\section{Introduction}
\label{intro}

Exoplanetary science has undergone rapid expansion over the past three
decades. As observational techniques have improved, the sensitivity
limits have allowed the detection of increasingly smaller exoplanets
\cite{butler2006,akeson2013}. The ``deep dive'' into the terrestrial
regime of exoplanet detection was largely enabled by the {\it Kepler}
mission \cite{borucki2016}; a legacy that is now being continued with
the Transiting Exoplanet Survey Satellite ({\it TESS})
\cite{ricker2015}. Moreover, these discoveries have revealed the
diversity of planetary system architectures \cite{ford2014,winn2015}
including compact systems of planets close to the host star
\cite{funk2010,kane2013e}. The proximity of exoplanets to their host
star has spurred further study into tidal locking scenarios, including
the time scales and implications for the planets
\cite{barnes2017b}. As such, the local analogs to tidally locked
terrestrial planets are exceptionally valuable subjects of
examination, as they provide the means to study the pathway to tidal
locking and the influence on their atmospheric evolution.

A particular area of focus has been the investigation of planets that
reside within their star's Habitable Zone (HZ), defined as the region
around a star where a planet may have surface liquid water provided
sufficient atmospheric pressure
\cite{kasting1993a,kane2012a,kopparapu2013a,kopparapu2014}. Many HZ
planets have been detected, including several hundreds from the {\it
  Kepler} mission \cite{kane2016c}. In parallel, the development of
climate models and their applications to exoplanets has seen a similar
rise in activity \cite{forget2014,shields2019a}. These climate
simulations are often constructed from parent Earth-based models
\cite{way2017b}, and require a substantial amount of assumptions
regarding intrinsic planetary properties
\cite{fauchez2021}. Furthermore, the effect of tidal locking on
potential surface habitability is unresolved, and may accelerate
\cite{hamano2013,turbet2021} or decelerate \cite{way2016} the
transition of terrestrial planet atmospheres into a runaway greenhouse
state. It is expected that exoplanet atmospheric compositional data
will provide additional insights that may substantially aid the
climate modeling approach \cite{kempton2018}. Importantly, the
detailed inference of planetary surface conditions relies upon a
complete understanding of the limited inventory of terrestrial
atmospheres within the Solar System, for which in-situ data form the
basis of atmospheric models \cite{kane2021d}.

The nearest Earth-size planet is Venus, whose complicated atmosphere
remains an enigma in many respects \cite{taylor2009,taylor2018}. The
surface conditions are among the most extreme observed in the Solar
System, with an atmospheric mass two orders of magnitude larger than
Earth, creating a surface pressure that renders its CO$_2$ dominated
atmosphere in a super-critical fluid state
\cite{lebonnois2020a}. Diagnosing the evolution of Venus from
formation to its present state is fundamental to understanding the
divergence of Venus and Earth \cite{kasting1988c} and possible similar
evolutionary pathways for exoplanets \cite{kane2019d}. Venus is
considered an asynchronous rotator \cite{leconte2015a}, whose present
rotational state is likely the result of complex interactions between
solar and atmospheric tides
\cite{ingersoll1978b,correia2001,auclairdesrotour2017b}. Similarly,
the dynamics and super-rotation of the Venusian atmosphere is a
consequence of the combined effects of relatively high incident flux,
slow rotation, atmospheric structure, and interaction with the surface
topography \cite{lee2007c,takagi2007,lebonnois2010}. The particular
relevance to exoplanets that lie near the tidal locking threshold is
acute \cite{sergeev2020}, for which Venus will always be our best
studied example \cite{kane2019d}.


