
J1402+09    & 0.0195 &  8.83        & ---                  & 0.79      &  AGN       & AGN    &  26  & \checkmark & -- & -- & -- \\     
J1405+11    & 0.0178 &  9.23        & ---                  & 1.15      &  AGN       & AGN    &   4  & -- & -- & -- & -- \\
J1407+50    & 0.0070 &  8.72        & ---                  & 0.77      &  Comp.     & AGN    &   8  & -- & -- & -- & -- \\ 
J1412+10    & 0.0324 &  8.99        & ---                  & 0.56      &  AGN       & AGN    &   3  & \checkmark & -- & -- & -- \\
J1442+20    & 0.0426 &  8.89        & ---                  & 0.89      &  AGN       & AGN    &   1  & \checkmark & -- & \checkmark & \checkmark \\
J1458+11    & 0.0198 &  9.91        & ---                  & 2.40      &  SF        & SF     &   0  & -- & -- & -- & -- \\
J1511+23    & 0.0143 &  9.68        & ---                  & 1.01      &  SF        & SF     &   0  & -- & -- & -- & -- \\
J1546+03    & 0.0132 &  9.49        & ---                  & 2.05      &  SF        & AGN    &   3  & -- & -- & -- & -- \\
J1608+12    & 0.0166 &  9.75        & ---                  & 2.65      &  SF        & SF     &   0  & -- & -- & -- & -- \\
J1623+39    & 0.0172 &  9.22        & ---                  & 2.68      &  SF        & SF     &   2  & \checkmark & -- & -- & -- \\
J1623+45    & 0.0064 &  9.41        & ---                  & 0.82      &  AGN       & AGN    &   0  & \checkmark & -- & -- & -- \\
J1644+43    & 0.0178 &  9.53        & ---                  & 0.86      &  SF        & SF     &   0  & -- & -- & -- & -- \\
J1706+33    & 0.0301 &  9.41        & ---                  & 1.95      &  SF        & SF     &   7  & -- & -- & -- & -- \\
J1717+33    & 0.0151 &  9.85        & ---                  & 1.03      &  SF        & SF     &   1  & \checkmark & -- & \checkmark & -- \\
J1721+28    & 0.0280 &  10.0        & ---                  & 3.49      &  SF        & SF     &   0  & -- & -- & -- & -- \\
J1722+28    & 0.0281 &  9.23        & ---                  & 1.71      &  SF        & SF     &   3  & \checkmark & -- & -- & -- \\
J2320+15    & 0.0130 &  9.57        & 3.7$^b$              & 0.59      &  AGN       & AGN    &   6  & -- & -- & -- & -- \\
\hline
\end{tabular}
\caption{
(1) * indicates objects excluded from this study.
(2) Redshift is calculated by fits to stellar absorption lines in LRIS spectra using \textsc{ppxf}.
(3) Stellar mass reported in the MPA-JHU catalogue.
(4) $^b$ Black hole mass lower limits derived using Eddington Luminosity arguments (M14) $^c$ Black hole mass estimated using as $M_{BH}\propto R\Delta V^2/G$, where $\Delta V$ is measured from broad H$\alpha$, extrapolating the BLR radius -- luminosity relation extends into the low mass regime (R13)
(5) SDSS Petrosian radius containing 50\% of r-band flux, in kiloparsecs.
(6) Classification of dominant ionization source based on Gaussian fits to emission lines using the process described in Section \ref{sec:emission}.  The spectra were extracted from the central 1kpc of each galaxy.
(7) Same as (6) but for HeII classification (S15)
(8) Number of galaxies with comparable mass within 1.5 Mpc. 
(9) Classified as disturbed (see Section \ref{sec:peculiar})
(10) Gas is clearly rotating and offset from stellar component. 
(11) Has an outflow identified by an additional broad component in as defined in Paper I.
(12) Narrow emission lines are stratified (see Section \ref{subsec:stratification})}
\label{tab:sample}
\end{table*}




\begin{center}
\begin{table}
\begin{tabular}{|c|c|c|c|c|c|}
    name &  $\log(M_\star)$ & AGN & counter-  & outflow & u$-$r \\ 
    &&& rotating & (Paper I) &colour  \\\hline
J0802+20   & 10.6 & \checkmark & \checkmark &    &  2.39 \\
J0932+31   &  9.6 & \checkmark & \checkmark &    &  2.23 \\
J0954+47   &  9.5 & \checkmark &    & \checkmark &  2.20 \\
J1005+12   &  9.6 & \checkmark &    & \checkmark &  2.16 \\
J1009+26   &  8.7 & \checkmark &    & \checkmark &  1.91 \\
J1014+19   &  8.6 &    &    & \checkmark &  1.25 \\ 
J1623+45   &  9.4 & \checkmark &    &    &  2.13 \\\hline

