\section{Introduction} \label{sec:intro}

\begin{figure*}
    \centering
   
   
    \includegraphics[width=0.475\hsize]{images/70micron+ring.png}
    \includegraphics[width=0.515\hsize]{images/Halpha_ColDens_0p1-0p2-0p40p8_1.png}
    \caption{{\bf Left}: The \textit{Herschel} 70 $\mu$m map of RCW 36 \citep{Minier2013}. The red box outlines the region that was already observed for the FEEDBACK program and the dashed white box shows the area that will be mapped.
    The blue crosses mark the location of the two O star candidates. Note that the close proximity of the two O star candidates does not allow to distinguish them clearly in this figure. The black dashed ellipse indicates the location of the central molecular ring, first reported by \citet{Minier2013}. The \textit{Herschel} 70 $\mu$m map also traces the limb-brightened shells at the cavity walls. The white contours indicate the \textit{Herschel} column density at N$_{\rm H_{2}}$ = 1, 2, 4 and 8$\times$10$^{22}$ cm$^{-2}$ determined using the method presented in \citet{Palmeirim2013}.  
    {\bf Right}: H$\alpha$ intensity map towards RCW 36 from the SuperCOSMOS H$\alpha$ Survey. The intensity units of the map are not calibrated to a specific unit and are only relative \citep{Hambly2001,Parker2005}. The white contours again indicate the \textit{Herschel} column density.
    }
    \label{fig:observedMap}
\end{figure*}

The interstellar medium (ISM) is a complex mixture of multiple phases \citep[][]{McKee1977,Wolfire1995,Wolfire2003,Walch2015b} where stars form in the densest regions \citep{Bergin2007} which are mostly organised in dense filaments \citep{Andre2010,Molinari2010,Schneider2012}. Feedback from the star formation process in the form of ionizing radiation and stellar winds provides substantial energy injection into the ISM which can drive its chemical and dynamical evolution. Feedback might also play a significant role in suppressing the star formation rate (SFR) in molecular clouds. It has been proposed that massive stars form in gravitationally collapsing hubs and ridges \citep{Motte2018} which results in the rapid accumulation of mass at the center of collapse (i.e. in a few free-fall timescales). This would result in high SFRs, which are not observed, if not counteracted by feedback processes \citep[e.g.][]{MacLow2017,VazquezSemadeni2019}. Additionally, with astrophysical simulations it remains extremely challenging to predict the impact and role of the different stellar feedback processes on the molecular cloud evolution because of the large computational requirements and complex subgrid physics  \citep[e.g.][]{Dale2014,Geen2020,Grudic2021,Kim2021}.\\
Stellar feedback leads to the formation of H\,{\scriptsize II}\ regions which come in the form of H\,{\scriptsize II}\ bubbles \citep{Churchwell2006,Deharveng2010,Beaumont2010,Kendrew2012}, bipolar H\,{\scriptsize II}\ regions \citep{Bally1982,Deharveng2015,Schneider2018,Samal2018} and more irregular features \citep{Anderson2011,Anderson2014}. Recently, the kinematics of a couple of H\,{\scriptsize II}\ bubbles have been studied with the [C\,{\scriptsize II}]\ 158 $\mu$m fine-structure line  \citep[][]{Anderson2019,Pabst2019,Pabst2020,Luisi2021,Tiwari2021,Beuther2022} because it traces the photodissociation regions (PDRs) at the interfaces between H\,{\scriptsize II}\ regions and molecular clouds, where mostly far-ultraviolet (FUV) photons in the energy range of 6 - 13.6 eV regulate the physical conditions of the ISM \citep[][]{Hollenbach1999}. The [C\,{\scriptsize II}]\ kinematics in some of these regions demonstrated the presence of expanding shells with velocities up to 15 km s$^{-1}$  \citep[][]{Pabst2019,Pabst2020,Luisi2021,Tiwari2021,Beuther2022}. 
However, they often show expansion in only one direction, mostly blue-shifted, which suggests that the bubbles might not be fully spherical.  
This more complex geometry is important for the interpretation of the various emission distributions. Observations of hot X-ray emitting plasmas, produced by stellar winds from OB stars, showed that these plasmas have 
an unbalanced energy budget, i.e. the energy of the hot plasmas is significantly lower than the energy injected by stellar winds  \citep[e.g.][]{Townsley2003,Townsley2006,Townsley2011,HarperClark2009,Lopez2011,Lopez2014,Rosen2014,Tiwari2021}. The more complex geometry of expanding H\,{\scriptsize II}\ regions could thus allow the hot plasma to leak out of the region, which might explain the mismatch in the energy budget. The lack of an expanding shell at one side of a region leading to rapid hot plasma leakage was recently demonstrated for RCW 49 by \citet{Tiwari2021}. Studying the [C\,{\scriptsize II}]\ emission dynamics can also help to constrain the role of stellar feedback in suppressing the star formation of a molecular cloud as well as triggering a second generation of star formation, which is still highly debated \citep[e.g.][]{Zavagno2010,Zavagno2020,Dale2013,Walch2015a}. \citet{Luisi2021} proposed, based on [C\,{\scriptsize II}]\ data taken within the SOFIA (Stratospheric Observatory for Infrared Astronomy) legacy program FEEDBACK\footnote{\href{https://feedback.astro.umd.edu}{https://feedback.astro.umd.edu}} \citep{Schneider2020}, that star-formation is triggered in RCW120. They propose a model in which a wind-driven expanding [C\,{\scriptsize II}]\ shell sweeps up a gas shell that  fragments and forms stars on very short time scales ($\sim$ 0.1 Myr). \\ 
The formation of bipolar H\,{\scriptsize II}\ regions has received less attention than single bubbles, which might be related to the fact that bipolar H\,{\scriptsize II}\ regions are not as common \citep[e.g.][]{Samal2018}. Early work by \citet{Bodenheimer1979} demonstrated that a bipolar H\,{\scriptsize II}\ region can form by expansion in a flattened molecular cloud, consistent with simulations by \citet{Wareing2017}. \citet{Whitworth2018} proposed that bipolar H\,{\scriptsize II}\ regions emerge from a sheet that was formed by a cloud-cloud collision, whereas \citet{Kumar2020} propose that bipolar H\,{\scriptsize II}\ regions form from a hub-filament cloud that was flattened by rotation. Numerical simulations predict that a significant fraction of the dense molecular gas is organized in filaments and sheets \citep[e.g.][]{Padoan2001,VazquezSemadeni2006,Banerjee2009,Wareing2019}, allowing for the formation of bipolar H\,{\scriptsize II}\ regions. This view of the molecular ISM organized in filaments and sheets is now increasingly supported by observations \citep[e.g.][]{Andre2014,Qian2015,Tritsis2018,Shimajiri2019,Bonne2020b}.\\\\
Here, we focus on the bipolar H\,{\scriptsize II}\ region RCW 36 which is located in the dense ridge of the Vela C molecular cloud \citep{Hill2011,Minier2013,Fissel2016}. The distance of the Vela C molecular cloud has recently been updated to 900 $\pm$ 50 pc with the GAIA data \citep{Zucker2020,GAIAcollaboration2018}. Earlier distance estimates \citep{Liseau1992,Yamaguchi1999,Massi2019} 
derived values between 700 and 1000 pc. 
RCW 36 is probably the first developing H\,{\scriptsize II}\ region in Vela C, which is well illustrated by Fig. 1 from \citet{Hill2011}, suggesting Vela C is still in a relatively early stage of star formation. The young cluster at the origin of the bipolar cavities has more than 350 stars located within a radius of 0.5 pc \citep{Baba2004}, an estimated age of 1.1 $\pm$ 0.6 Myr \citep{Ellerbroek2013a} and is proposed to host two O stars of type O9.5 V \& O9 V \citep{Massi2003,Bik2005,Ellerbroek2013a}. This  is consistent with the estimated total luminosity of 1.3$\times$10$^{5}$ L$_{\odot}$ for the cluster (scaled to the adopted distance in this work: d = 900 pc) \citep{Verma1994}. \textit{Herschel} observations indicated that the young cluster is surrounded by a dense molecular ring of swept-up gas with a radius of $\sim$ 1 pc which is proposed to expand with a velocity of 1-2 km s$^{-1}$ \citep{Minier2013}. In Fig. \ref{fig:observedMap}, the H$\alpha$ absorption in the eastern part of the ring would then suggest that this part of the ring is expanding towards us and that the western part is expanding away from us \citep{Minier2013}. Multiwavelength observations of RCW 36 have also established the presence of several protostar and young stellar object (YSO) candidates \citep{Bik2006,Hill2011,Ellerbroek2011,Giannini2012,Massi2019}, indicating relatively low-mass ongoing star formation in the region, as well as the presence of two Herbig-haro (HH) jets \citep{Ellerbroek2013b}.\\\\
In this paper, we present the first [C\,{\scriptsize II}]\ and [O\,{\scriptsize I}]\ observations of RCW 36 obtained by the SOFIA FEEDBACK Legacy survey
in combination with complementary data to acquire a global understanding of the evolution of this region. Both the [C\,{\scriptsize II}]\ and [O\,{\scriptsize I}]\ line are PDR tracers where [O\,{\scriptsize I}], with a critical density of 5$\times$10$^{5}$ cm$^{-3}$, is particularly used to trace dense PDRs \citep{Roellig2006}. These FEEDBACK observations unveil new dynamical information that was not available before.
 Sect.~\ref{obs} describes our new [CII], [OI], and CO(3-2) observations, as well as archival X-ray and submillimeter continuum  datasets. The results of these observations are presented in Sect.~\ref{sec:results}. In Sect.~\ref{sec:analysis}, the expansion energetics and mass ejection parameters are calculated, and in Sect.~\ref{sec:chandra} the [C\,{\scriptsize II}]\ data is compared with Chandra X-ray observations of RCW 36. In Sect.~\ref{sec:discussion}, these results are combined to propose a scenario for the evolution of RCW 36 and discuss the results in the global context of stellar feedback on molecular clouds.

\section{Observations} \label{obs}
\subsection{SOFIA}
The FEEDBACK C$^{+}$ Legacy survey observed the [C\,{\scriptsize II}]\ $^{3}$P$_{3/2}$ $\to$ $^{3}$P$_{1/2}$ transition, at 158 $\mu$m, and [O\,{\scriptsize I}]\ $^{3}$P$_{1}$ $\to$ $^{3}$P$_{2}$ transition, at 63 $\mu$m, simultaneously with the upGREAT instrument \citep{Risacher2018} onboard of the airborne Stratospheric Observatory for Infrared Astronomy 
(SOFIA) \citep{Young2012} during a flight on June 6th 2019 from Christchurch, New Zealand. 
The observation strategy was to carry out [C\,{\scriptsize II}]\ and [O\,{\scriptsize I}]\ on-the-fly (OTF) maps and is described in detail in \citet{Schneider2020}.
For RCW 36, the planned map within the legacy program has a size of 14.4$^{\prime}\times$14.4$^{\prime}$, indicated in Fig. \ref{fig:observedMap}. Here, we present the lower part of the map (14.4$^{\prime}\times$7.2$^{\prime}$) that has been observed so far. 
The center of the full map is located at $\alpha_{(J2000)}$ = 08$^h$59$^m$26.8$^s$ and $\delta_{(J2000)}$ = -43$^\circ$44$'$14.1$''$, and the emission-free OFF position is at $\alpha_{(J2000)}$ = 09$^h$01$^m$31.7$^s$ and $\delta_{(J2000)}$ = -43$^\circ$22$'$50.0$''$.\\ 
 Both, the reduced [C\,{\scriptsize II}]\ (smoothed to 20$^{\prime\prime}$) and [O\,{\scriptsize I}]\ (smoothed to 30$^{\prime\prime}$) map, used in this paper, have a spectral binning of 0.2 km s$^{-1}$. The typical noise rms of this smoothed data within 0.2 km s$^{-1}$ is 0.8-1.0 K for [C\,{\scriptsize II}]\ and $\sim$ 0.8-1.5 K for [O\,{\scriptsize I}].
The calibration was done using the GREAT pipeline \citep{Guan2012}. To convert the antenna to main beam temperatures, a forward efficiency $\eta_{f}$ = 0.97 and main beam efficiency $\eta_{mb}$ = 0.65 for [C\,{\scriptsize II}]\ and 0.69 for [O\,{\scriptsize I}]\ were applied.
To improve the baseline removal of the data, a new method based on Principal Component Analysis (PCA) was used 
(Buchbender et al. in prep.). This technique was also employed for the data published in \citet{Luisi2021}, \citet{Tiwari2021} and \citet{Kabanovic2022}. Specifically, PCA identifies the systematic components of baseline variation in different spectra which allows to accurately remove them and recover the actual spectrum. For a more general overview of PCA we refer the reader to \citet{Jolliffe2011}.

   
   

\begin{figure*}
    \centering
   
    \includegraphics[width=\hsize]{images/fig3_final.png}
   
   
    \caption{The middle panel shows the line integrated intensity map of [C\,{\scriptsize II}]\ from -20 to 20 km s$^{-1}$ with the white contours indicating the \textit{Herschel} column density N$_{H_{2}}$ at 1, 2, 4 and 8$\times$10$^{22}$ cm$^{-2}$. The [C\,{\scriptsize II}], [O\,{\scriptsize I}], $^{12}$CO(3-2) and $^{13}$CO(3-2) spectra at the indicated positions are shown around the map. These spectra are named after their position in the map. The spectra from the central molecular ring are indicated with a `C', the spectra to the east with `E' and the spectra to the west with `W'. The spectra indicate the presence of multiple velocity components and show signatures of self-absorption towards the ring (C). In several spectra (C1-C3), high-velocity blue- and red-shifted wings are detected. The spectrum `W3' at the top right highlights the color legend for the spectra. When inspecting the spectra, note that the y-scale is different in each sub-panel.}
    \label{fig:integratedIntensities}
\end{figure*}

\begin{figure}
    \centering
    \includegraphics[width=\hsize]{images/integratedMap_ColDens0p1-0p2-0p4-0p8e23_half_OI.png}
   
    \caption{The integrated intensity map of [O\,{\scriptsize I}]\ at 63 $\mu$m from -20 to 20 km s$^{-1}$ with the white contours indicating the column density 
    N$_{H_{2}}$ at 1, 2, 4, and 8$\times$10$^{22}$ cm$^{-2}$.}
   
   
    \label{fig:integratedOI}
\end{figure}

\subsection{APEX}
Complementary $^{12}$CO(3-2) and $^{13}$CO(3-2) data were simultaneously obtained with the LAsMA 7-pixel receiver on September 27, 2019 and July 21, 2021 in good weather conditions (precipitable water vapor, pwv $\approx$ 1 mm) using the APEX telescope\footnote{APEX, the Atacama Pathfinder EXperiment is a collaboration between the Max-Planck-Institut f\"ur Radioastronomie, Onsala Space Observatory (OSO), and the European Southern Observatory (ESO).} \citep{Guesten2006}. This heterodyne spectrometer allows simultaneous observations of the two CO isotopomers in the upper ($^{12}$CO(3-2) at 345.7959899 GHz) and lower ($^{13}$CO(3-2), 330.5879653 GHz) sideband of the receiver. The LAsMA backends are fast Fourier transform spectrometers (FFTS) with 2$\times$4 GHz bandwidth \citep{Klein2012} and a native spectral resolution of 61 kHz. The main beam size of the APEX observations ($\theta_{mb}$ = 18.2$^{\prime\prime}$ at 345.8 GHz) is similar to the resolution of the [C\,{\scriptsize II}]\ data. The mapped field with a size of 20$^{\prime}\times$15$^{\prime}$ was scanned in total power on-the-fly mode, with a spacing of 9$^{\prime\prime}$ between rows (while oversampling to 6$^{\prime\prime}$ in scanning direction, R.A.). The map data were calibrated against a sky reference position at $\alpha_{(J2000)}$ = 09$^h$01$^m$31.7$^s$ and $\delta_{(J2000)}$ = -43$^\circ$22$'$50.0$''$. 
For the APEX observations, a first order baseline was removed, and a main beam efficiency $\eta_{mb}$ = 0.68 was used to convert the antenna temperatures to main beam temperatures. The baseline-subtracted spectra have been binned to a spectral resolution of 0.2 km s$^{-1}$. The final data cubes (with a pixel size of 9.1$^{\prime\prime}$) have an rms of 0.45 K.