\section{The Terrestrial Exoplanet Population}
\label{population}

The currently known exoplanet inventory consists of a population
number that lies in the thousands \cite{akeson2013}, from which the
diversity of system architectures begins to emerge
\cite{ford2014,clanton2014b,winn2015}. Shown in Figure~\ref{fig:radii}
are histograms of the exoplanet radii distribution for discoveries up
until 2012, 2015, and 2021. The data were extracted from the NASA
Exoplanet Archive \cite{akeson2013} and are current as of 2021, June
10. The green shaded region indicates which planets may be
terrestrial, accounting for uncertainties in the radii measurements
\cite{rogers2015a,wolfgang2016}. The figure demonstrates the dramatic
rise in terrestrial planet detection that occurred between 2012 and
2021, largely due to the results from the {\it Kepler} mission
\cite{borucki2016}. Figure~\ref{fig:radii} also shows the gradual
appearance of the a gap in the radius distribution, referred to as the
``Fulton gap'' or ``photoevaporation valley''. This radius gap has
been suggested to be the result of photo-evaporation
\cite{lopez2013,owen2013a,fulton2017}, suggesting that short-period
super-Earths may primarily consist of a ``bare'' core from which the
atmosphere has been stripped within 100~Myrs of formation. Though the
transit and radial velocity exoplanet detection techniques are biased
toward short-period planets, the occurrence of terrestrial planets
within their sensitivity regimes have been broadly quantified
\cite{dressing2013,bryson2021}. These occurrence rates include those
for planets that lie interior to the system HZ, where the planets may
be stronger candidates for atmospheric evolution into post runaway
greenhouse environments \cite{kane2014e}.

\begin{figure}
  \begin{center}
      \includegraphics[width=0.9\linewidth]{fig_radii.png}
  \end{center}
  \caption{Histogram of the radius distribution for the known
    exoplanet population. The largest histogram (solid line, light
    blue) represents the currently known distribution. The middle
    histogram (dashed line, medium blue) and the smallest histogram
    (dotted line, dark blue) represent the distributions as of 2015
    and 2012, respectively. The green shaded region indicates which
    planets may be terrestrial in nature.}
  \label{fig:radii}
\end{figure}

\begin{figure*}[t]
  \begin{center}
      \includegraphics[width=0.9\linewidth]{fig_tidallock.png}
  \end{center}
  \caption{The HZ boundaries (solid and dotted lines) and tidal
    locking distance (gray dashed line) as a function of stellar
    effective temperature and stellar flux received by the
    planet. Solar System planets and numerous known exoplanets are
    included \cite{yang2014b}.}
  \label{fig:tidallock}
\end{figure*}

The vast majority of detected exoplanets are relatively close to their
host stars, and are often considered to be susceptible to tidal
locking \cite{barnes2017b}, a process that can have significant
consequences for climate evolution
\cite{barnes2013a,yang2014b,leconte2015a,kane2020e}. Furthermore, the
rotational state of a planet can be a strong driver of its magnetic
field strength \cite{christensen2006,driscoll2015} which, in turn, may
play an important role in atmospheric erosion
\cite{zhang2009,gunell2018a}. Shown in Figure~\ref{fig:tidallock} is a
representation of HZ boundaries (solid and dotted lines) and tidal
locking distance (gray dashed line) as a function of stellar effective
temperature and stellar flux received by the planet
\cite{yang2014b}. The figure also includes numerous known exoplanets,
where those below the gray dashed line are considered to be tidally
locked to the host star. Note that those planets near or below the
tidal locking boundary are dominated by systems with Gliese host stars
which, since the catalog only extends to 25~pcs, tend to be low-mass
stars \cite{stauffer2010b}. The dotted lines are modified HZ
boundaries depending on the rotational state of the planet. It is
worth noting that there are many other aspects of the planet and star,
such as planetary obliquity and stellar type, that play major roles in
governing the atmospheric evolution of terrestrial planets.

The present state of a planet's angular momentum depends on the age of
the system and the tidal forces that are acting upon the planet. The
time scale for a planet to become tidally locked to the host star may
be expressed as
\begin{equation}
  \tau_\mathrm{lock} = \frac{\omega a^6 I Q}{3 G M_\star^2 k_2 R_p^5}
  \label{eq:lock}
\end{equation}
where $\omega$ is the rotation rate, $a$ is the semi-major axis, $I$
is the moment of inertia, $Q$ is the dissipation function, $G$ is the
gravitational constant, $M_\star$ is the mass of the star, $k_2$ is
the Love number, and $R_p$ is the radius of the planet
\cite{gladman1996b}. Note that, with the exception of the stellar
mass, all variables in Equation~\ref{eq:lock} pertain to the planetary
properties. The known properties of Venus may be used to thus estimate
the time until Venus may be tidally locked. Based on the analysis of
{\it Magellan} and {\it Pioneer Venus} data, we adopt values of $Q =
12$ and $k_2 = 0.299$ \cite{konopliv1996,dumoulin2017}. The subsequent
calculations yield a time scale for Venus tidal locking of $\sim 6.5
\times 10^6$~years. Such a relatively short time period must account
for the highly uncertain values of $Q$ and $k_2$. Additionally, the
precise nature of the change in the Venusian angular momentum remains
unclear \cite{bills2005e,campbell2019}, and the above calculation
neglects the non-negligible interaction of the atmosphere with the
surface \cite{leconte2015a,auclairdesrotour2017b}. Therefore, the
climate dynamics of a planet such as Venus are critical to
understanding the rotational evolution for those planets susceptible
to tidal locking.