\end{tabular}
\caption{Seven galaxies in our sample have disturbed gas kinematics and no neighbours of comparable mass within 1.5 Mpc and $\pm 1000$ km s$^{-1}$.  Six of them host AGN, two have counter-rotating gas, and four have outflows indicated by broad wings in their [OIII]5007 emission line profiles.  $u-r$ colour is based on SDSS cModelMag photometry.}
\label{tab:isolated}
\end{table}
\end{center}








\section{Summary}
\label{sec:Summary}
From Keck LRIS longslit spectroscopy, we measured rotational velocity curves of 45 dwarf galaxies.  Our sample consists of  26 galaxies with AGN and a control sample of 19 star forming galaxies with no optical or IR evidence of AGN.  The rotation curves are decomposed into stellar, Balmer emission, and forbidden emission components.  In order to investigate the potential effects of AGN on gas kinematics in this sample, we quantified velocity offsets between stellar and gas components.  We summarize our conclusions below.


\begin{enumerate}




\item We detect counter-rotating gas in five of 45 galaxies, and AGN are present in all five cases. A study of the occurrence, properties, and evolutionary history of counter-rotating galaxies in Illustris \citep{Starkenburg2019} finds that removal and re-accretion of gas is necessary for counter-rotating gas discs to form, and that periods of AGN activity are sometimes associated with large drops in gas mass.  We find that the properties of the counter-rotating dwarfs in our sample agree with present-day properties of counter-rotating dwarf galaxies predicted from Illustris.

\item We use the weighted average of velocity offsets between stellar spectra and emission lines to identify disturbed gas kinematics. We find disturbed gas in 25 out of 45 galaxies in our sample.  Of the 26 AGN in our sample, 19 (or 73\%) have disturbed gas.  Star forming galaxies tend to have orderly, co-rotating gas discs, with only 32\% showing disturbed gas.  

\item At least three galaxies in our sample have line of sight velocities far exceeding those expected based on their stellar masses.  These line of sight velocities constitute a lower limit estimate of true halo mass, indicating that these galaxies inhabit much more massive dark matter haloes than expected based on their small stellar masses. This potential evidence of ongoing star formation suppression is most apparent in three AGN-hosting galaxies within our sample, two of which have counter-rotating gas.  This suggests that AGN could be associated with gas removal and star formation suppression in dwarf galaxies.  A detailed study of the star formation histories of these galaxies is warranted.

\item In the absence of environmental influence, kinematically disturbed gas is expected to be caused by secular processes.  Fifteen dwarfs in our sample are isolated, with no neighbouring galaxies of comparable mass within 1.5 Mpc and $\pm1000$ km s$^{-1}$.  Of these, seven galaxies have disturbed gas.  We find that six out of seven isolated galaxies with disturbed gas host AGN. 

\end{enumerate}

Our findings imply that AGN play an important, and perhaps dominant, role in disturbing gas and limiting star formation in dwarf galaxies.  This represents additional evidence of the importance of AGN-driven winds in dwarf galaxy evolution and further highlights the importance of including AGN feedback in galaxy formation models.  A detailed follow-up IFU study of ionized gas kinematics in a subset of these galaxies is in progress (Liu et. al., in prep). Multiphase gas kinematic measurements, gas mass measurements, and comparison with simulations run with detailed AGN feedback models are necessary for a full understanding of AGN feedback in dwarf galaxies.