\subsection{Ancillary data}
The Chandra X-ray Observatory ACIS camera \citep{Garmire2003} observed a 17$'$x17$'$ field centred on RCW~36 for $\sim$70~ksec in 2006.  The MYStIX project \citep{Kuhn2013} found 502 X-ray point sources in this field.  These were excised, and the remaining data smoothed, to obtain an 0.5--7~keV diffuse X-ray image of the field \citep{Townsley2014}.  ACIS is an intrinsic spectrometer, tagging every X-ray event with its energy as well as its position.  We will use the Chandra/ACIS data to study the X-ray spectra in a variety of regions in and around RCW~36.\\
The RCW 36 region, being part of the Vela C molecular cloud, was observed with the PACS \citep{Poglitsch2010} and SPIRE \citep{Griffin2010} bolometers on the \textit{Herschel} telescope as part of the {\sl Herschel} imaging survey of OB young stellar objects (HOBYS) program \citep{Motte2010}.  In this work, we use the flux map at 70 $\mu$m with an angular resolution of $\sim$6$''$ as it clearly outlines the bipolar H\,{\scriptsize II}\ region.  Further, we use the dust temperature map at 36$''$ resolution and a dust column density map at 18.2$^{\prime\prime}$ resolution. 
This dust temperature and column density map was obtained by fitting the spectral energy distribution (SED) to the 160 to 500 $\mu$m data, using the method presented in \citet{Palmeirim2013}.\\
We further make use of data from the WISE telescope from 3.4 $\mu$m to 22 $\mu$m \citep{Wright2010}, a H$\alpha$ map of RCW 36 from the Southern H$\alpha$ Sky Survey Atlas (SHASSA) \citep{Gaustad2001}, and a large scale dust polarization map at 500 $\mu$m with a spatial resolution of 2.5$^{\prime}$ that was observed with the BLASTPol balloon-borne receiver \citep{Fissel2016,Fissel2019,Gandilo2016}.

\section{Results}\label{sec:results}

\subsection{The integrated intensity map}
 Figures~\ref{fig:integratedIntensities} and \ref{fig:integratedOI} present the integrated intensity map for [C\,{\scriptsize II}]\ and [O\,{\scriptsize I}], respectively. [C\,{\scriptsize II}]\ is brightest towards the region that is surrounded by the high-column density ring and shows more extended emission towards the two cavities. 
 Outside of the cavity walls, the [C\,{\scriptsize II}]\ intensity decreases rapidly. [O\,{\scriptsize I}]\ on the other hand is only detected towards the high column density ring where a high-density PDR can be expected.\\
The line integrated intensity maps of $^{12}$CO(3-2) and $^{13}$CO(3-2), presented in Fig. \ref{fig:integratedMapsCO}, show a different structure. The emission follows the ring-like \textit{Herschel} dust column density maps rather closely and shows that the CO emission is brightest at the edge around the bright [C\,{\scriptsize II}]\ emission, which would be expected for a PDR irradiated by the central cluster. This is not a resolution effect since both beams have 
similar spatial resolution. 
To the south-west of the ring there is a region (local peak in dust column density), where the ring is significantly less bright in $^{12}$CO(3-2) and $^{13}$CO(3-2) (by a factor 2-3), but the [C\,{\scriptsize II}]\ contours show a protrusion toward the west. This may indicate that there is a puncture in the ring so that the [C\,{\scriptsize II}]\ emitting gas can freely expand into a lower density region, driven by the stellar feedback from the east. On the other hand, the weaker CO emission at this location (C3 in Fig.~\ref{fig:integratedIntensities}) can be partly caused by self-absorption. This self-absorption can be related to the protrusion as it would give rise to warm and cold gas layers along the line of sight while there still appears to be a significant column density based on the Herschel data. 
On a larger scale outside the ring in Fig. \ref{fig:integratedMapsCO}, $^{12}$CO(3-2) shows filamentary emission that is perpendicular to the dense ring. Several of these filamentary structures are also detected in [C\,{\scriptsize II}]\ and show a curvature that appears to originate in the central cluster. This suggests that pre-existing filaments are being swept up. \\%, but are less prominent than in CO.\\
Recently, [C\,{\scriptsize II}]\ integrated intensity observations at an angular resolution of 90$^{\prime\prime}$ were presented in \citet{Suzuki2021} using a 100 cm balloon-borne infrared telescope. Smoothing the FEEDBACK integrated intensity map to a resolution of 90$^{\prime\prime}$, presented in App. \ref{sec:90arcsec}, the results look extremely similar to the maps presented in \citet{Suzuki2021}. The intensity maps appear to agree within 10\%, which corresponds to typical calibration errors. Comparing the smoothed map in Fig. \ref{fig:compSuzuki} with the FEEDBACK map in Fig. \ref{fig:integratedIntensities}, it is evident that the higher spatial resolution of the SOFIA observations is necessary to resolve e.g. the ring and filamentary structures in [C\,{\scriptsize II}]. Another major advantage of the FEEDBACK observations is the high spectral resolution of the observations that allows to study the dynamics of the region.

\begin{figure}
    \centering
   
    \includegraphics[width=\hsize]{images/12CO+filaments.png}
    \includegraphics[width=\hsize]{images/integrated13CO+colDens+CII_3.png}
   
   
   
    \caption{{\bf Top}: The integrated $^{12}$CO(3-2) emission map from -20 to 20 km s$^{-1}$ with \textit{Herschel} column density contours in white and [C\,{\scriptsize II}]\ integrated intensity contours starting at 50 K km~s$^{-1}$ with increments of 100 K km~s$^{-1}$ in red to delineate their structure. Outside the molecular ring, the $^{12}$CO(3-2) emission shows filamentary structures that are oriented perpendicular to the ring (indicated by the white arrows). {\bf Bottom}: The same for $^{13}$CO(3-2), in the green box indicated in the figure above, which follows the column density contours of the high-column density ring closely. The [C\,{\scriptsize II}]\ emission shows a structure perpendicular to the high-column density ring in the south-west at the location where there is a drop in $^{13}$CO(3-2) intensity. The white crosses indicate the location of the two O star candidates.}
    \label{fig:integratedMapsCO}
\end{figure}

\subsection{Multiple velocity components, absorption and high-velocity wings}\label{sec:velComps}

The [C\,{\scriptsize II}], CO, and [O\,{\scriptsize I}]\ spectra shown in Fig. \ref{fig:integratedIntensities} are all very complex and cannot be described by a single Gaussian velocity component. 
The bulk emission of the molecular cloud/dense ring is best traced with the $^{13}$CO(3-2) line that is visible for all center positions (C1-5) around 7-8 km s$^{-1}$ but mostly absent for all western (W1-W3) and eastern (E1-E2) positions. The $^{12}$CO(3-2) line profile shows significant variation depending on the position. For the spectra at the central molecular ring, we observe two apparent line components that are caused by foreground or self-absorption because the $^{13}$CO line peaks in the $^{12}$CO dip at $\sim$7 km s$^{-1}$. Note that the optically thin dense gas tracers N$_{2}$H$^{+}$(2-1) and NH$_{3}$(1,1), presented in  \citet{Fissel2019},  also peak at velocities around 7-8 km s$^{-1}$. The absorption thus mimics two separate  
velocity components that were interpreted by \citet{Sano2018} as two velocity components tracing a cloud-cloud collision. 
We observe that the absorption in $^{12}$CO continues towards the east and west because the dip in the line profile is always around 7 km s$^{-1}$ and the $^{13}$CO emission clearly peaks in the $^{12}$CO dip for position W1 (but is too weak for W2 and E1 and E2). For all center positions, the self-absorption is dominant towards the blue-shifted part of the main velocity component which is generally associated with expansion \citep[e.g.][]{Castor1979}. \\
The [C\,{\scriptsize II}]\ line has a bright, prominent component (main beam temperatures up to $\sim$100~K for the center positions) around 8-9 km s$^{-1}$. This bright component is also found in the eastern spectra, but is less strong for the three western positions (W1-W3). This component is also affected by absorption which we can prove with our [$^{\rm 13}$C\,{\scriptsize II}]\ line observations shown in Fig. \ref{fig:13CIIline} and Appendix \ref{sec:selfAbs}. The intensity of the [C\,{\scriptsize II}]\ main component drops where [$^{\rm 13}$C\,{\scriptsize II}]\ has its emission peak, similar to what was observed for several other bright [C\,{\scriptsize II}]\ sources with SOFIA \citep[e.g.][]{Graf2012,Guevara2020,Kirsanova2020,Mookerjea2021,Kabanovic2022}. There is also a separate second velocity component between 0 and 5 km s$^{-1}$ (hereafter the blue-shifted component) which is well visible in [C\,{\scriptsize II}]\ and even brighter than the 7-8 km s$^{-1}$ component in the west of the ring (W1-W3). At some locations (C3, C4, W3) this component is also detected in $^{12}$CO(3-2), see Fig. \ref{fig:integratedIntensities}, but mostly at slightly higher velocities (3-5 km s$^{-1}$).\\
The [O\,{\scriptsize I}]\ spectra, detected towards the dense ring, look slightly different than $^{12}$CO(3-2) and [C\,{\scriptsize II}]. [O\,{\scriptsize I}]\ is only detected at velocities higher than 7 km s$^{-1}$. At lower velocities, i.e. between 3 and 7 km s$^{-1}$, the spectra indicate absorption since the emission in this velocity interval goes under the baseline in C1-C5. This is demonstrated in more detail in App. \ref{sec:selfAbs} which shows that the integrated intensity of [O\,{\scriptsize I}]\ from 3 to 7 km s$^{-1}$ becomes negative towards the dense ring, in particular towards the \textit{Herschel} column 
density peaks. This suggests significant [O\,{\scriptsize I}]\ 63 $\mu$m foreground absorption at the same velocities where [C\,{\scriptsize II}]\ and $^{12}$CO(3-2) are absorbed, similar to what was recently found towards several bright [O\,{\scriptsize I}]\ 63 $\mu$m sources in \citet{Goldsmith2021}. Based on detailed studies of several clouds,  i.e.  M17 and MonR2 (Guevara et al., to be submitted) and RCW120 \citep{Kabanovic2022}, it has been proposed this could be due to a foreground cloud or cold atomic oxygen and C$^{+}$ in the low-density halo of the cloud.
Lastly, in several spectra of Fig. \ref{fig:integratedIntensities}, high-velocity blue- and red-shifted wings are observed in the intervals from -8
to 0 km s$^{-1}$ and 14 to 23 km s$^{-1}$.  Even though these high-velocity wings are not always very clear on the presented figures because of the very bright emission at 5-12 km s$^{-1}$, associated with the central ring, they are well above the noise level (which is 0.8 K in individual spectral bins). The wings are particularly evident at positions C2, C3 and W3 in Fig. \ref{fig:integratedIntensities}. For the red-shifted wing, it has to be noted that the [$^{\rm 13}$C\,{\scriptsize II}]\ F=2-1 transition is located between 17 and 23 km s$^{-1}$ which provides a contribution (1.5 K km s$^{-1}$ on average) to the wing at these velocities
\begin{figure}
    \centering
   
    \includegraphics[width=\hsize]{images/13CIIf2-1+CII_fit_2.png}
    \caption{The [$^{\rm 13}$C\,{\scriptsize II}]\ F = 2-1 line emission (magenta), averaged over the dense molecular ring, compared to the [C\,{\scriptsize II}]\ line profile (blue) which is averaged over the same area. Even though there is confusion by the redshifted high-velocity wing seen with [C\,{\scriptsize II}], indicated by the fitted curve to the wing (part of a gaussian), the [$^{\rm 13}$C\,{\scriptsize II}]\ emission profile clearly shows that the intensity dip at $\sim$ 7 km s$^{-1}$ in [C\,{\scriptsize II}]\ and $^{12}$CO(3-2) is the result of self-absorption.}
    \label{fig:13CIIline}
\end{figure}
\subsection{Gas dynamics in [C\,{\scriptsize II}]\ and CO}

\begin{figure}
   
   
    \includegraphics[width=0.88\hsize]{images/RGB_velocity_0-5_5-7_7-12+colDens+box_2.png}
    \includegraphics[width=0.88\hsize]{images/RGB_velocity_7-8p4_8p4-9p8_9p8-11p2+colDens+box.png}
    \includegraphics[width=\hsize]{images/expandingShellPV+fit+names.png}
   
   
   
   
    \caption{{\bf Top}:  
   
    [C\,{\scriptsize II}]\ RGB map presenting the global kinematic structure of RCW 36 between 0 and 12 km s$^{-1}$. 
    The color coding is given in the panel. The white contours indicate the column density 
    N$_{H_{2}}$ at 1, 2, 4, and 8$\times$10$^{22}$ cm$^{-2}$.  
   