\section{Climates of Tidally Locked Worlds}
\label{climates}

\begin{figure*}[t]
  \begin{center}
      \includegraphics[width=0.9\linewidth]{fig_rocke3d.png}
  \end{center}
  \caption{A Robinson projection of the results from a ROCKE-3D
    simulation for the exoVenus candidate, Kepler-1649b
    \cite{kane2018d}, showing the surface temperature and a Venus
    topography overlay. The surface temperature reached a maximum of
    270$^\circ$C and a global mean of 112$^\circ$C at the limit of the
    ROCKE-3D radiation tables.}
  \label{fig:rocke3d}
\end{figure*}

As described in Section~\ref{population}, a significant fraction of
the known terrestrial exoplanet population are expected to be near or
in a tidally locked state. Consequently, significant effort has been
expended toward adapting climate models to slow rotational states,
including synchronized rotation. Functionally, this is generally
achieved by setting the rotation period to a value similar to the
orbital period, and adjusting the spectral energy distribution
received at the top of the atmosphere. The application of these
simulations has been successfully demonstrated on numerous occasions,
some with far-reaching consequences. For example, climate simulations
of tidally locked planets have revealed conditions that lead to
climate instability, whereby positive or negative feedbacks result in
a runaway climate shift \cite{kite2011c}, and potential atmospheric
collapse, whereby cooling and condensation of the atmosphere result in
dramatic changes in atmospheric conditions
\cite{wordsworth2015a,auclairdesrotour2020}. Others have studied the
relationship between atmospheric circulation, convection, and thermal
structure that tidal locking produces
\cite{koll2016,sergeev2020,hammond2021}. The HZ boundaries,
particularly the inner edge, have been found to have a strong
rotational dependence, emphasizing the importance of tidal locking for
target selection of potentially habitable worlds
\cite{yang2013,leconte2015a}. Additional simulations have shown the
effects of water trapping and specific cloud features on the dayside
of tidally locked planets
\cite{yang2014c,yang2019b,ding2020a}. Climate simulations have also
demonstrated the dependence of the climate dynamics of tidally locked
planets on surface topography \cite{carone2016,lewis2018}, discussed
further in Section~\ref{venus}.

To date, climate simulations have been applied to numerous known
exoplanets suspected of being in a tidally locked state, including the
nearest exoplanet: Proxima Centauri b
\cite{turbet2016,delgenio2019a}. An example of such simulations is the
case of Kepler-1649b, a short-period planet orbiting an M dwarf star
that is a strong candidate as an exoVenus analog
\cite{angelo2017a}. Various simulations of the climate evolution using
the general circulation model ROCKE-3D \cite{way2017b} found that, in
all cases, the surface temperature quickly rises to the limit of the
radiation tables utilized, indicating a progression into a moist or
runaway greenhouse state \cite{kane2018d}. Shown in
Figure~\ref{fig:rocke3d} is an example output from these simulations
in the form of a Robinson projection of the final surface temperature
map with a Venus topography overlay. The initial conditions in this
case included an incident flux of double the solar constant, CO$_2$
and CH$_4$ atmospheric compositions of 400 and 1 ppmv, respectively,
and a paleo-Venus topography with all-ocean grid cells set to 1360~m
in depth. Before reaching the limit of the radiation tables, the
surface temperature reached a maximum value of 270$^\circ$C, with a
global mean of 112$^\circ$C. Similar simulations have been used to
suggest that Venus may have experienced a significant period of
temperate surface conditions \cite{way2016}, with substantial cloud
feedback near the substellar point producing a cooling effect
\cite{way2020}. Such scenarios assume that water inventory in the
atmosphere was able to condense at the surface to form oceans, which
may have been prevented via early magma oceans and/or insolation flux
\cite{hamano2013,turbet2021}. Regardless, the atmospheric dynamics of
a nearby, slowly rotating, Earth-size planet, and how it has evolved
through time, is a critically important laboratory to test many of
these principles.