\vspace{1cm}
{\bf Acknowledgements}
We would like to thank the anonymous referee,
whose careful reading and thoughtful feedback 
has helped to improve and clarify this manuscript. 
Support for this program was provided
by the National Science Foundation, under
grant number AST 1817233.  Additional support
was provided by NASA through a grant from the
Space Telescope Science Institute (Program AR-
14582.001-A), which is operated by the Association of
Universities for Research in Astronomy, Incorporated,
under NASA contract NAS5-26555.  
The data presented herein were obtained at the W. M.
Keck Observatory, which is operated as a scientific partnership 
among the California Institute of Technology,
the University of California and the National Aeronautics 
and Space Administration. The Observatory was made 
possible by the generous financial support of the
W. M. Keck Foundation.
The authors wish to recognize and acknowledge the
very significant cultural role and reverence that the 
summit of Mauna Kea has always had within the Indigenous
Hawaiian community. We are most fortunate to have the
opportunity to conduct observations from this mountain.
Some of the data presented herein were obtained using the UCI
Remote Observing Facility, made possible by a generous gift 
from John and Ruth Ann Evans. 
This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

{\bf Data Availability}\\
The data underlying this article will be shared on reasonable request to the corresponding author.
\bibliographystyle{mnras}

\section{Introduction}

The journal \textit{Monthly Notices of the Royal Astronomical Society} (MNRAS) encourages authors to prepare their papers using \LaTeX.
The style file \verb'mnras.cls' can be used to approximate the final appearance of the journal, and provides numerous features to simplify the preparation of papers.
This document, \verb'mnras_guide.tex', provides guidance on using that style file and the features it enables.

This is not a general guide on how to use \LaTeX, of which many excellent examples already exist.
We particularly recommend \textit{Wikibooks \LaTeX}\footnote{\url{https://en.wikibooks.org/wiki/LaTeX}}, a collaborative online textbook which is of use to both beginners and experts.
Alternatively there are several other online resources, and most academic libraries also hold suitable beginner's guides.

For guidance on the contents of papers, journal style, and how to submit a paper, see the MNRAS Instructions to Authors\footnote{\label{foot:itas}\url{http://www.oxfordjournals.org/our_journals/mnras/for_authors/}}.
Only technical issues with the \LaTeX\ class are considered here.


\section{Obtaining and installing the MNRAS package}
Some \LaTeX\ distributions come with the MNRAS package by default.
If yours does not, you can either install it using your distribution's package manager, or download it from the Comprehensive \TeX\ Archive Network\footnote{\url{http://www.ctan.org/tex-archive/macros/latex/contrib/mnras}} (CTAN).

The files can either be installed permanently by placing them in the appropriate directory (consult the documentation for your \LaTeX\ distribution), or used temporarily by placing them in the working directory for your paper.

To use the MNRAS package, simply specify \verb'mnras' as the document class at the start of a \verb'.tex' file:

\begin{verbatim}
\documentclass{mnras}
\end{verbatim}
Then compile \LaTeX\ (and if necessary \bibtex) in the usual way.

\section{Preparing and submitting a paper}
We recommend that you start with a copy of the \texttt{mnras\_template.tex} file.
Rename the file, update the information on the title page, and then work on the text of your paper.
Guidelines for content, style etc. are given in the instructions to authors on the journal's website$^{\ref{foot:itas}}$.
Note that this document does not follow all the aspects of MNRAS journal style (e.g. it has a table of contents).

If a paper is accepted, it is professionally typeset and copyedited by the publishers.
It is therefore likely that minor changes to presentation will occur.
For this reason, we ask authors to ignore minor details such as slightly long lines, extra blank spaces, or misplaced figures, because these details will be dealt with during the production process.

Papers must be submitted electronically via the online submission system; paper submissions are not permitted.
For full guidance on how to submit a paper, see the instructions to authors.

\section{Class options}
\label{sec:options}
There are several options which can be added to the document class line like this:

\begin{verbatim}
\documentclass[option1,option2]{mnras}
\end{verbatim}
The available options are:
\begin{itemize}
\item \verb'letters' -- used for papers in the journal's Letters section.
\item \verb'onecolumn' -- single column, instead of the default two columns. This should be used {\it only} if necessary for the display of numerous very long equations.
\item \verb'doublespacing' -- text has double line spacing. Please don't submit papers in this format.
\item \verb'referee' -- \textit{(deprecated)} single column, double spaced, larger text, bigger margins. Please don't submit papers in this format.
\item \verb'galley' -- \textit{(deprecated)} no running headers, no attempt to align the bottom of columns.
\item \verb'landscape' -- \textit{(deprecated)} sets the whole document on landscape paper.
\item \verb"usenatbib" -- \textit{(all papers should use this)} this uses Patrick Daly's \verb"natbib.sty" package for citations.
\item \verb"usegraphicx" -- \textit{(most papers will need this)} includes the \verb'graphicx' package, for inclusion of figures and images.
\item \verb'useAMS' -- adds support for upright Greek characters \verb'\upi', \verb'\umu' and \verb'\upartial' ($\upi$, $\umu$ and $\upartial$). Only these three are included, if you require other symbols you will need to include the \verb'amsmath' or \verb'amsymb' packages (see section~\ref{sec:packages}).
\item \verb"usedcolumn" -- includes the package \verb"dcolumn", which includes two new types of column alignment for use in tables.
\end{itemize}

Some of these options are deprecated and retained for backwards compatibility only.
Others are used in almost all papers, but again are retained as options to ensure that papers written decades ago will continue to compile without problems.
If you want to include any other packages, see section~\ref{sec:packages}.