    The red bar outlines the area of the map used to produce the position-velocity (PV) diagram below. The small black vertical line inside the red bar indicates the center (0 pc) for the PV diagram. 
    {\bf Middle}: The same as above, but focusing on the velocity structure in the most red-shifted velocity interval between 7 and 11.2 km s$^{-1}$.
    {\bf Bottom}: The [C\,{\scriptsize II}]\ PV diagram parallel to the bipolar cavities and the $^{12}$CO(3-2) emission in white contours (starting at 5 K km s$^{-1}$ with increments of 10 K km s$^{-1}$). The full and dashed red curves, which closely overlap and thus are difficult to separate on this figure, show the fitted functions (2$^{nd}$ order polynomial: full, sine function: dashed) to the two identified blue-shifted expanding [C\,{\scriptsize II}]\ shells that are found in the two cavities. The black line follows the peak intensity along the expanding shells as a function of radius.
   
   
    At velocities $<$ 0 km s$^{-1}$ and $>$ 12 km s$^{-1}$, the emission from the high-velocity wings is observed. This emission does not show an elliptical shape in the PV diagram, which would be predicted for expanding shells. 
   
   
   
    }
    \label{fig:pvCavities}
\end{figure}

\subsubsection{The expanding shells}\label{sec:expShells}
The [C\,{\scriptsize II}]\ position-velocity (PV) diagram presented in Fig. \ref{fig:pvCavities} is a cut through RCW 36, parallel to the central axis of the bipolar cavities. This provides a view on the large scale kinematics in RCW 36. It displays a blue-shifted expanding shell signature in the western region of the observed map, i.e. r $>$ 0 pc in Fig. \ref{fig:pvCavities} (indicated with 'cavity 2'), where the western cavity is located. This expanding structure is similar to the ones observed towards bubble-like structures in Orion, RCW 120 and RCW 49 \citep[][]{Pabst2020,Luisi2021,Tiwari2021}. The expansion feature is observed between 1 and 6 km s$^{-1}$ which suggests that this expanding shell has an expansion velocity of $\sim$ 5 km s$^{-1}$. Later in this section we will constrain the expansion velocity quantitatively. The emission from the shell is also clearly identified in the individual spectra of Fig. \ref{fig:integratedIntensities} as a separate velocity component in the same velocity interval.
This feature is most prominent in the spectra of the western cavity (W1-3) and dominates over the component associated with the velocity of the molecular ring.  
The cavity to the east (r $<$ 0 pc) has a similar, though less bright, expanding shell that covers the same velocity range, see Fig. \ref{fig:pvCavities}. As the eastern cavity is less bright, it is not as clear in the PV diagram, but when inspecting the [C\,{\scriptsize II}]\ channel maps in Fig. \ref{fig:chanMapsFull}, it becomes evident that the [C\,{\scriptsize II}]\ emission between 1 and 6 km s$^{-1}$ shows the same morphology as the western cavity. This blue-shifted expanding shell morphology is also seen in the upper RGB image of Fig. \ref{fig:pvCavities}, where the center of both cavities shows blue-shifted emission confined within the green limb brightened cavity walls. Both the western and eastern cavity thus show a blue-shifted expanding shell in [C\,{\scriptsize II}]\ with similar expansion velocity. 
To quantify the expansion velocity of these shells in the cavities, we determined the velocity of peak intensity for the shells (i.e. at v$_{LSR} <$ 6.5 km s$^{-1}$), see Fig. \ref{fig:pvCavities}. This curve was then fitted in each cavity by both a second order polynomial and a sine function which assumes that the reference velocity for expansion is v$_{LSR} =$ 6.5 km s$^{-1}$. To calculate the expansion velocity, we then determined the point of minimal v$_{LSR}$ obtained from the fit. The difference between this minimal velocity and v$_{LSR}$ = 6.5 km s$^{-1}$, is the expansion velocity. The results of these fits are summarized in Tab. \ref{tab:shellVelocities}. The expansion velocity in the cavities is then estimated by taking the average of all obtained expansion velocities, which gives: 5.2 $\pm$ 0.5 $\pm$ 0.5 km s$^{-1}$. The first estimated error corresponds to the spread of all obtained expansion velocities. The second estimated error is a systematic error caused by the uncertainty on the rest v$_{LSR}$ for the expanding shell which should be between v$_{LSR}$ = 6 and 7 km s$^{-1}$.  
The two expanding shells appear to spatially come together in projection at the central molecular ring, which is also observed in the channel maps in Fig. \ref{fig:chanMapsFull}. The $^{12}$CO(3-2) channel maps in Fig. \ref{fig:chanMapsFullCO} show indications that the outer layer of the western expanding shell is also detected in $^{12}$CO(3-2) between 1.4 and 3 km s$^{-1}$. This is not the case for all expanding [C\,{\scriptsize II}]\ shells \citep[e.g.][]{Luisi2021}.
In PDRs, CO generally exists in regions with A$_{\text{V}} \ge$ 2-3 \citep[e.g.][]{Tielens1985,Roellig2007} which implies that the expanding shell has a thickness of several A$_{\text{V}}$. This is consistent with the \textit{Herschel} column density map of Vela C which shows an A$_{\text{V}}$ of 3-6 towards the cavities.
\begin{figure*}
    \centering
   
   
    \includegraphics[width=0.49\hsize]{images/channelmaps_res25arcsec_0p6_CII_12CO32cont_5.png}
    \includegraphics[width=0.49\hsize]{images/channelmaps_res25arcsec_0p6_12CO32_CIIcont_5.png}
    \caption{{\bf Left}: Channel maps of [C\,{\scriptsize II}]\ from -1.8 km s$^{-1}$ to 13.8 km s$^{-1}$ with velocity intervals of 1.2 km s$^{-1}$ present the velocity structure of RCW 36. Below 6 km s$^{-1}$, the blueshifted expanding shells are observed in the colormap for [C\,{\scriptsize II}]. {\bf Right}: The same for $^{12}$CO(3-2) covering the same area as the [C\,{\scriptsize II}]\ map. It appears that $^{12}$CO(3-2) only marginally traces the expanding shell. At higher velocities, $^{12}$CO(3-2) mostly traces the kinematics of the Vela C molecular cloud.}
    \label{fig:chanMapsFull}
\end{figure*}

\begin{table*}[]
    \centering
    \begin{tabular}{ccccc}
    \hline
    \hline
        function & v$_{LSR,min,west}$ (km s$^{-1}$) & v$_{exp,west}$ (km s$^{-1}$) & v$_{LSR,min,east}$ (km s$^{-1}$) & v$_{exp,east}$ (km s$^{-1}$)\\
        \hline
        sine & 1.4 $\pm$ 0.1 & 5.1 $\pm$ 0.1 $\pm$ 0.5 & 0.8 $\pm$ 0.9 & 5.7 $\pm$ 0.9 $\pm$ 0.5\\ 
        poly & 1.5 $\pm$ 0.1 & 5.0  $\pm$ 0.1 $\pm$ 0.5 & 1.6 $\pm$ 0.1 & 4.9 $\pm$ 0.1 $\pm$ 0.5 \\
        \hline
    \end{tabular}
    \caption{Minimal velocity (v$_{LSR,min}$) and corresponding expansion velocity (v$_{exp}$) obtained for the two fitted functions to the expanding shells in the west and the east, respectively. The fitted functions are a sine function (sine) and a second order polynomial (poly). The indicated errors for the minimal v$_{LSR}$ correspond to the error on the fit. The two indicated errors for the expansion velocities correspond to the fitting error and uncertainty on the assumed rest v$_{LSR}$ for the shells.}
    \label{tab:shellVelocities}
\end{table*}

\subsubsection{The kinematics of the molecular ring}\label{sec:ringExp}

\begin{figure}
    \centering
    \includegraphics[width=\hsize]{images/CII+13CO5-35_ringRCW36_2.png}
   
    \caption
    A zoom of the [C\,{\scriptsize II}]\ channel maps on the ring around the young OB cluster, to focus on the velocity structure in the ring. The overlaid black contours indicate the $^{13}$CO(3-2) channel maps at the same velocity starting at 5 K km s$^{-1}$ with increments of 10 K km s$^{-1}$. It shows that the kinematics in [C\,{\scriptsize II}]\ and $^{13}$CO(3-2) are very similar towards the ring, unlike the cavities. The eastern part of the ring is already detected starting at 5 km s$^{-1}$ while the western part of the ring is only detected starting at 7-8 km s$^{-1}$.} 
    \label{fig:chanMapRing}
\end{figure}
Our observations also resolve the central molecular ring which is best visible in the dust column density map and in the $^{13}$CO(3-2) emission (Fig.~\ref{fig:integratedMapsCO}). However, the ring is also associated with [C\,{\scriptsize II}]\ emission as shown in the  
RGB images of Fig. \ref{fig:pvCavities}. The top panel indicates that the eastern part of the ring is more blue-shifted than the western part. Since it was proposed, by \citet{Minier2013} and from Fig. \ref{fig:observedMap}, that the eastern part of the ring is in front of the western part, this velocity structure fits with the proposed expansion of the molecular ring. A zoom into the ring kinematics by the channel maps in Fig. \ref{fig:chanMapRing} confirms this expansion and demonstrates that the expansion is also seen in $^{13}$CO(3-2). Unfortunately, it is very difficult to accurately estimate an expansion velocity for the ring. There are several reasons for this: self-absorption effects in all available lines limits an accurate determination of the typical velocity of the gas, stellar feedback breaking through the ring affects the velocity field, and the presence of additional velocity structure in the line of sight (see also Bij et al. in prep.) limits the possibility to use the moment 1 map. Therefore, we estimate the expansion velocity from inspecting the channel maps in Fig. \ref{fig:chanMapRing}. The eastern area of the ring is found at 5-6 km s$^{-1}$ whereas the western part is at $\sim$8.0 - 8.8 km s$^{-1}$. This suggests a typical expansion velocity of 1.0-1.9 km s$^{-1}$.
More generally, Fig. \ref{fig:chanMapRing} shows that [C\,{\scriptsize II}]\ and CO have the same kinematic structure towards the ring which implies that they trace the same expansion dynamics. The full ring is thus swept up by the expansion from the cluster with the CO emission at the outer side of the [C\,{\scriptsize II}]\ emission as would be expected in a PDR structure with internal FUV irradiation. Lastly, in the south-west of the ring, where Fig. \ref{fig:integratedMapsCO} shows that the integrated [C\,{\scriptsize II}]\ emission crosses the molecular ring, Fig. \ref{fig:chanMapRing} now shows that $^{13}$CO and [C\,{\scriptsize II}]\ have the same kinematic morphology between 8.0 and 9.6 km s$^{-1}$. 

\subsubsection{Filamentary structures in [C\,{\scriptsize II}]}\label{sec:filsExp}
The PV diagram in Fig. \ref{fig:pvCavities} also shows significant [C\,{\scriptsize II}]\ emission around 10 km s$^{-1}$, with corresponding $^{12}$CO(3-2) emission towards the eastern cavity.  This emission is indicated with the name $'$filaments$'$ in the PV diagrams. The typical elliptical signature expected in PV diagrams for expanding shells is not as evident for this [C\,{\scriptsize II}]\ emission which could be due to the small velocity difference with the ring ($<$~2-3 km s$^{-1}$). In the channel maps in Figs. \ref{fig:chanMapsFull} and \ref{fig:chanMapsFullCO}, this 10 km s$^{-1}$ emission displays a filamentary structure which is not typical for expanding shells. However, Fig. \ref{fig:chanMapsFullCO} in particular also shows that these filaments have a curved morphology that appear to have their origin towards the central cluster. This [C\,{\scriptsize II}]\ and CO emission might thus originate from low-density filaments, originally converging towards the ridge where RCW 36 formed, which are now being swept away at velocities $<$~3 km s$^{-1}$ by the feedback from the stellar cluster. Such filamentary gas, which might originally be flowing towards a central filament or ridge, was observed for a wide variety of low- to high-mass star formation regions such as e.g. Musca, B211/3 and DR21 \citep{Goldsmith2008,Schneider2010,Palmeirim2013,Cox2016,Bonne2020b}. The observed small expansion velocity for these filaments around RCW 36 is quite similar to the expansion velocity in the ring which suggest that overdensities, which are clearly detected in CO,  experience significantly slower expansion driven by stellar feedback. Lastly, no corresponding bright filamentary [C\,{\scriptsize II}]\ emission at 10 km s$^{-1}$ is observed towards the western cavity, which might be the result of the molecular cloud morphology around RCW 36 before the onset of stellar feedback. 

\begin{figure*}
    \centering
   
    \includegraphics[width=0.9\hsize]{images/channelmaps_12CO32_20_5.png}
    \caption{Channel maps of $^{12}$CO(3-2) from 1.0 km s$^{-1}$ to 12.4 km s$^{-1}$ over the full APEX map of RCW 36. The white box indicates the currently observed [C\,{\scriptsize II}]\ map. Below 4 km s$^{-1}$, emission in an arc is observed that indicates that the shell is also (weakly) detected in $^{12}$CO(3-2). Note the clumpy nature of this $^{12}$CO emission originating from the shell. At velocities above 8 km s$^{-1}$, filamentary gas perpendicular to the central ring is observed.}
    \label{fig:chanMapsFullCO}
\end{figure*}

\subsection{High-velocity wing emission}
The spectra in Sec. \ref{sec:velComps} showed the presence of blue- (v$_{LSR} <$ 0 km s$^{-1}$) and red-shifted (v$_{LSR} >$ 14 km s$^{-1}$) high-velocity [C\,{\scriptsize II}]\ wings. These high-velocity wings have a brightness up to 5-10 K in individual spectral bins, see Fig. \ref{fig:integratedIntensities}, which is well above the detection limit for [C\,{\scriptsize II}]\ with a noise rms of 0.8 - 1.0 K. In Fig. \ref{fig:outflowColdens} the integrated intensity map of the high-velocity wings shows that the blue- and red-shifted wings display a bipolar distribution, similar to what is observed for protostellar outflows in CO \citep[e.g.][]{Bachiller1996,Arce2007}. However, for RCW 36, there are no known driving protostars or young stellar objects \citep{Ellerbroek2013a} at the location where the blue- and red-shifted outflow wings come together in the plane of the sky. 
Furthermore, the high-velocity wings are only detected in [C\,{\scriptsize II}]. Even at the high column density ring the wings are at no point detected in $^{12}$CO (see spectra C1-C3 in Fig. \ref{fig:integratedIntensities}), and higher angular resolution observations (Bij et al., in prep.) indicate there are no protostellar sources in the ring that could drive such powerful mass ejection. The observed [C\,{\scriptsize II}]\ wings are thus most likely not of protostellar nature.\\
In the currently covered area of RCW 36, there is a significant disparity between the blue- and red-shifted integrated wings. Even when integrating over the full 14-22 km s$^{-1}$ interval, which contains contamination from [$^{\rm 13}$C\,{\scriptsize II}], the red-shifted wing remains 2 times less bright and covers a significantly smaller area than the blue-shifted wing. These high-velocity wings also do not appear to be directly associated with expanding shells as it does not show an expanding shell velocity structure in the PV diagram in Fig. \ref{fig:pvCavities} (i.e. an elliptical velocity profile). 
The brightest part of the blue-shifted wing can be found relatively close to the two reported HH objects in \citet{Ellerbroek2013b}. However, Fig. \ref{fig:outflowColdens} also shows the position angle of the HH jets which indicates that the wings seen in [C\,{\scriptsize II}]\ are not associated with these HH jets. Lastly, Fig. \ref{fig:outflowColdens} shows that the brightest wings are located around the dense molecular ring and towards the cavity walls. This suggests that the wings might be the result of gas that is entrained from the ring and cavity walls by the impact of feedback processes.
\begin{figure}
    \centering
    \includegraphics[width=\hsize]{images/colDens+outflowContours_b15-45_r14-17-5-20+HH+OB_large_3.png}
    \caption{\textit{Herschel} column density map overlaid with the contours from the integrated blue-shifted high-velocity wing (in blue) and the red-shifted high-velocity wing (in red) of [C\,{\scriptsize II}]. The location of the two O stars and HH objects, with the orientation of their observed jet (black lines), is also indicated. This shows that the observed high-velocity wings are not associated with the HH jets.}
    \label{fig:outflowColdens}
\end{figure}