\section{Venus Atmospheric Dynamics}
\label{venus}

Despite a slow rotation, Venus maintains an extremely dynamic
climate. The Venusian surface conditions are exceptionally different
from those found on Earth, with a mean surface temperature and
pressure of $\sim$735~K and 93~bar, respectively. Although these
surface conditions are globally consistent, the day-side and
night-side temperature diverge considerably above an altitude of
$\sim$100~km \cite{schubert1980c}. Since only $\sim$3\% of the
sunlight incident at the top of the atmosphere reaches the surface,
almost all of the solar energy absorbed by the planet is deposited
into the atmosphere \cite{crisp1986a}. Despite the slow rotation and
nearly zero eccentricity and obliquity, the atmosphere of Venus
consistently produces convective cells that results in a non-uniform
atmospheric circulation \cite{schubert1980c}. Furthermore, the
turbulence produced in the atmosphere may be the driver for the
super-rotation of the middle and upper atmosphere
\cite{horinouchi2020}, which rotates 60 times faster than the solid
planet, and may play an important role in the dynamics of many
exoplanetary atmospheres \cite{imamura2020}. The super-rotation for
terrestrial planets differs from those that occur for giant planets,
such as Jupiter and Saturn, due to the interaction of terrestrial
atmospheres with the solid planet and the internal heat flux and
interior convection of giant planets that provides an additional
driver of super-rotation in the cloud top layers \cite{kaspi2020}. The
atmospheric super-rotation observed for Venus (and also Titan) and the
mechanisms that drive them thus remain a significant challenge for
numerical models \cite{read2018b}.

\begin{figure}
  \begin{center}
      \includegraphics[width=0.9\linewidth]{fig_akatsuki.jpg}
  \end{center}
  \caption{{\it Akatsuki} data showing the brightness temperature
    (a--e) and UV brightness (f) of the Venusian disk. The bow-shaped
    structure is an atmospheric gravity wave passing over the surface
    topography \cite{fukuhara2017a}.}
  \label{fig:akatsuki}
\end{figure}

Climate simulations of tidally locked planets have produced strong
evidence that climates can interact significantly with surface
topography \cite{carone2016,lewis2018}. Such evidence has been
observed directly in the Venusian atmosphere, such as the detection
and subsequent analysis of stationary gravity waves detected using
data from the {\it VEGA} Balloon \cite{young1987b,young1994c}, and the
{\it Venus Express} mission \cite{peralta2017c}. These observations
were verified by data from the {\it Akatsuki} mission, which indicate
the presence of stationary waves in the upper atmosphere of Venus
\cite{fukuhara2017a}, as shown in Figure~\ref{fig:akatsuki}. The
center of the wave features, visible in the brightness temperature
maps (a--e), are located approximately above the Aphrodite Terra
highland region, which suggest that the causation is the direct result
of deep atmosphere movement over, and interaction with, the elevated
terrain \cite{bertaux2016}. The structure of these waves is not
uniform, indicating a dependence on latitudinal and diurnal effects,
and thus their production resulting from a complex interaction between
atmospheric dynamics and solar heating \cite{kouyama2017}. The
explanation of the atmospheric features as stationary gravity waves
was further validated via numerical simualtions that also contribute
to the atmospheric torque that acts upon the solid planet
\cite{navarro2018}. This interplay between incident flux, rotation,
atmospheric dynamics, and topography leads to correlated behavior that
is both important to include in simulations and may also enable
inferences regarding surface conditions and topography.