\section{Title page}

If you are using \texttt{mnras\_template.tex} the necessary code for generating the title page, headers and footers is already present.
Simply edit the title, author list, institutions, abstract and keywords as described below.

\subsection{Title}
There are two forms of the title: the full version used on the first page, and a short version which is used in the header of other odd-numbered pages (the `running head').
Enter them with \verb'\title[]{}' like this:
\begin{verbatim}
\title[Running head]{Full title of the paper}
\end{verbatim}
The full title can be multiple lines (use \verb'\\' to start a new line) and may be as long as necessary, although we encourage authors to use concise titles. The running head must be $\le~45$ characters on a single line.

See appendix~\ref{sec:advanced} for more complicated examples.

\subsection{Authors and institutions}

Like the title, there are two forms of author list: the full version which appears on the title page, and a short form which appears in the header of the even-numbered pages. Enter them using the \verb'\author[]{}' command.

If the author list is more than one line long, start a new line using \verb'\newauthor'. Use \verb'\\' to start the institution list. Affiliations for each author should be indicated with a superscript number, and correspond to the list of institutions below the author list.

For example, if I were to write a paper with two coauthors at another institution, one of whom also works at a third location:
\begin{verbatim}
\author[K. T. Smith et al.]{
Keith T. Smith,$^{1}$
A. N. Other,$^{2}$
and Third Author$^{2,3}$
\\
$^{1}$Affiliation 1\\
$^{2}$Affiliation 2\\
$^{3}$Affiliation 3}
\end{verbatim}
Affiliations should be in the format `Department, Institution, Street Address, City and Postal Code, Country'.

Email addresses can be inserted with the \verb'\thanks{}' command which adds a title page footnote.
If you want to list more than one email, put them all in the same \verb'\thanks' and use \verb'\footnotemark[]' to refer to the same footnote multiple times.
Present addresses (if different to those where the work was performed) can also be added with a \verb'\thanks' command.

\subsection{Abstract and keywords}

The abstract is entered in an \verb'abstract' environment:
\begin{verbatim}
\begin{abstract}
The abstract of the paper.
\end{abstract}
\end{verbatim}
\noindent Note that there is a word limit on the length of abstracts.
For the current word limit, see the journal instructions to authors$^{\ref{foot:itas}}$.

Immediately following the abstract, a set of keywords is entered in a \verb'keywords' environment:
\begin{verbatim}
\begin{keywords}
keyword 1 -- keyword 2 -- keyword 3
\end{keywords}
\end{verbatim}
\noindent There is a list of permitted keywords, which is agreed between all the major astronomy journals and revised every few years.
Do \emph{not} make up new keywords!
For the current list of allowed keywords, see the journal's instructions to authors$^{\ref{foot:itas}}$.

\section{Sections and lists}

Sections and lists are generally the same as in the standard \LaTeX\ classes.

\subsection{Sections}
\label{sec:sections}
Sections are entered in the usual way, using \verb'\section{}' and its variants. It is possible to nest up to four section levels:
\begin{verbatim}
\section{Main section}
 \subsection{Subsection}
  \subsubsection{Subsubsection}
   \paragraph{Lowest level section}
\end{verbatim}
\noindent The other \LaTeX\ sectioning commands \verb'\part', \verb'\chapter' and \verb'\subparagraph{}' are deprecated and should not be used.

Some sections are not numbered as part of journal style (e.g. the Acknowledgements).
To insert an unnumbered section use the `starred' version of the command: \verb'\section*{}'.

See appendix~\ref{sec:advanced} for more complicated examples.

\subsection{Lists}

Two forms of lists can be used in MNRAS -- numbered and unnumbered.