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

\subsection{The expanding shell energetics from \textit{Herschel}}
Both cavities have blue-shifted expanding [C\,{\scriptsize II}]\ shells. In contrast to the shells in previously studied bubble H\,{\scriptsize II}\ regions \citep[e.g.][]{Pabst2020,Luisi2021,Tiwari2021}, the analysis for RCW 36 is a bit more involved as it has two expanding cavities and an expanding molecular ring around the cluster. There are two approaches to estimate the expansion energetics. One is based on the \textit{Herschel} data and the second one on the [C\,{\scriptsize II}]\ data. \\ 
First we will work with the \textit{Herschel} data of Vela C. 
The column density map produced from SED fitting to the 160 to 500 $\mu$m data might not be ideal to calculate the shell mass as most of 
these wavelengths particularly trace the cold dust ($<$ 20-30 K). Furthermore, the shells in the bipolar cavities are prominent at 160 $\mu$m and shorter wavelengths, which could be expected for the strongly irradiated expanding shells if they have a relatively low A$_{V}$ ($\lesssim$5). In this case, the shell is mostly dominated by the presence of PDRs which would lead to higher temperatures. A method that would be more sensitive to relatively warm shells was presented in \citet{Tiwari2021}, using a column density map produced based on the \textit{Herschel} 70 $\mu$m and 160 $\mu$m map. This makes use of the fact that the optical depth at 160 $\mu$m ($\tau_{160}$) can be converted to a hydrogen nucleus column density N$_{H}$ using the dust extinction cross section at this wavelength which is given by C$_{ext,160}$/H = 1.9$\times$10$^{-25}$ cm$^{2}$/H \citep{Draine2003}. The optical depth is related to the observed intensity by I$_{\nu}$ = B$_{\nu}$(T$_{d}$)$\tau_{\nu}$, assuming optically thin emission and limited fore/background emission. B$_{\nu}$(T$_{d}$) is the Planck function at a specific dust temperature T$_{d}$. In order to calculate the dust temperature map, the method presented in \citet{Peretto2016} and \citet{Bonne2022}, based on the intensity ratio of 70 $\mu$m (after smoothing to the resolution of 
the 160 $\mu$m data) and 160 $\mu$m, is used. From this dust temperature map, it is then possible to calculate the optical depth and the column density \citep{Draine2003}.\\
Based on a visual inspection of the \textit{Herschel} and WISE data at 160 $\mu$m and shorter wavelengths, the limb-brightened part of the shell in the cavities corresponds to a width of $\sim$0.3 pc, which is $\sim$30 \% of the 1.0 pc radius for both cavities, see Fig. \ref{fig:defineShells}. This figure also defines the area of the expanding ring. The estimated mass of the ring and shells are presented in Tab. \ref{tab:shellEnergetics}. To obtain the full mass of the expanding shells in the cavities, the calculated mass in the limb-brightened shells is multiplied by a geometric correction factor of 2.7. This correction factor was calculated using a code that determines the fraction of the shell located in the limb-brightened part of the shell in a 1D cut through the spherical half-shell and then assumes an axial symmetry. Using an expansion velocity of 1.0-1.9 km s$^{-1}$ for the ring and 5.2 km s$^{-1}$ for the two expanding shells in the cavities, we then arrive at a total kinetic energy of 2.4-2.6$\times$10$^{47}$ erg, see Tab. \ref{tab:shellEnergetics}.\\
We note that the expanding central ring contains dust that is also detected at wavelengths $>$ 160 $\mu$m. When using the mass for the ring from the column density map produced by the SED fitting between 160 $\mu$m and 500 $\mu$m, the mass agrees roughly within a factor 2 with the method based on the 160 $\mu$m and 70 $\mu$m ratio (i.e. the mass of the ring obtained from SED fitting is about a factor 2 lower, see Tab. \ref{tab:shellEnergetics}). In fact, the results for the bipolar cavities also agree within a factor 2. Identifying the best column density map to calculate the contribution from the central ring is a non-trivial issue, but these results indicate that an uncertainty of at least a factor 2 should be taken into account.
\begin{figure}
    \centering
   
    \includegraphics[width=\hsize]{images/columnDensity+Shells_zoom_2.png}
    \caption{\textit{Herschel} column density map with overlaid \textit{Herschel} contours at 160 $\mu$m (in white) which is bright towards the ring and cavity walls. In order to calculate the masses for the expansion energetics, the ring is defined by the region encompassed by the green ellipse and the expanding shells in the cavities by the two red annuli. The regions where the annuli overlap with the green ellipse are excluded for the mass calculation of the expanding shells.
    }
    \label{fig:defineShells}
\end{figure}

\begin{table}[]
    \centering
     \caption{The mass, and the resulting kinetic energy of the expanding ring and shells, calculated with the different methods. This was calculated using E$_{K}$ = $\frac{1}{2}$Mv$_{exp}^{2}$. An expansion velocity range of 1 - 1.9 km s$^{-1}$ was used for the ring, and expansion velocity of 5.2$\pm$0.5$\pm$0.5 km s$^{-1}$ was assumed for the shells in the cavities. The error on the energy values for the cavity was estimated based on the uncertainty on the expansion velocity. Note that this does not take into account errors on the mass. In the table, `full cavity' indicates that the eastern and western cavity were not separated. Based on the calculations using different C$_{ul}$/A$_{ul}$ values, we obtain an uncertainty of 30\% on the calculated mass from [C\,{\scriptsize II}].
     }
    
     \label{tab:shellEnergetics}
     \begin{tabular}{ccc}
     \hline
     \hline
        Region & Mass & Kinetic energy \\
        \hline
        \hline
        \multicolumn{3}{c}{70 $\mu$m and 160 $\mu$m column density map}\\
        \hline
        ring &  9.1$\times 10^{2}$ M$_{\odot}$ & 0.9-3.3$\times 10^{46}$ erg\\ 
        east cavity &  4.5$\times 10^{2}$ M$_{\odot}$ & 1.2$\pm$0.2$\pm$0.2$\times 10^{47}$ erg \\
        west cavity &  3.9$\times 10^{2}$ M$_{\odot}$ & 1.1$\pm$0.2$\pm$0.2$\times 10^{47}$ erg \\
        total & & 2.4-2.6$\times 10^{47}$ erg \\
        \hline
        \hline
        \multicolumn{3}{c}{SED fitted column density map}\\
        \hline
        ring &  4.1$\times 10^{2}$ M$_{\odot}$ & 0.4-1.5$\times 10^{46}$ erg\\ 
        east cavity &  2.5$\times 10^{2}$ M$_{\odot}$ & 6.8$\pm$1.3$\pm$1.3$\times 10^{46}$ erg \\
        west cavity &  2.3$\times 10^{2}$ M$_{\odot}$ & 6.2$\pm$1.2$\pm$1.2$\times 10^{46}$ erg \\
        total & & 1.2-1.4$\times 10^{47}$ erg \\
        \hline
        \hline
        \multicolumn{3}{c}{[C\,{\scriptsize II}]\ shell}\\
        \hline
        full cavity (100 K) & 1.5$\pm$0.5$\times 10^{2}$ M$_{\odot}$ & 4.1$\pm$1.4$\pm$0.8$\times 10^{46}$ erg\\
        full cavity (250 K)  & 1.1$\pm$0.3$\times 10^{2}$ M$_{\odot}$ & 3.0$\pm$1.1$\pm$0.6$\times 10^{46}$ erg\\
        full cavity (500 K) & 1.0$\pm$0.3$\times 10^{2}$ M$_{\odot}$ & 2.7$\pm$1.0$\pm$0.5$\times 10^{46}$ erg\\
        \hline
    \end{tabular}
 
\end{table}

\subsection{The expanding shell energetics from [C\,{\scriptsize II}]}
[C\,{\scriptsize II}]\ is a direct tracer of the expanding shells at velocities between 0 and 5 km s$^{-1}$ in the cavities and can thus be used to calculate its mass and kinetic energy. Note, however, that currently only 50 \% of the planned region is observed in [C\,{\scriptsize II}]. Therefore, we apply a correction factor to the calculations. The correction factor is calculated by determining the fraction of the 70 $\mu$m emission from RCW 36 covered by the current [C\,{\scriptsize II}]\ map.  Using different minimal 70 $\mu$m intensities (i.e. 500-1500 MJy/sr) to define RCW 36, we find that typically 47 - 55 \% of RCW 36 was covered. Therefore we apply a correction factor of 2.0$\pm$0.2. In order to calculate the C$^{+}$ column densities in the expanding shell we need the excitation temperature. Generally, this is calculated using the [$^{\rm 13}$C\,{\scriptsize II}]\ line \citep[e.g.][]{Guevara2020}. However, this is not possible for RCW 36 at the moment because there is no convincing [$^{\rm 13}$C\,{\scriptsize II}]\ detection corresponding to the emission between 0 and 5 km s$^{-1}$. 
Therefore, we calculate the kinetic temperature of the expanding shell from estimating the FUV-field strength at the location of the expanding shells and converting this into a C$^{+}$ kinetic temperature using the PDR Toolbox \citep{Kaufman2006,Pound2008}. This method is further specified in Appendix \ref{sec:fuvEstimate} and results in an estimated surface temperature range of 100-500 K which is a good proxy for the gas temperature that is traced by [C\,{\scriptsize II}]\ emission and in agreement with work towards other H\,{\scriptsize II}\ regions \citep[e.g.][]{Schneider2018,Pabst2020}. Assuming optically thin [C\,{\scriptsize II}]\ emission for the shell, which is currently justified by the non-detection of [$^{\rm 13}$C\,{\scriptsize II}]\ emission at velocities lower than 6 km s$^{-1}$, we use Eq.~26 from \citet{Goldsmith2012} to calculate the C$^{+}$ column density. We assume that [C\,{\scriptsize II}]\ emission is thermally excited and work with a ratio C$_{ul}$/A$_{ul}$ = 2 (C$_{ul}$ is the collision rate and A$_{ul}$ the Einstein-coefficient for radiative excitation) because H and H$_{2}$ number densities are expected to be around 3-6$\times$10$^{3}$ cm$^{-3}$ in the shells. 
Varying this ratio between 1 and 5, the resulting column density variations remain within 30\% at each temperature, which is not significantly larger than other uncertainties such as the temperature (leading to variations up to 50\%) or the optically thin assumption. Decreasing the ratio of Einstein coefficients down to C$_{ul}$/A$_{ul}$ = 0.3 would increase the mass by a factor 2. The column density map for the [C\,{\scriptsize II}]\ emission between 0 and 5 km s$^{-1}$ is presented in Fig. \ref{fig:CIIcolDensShell}. 
Integrating the column density map, using the value C/H = 1.6$\times$10$^{-4}$ from \citet{Sofia2004}, the total mass of the expanding shells in the cavities are: 1.5$\times$10$^{2}$ M$_{\odot}$, 1.1$\times$10$^{2}$ M$_{\odot}$ and 1.0$\times$10$^{2}$ M$_{\odot}$, respectively at a mean kinetic temperature (T$_{\text{kin}}$) of 100 K, 250 K and 500 K. Note that this conversion factor might give a lower limit for the total column density since the expanding shell is also weakly detected in the $^{12}$CO(3-2) line and the densities towards the shell of RCW 36 are far higher than the typical densities reported in \citet{Sofia2004} where C/H = 1.6$\times$10$^{-4}$ is mostly found to be an upper limit for the higher densities in their sample. These uncertainties might be part of the explanation why these masses, and resulting expansion energetics, are significantly lower than the values obtained with the \textit{Herschel} methods. They are about a factor 4 smaller than the values obtained using the SED fitted column density map which gives the lowest values for the \textit{Herschel} based calculations. Another reason for this difference might be the spherical assumption when correcting the \textit{Herschel} limb-brightened shells to a total mass. Recently, \citet{Kabanovic2022} demonstrated with detailed radiative transfer and self-absorption analysis that the expanding shell in RCW 120 is expanding in a flattened, and not a spherical, molecular cloud. A similar point might be valid for the cavities in RCW 36, which would reduce the mass estimated based on the \textit{Herschel} data.

\begin{figure}
    \centering
   
    \includegraphics[width=\hsize]{images/shell_NCII_250_paper_1.png}
   
    \caption{C$^{+}$ column density map of the blue-shifted expanding shells in the cavities, i.e. the [C\,{\scriptsize II}]\ emission between 0 and 5 km s$^{-1}$, assuming T$_{kin}$ = 250 K. When working with a different temperature, the [C\,{\scriptsize II}]\ column density structure is exactly the same only with different absolute values. The white contours indicate the \textit{Herschel} column density and the white crosses indicate the location of the two O stars.}
    \label{fig:CIIcolDensShell}
\end{figure}

\subsection{The mass and momentum flux of the high-velocity wings}\label{sect:outflowAnalysis}

At velocities around -8 to 0 km s$^{-1}$ and 14-22 km s$^{-1}$ we observe [C\,{\scriptsize II}]\ emission features that are not associated with expanding shell(s). These blue- and red-shifted high-velocity wings rather resemble what is observed for protostellar outflows in CO. 
However, there are no indications of classical outflow wings in $^{12}$CO(3-2) at any location in the map. In addition, [C\,{\scriptsize II}]\ emission is not a typical tracer for protostellar outflows. Nevertheless, we perform a first order approximation to calculate the mass and momentum flux of these bipolar [C\,{\scriptsize II}]\ high-velocity wings using the method presented in \citet{Cabrit1992,Beuther2002} for bipolar molecular outflows\footnote{See the equations in section 3.2 in \citet{Beuther2002}.}. We first calculate the C$^{+}$ column density maps associated with the high-velocity wings with the same method used in the previous section for the shells. Again, the resulting C$^{+}$ mass associated with the wings depends on T$_{\text{kin}}$ and C$_{ul}$/A$_{ul}$. T$_{\text{kin}}$, between 100 and 500 K, is again quite well constrained from the PDR models. C$_{ul}$/A$_{ul}$ is less constrained as the density and collision partners of C$^{+}$ in these high-velocity wings is uncertain. Therefore, taking C$_{ul}$/A$_{ul} \sim$ 2 will give a reasonable view on the plausible mass range (within a factor 2).
The resulting C$^{+}$ column density maps of the velocity intervals from -8 to 0 km s$^{-1}$ (blue-shifted wing) and 14 to 22 km s$^{-1}$ (red-shifted wing) are presented in Fig. \ref{fig:blueOutflowColdens}. In the red-shifted wing a correction of 1.5 K km s$^{-1}$ is made to take into account the contribution from the [$^{\rm 13}$C\,{\scriptsize II}]\ line at velocities above 17 km s$^{-1}$. Measured with respect to the central velocity of 7 km s$^{-1}$, these velocity ranges give an observed velocity of 15 km s$^{-1}$ for both the blue- and red-shifted wings, respectively. Since the driving mechanism, and thus the inclination, of the mass ejection is uncertain, we work with an average angle of 57$^{o}$ \citep{Bontemps1996}, which also seems reasonable for mass flows in the cavities that are close to the plane of the sky. From the integrated intensity map of the high-velocity wings, we get a radial extent of 1.5 pc. Taking again into account that currently only half of the cavity is observed, the obtained values are corrected by a factor 2.0$\pm$0.2. The resulting mass, mass ejection rate and momentum flux of the bipolar high-velocity wings, assuming a kinetic temperature of 100-500 K for [C\,{\scriptsize II}], are presented in Table~\ref{tab:outflowParams}.
\begin{figure}
    \centering
   
    \includegraphics[width=\hsize]{images/blueOutflow_NCII_250_paper_1.png}
   
    \includegraphics[width=\hsize]{images/redOutflow_NCII_250_paper_2.png}
    \caption{{\bf Top}: C$^{+}$ column density map of the blue-shifted high-velocity wing between -8 km s$^{-1}$ and 0 km s$^{-1}$, assuming T$_{kin}$ = 250 K. The white crosses indicate the location of the two O stars. {\bf Bottom}: The same for the red-shifted high-velocity wing between 14 km s$^{-1}$ and 22 km s$^{-1}$.}
    \label{fig:blueOutflowColdens}
\end{figure}

   

\begin{table*}[]
    \centering
     \caption{The calculated mass, momentum flux (F$_{m}$) and mass ejection rate ($\dot{\text{M}}_{out}$) of the bipolar wings observed with [C\,{\scriptsize II}]\ in the RCW 36 cavities for kinetic temperatures of 100 K, 250 K and 500 K. Based on arguments presented in the text, the errors, which are difficult to quantify for all sources of uncertainty, on these values are easily a factor 2.}
    \label{tab:outflowParams}
    \begin{tabular}{cccc}
    \hline
    \hline
         T$_{kin}$ & Mass & F$_{m}$ & $\dot{\text{M}}_{out}$ \\
         \hline
         100 K & 4$\times$10$^{2}$ M$_{\odot}$ & 2$\times$10$^{-2}$ M$_{\odot}$ km s$^{-1}$ yr$^{-1}$ & 7$\times$10$^{-4}$ M$_{\odot}$ yr$^{-1}$\\
         250 K & 3$\times$10$^{2}$ M$_{\odot}$ & 1$\times$10$^{-2}$ M$_{\odot}$ km s$^{-1}$ yr$^{-1}$ & 5$\times$10$^{-4}$ M$_{\odot}$ yr$^{-1}$\\
         500 K & 3$\times$10$^{2}$ M$_{\odot}$ & 1$\times$10$^{-2}$ M$_{\odot}$ km s$^{-1}$ yr$^{-1}$ & 4$\times$10$^{-4}$ M$_{\odot}$ yr$^{-1}$\\
         \hline
    \end{tabular}
 
\end{table*}

\section{Chandra}\label{sec:chandra}
Chandra observations trace the presence of hot plasma formed in the winds of massive stars. A map of diffuse X-ray emission for RCW 36 was presented in \citet{Townsley2014}. The methods to extract this diffuse X-ray emission are described in detail in  \citet{Broos2010,Broos2012,Broos2018}. Analysing the Chandra data will thus allow a more comprehensive view of the feedback processes that are driving the observed dynamics around RCW 36.

\subsection{The diffuse X-ray emission map}\label{sec:diffXrayEmission}
The diffuse X-ray emission is presented in Fig. \ref{fig:DiffuseXrayEmission}. The brightest peak is centered on the two O star candidates of the young cluster. Fainter emission is seen inside the bipolar cavities, which is explained by extinction from the cavity walls when analyzing the X-ray spectra (see App. \ref{sec:xpecFit}). The morphology of the diffuse X-ray emission in Fig. \ref{fig:DiffuseXrayEmission} hints that the hot plasma formed in the OB cluster is leaking out of the H\,{\scriptsize II}\ region into the ISM beyond the cavities of RCW 36.\\\\
\begin{figure}
    \centering
    \includegraphics[width=\hsize]{images/chandra+70micron+CIIoutline_3.png}
    \includegraphics[width=0.9\hsize]{images/rcw36_acisfulldiffuse+wiseband3+spire250_sm.pdf}
   
   
    \caption{{\bf Top}: Diffuse X-ray emission observed with the ACIS instrument on Chandra. The white contours show the 70 $\mu$m emission of RCW 36 from Fig. \ref{fig:observedMap} starting at 10$^{-1.5}$ Jy pixel$^{-1}$ with increments of 0.5 in the exponent. The brightest Chandra emission is centered on the O stars of the cluster, which are indicated by the black cross. In the cavities, there is diffuse emission detected which is significantly weaker than extended emission outside the cavities (outlined by the 70 $\mu$m emission). 
   
    The diffuse emission outside the cavities likely is the result of hot plasma leaking out of the H\,{\scriptsize II}\ region, which fits with the observed physical connection to the emission inside the H\,{\scriptsize II}\ region and the fact that the hot plasma fitting blindly converged to very similar properties for the different regions. Two locations where this physical connection is seen, are indicated with the red lines. The red box indicates the outline of the currently observed [C\,{\scriptsize II}]\ map.
    {\bf Bottom}: A smoothed image of Chandra/ACIS diffuse X-ray emission in the context of WISE and Herschel images.  The five regions used to extract diffuse X-ray spectra are overlaid.  The small blue ellipse at field center marks a region excluded from the $'$Center$'$ diffuse X-ray spectrum because it is dominated by emission from unresolved young stars at the center of the cluster.  See Appendix D for details of the X-ray spectral fitting.}
    \label{fig:DiffuseXrayEmission}
\end{figure}
To constrain the excitation conditions of the diffuse X-ray emission, X-ray spectra of several regions in RCW 36 are fitted using plasma models in XSPEC \citep{Arnaud1996}. Five diffuse extraction regions, shown in Fig. 14, were defined to obtain spectra with sufficient S/N for fitting.  X-ray events from hundreds of X-ray point sources were excised from these regions, to minimize their influence on the diffuse X-ray spectra.  Details on our methods for fitting diffuse X-ray emission in and around massive star-forming regions are given in \citet{Townsley2019}.\\
The extracted diffuse X-ray spectra and fitting results are presented in App. \ref{sec:xpecFit} and Tab. \ref{tbl:diffuse_spectroscopy_style2}. The central region is filled by a soft, single-temperature thermal plasma plus residual emission from unresolved pre-main sequence stars in the young cluster. The eastern and western cavities are filled with a thermal plasma of similar temperature. The intrinsic surface brightness of this emission, which corrects for the intervening absorption, is higher than that outside the cavities, confirming that the morphology of the apparent surface brightness map is influenced by intervening absorption.  Hot plasma in the ISM surrounding RCW 36 shows two thermal plasma components, one similar in temperature to the RCW 36 emission and one substantially hotter.  While the hotter component is likely unrelated background emission (often seen along Galactic Plane sightlines), the cooler component is strong evidence that the plasma generated by massive star winds in RCW 36 is leaking out of its H\,{\scriptsize II}\ region into the surrounding molecular cloud.

\subsection{Properties of the hot plasma}
From the fitted spectra of the hot plasma, the physical properties (plasma density, pressure,...) can be calculated with an assumed emissivity curve and a filling factor which was taken to be unity \citep{Townsley2003}. The assumed emissivity curve from \citet{Landi1999} assumes collisional ionization equilibrium (CIE) for the plasma. This assumption is justified since non-equilibrium effects only become notable below plasma temperatures of 10$^{6}$ K \citep{Vasiliev2011,Vasiliev2013} whereas the hot plasma temperature in RCW 36 (1.7-2$\times$10$^{6}$ K) is above this value, see also Tab. \ref{tab:PlasmaFit}. The calculation of the physical properties was not done for the regions outside the bipolar H\,{\scriptsize II}\ region (north and southeast) as there is no evident assumption for the 3D geometry at these locations. This calculation of the physical properties also was not done for the central region directly around the OB cluster because of the non-equilibrium ionization (NEI) of the plasma and relatively low temperature. As a result, the bandpass correction factor necessary for the limited ACIS bandpass is larger than 40 which would make the results for the center highly uncertain. For the cavities, the bandpass correction factors are 4.4 and 3.4 for the east and west, respectively, which makes their estimated properties less uncertain. The resulting physical properties of the plasma are presented in Tab. \ref{tab:PlasmaProperties}. Both cavities have an estimated temperature around 2$\times$10$^{6}$ K and electron densities around 0.2 cm$^{-3}$, which results in an estimated pressure of 0.6-0.9$\times$10$^{6}$ K cm$^{-3}$.\\
The resulting estimated energy of the plasma in both cavities match the expansion energy of the expanding shells, presented in Tab. \ref{tab:shellEnergetics}, well (i.e. it is slightly higher than the estimated expansion energy based on [C\,{\scriptsize II}]\ and slightly lower than the estimates based on \textit{Herschel}). This suggests that under adiabatic conditions the expanding shells in the cavities might be driven by the hot plasma \citep[e.g.][]{Weaver1977,Lancaster2021a}. This will be examined in more detail later on as other processes such as photo-ionized gas pressure and direct radiation pressure could also play a role. Note that the unity filling factor is an assumption. The appropriate scaling factor ($\eta^{-1/2}$, with $\eta$ the filling factor) to correct for a lower filling factor is also presented in Column 2 of Tab. \ref{tab:PlasmaProperties}.  This indicates that the resulting plasma properties are not extremely sensitive to the filling factor.

\begin{deluxetable}{@{\hspace{2em}}lcccc@{}}
\centering  \tabletypesize{\footnotesize} \tablewidth{0pt}

\tablecaption{Physical Properties of the Diffuse X-ray Plasma Components for RCW~36, D = 900~pc. \label{tbl:physics}}


\tablehead{
\colhead{Parameter} & \colhead{~Scale factor~~} & 
\multicolumn{2}{c}{RCW 36 Diffuse Region}\\[-7pt]
\colhead{}{\hrulefill} & \colhead{}{\hrulefill} &
\multicolumn{2}{c}{\hrulefill}\\[-7pt]
\colhead{} & \colhead{} &
\colhead{East Bubble}  & \colhead{West Bubble}
}

\startdata
\multicolumn{4}{l}{Observed X-ray properties} \\
\hline
$kT_x$ (keV)                & \nodata     &  0.15                &  0.17                 \\
$L_{X,bol}$ (erg~s$^{-1}$)  & \nodata     &$4.4 \times 10^{33}$  & $1.9 \times 10^{33}$  \\
$V_x$ (cm$^3$)              & $\eta$      &$4.1 \times 10^{56}$  & $4.1 \times 10^{56}$  \\
                            &             &                      &                       \\
\hline
\multicolumn{3}{l}{Derived X-ray plasma properties} \\
\hline
$T_x$ (K)                   & \nodata      & $1.7 \times 10^6$    & $2.0 \times 10^6$     \\
$n_{e,x}$ (cm$^{-3}$)       &$\eta^{-1/2}$ &  0.22                &  0.15                 \\
$P_x/k$ (K~cm$^{-3}$)  	    &$\eta^{-1/2}$ & $0.9 \times 10^6$    & $0.6 \times 10^6$     \\
$E_x$ (erg)                 &$\eta^{1/2}$  & $7.2 \times 10^{46}$ & $5.4 \times 10^{46}$  \\
$\tau_{cool}$ (Myr)         & $\eta^{1/2}$ & 0.5                  & 0.9                   \\
$M_x$ (M$_\odot$)           & $\eta^{1/2}$ & 0.05                 & 0.03                  \\
\enddata

\tablecomments{Equations detailing how the derived properties were obtained from the observed properties are given in \citet{Townsley2003}.  
The quantity $\eta$ is a ``filling factor,'' $0 < \eta < 1$, accounting for partial filling of the volume with the X-ray-emitting plasmas.  The parameters in the table should be multiplied by the appropriate scale factor (Column 2) to account for this filling factor.  Derived plasma properties are proportional to $\eta^{1/2}$ and are thus only weakly sensitive to this correction.}