For a numbered list, use the \verb'enumerate' environment:
\begin{verbatim}
\begin{enumerate}
 \item First item
 \item Second item
 \item etc.
\end{enumerate}
\end{verbatim}
\noindent which produces
\begin{enumerate}
 \item First item
 \item Second item
 \item etc.
\end{enumerate}
Note that the list uses lowercase Roman numerals, rather than the \LaTeX\ default Arabic numerals.

For an unnumbered list, use the \verb'description' environment without the optional argument:
\begin{verbatim}
\begin{description}
 \item First item
 \item Second item
 \item etc.
\end{description}
\end{verbatim}
\noindent which produces
\begin{description}
 \item First item
 \item Second item
 \item etc.
\end{description}

Bulleted lists using the \verb'itemize' environment should not be used in MNRAS; it is retained for backwards compatibility only.

\section{Mathematics and symbols}

The MNRAS class mostly adopts standard \LaTeX\ handling of mathematics, which is briefly summarised here.
See also section~\ref{sec:packages} for packages that support more advanced mathematics.

Mathematics can be inserted into the running text using the syntax \verb'$1+1=2$', which produces $1+1=2$.
Use this only for short expressions or when referring to mathematical quantities; equations should be entered as described below.

\subsection{Equations}
Equations should be entered using the \verb'equation' environment, which automatically numbers them:

\begin{verbatim}
\begin{equation}
 a^2=b^2+c^2
\end{equation}
\end{verbatim}
\noindent which produces
\begin{equation}
 a^2=b^2+c^2
\end{equation}

By default, the equations are numbered sequentially throughout the whole paper. If a paper has a large number of equations, it may be better to number them by section (2.1, 2.2 etc.). To do this, add the command \verb'\numberwithin{equation}{section}' to the preamble.

It is also possible to produce un-numbered equations by using the \LaTeX\ built-in \verb'\['\textellipsis\verb'\]' and \verb'$$'\textellipsis\verb'$$' commands; however MNRAS requires that all equations are numbered, so these commands should be avoided.

\subsection{Special symbols}


\begin{table}
 \caption{Additional commands for special symbols commonly used in astronomy. These can be used anywhere.}
 \label{tab:anysymbols}
 \begin{tabular}{lll}
  \hline
  Command & Output & Meaning\\
  \hline
  \verb'\sun' & \sun & Sun, solar\\[2pt]
  \verb'\earth' & \earth & Earth, terrestrial\\[2pt]
  \verb'\micron' & \micron & microns\\[2pt]
  \verb'\degr' & \degr & degrees\\[2pt]
  \verb'\arcmin' & \arcmin & arcminutes\\[2pt]
  \verb'\arcsec' & \arcsec & arcseconds\\[2pt]
  \verb'\fdg' & \fdg & fraction of a degree\\[2pt]
  \verb'\farcm' & \farcm & fraction of an arcminute\\[2pt]
  \verb'\farcs' & \farcs & fraction of an arcsecond\\[2pt]
  \verb'\fd' & \fd & fraction of a day\\[2pt]
  \verb'\fh' & \fh & fraction of an hour\\[2pt]
  \verb'\fm' & \fm & fraction of a minute\\[2pt]
  \verb'\fs' & \fs & fraction of a second\\[2pt]
  \verb'\fp' & \fp & fraction of a period\\[2pt]
  \verb'\diameter' & \diameter & diameter\\[2pt]
  \verb'\sq' & \sq & square, Q.E.D.\\[2pt]
  \hline
 \end{tabular}
\end{table}

\begin{table}
 \caption{Additional commands for mathematical symbols. These can only be used in maths mode.}
 \label{tab:mathssymbols}
 \begin{tabular}{lll}
  \hline
  Command & Output & Meaning\\
  \hline
  \verb'\upi' & $\upi$ & upright pi\\[2pt]
  \verb'\umu' & $\umu$ & upright mu\\[2pt]
  \verb'\upartial' & $\upartial$ & upright partial derivative\\[2pt]
  \verb'\lid' & $\lid$ & less than or equal to\\[2pt]
  \verb'\gid' & $\gid$ & greater than or equal to\\[2pt]
  \verb'\la' & $\la$ & less than of order\\[2pt]
  \verb'\ga' & $\ga$ & greater than of order\\[2pt]
  \verb'\loa' & $\loa$ & less than approximately\\[2pt]
  \verb'\goa' & $\goa$ & greater than approximately\\[2pt]
  \verb'\cor' & $\cor$ & corresponds to\\[2pt]
  \verb'\sol' & $\sol$ & similar to or less than\\[2pt]
  \verb'\sog' & $\sog$ & similar to or greater than\\[2pt]
  \verb'\lse' & $\lse$ & less than or homotopic to \\[2pt]
  \verb'\gse' & $\gse$ & greater than or homotopic to\\[2pt]
  \verb'\getsto' & $\getsto$ & from over to\\[2pt]
  \verb'\grole' & $\grole$ & greater over less\\[2pt]
  \verb'\leogr' & $\leogr$ & less over greater\\
  \hline
 \end{tabular}
\end{table}