\label{tab:PlasmaProperties}
\end{deluxetable}

\section{Discussion}\label{sec:discussion}
\subsection{3D structure of RCW 36}
RCW 36 consists of a bipolar cavity and a dense central ring surrounding the waist of the H\,{\scriptsize II}\ region created by the central OB cluster. In the cavities, the expanding [C\,{\scriptsize II}]\ shell is only observed at blue-shifted velocities, which implies it is expanding towards us.  Fitting the foreground column to the Chandra data towards the cavities, in particular the eastern one, suggests that most column density, observed with {\sl Herschel}, is associated with and on the near side of RCW 36 from our point of view. The observed [C\,{\scriptsize II}]\ shells are thus expanding into the predominant nearby column density reservoir of RCW 36. This can offer an explanation why no corresponding red-shifted expanding shell is detected for the cavities even though a few expanding filamentary structures are observed towards slightly more redshifted velocities. As most of the column density appears to be located in front, the gas behind the ridge might be mostly diffuse gas. As a result, the hot plasma created by the OB stars would be able to leak from RCW 36 in that direction, as sketched in Fig. \ref{fig:3dMorph}. This is in essence the same scenario observed for RCW 49 in \citet{Tiwari2021}. Interestingly, in contrast to RCW 36 (2 O star candidates and $\sim$ 1 Myr), RCW 49 contains 37 OB identified stars and is slightly older with an estimated age $\sim$ 2 Myr.\\
To obtain a first idea of the expansion timescale for the dense molecular ring, we use the estimated expansion velocity between 1.0 and 1.9 km s$^{-1}$ and an estimated radius of 0.9 pc.
As it is unclear what drives the expansion of the ring, we calculated the Spitzer expansion timescale for expansion driven by ionizing radiation \citep{Spitzer1978}, the Weaver solution for expansion driven by stellar winds \citep{Weaver1977} and the ballistic expansion timescale which can be expected if shell expansion is driven by stellar winds in an isothermal density field with a power law index of -2 \citep{Geen2022}. The Spitzer solution gives an expansion timescale of 1.2-1.7 Myr, the Weaver solution gives a timescale of 0.3-0.6 Myr and the ballistic expansion give a timescale of 0.5-0.9 Myr. The calculations of the Spitzer and Weaver solutions are further specified in App. \ref{sec:SpitzerWeaverCalc}. Broadly speaking, the Spitzer and ballistic solution for the dense ring appear to be in better agreement with the cluster age than the Weaver solution \citep{Ellerbroek2013a}. However, the upper value of the Spitzer solution, which might be the most representative one (see App. \ref{sec:SpitzerWeaverCalc}), has an equally large deviation from the estimated cluster age as the Weaver solution. The cavities on the other hand have a radius of $\sim$1.0 pc and an expansion velocity of 5.2$\pm$0.5$\pm$0.5 km s$^{-1}$ which results in an estimated Spitzer expansion timescale of 0.2-0.4 Myr (see App. \ref{sec:SpitzerWeaverCalc}), a Weaver expansion timescale of 0.1 Myr and a ballistic expansion timescale of $\sim$ 0.2 Myr. This is roughly a factor 3-5 shorter than for the ring and suggests that the expansion in the cavities is a recent feature. Note that this assumes the cavity expands from the center of the cavity, which might not be fully correct. Considering the expansion starts from the center of RCW 36, we get a radius between 1.5-2.0 pc. This results in an estimated ballistic expansion timescale of 0.3-0.4 Myr which still is shorter than the expansion of the dense ring. RCW 36 thus shows inhomogeneous expansion: relatively slow expansion in the dense gas followed by increasing expansion velocity once the expansion reaches the lower density gas. This fits with relatively low ($<$ 3 km s$^{-1}$) expansion velocity of the denser filamentary structures perpendicular to the ring.\\\\% bipolar cavities form perpendicular to it because of more rapid expansion in the low-density gas.\\% If the expansion in RCW 36 was indeed mostly confined to the sheet until 0.2 Myr ago, this suggests that protostellar outflows during the embedded phases of star formation did not affect these expansion dynamics.\\
\citet{Samal2018} noted that only 16 of the 1377 H\,{\scriptsize II}\ regions considered in their sample are visibly identified as bipolar H\,{\scriptsize II}\ regions. A correction factor has to be taken into account based on inclination selection effects but, as mentioned in \citet{Samal2018}, this still implies that bipolar H\,{\scriptsize II}\ regions are rather rare. From the faster expansion in the bipolar cavities of RCW 36 compared to the ring, it can be argued that the morphology of RCW 36 is changing rapidly (on $\sim$ 0.2 Myr timescales) and thus that a H\,{\scriptsize II}\ region might only be observed as bipolar for a part of its evolution.
As a short exercise, assuming a correction factor 5 for the inclination \footnote{A factor 5 correction for the inclination assumes that we can only identify a bipolar H\,{\scriptsize II}\ region if the inclination angle with the line of sight is larger than 70-75$^{o}$.  This might be a bit of an overestimate, but most identified bipolar nebulae in \citet{Samal2018} have clearly separated cavities which suggests their identification is constrained to high inclination angles.}, and a potential correction factor 5 for the short timescale\footnote{Based on the expansion timescale results, a bipolar H\,{\scriptsize II}\ region would be identified for $\sim$0.2-0.5 Myr. Most mass around a H\,{\scriptsize II}\ region might be removed in a few Myr (e.g.  1-3 Myr), see for example later sections in the discussion. This suggests a correction factor of the order 5, assuming the presence of some mass is required to identify the structure of a H\,{\scriptsize II}\ region in the study of Spitzer images by \citet{Samal2018}.} would imply that up to 30 \% of the H\,{\scriptsize II}\ regions might go through a bipolar phase. However, this remains speculative at the moment since this is based on a single case. More generally, the observation of expanding half-shells, instead of fully spherical shells, in [C\,{\scriptsize II}]\ emission towards H\,{\scriptsize II}\ regions \citep[e.g.][]{Anderson2019,Pabst2020,Luisi2021,Tiwari2021}, and the evidence of important hot plasma leakage, 
 can fit in the view of the ISM where (massive) stars form in a complex organization of filaments and sheets. The creation of bipolar H\,{\scriptsize II}\ regions can then occur when an O star forms close to the mid-plane of a sheet-like structure such that the radiation and wind breaks out on both sides at about the same time. The hot plasma can then start driving expanding shells in the lower density gas outside the sheet. This is however speculative since it is based on a single case while the observations also indicate that the expansion strongly depends on the density structure. Furthermore, simulations by \citet{Wareing2017} suggest that the bipolar morphology remains present for a significant part of their simulation. This is due to the apparent low expansion velocity ($<$ 1 km s$^{-1}$) for the cavities in their simulation which is not in agreement with the observed velocities in the cavities for RCW 36. As the expansion dynamics might depend from region to region, a detailed analysis of age and dynamics of a sample of bipolar H\,{\scriptsize II}\ regions will be required to fully address this question.

\begin{figure}
    \centering
    \includegraphics[width=\hsize]{images/3dMorphology.png}
    \caption{Sketch of RCW 36 seen from the side and indicating our point of view (telescope). With [C\,{\scriptsize II}], we observe blue-shifted expanding shells (blue) in the bipolar cavities. The ring (green) is expanding at a lower velocity into the Vela C molecular cloud. The blue and red arrows indicate the high-velocity mass ejection in the cavities associated with the wings (blue and red) in the spectra. The brown arrows indicate the hot plasma leakage which is presumably most effective towards the back of RCW 36 where no red-shifted expanding shells are observed with the [C\,{\scriptsize II}]\ data, but we also observed it can channel through punctures in the ring as well (brown patches on the ring).}
    \label{fig:3dMorph}
\end{figure}


\subsection{The pressure and energy budget in RCW 36}\label{sec:pressEnergyBudget}

Analysis of the Chandra data shows that a hot plasma, created by the stellar winds, pervades RCW 36 and that it has the required energy to drive the observed expanding shells in both cavities. To discuss the role of different physical process, the associated pressure terms were estimated and are presented in Tab. \ref{tab:pressureTable}. Specific assumptions made for these calculations are specified in App. \ref{sec:linewidthShell}.
The thermal pressure from the hot plasma in both cavities is $\sim$ 0.6-1.0$\times$10$^{6}$ K cm$^{-3}$, which is slightly larger than the estimated thermal pressure of the photo-ionized gas, i.e. 4.6-5.0$\times$10$^{5}$ K cm$^{-3}$, derived from the SHASSA H$\alpha$ observations \citep{Gaustad2001}. However, as for the hot plasma, if the photo-ionized gas is confined in a sub-region of the cavities, this will increase the estimated pressure. As a result, these terms probably dominate over the direct radiation pressure in the cavities, see Tab. \ref{tab:pressureTable}. Since cavities are filled by both the hot plasma and photo-ionized gas, the photo-ionized and collisionally ionized gas can thus be in pressure equilibrium across the contact discontinuity.\\
The physical processes that drive expanding motion of H\,{\scriptsize II}\ regions is still a matter of debate. Simulations generally predict that ionizing radiation is the main driver of expansion compared to stellar winds \citep[e.g.][]{Haid2018,Geen2021,Ali2022}. Yet, simulating the high dynamic range of temperatures and densities associated with the presence of stellar winds in the ISM is challenging \citep[e.g.][]{Dale2015}. Observations by \citet{Lopez2014} also indicate that the ionized gas pressures appear to dominate most H\,{\scriptsize II}\ regions, however other observational studies \citep[e.g.][]{Pabst2019,Luisi2021,Tiwari2021} have proposed that stellar winds drive the high-velocity expansion detected with spectrally resolved [C\,{\scriptsize II}]\ observations. Above we already noted that thermal pressure of the ionized gas and hot plasma seem to be of the same order for RCW 36. Here, we will discuss the associated energy terms. Based on the SHASSA H$\alpha$ intensity, the ionizing photon flux in each cavity is $\sim$8.5$\times$10$^{46}$ s$^{-1}$, see App. \ref{sec:linewidthShell}. This results in a  total injected energy of $\sim$ 6.2$\times$10$^{49}$ erg over the estimated lifetime of the cluster (i.e. 1.1 Myr) when assuming an energy of 13.6 eV for the ionizing photons. Taking into account that the coupling efficiency of ionizing radiation energy to radial expansion typically is $<$ 10$^{-4}$ \citep{Haid2018}, this is about an order of magnitude too small to explain the expanding motion of the shells in the cavities. We do note that at very early evolutionary stages in \citet{Haid2018}, the coupling efficiency for ionizing photons is significantly higher. However, considering a coupling efficiency of 10$^{-3}$ over the first 0.3 Myr remains insufficient to explain the observed expansion. Therefore, unless the coupling efficiency for ionizing photons in \citet{Haid2018} is about an order of magnitude lower than in RCW 36, we propose that the hot plasma created by stellar winds drives the expansion of the blueshifted shells in the cavities.\\
On the other side of the shell, ram pressure, thermal pressure and magnetic pressure from the ambient cloud confine the shell.  The values in Tab. \ref{tab:pressureTable} indicate that in this low-density region, the ram pressure confines the shell. Inside the compressed shell, turbulent pressure seems to be the dominant term to prevent the shell from being further compressed between the hot plasma on one side and ram pressure on the other side.
Even though the estimated magnetic pressure in the shell is significantly smaller than the turbulent pressure, it might play a role in limiting the initial compression rate of the propagating shock that is driven by the expansion. Inspecting the BLASTPol magnetic field map towards RCW 36 in Fig. \ref{fig:blastPolIm}, it is observed that the magnetic field morphology follows the bipolar cavities and forms a kink near the ring where the polarization fraction drops. This behaviour where the magnetic field orientation is aligned with the shell morphology around a H\,{\scriptsize II}\ region, as it is dragged along by the expansion, was recently also observed in the Keyhole Nebula \citep{Seo2021} and NGC 6334 \citep{Arzoumanian2021}. The magnetic field morphology in the ring and whether it significantly affects the expansion remains unclear with current data. This requires higher angular resolution observations (Bij et al. in prep.). In the ring, it is also unclear which process (ionizing radiation or the hot plasma) drives the expansion. The number of ionizing photons and coupling efficiency is sufficient to drive the ring expansion, but the hot plasma in the ring remains unconstrained. As a result, we cannot reach a firm conclusion.

\subsection{Feedback driven turbulence}\label{sec:turbRing}
In Fig. \ref{fig:13coSigmaMap}, a noteworthy increase in $^{13}$CO(3-2) velocity dispersion is observed in the ring of RCW 36 compared to the surrounding regions of the Vela C molecular ridge which does not seem to be explained by opacity broadening, see App. \ref{sec:linewidthShell}. This indicates that the mechanical energy input from stellar feedback can significantly increase the turbulent energy in the compressed gas. This energy injection might thus play a role in setting the thickness of the shell, as it provides a rough pressure equilibrium with both sides of the shell. Specifically, the turbulent pressure in the ring, derived from the spectral linewidth, is similar to or higher than the ram pressure provided by the ambient gas, see Tab. \ref{tab:pressureTable}. Otherwise, the shell would be further compressed until an increased temperature (or magnetic field strength or turbulence) due to this compression would halt it. From the information provided by the $^{13}$CO(2-1) linewidth, corrected for optically thick line broadening (App.~\ref{sec:linewidthShell}), it is possible to estimate the turbulence injection by stellar feedback in the molecular ring. The calculated total turbulent energy injection in the ring and cavity shells is given in Tab. \ref{tab:turbulenceTable}. From Fig. \ref{fig:13coSigmaMap}, it is reasonable to assume a linewidth for this gas of 0.7 km s$^{-1}$ before the onset of stellar feedback, which would give a total turbulent energy of 2.5$\times$10$^{2}$ M$_{\odot}$ (km s$^{-1}$)$^{2}$ for the gas now located in the ring. Comparing this with the value for the ring in Tab. \ref{tab:turbulenceTable}, this implies that the turbulent energy of the gas, after opacity broadening correction, has roughly increased by more than 60 \% compared to the onset of stellar feedback. Turbulence typically dissipates over a few crossing timescales (t$_{cross}$ = d/$\sigma_{los}$) \citep[][]{Ostriker2001}. For the ring, with a width of $\sim$0.1 pc, this gives a crossing timescale of 1.1$\times$10$^{-1}$ Myr. Using this timescale results in a turbulence dissipation rate of 2.4$\times$10$^{33}$ erg s$^{-1}$ that has to be injected to maintain the turbulent linewidth. This is only a small fraction of the probable energy injection rate by the O star candidates, which will be discussed in more detail in the next section.

\begin{figure}
    \centering
    \includegraphics[width=\hsize]{images/70micron_BLASTpol_polFracLength_1.png}
    \caption{\textit{Herschel} 70 $\mu$m map of RCW 36 overlaid with the magnetic field orientation obtained from BLASTPol at 500 $\mu$m \citep{Fissel2016,Fissel2019}. The magnetic field orientation tends to follow the edges of the shells and associated kink near the central ring. It is also observed that the polarization fraction quickly drops towards the central ring which might be associated with the complex morphology in this region that remains unresolved with the BLASTPol data.}
    \label{fig:blastPolIm}
\end{figure}

\begin{figure}
    \centering
    \includegraphics[width=\hsize]{images/sigma13COringMap_1.png}
    \caption{The velocity dispersion map of $^{13}$CO(3-2) for RCW 36. The contours indicate the \textit{Herschel} column density map. Despite the relatively limited extent of the map, it becomes clear that there is a significant velocity dispersion increase at the ring surrounding the OB cluster.}
    \label{fig:13coSigmaMap}
\end{figure}

\begin{table*}[]
\caption{The estimated pressure (range) for the different components associated to the expanding shells in the cavities and the dense molecular ring around the central cluster. The calculation of the values are presented in more detail in App. \ref{sec:linewidthShell}.}
\footnotesize
    \begin{center}
    \setlength{\tabcolsep}{12pt}
    \begin{tabular}{cccccc}
        \multicolumn{5}{c}{Bipolar cavities}\\
        \hline
        \hline
         & P$_{th}$/k (K cm$^{-3}$) & P$_{rad}$ (K cm$^{-3}$)  & P$_{turb}$/k (K cm$^{-3}$) & P$_{B}$/k (K cm$^{-3}$) & P$_{ram}$/k (K cm$^{-3}$) (1)\\
         \hline
        Hot plasma &  0.6-0.9$\times$10$^{6}$ & & & & \\
        H\,{\scriptsize II}\ region & 4.6-5.0$\times$10$^{5}$ & 4.5$\times$10$^{5}$ & & & \\
        Ambient cloud & 0.5-2.5$\times$10$^{4}$ & & $<$1.3-6.7$\times$10$^{5}$ & 0.3-1.4$\times$10$^{5}$ & 0.7-3.5$\times$10$^{6}$\\
        Shell (internal) & 2.5-7.5$\times$10$^{5}$ & & 0.5-1.7$\times$10$^{6}$  & $<$ 0.8-3.8$\times$10$^{5}$ \\
        \hline
    \end{tabular}
    \newline
    \vspace*{0.5 cm}
    \newline
    \begin{tabular}{cccccc}
    \multicolumn{5}{c}{Center + Dense ring}\\
    \hline
    \hline
     & P$_{th}$/k (K cm$^{-3}$) & P$_{rad}$ (K cm$^{-3}$)  & P$_{turb}$/k (K cm$^{-3}$) & P$_{B}$/k (K cm$^{-3}$) & P$_{ram}$/k (K cm$^{-3}$) (1)\\
    \hline
    Hot plasma & \\
    H\,{\scriptsize II}\ region & 2$\times$10$^{6}$ (2) & 1.2$\times$10$^{6}$ \\
    Ambient cloud & 0.2-2.0$\times$10$^{5}$ & & $<$1.3-13$\times$10$^{6}$ & 0.4-7.8$\times$10$^{6}$ & 0.3-2.8$\times$10$^{6}$ \\
    Ring (internal) & 2.4-3.6$\times$10$^{5}$ & & 3.0-3.7$\times$10$^{6}$ & & \\
    \hline
    \end{tabular}
    \end{center}
    NOTE\hspace{0.3 cm}
   
   
    (1) Ram pressure provided by the ambient cloud on the expanding shell/ring. 
    (2) \citet{Minier2013}
    \label{tab:pressureTable}
\end{table*}

\begin{table*}[]
\caption{The turbulent energy (E$_{turb}$), dissipation timescale (t$_{diss}$), turbulent dissipation rate ($\dot{E}_{turb}$) and the total injected turbulent energy (E$_{turb,tot}$) for the dense ring and the full expanding shell associated with the bipolar cavities.}
    \begin{center}
    \setlength{\tabcolsep}{12pt}
    \begin{tabular}{ccccc}
       
        \hline
        \hline
         & E$_{turb}$ (erg) & t$_{diss}$ (Myr) & $\dot{E}_{turb}$ (erg s$^{-1}$) & E$_{turb,tot}$ (erg)\\
         \hline
        Ring & 8.2$\times$10$^{45}$ & 1.1$\times$10$^{-1}$ & 2.4$\times$10$^{33}$ & 8.2$\times$10$^{46}$ (over 1.1 Myr)\\
        Shells (from [C\,{\scriptsize II}]) & 2.2$\times$10$^{46}$ & 2.0$\times$10$^{-1}$ & 3.2$\times$10$^{33}$ & 2.2$\times$10$^{46}$ (over 0.2 Myr)\\
        \hline
    \end{tabular}
    \end{center}
     NOTE\hspace{0.3 cm} These calculations for the shell make use of the typical velocity dispersion of 1.5 km s$^{-1}$ in the expanding shell and the shell mass deduced from [C\,{\scriptsize II}].
    \label{tab:turbulenceTable}
\end{table*}

\subsection{Leakage of the hot plasma}\label{sec:plasmaLeakage}
In Sect. \ref{sec:diffXrayEmission} we proposed that there is leakage of the hot plasma through the diffuse medium around RCW 36 which leads to the hot plasma found outside RCW 36 in Fig. \ref{fig:DiffuseXrayEmission}. To quantify the leakage, we have to estimate the total energy injected in the ISM by the stellar winds of the OB cluster. This is done using several stellar atmosphere models as there is a large uncertainty on the actual stellar wind mass-loss rates which from observations appear to be lower than predicted by the standard models \citep[e.g.][]{Martins2004,Martins2005b,deAlmeida2019}. However, recently it was proposed that the observed values are underestimated because observations miss a significant part of the stellar winds as a large fraction of the stellar wind might be in a hot phase that is not traced by the observations \citep{Lagae2021}. To cover the range of possibilities, we will use the relations that were put forward in Eq. 12 of \citet{Vink2000}, Eq. 3 of \citet{Lucy2010}, Eq. 11 of \citet{Krticka2017} and Eq. 20 of \citet{Bjorklund2021}, all with a terminal velocity of 2500 km s$^{-1}$ \citep[e.g.][]{Lamers1995,Krticka2017,Lagae2021}. The formulas differ in the choice of critical parameters and their dependencies (luminosity, metallicity, effective temperature, terminal velocity etc.), but it is beyond the scope of this paper to discuss their differences in more detail. In any case, employing a range of 
relations allows to cover the standard predicted mass ejection rate from stellar models \citep{Vink2000} to predictions that are more adapted to fit with the current observations \citep{Bjorklund2021}. For the 09V and 09.5V star candidates in the cluster we use the stellar parameters from \citet{Martins2005a} and \citet{Pecaut2013} to take into account the effects of different stellar models. The results are summarized in Tab. \ref{tab:SWmodelsTable}, which indicates a significant change depending on the stellar model used and an even larger effect related to the the stellar wind mass loss rate prescription used. Only taking into account the two O star candidates of RCW 36, this results in a total injected energy in the range of 4.7$\times$10$^{47}$-8.3$\times$10$^{48}$ erg over 1.1 Myr, see Tab. \ref{tab:SWmodelsTable}. This order of magnitude difference depending on the model might be overcome by the missing hot phase proposed in \citet{Lagae2021}, however future observations will have to address if there is indeed such a large fraction of the stellar winds in the hot phase. The energy in the hot plasma of RCW 36, from Tab. \ref{tab:PlasmaProperties}, is of the order of 1-2$\times$10$^{47}$ erg, implying that $>$50\%, and potentially up to 97\%, of the total injected stellar wind energy is no longer found in the hot plasma.\\\\
Stellar wind energy loss methods were listed in \citet{Townsley2003}, \citet{HarperClark2009} and \citet{Rosen2014}. Here we will explore the options. From Tab. \ref{tab:PlasmaProperties}, it is found that the hot plasma luminosity is a factor 3 to more than an order of magnitude lower than required to explain the missing energy in the hot plasma. The injected turbulent energy in the molecular ring, presented in Tab. \ref{tab:turbulenceTable}, is a factor 5 to two orders of magnitude smaller than total injected energy as well. Thermal conduction at the interface of the hot plasma and the turbulent shell layer is another potential way to lose the plasma energy. Recently, work by \citet{Lancaster2021a,Lancaster2021b} indicated that cooling can be very efficient at the interface because of turbulent substructure and that this could even explain all the observed missing hot plasma energy. However, it was also noted that thermal conduction is strongly reduced when a (weak) magnetic field is parallel to the shell \citep{Soker1994,Rosen2014}. This is the case for RCW 36 based on Fig. \ref{fig:blastPolIm} and it should be noted that \citet{Lancaster2021a,Lancaster2021b} currently do not include the magnetic field. Simulations in \citet{Arthur2011} indicate that the magnetic field will be mostly perpendicular to the shell in the ionized gas and aligned with the shell in the neutral gas. \citet{Rosen2014} note that a parallel magnetic field with 1 $\mu$G would decrease the thermal conduction by several orders of magnitude. In RCW 36, a magnetic field strength of at least several $\mu$G is expected \citep{Crutcher2012}, 
which seems to exclude thermal conduction based on this work. However, more in depth theoretical studies of energy loss at the turbulent interface, including the magnetic field, would be invaluable to better constrain this. Lastly, wind energy transfer to dust grains through collisions was also excluded in \citet{Rosen2014} as a plausible explanation. This suggests that the majority of the stellar wind energy might have leaked through lower-density regions out of RCW 36. Therefore, we here try to estimate the plasma energy leakage from RCW 36 based on Eq 8 from \citet{HarperClark2009}. As we propose the region is fully open at one side of the region we use a shell cover fraction (C$_{f}$) of 0.5 for RCW 36 and radius of 1 pc. Plugging in these values with the hot plasma parameters from Tab. \ref{tab:PlasmaProperties} gives a current energy leakage per cavity of -2.0$\times$10$^{35}$ erg s$^{-1}$ which is almost two orders of magnitude larger than derived values from other processes in this work. Since leakage probably occurred over the evolution of the H\,{\scriptsize II}\ region, we use an intermediate radius of 0.5 pc to estimate the leakage over the lifetime of RCW 36. Note that this is only an approximation as we have no detailed information on the time evolution of RCW 36. It should also be noted that the C$_{f}$ definition in \citet{HarperClark2009} assumes equal leakage in all directions, whereas in RCW 36 we propose that leakage has a preferential direction. This then gives a total leaked plasma energy of -1.7$\times$10$^{48}$ erg over 1.1 Myr. Compared to the values in Tab. \ref{tab:SWmodelsTable}, this suggests that leakage indeed has the potential to account for most missing hot plasma energy.\\ 
If there is indeed such strong hot plasma leakage, it could be wondered if the leaking plasma still has an effect on the molecular cloud. Studying the large scale molecular cloud structure around RCW 36 with sensitive dust continuum observations (i.e. \textit{Herschel} \& BLASTPol), it can be noted that RCW 36 is located at the center of a large low-column density region in Vela C \citep{Hill2011,Fissel2016}, see Fig. \ref{fig:largeCavities}. Furthermore, inspecting Fig. \ref{fig:largeCavities} we observe that the leaking hot plasma shows hints it correlates with the structure of this large low-column density region. It is thus possible that the potential large fraction of leaking hot plasma clears the low-density ambient cloud on a larger scale. When the injected feedback energy escapes into the diffuse ISM through such lower-density regions or $'$chimneys$'$ in the cloud it can thus further disrupt these regions and their mass provision to the ridge around RCW 36. From the large scale SHASSA H$\alpha$ map presented in Fig. \ref{fig:largeCavitiesHalpha}, we confirm that this low density region is indeed a channel of feedback energy leaking into the larger cloud. Estimating the number of photons in these larger cavities is relatively uncertain as their extent is not strongly constrained. Excluding the H$\alpha$ emission in the cavities defined by the 70 $\mu$m emission, we obtain ionizing photon fluxes as high as 6-7$\times$10$^{46}$ s$^{-1}$ in these larger cavities. This is fairly similar to the values obtained inside the 70 $\mu$m cavities and thus supports significant leakage from RCW 36 into the diffuse cloud.\\
As Vela C still is a relatively young molecular cloud where RCW 36 is the first H\,{\scriptsize II}\ region, this suggests that the leakage is the result of the molecular cloud morphology before feedback sets in. This presence of lower-density gas (or voids) is expected if molecular clouds are indeed built out of filaments and sheets. 
\begin{table*}[]
\caption{{\bf Top}: The stellar wind mass ejection rates ($\dot{\rm M}_{\rm SW}$) for the individual O stars. {\bf Bottom}: The resulting total ejected energy over the lifetime of the cluster (1.1 Myr) using terminal wind velocities of 2500 km s$^{-1}$.}
    \centering
    \begin{tabular}{cccccc}
    \hline
    \hline
       \multicolumn{2}{c}{}  & \citet{Vink2000} & \citet{Lucy2010} & \citet{Krticka2017}  & \citet{Bjorklund2021}\\
        Model & star & log[$\dot{\rm M}_{\rm SW}$ (M$_{\odot}$ yr$^{-1}$)] & log[$\dot{\rm M}_{\rm SW}$ (M$_{\odot}$ yr$^{-1}$)] & log[$\dot{\rm M}_{\rm SW}$ (M$_{\odot}$ yr$^{-1}$)] & log[$\dot{\rm M}_{\rm SW}$ (M$_{\odot}$ yr$^{-1}$)]\\
        \hline
         \citet{Martins2005a} & O9V & -7.35 & -8.56 & -7.78 & -8.31 \\
         \citet{Martins2005a} & O9.5V & -7.57 & -9.00 & -7.94 & -8.53\\
         \hline
         \citet{Pecaut2013} & O9V & -7.12 & -8.56 & -7.61 & -8.10 \\
         \citet{Pecaut2013} & O9.5V & -7.35 & -8.58 & -7.78 & -8.31\vspace{0.4 cm}\\
         \hline
         \hline
         & & E$_{\rm SW}$ (erg) & E$_{\rm SW}$ (erg) & E$_{\rm SW}$ (erg) & E$_{\rm SW}$ (erg)\\
         \hline
         \citet{Martins2005a} & O9V & 2.7$\times$10$^{48}$ & 1.7$\times$10$^{47}$ & 1.0$\times$10$^{48}$ & 3.0$\times$10$^{47}$\\
         \citet{Martins2005a} & O9.5V & 1.6$\times$10$^{48}$ & 5.7$\times$10$^{46}$ & 6.7$\times$10$^{47}$ & 1.7$\times$10$^{47}$\\
         \citet{Martins2005a} & total & 4.3$\times$10$^{48}$ & 2.3$\times$10$^{47}$ & 1.7$\times$10$^{48}$ & 4.7$\times$10$^{47}$\\
         \hline
         \citet{Pecaut2013} & O9V & 5.4$\times$10$^{48}$ & 1.9$\times$10$^{47}$ & 1.7$\times$10$^{48}$ & 5.4$\times$10$^{47}$\\
         \citet{Pecaut2013} & O9.5V & 2.9$\times$10$^{48}$ & 1.7$\times$10$^{47}$ & 1.1$\times$10$^{48}$ & 3.1$\times$10$^{47}$\\
         \citet{Pecaut2013} & total & 8.3$\times$10$^{48}$ & 3.6$\times$10$^{47}$ & 2.8$\times$10$^{48}$ & 8.5$\times$10$^{47}$\\
         \hline
    \end{tabular}
    \label{tab:SWmodelsTable}
\end{table*}

\begin{figure*}
   
    \includegraphics[width=0.95\hsize]{images/LargeCavities_3.png}
    \caption{\textit{Herschel} column density map of the region in Vela C around RCW 36 (outlined by the green 70 $\mu$m contour). The bipolar cavity only fills up a part of the large low column density region around RCW 36, indicated by the dashed white circles. The black to orange contours indicate the increasing diffuse Chandra X-ray emission. This shows some hints of a correlation between the diffuse X-ray emission and the column density structure in the larger low-density regions surrounding RCW 3
    , e.g. in the north and south-east of the map. The red box indicates the region covered by the Chandra data.}
    \label{fig:largeCavities}
\end{figure*}

\begin{figure*}
    \centering
    \includegraphics[width=0.85\hsize]{images/LargeCavities_7.png}
    \caption{SHASSA H$\alpha$ map of the larger region around RCW 36. The peak H$\alpha$ emission corresponds to the center of RCW 36. The yellow and red contours indicated the \textit{Herschel} column density contours at N$_{H_{2}}$ = 4$\times$10$^{21}$ cm$^{-2}$ and 6$\times$10$^{21}$ cm$^{-2}$. The white dashed circles indicate the same large-scale low density cavities as in Fig. \ref{fig:largeCavities}. These cavities are clearly emitting H$\alpha$ emission, associated with the leakage of ionizing photons, compared to unperturbed regions in the Vela C molecular cloud.}
    \label{fig:largeCavitiesHalpha}
\end{figure*}