Some additional symbols of common use in astronomy have been added in the MNRAS class. These are shown in tables~\ref{tab:anysymbols}--\ref{tab:mathssymbols}. The command names are -- as far as possible -- the same as those used in other major astronomy journals.

Many other mathematical symbols are also available, either built into \LaTeX\ or via additional packages. If you want to insert a specific symbol but don't know the \LaTeX\ command, we recommend using the Detexify website\footnote{\url{http://detexify.kirelabs.org}}.

Sometimes font or coding limitations mean a symbol may not get smaller when used in sub- or superscripts, and will therefore be displayed at the wrong size. There is no need to worry about this as it will be corrected by the typesetter during production.

To produce bold symbols in mathematics, use \verb'\bmath' for simple variables, and the \verb'bm' package for more complex symbols (see section~\ref{sec:packages}). Vectors are set in bold italic, using \verb'\mathbfit{}'.

For matrices, use \verb'\mathbfss{}' to produce a bold sans-serif font e.g. \mathbfss{H}; this works even outside maths mode, but not all symbols are available (e.g. Greek). For $\nabla$ (del, used in gradients, divergence etc.) use \verb'$\nabla$'.

\subsection{Ions}

A new \verb'\ion{}{}' command has been added to the class file, for the correct typesetting of ionisation states.
For example, to typeset singly ionised calcium use \verb'\ion{Ca}{ii}', which produces \ion{Ca}{ii}.

\section{Figures and tables}
\label{sec:fig_table}
Figures and tables (collectively called `floats') are mostly the same as built into \LaTeX.

\subsection{Basic examples}
\begin{figure}
 \includegraphics[width=\columnwidth]{example}
 \caption{An example figure.}
 \label{fig:example}
\end{figure}
Figures are inserted in the usual way using a \verb'figure' environment and \verb'\includegraphics'. The example Figure~\ref{fig:example} was generated using the code:
\begin{verbatim}
\begin{figure}
 \includegraphics[width=\columnwidth]{example}
 \caption{An example figure.}
 \label{fig:example}
\end{figure}
\end{verbatim}

\begin{table}
 \caption{An example table.}
 \label{tab:example}
 \begin{tabular}{lcc}
  \hline
  Star & Mass & Luminosity\\
   & $M_{\sun}$ & $L_{\sun}$\\
  \hline
  Sun & 1.00 & 1.00\\
  $\alpha$~Cen~A & 1.10 & 1.52\\
  $\epsilon$~Eri & 0.82 & 0.34\\
  \hline
 \end{tabular}
\end{table}
The example Table~\ref{tab:example} was generated using the code:
\begin{verbatim}
\begin{table}
 \caption{An example table.}
 \label{tab:example}
 \begin{tabular}{lcc}
  \hline
  Star & Mass & Luminosity\\
   & $M_{\sun}$ & $L_{\sun}$\\
  \hline
  Sun & 1.00 & 1.00\\
  $\alpha$~Cen~A & 1.10 & 1.52\\
  $\epsilon$~Eri & 0.82 & 0.34\\
  \hline
 \end{tabular}
\end{table}
\end{verbatim}

\subsection{Captions and placement}
Captions go \emph{above} tables but \emph{below} figures, as in the examples above.

The \LaTeX\ float placement commands \verb'[htbp]' are intentionally disabled.
Layout of figures and tables will be adjusted by the publisher during the production process, so authors should not concern themselves with placement to avoid disappointment and wasted effort.
Simply place the \LaTeX\ code close to where the figure or table is first mentioned in the text and leave exact placement to the publishers.

By default a figure or table will occupy one column of the page.
To produce a wider version which covers both columns, use the \verb'figure*' or \verb'table*'  environment.

If a figure or table is too long to fit on a single page it can be split it into several parts.
Create an additional figure or table which uses \verb'\contcaption{}' instead of \verb'\caption{}'.
This will automatically correct the numbering and add `\emph{continued}' at the start of the caption.
\begin{table}
 \contcaption{A table continued from the previous one.}
 \label{tab:continued}
 \begin{tabular}{lcc}
  \hline
  Star & Mass & Luminosity\\
   & $M_{\sun}$ & $L_{\sun}$\\
  \hline
  $\tau$~Cet & 0.78 & 0.52\\
  $\delta$~Pav & 0.99 & 1.22\\
  $\sigma$~Dra & 0.87 & 0.43\\
  \hline
 \end{tabular}
\end{table}
Table~\ref{tab:continued} was generated using the code:

\begin{verbatim}
\begin{table}
 \contcaption{A table continued from the previous one.}
 \label{tab:continued}
 \begin{tabular}{lcc}
  \hline
  Star & Mass & Luminosity\\
   & $M_{\sun}$ & $L_{\sun}$\\
  \hline
  $\tau$~Cet & 0.78 & 0.52\\
  $\delta$~Pav & 0.99 & 1.22\\
  $\sigma$~Dra & 0.87 & 0.43\\
  \hline
 \end{tabular}
\end{table}
\end{verbatim}

To produce a landscape figure or table, use the \verb'pdflscape' package and the \verb'landscape' environment.
The landscape Table~\ref{tab:landscape} was produced using the code:
\begin{verbatim}
\begin{landscape}
 \begin{table}
  \caption{An example landscape table.}
  \label{tab:landscape}
  \begin{tabular}{cccccccccc}
    \hline
    Header & Header & ...\\
    Unit & Unit & ...\\
    \hline
    Data & Data & ...\\
    Data & Data & ...\\
    ...\\
    \hline
  \end{tabular}
 \end{table}
\end{landscape}
\end{verbatim}
Unfortunately this method will force a page break before the table appears.
More complicated solutions are possible, but authors shouldn't worry about this.

\begin{landscape}
 \begin{table}
  \caption{An example landscape table.}
  \label{tab:landscape}
  \begin{tabular}{cccccccccc}
    \hline
    Header & Header & Header & Header & Header & Header & Header & Header & Header & Header\\
    Unit & Unit & Unit & Unit & Unit & Unit & Unit & Unit & Unit & Unit \\
    \hline
    Data & Data & Data & Data & Data & Data & Data & Data & Data & Data\\
    Data & Data & Data & Data & Data & Data & Data & Data & Data & Data\\
    Data & Data & Data & Data & Data & Data & Data & Data & Data & Data\\
    Data & Data & Data & Data & Data & Data & Data & Data & Data & Data\\
    Data & Data & Data & Data & Data & Data & Data & Data & Data & Data\\
    Data & Data & Data & Data & Data & Data & Data & Data & Data & Data\\
    Data & Data & Data & Data & Data & Data & Data & Data & Data & Data\\
    Data & Data & Data & Data & Data & Data & Data & Data & Data & Data\\
    \hline
  \end{tabular}
 \end{table}
\end{landscape}

\section{References and citations}

\subsection{Cross-referencing}

The usual \LaTeX\ commands \verb'\label{}' and \verb'\ref{}' can be used for cross-referencing within the same paper.
We recommend that you use these whenever relevant, rather than writing out the section or figure numbers explicitly.
This ensures that cross-references are updated whenever the numbering changes (e.g. during revision) and provides clickable links (if available in your compiler).

It is best to give each section, figure and table a logical label.
For example, Table~\ref{tab:mathssymbols} has the label \verb'tab:mathssymbols', whilst section~\ref{sec:packages} has the label \verb'sec:packages'.
Add the label \emph{after} the section or caption command, as in the examples in sections~\ref{sec:sections} and \ref{sec:fig_table}.
Enter the cross-reference with a non-breaking space between the type of object and the number, like this: \verb'see Figure~\ref{fig:example}'.

The \verb'\autoref{}' command can be used to automatically fill out the type of object, saving on typing.
It also causes the link to cover the whole phrase rather than just the number, but for that reason is only suitable for single cross-references rather than ranges.
For example, \verb'\autoref{tab:journal_abbr}' produces \autoref{tab:journal_abbr}.

\subsection{Citations}
\label{sec:cite}

MNRAS uses the Harvard -- author (year) -- citation style, e.g. \citet{author2013}.
This is implemented in \LaTeX\ via the \verb'natbib' package, which in turn is included via the \verb'usenatbib' package option (see section~\ref{sec:options}), which should be used in all papers.