\subsection{The implication of the high-velocity [C\,{\scriptsize II}]\ wings}\label{sec:massEjection}

The bipolar wings at high velocities in [C\,{\scriptsize II}]\ show no clear expanding shell morphology and are not driven by protostars in the ring, but rather by feedback from the OB cluster. This could explain why the wings become less clear at the high-column density region of the ring in Fig. \ref{fig:outflowColdens}. [C\,{\scriptsize II}]\ high-velocity wings were also found in the bipolar regions S106 \citep{Simon2012} and NGC 7538 IRS1 \citep{Sandell2020}. Unlike S106 \citep{Schneider2018}, [O\,{\scriptsize I}]\ is not clearly detected in the wings of RCW 36 which suggests that the density in these wings is comparatively low. In NGC 7538 IRS1, the wings are also detected in $^{12}$CO(3-2) which suggests that for NGC 7538 IRS1 the [C\,{\scriptsize II}]\ wings might trace a protostellar outflow there.\\
To investigate whether ablation by stellar winds can drive the mass ejection observed with the [C\,{\scriptsize II}]\ wings, we compare the energy (and momentum) rates for the stellar winds and the [C\,{\scriptsize II}]\ wings.  
The energy injection rate of the most favorable stellar wind models ($\sim$3.9-7.5$\times$10$^{42}$ erg yr$^{-1}$, from \citet{Vink2000}) is of the same order as the outflow energy rate seen with the [C\,{\scriptsize II}]\ wings ($\sim$ 3-5$\times$10$^{42}$ erg yr$^{-1}$). As the [C\,{\scriptsize II}]\ outflow parameters should be accurate within a factor 2-3 according to our evaluation in Sec. \ref{sect:outflowAnalysis}, this suggests that stellar wind ablation might be able to continuously drive the observed [C\,{\scriptsize II}]\ wings. If these high-velocity wings are continuously ejected from RCW 36, it might account for a significant fraction of the missing plasma energy. However, it has to be taken into account that we also observe actual leakage of the hot plasma and that there are other potential stellar wind energy sinks discussed in previous sections.  In addition this conclusion is only valid for the \citet{Vink2000} models. The estimated energy injection rate by all other models would not be able to explain the observed wings.When considering the total momentum injection rate of the stellar winds, this is about two orders of magnitude lower than the momentum flux observed for the [C\,{\scriptsize II}]\ wings.\\
Another potential driver would be the radiation from the OB cluster. In the simulations by \citet{Kim2018}, which focus on radiation feedback in molecular clouds, they found mass ejection with velocities between $\sim$ 6 and 40 km s$^{-1}$ as a result of thermal and radiation pressure from ionizing radiation. Radiation might thus be able to drive the observed mass ejection from the center of RCW 36. The calculated radiation pressure (I/c) at r = 0.9 pc (corresponding to the ring) is 1.2$\times$ 10$^{6}$ K cm$^{-3}$ and thus not significantly higher than the pressure from the hot plasma in the cavities. If the acceleration originates in the ionized gas closer to the OB cluster the radiation pressure would be higher and could thus more easily drive high-velocity mass ejection into the low density cavities.  As the ionized gas does not cover the full region, because of the hot plasma, this also increases the thermal pressure of the ionized gas. However, there is very little mass inside the central ring \citep{Minier2013} which implies that the mass ejection should happen at the surface of the ring and/or bipolar cavities. The mass ejection seen with the wings might thus be driven by a combination of stellar wind and pressure from the ionizing radiation. This combination would leave more room for the observed hot plasma leakage and other energy sinks. In general it thus remains challenging to explain the observed wings with the constrained feedback mechanisms for RCW 36.\\\\
The mass ejection rate derived from the [C\,{\scriptsize II}]\ wings in Tab. \ref{tab:outflowParams} is high. It suggests that 4.8-7.4$\times$10$^{2}$ M$_{\odot}$ can be removed from the region confined by the ring in RCW 36 over the current lifetime of the OB cluster (or 0.9-1.3$\times$10$^{2}$  M$_{\odot}$ over 0.2 Myr). This could have important implications for the star formation efficiency (SFE) in the cloud. 
If this mass ejection is going on for 1.1 Myr, which could fit with the missing hot plasma energy, it would have already removed about the same mass from the original star forming region as what is now found in the molecular ring and more than an order of magnitude more than the $\sim$ 20 M$_{\odot}$ of ionized gas confined by the ring \citep{Minier2013}. We found no indications of inflow towards RCW36 from the ambient gas as it is actively being swept away, so the main mass inflow would happen along the ridge of Vela C. Using $\pi$R$^{2}$v$_{\rm inf}\rho$ it is then possible to calculate the remaining mass inflow to the RCW 36 ring through the ridge, where R is the radius, v$_{inf}$ the inflow velocity and $\rho$ the density. Here, we assume that the 1.5 km s$^{-1}$ velocity gradient along RCW 36 \citep{Fissel2019} is associated with inflow though it is equally plausible this is mainly the result of expansion. This gives $\dot{\rm M}_{\rm inf}$ = 0.7$\times$10$^{-4}$ M$_{\odot}$ yr$^{-1}$ when we further assume R = 0.1 pc \citep{Minier2013} and n$_{H_{2}}$ = 2.4$\times$10$^{4}$ cm$^{-3}$ (converted to the density assuming a mean molecular mass $\mu$ = 2.33). The inflow rate is thus more than a factor 5 lower than the mass ejected from RCW 36 and therefore has a small effect on the disruption. The observed mass ejection rate could thus stop any new star formation around RCW 36 on the timescale of 1-2 Myr.\\
It is also interesting that the mass ejection rate is within a factor two of the typical proposed mass inflow rates ($\sim$ 10$^{-3}$ M$_{\odot}$ yr$^{-1}$) in globally collapsing hubs and ridges before massive stars have formed \citep[e.g.][]{Schneider2010,Peretto2013}. This implies that the observed mass ejection can remove the mass from the central region on roughly the same timescale that the collapsing hub/ridge provides mass inflow (i.e. a few free fall timescales of the hub), which is consistent with several simulations that emphasize the importance of stellar feedback to maintain a low SFE in molecular clouds \citep[e.g.][]{Dale2012,Walch2012}. The observations of RCW 36 thus suggest that stellar feedback is essential in preserving the low SFE in proposed dynamic high-mass star forming scenarios due to effective mass removal from the originally collapsing pc scale region.\\ 
There are still several uncertainties related to this rapid mass removal (e.g. when the high-velocity mass removal started exactly, the currently incomplete map, etc.), but future studies using the larger statistical sample that will be provided by the FEEDBACK Legacy program will give further insight into the timescale of this rapid mass removal and how it affects the SFE in high-mass star forming regions.


\section{Conclusions}
We presented the currently obtained [C\,{\scriptsize II}]\ and [O\,{\scriptsize I}]\ observations from the SOFIA FEEDBACK Legacy program towards RCW 36, a bipolar H\,{\scriptsize II}\ region in the young Vela C molecular cloud. These observations are complemented with $^{12}$CO(3-2) and $^{13}$CO(3-2) observations from APEX, Chandra X-ray observations, \textit{Herschel} photometric data, and the BLASTpol dust polarization observation at 500 $\mu$m. The main results can be listed as follows:\\\\
$\bullet$ The [C\,{\scriptsize II}]\ and $^{13}$CO(3-2) data show that the central molecular ring is expanding with an estimated velocity of 1.0-1.9 km s$^{-1}$ (see Sec.  \ref{sec:ringExp}).\\
$\bullet$ The [C\,{\scriptsize II}]\ and $^{12}$CO(3-2) data show the presence of several filaments in the ambient cloud that are being swept away with velocities $<$ 3 km s$^{-1}$ (see Sec.  \ref{sec:filsExp}).\\
$\bullet$ The [C\,{\scriptsize II}]\ line unveils blueshifted expanding shells in the bipolar cavities with a velocity of  $\sim$5.2$\pm$0.5$\pm$0.5 km s$^{-1}$  (see Sec.  \ref{sec:expShells}).\\
$\bullet$ The [C\,{\scriptsize II}], [O\,{\scriptsize I}], and $^{12}$CO(3-2) spectra have important absorption signatures towards the bright molecular ring (see Sec.  \ref{sec:velComps}).\\
$\bullet$ The [C\,{\scriptsize II}]\ emission indicates that the warm gas from the PDR layer has broken through the dense swept-up ring in the south-west of this ring (see Sec.  \ref{sec:ringExp}).\\
$\bullet$ The BLASTPol data shows that the magnetic field, dragged along by the expansion, follows the curvature of the shells around the bipolar cavities. However, the magnetic field orientation might have set the direction of the bipolar cavities. Higher resolution observations are needed to address this (see Sec. \ref{sec:pressEnergyBudget}).\\
$\bullet$ The $^{13}$CO(3-2) emission has an increased linewidth in the swept-up ring compared to the unaffected ridge in Vela C which might alter the outcome of the second generation of star formation towards RCW 36 (see Sec. \ref{sec:turbRing}).\\
$\bullet$ Diffuse Chandra emission traces a hot plasma, created by stellar winds, that fills RCW 36 and appears to be able to drive the 5.2 km s$^{-1}$ blueshifted expanding shells in the cavities (see Sec. \ref{sec:chandra}).\\
$\bullet$ Fitting the Chandra data also demonstrates that the observed hot plasma outside the H\,{\scriptsize II}\ region is likely hot plasma leaking from the H\,{\scriptsize II}\ region.\\
$\bullet$ We find that between 50\% and 97\%, depending on the stellar wind model, of the injected stellar wind energy is missing in RCW 36. Hot plasma leakage can provide a consistent explanation for this, but we can't fully constrain the contribution from energy sinks at the hot plasma-shell interface (see Sec. \ref{sec:plasmaLeakage}).\\
$\bullet$ We showed that the hot plasma and ionizing photon leakage has cleared a larger region around RCW 36 in the Vela C molecular cloud. (see Sec. \ref{sec:plasmaLeakage}).\\
$\bullet$ The [C\,{\scriptsize II}]\ spectra have bipolar high-velocity wings in the cavities without a visible expanding shell velocity structure, nor a counterpart in CO. These wings trace high-velocity (v $>$ 15 km s$^{-1}$) and effective ($\sim$ 5$\times$10$^{-4}$ M$_{\odot}$ yr$^{-1}$) mass ejection from RCW 36 (see Sec. \ref{sec:massEjection}).\\\\
The observed rapid shell expansion in the cavities compared to the ring indicates that the expansion accelerates when it reaches lower density gas. This suggests that this clear bipolar stage might only be a relatively short phase in the evolution of RCW 36 and thus even that a bipolar morphology at some point in expanding H\,{\scriptsize II}\ regions might be more common than previously thought. The observed multistage expansion morphology, as well as the proposed important leakage, point to a scenario where stellar feedback evolves in a structure of filaments, sheets and lower-density ambient gas that make up the Vela C molecular cloud. Lastly, the expansion timescale of the ring and rapid mass ejection indicate that stellar feedback can rapidly suppress local massive star formation in a cloud (in 1-2 Myr). This could even allow to maintain a low star formation rate in gravitationally collapsing regions of a molecular cloud where massive stars form. Additionally, the proposed clearing of the ambient low-density cloud can prevent further provision of cold gas necessary to continue high-mass star formation.

\acknowledgments
We thank the anonymous referee for detailed and very insightful comments that significantly improved the quality of this paper. We thank F. Martins and J-C Bouret for providing comments on the modeling and observations of stellar winds related to this work. We thank F. Comeron for fruitful discussions on the interpretation of the star cluster observations towards RCW 36. We further thank M. Pound and M. Wolfire for discussions related to PDR structure and the PDR Toolbox. \\
This work is based on observations made with the NASA/DLR Stratospheric Observatory for Infrared Astronomy
(SOFIA). SOFIA is jointly operated by the Universities Space Research Association, Inc. (USRA),
under NASA contract NNA17BF53C, and the Deutsches SOFIA Institut (DSI) under DLR contract 50 OK 0901
to the University of Stuttgart.\\
We thank the USRA and NASA staff of the Armstrong Flight Research
Center in Palmdale and of the Ames Research Center in Mountain View,
and the Deutsches SOFIA Institut for their work on the observatory. We
acknowledge the support by the upGREAT team for operating the
instrument, for planning the detailed observing scenarios and in the
calibration of the data. The development and operation of upGREAT was
financed by resources from the MPI f\"ur Radioastronomie, Bonn, from
Universit\"at zu K\"oln, from the DLR Institut für Optische Sensorsysteme,
Berlin, and by the Deutsche Forschungsgemeinschaft (DFG) within the
grant for the Collaborative Research Center 956 as well as by the Federal Ministry
of Economics and Energy (BMWI) via the German Space Agency (DLR)
under Grants 50 OK 1102, 50 OK 1103 and 50 OK 1104.\\
The FEEDBACK project is supported by the BMWI via DLR, Projekt Number 50 OR 1916
(FEEDBACK). \\
L.B. was supported by a USRA postdoctoral fellowship, funded through the NASA SOFIA contract NNA17BF53C. N.S. acknowledges supported by the Agence National
de Recherche (ANR/France) and the Deutsche Forschungsgemeinschaft
(DFG/Germany) through the project ‘GENESIS’ (ANR-16-CE92-0035-
01/DFG1591/2-1).


\vspace{5mm}
\facilities{SOFIA (upGREAT), Chandra, APEX, Herschel}


\software{astropy \citep{Astropy2013},  
          cygrid \citep{Winkel2016},
         
         
          }
          