Each entry in the reference list has a `key' (see section~\ref{sec:ref_list}) which is used to generate citations.
There are two basic \verb'natbib' commands:
\begin{description}
 \item \verb'\citet{key}' produces an in-text citation: \citet{author2013}
 \item \verb'\citep{key}' produces a bracketed (parenthetical) citation: \citep{author2013}
\end{description}
Citations will include clickable links to the relevant entry in the reference list, if supported by your \LaTeX\ compiler.

\defcitealias{smith2014}{Paper~I}
\begin{table*}
 \caption{Common citation commands, provided by the \texttt{natbib} package.}
 \label{tab:natbib}
 \begin{tabular}{lll}
  \hline
  Command & Ouput & Note\\
  \hline
  \verb'\citet{key}' & \citet{smith2014} & \\
  \verb'\citep{key}' & \citep{smith2014} & \\
  \verb'\citep{key,key2}' & \citep{smith2014,jones2015} & Multiple papers\\
  \verb'\citet[table 4]{key}' & \citet[table 4]{smith2014} & \\
  \verb'\citep[see][figure 7]{key}' & \citep[see][figure 7]{smith2014} & \\
  \verb'\citealt{key}' & \citealt{smith2014} & For use with manual brackets\\
  \verb'\citeauthor{key}' & \citeauthor{smith2014} & If already cited in close proximity\\
  \verb'\defcitealias{key}{Paper~I}' &  & Define an alias (doesn't work in floats)\\
  \verb'\citetalias{key}' & \citetalias{smith2014} & \\
  \verb'\citepalias{key}' & \citepalias{smith2014} & \\
  \hline
 \end{tabular}
\end{table*}

There are a number of other \verb'natbib' commands which can be used for more complicated citations.
The most commonly used ones are listed in Table~\ref{tab:natbib}.
For full guidance on their use, consult the \verb'natbib' documentation\footnote{\url{http://www.ctan.org/pkg/natbib}}.

If a reference has several authors, \verb'natbib' will automatically use `et al.' if there are more than two authors. However, if a paper has exactly three authors, MNRAS style is to list all three on the first citation and use `et al.' thereafter. If you are using \bibtex\ (see section~\ref{sec:ref_list}) then this is handled automatically. If not, the \verb'\citet*{}' and \verb'\citep*{}' commands can be used at the first citation to include all of the authors.

\subsection{The list of references}
\label{sec:ref_list}

It is possible to enter references manually using the usual \LaTeX\ commands, but we strongly encourage authors to use \bibtex\ instead.
\bibtex\ ensures that the reference list is updated automatically as references are added or removed from the paper, puts them in the correct format, saves on typing, and the same reference file can be used for many different papers -- saving time hunting down reference details.
An MNRAS \bibtex\ style file, \verb'mnras.bst', is distributed as part of this package.
The rest of this section will assume you are using \bibtex.

References are entered into a separate \verb'.bib' file in standard \bibtex\ formatting.
This can be done manually, or there are several software packages which make editing the \verb'.bib' file much easier.
We particularly recommend \textsc{JabRef}\footnote{\url{http://jabref.sourceforge.net/}}, which works on all major operating systems.
\bibtex\ entries can be obtained from the NASA Astrophysics Data System\footnote{\label{foot:ads}\url{http://adsabs.harvard.edu}} (ADS) by clicking on `Bibtex entry for this abstract' on any entry.
Simply copy this into your \verb'.bib' file or into the `BibTeX source' tab in \textsc{JabRef}.

Each entry in the \verb'.bib' file must specify a unique `key' to identify the paper, the format of which is up to the author.
Simply cite it in the usual way, as described in section~\ref{sec:cite}, using the specified key.
Compile the paper as usual, but add an extra step to run the \texttt{bibtex} command.
Consult the documentation for your compiler or latex distribution.

Correct formatting of the reference list will be handled by \bibtex\ in almost all cases, provided that the correct information was entered into the \verb'.bib' file.
Note that ADS entries are not always correct, particularly for older papers and conference proceedings, so may need to be edited.
If in doubt, or if you are producing the reference list manually, see the MNRAS instructions to authors$^{\ref{foot:itas}}$ for the current guidelines on how to format the list of references.

\section{Appendices and online material}

To start an appendix, simply place the \verb'