\section{Observational Diagnostics}
\label{model}

\begin{figure}
  \begin{center}
      \includegraphics[width=0.9\linewidth]{fig_spectra.jpg}
  \end{center}
  \caption{Spectra of Earth, Venus, and Mars the visible to near
    infrared wavelength range, where the reflected flux of Mars has
    been multiplied by 10 for better visibility
    \cite{kaltenegger2017}.}
  \label{fig:spectra}
\end{figure}

Exoplanet searches to the present date have a limited list of
observable parameters, most of which pertain to the orbital properties
of the planet \cite{pepe2014b}. These observables include orbital
period and eccentricity, and planet mass and radius. The next
significant step forward is expected to lie in the systematic
detection and inventorying of atmospheric compositions via
transmission spectroscopy using the James Webb Space Telescope ({\it
  JWST}) \cite{greene2016,kempton2018}. Though the majority of planets
studied in this manner will likely be gaseous in nature, strategies
have formulated for addressing the challenge of terrestrial planet
atmospheres
\cite{morley2017b,batalha2018b,lincowski2019,lustigyaeger2019a}. Such
methodology will be adapted with improved precision to distinguish
between the spectral signatures of Earth and Venus in an exoplanet
analog context
\cite{ehrenreich2006a,ehrenreich2012a,barstow2016a}. For example,
Figure~\ref{fig:spectra} shows the spectra of Venus, Earth, and Mars
at visible to near infrared (NIR) wavelengths \cite{kaltenegger2017}.
The high optical depth of the Venusian atmosphere results a small
fraction of the upper atmosphere being sampled via transmission
spectroscopy, neglecting the entire troposphere which contains 99\% of
the atmosphere by mass. The CO$_2$ absorption bands expected for Venus
are relatively narrow compared with the broad O$_2$ and H$_2$O
absorption features for Earth's atmosphere, due to the truncation of
absorption features caused the Venusian cloud decks, and the higher
temperature of Earth's atmosphere at high altitudes. Much attention is
directed toward the CO$_2$ absorption bands centered at 2.7 and 4.3
$\mu$m due to their potential detectability with JWST. However, given
the subtle difference in absorption features at those wavelengths for
Venus and Earth analogs, distinguishing between such planets using
transmission spectroscopy may require a broader wavelnegth criteria,
or the identification of Earth-based absorption features such as O$_3$
\cite{barstow2016a,fujii2018}. Since it is expected that many of the
transmission spectroscopy targets from transit surveys will be Venus
analog candidates \cite{kane2014e,lustigyaeger2019b,ostberg2019}, the
disconnect between the available observables, fraction of atmosphere
probed by transmission spectroscopy, and the degeneracy of models that
infer surface conditions, may present a significant barrier to a
complete characterization of terrestrial exoplanets in the near
future.

In the era of exoplanet direct imaging, the reflectance and emission
spectra of terrestrial planets provides an additional means to
characterize their atmospheres
\cite{seager2010,hu2012a,cowan2013a,madhusudhan2019}. Analysis of
disk-integrated reflectance spectra for directly imaged exoplanets
enable access to short wavelength absorption and Rayleigh-scattering
features, similar to those shown in Figure~\ref{fig:spectra}, that can
significantly aid in breaking degeneracy in atmospheric retrieval
models. Thermal emission spectra are measured at longer wavelengths
and reveal the temperature properties of the cloud layers, and
possibly the surface via infrared observing windows. In the context of
Venus, such observational diagnostics are incredibly powerful methods
to probe the deeper atmosphere through observing windows that
penetrate the cloud and haze layers that are largely opaque at optical
wavelengths. NIR observations of the nightside of Venus have
successfully probed beneath the sulfuric acid haze layer to measure
compositions and mixing ratios present in the middle and deep
atmosphere
\cite{bezard1990b,pollack1993b,meadows1996,arney2014}. Remarkably,
these NIR observations also reveal surface emissivity and
topographical features. As described in Section~\ref{venus}, the
temperature, pressure, and compositional profile of the Venusian
atmosphere is critical for a full model evaluation of the complex
climate dynamics and how these relate to the spin state of the
planet. Thus, the combination of transmission, reflectance, and
emission spectra will provide key diagnostics for establishing the
climate state of exoplanets, whose evolution may similarly be related
to the planetary rotation \cite{guzewich2020a}.

\begin{figure*}
  \begin{center}
      \includegraphics[width=0.9\linewidth]{fig_venusimage_combined.png}
  \end{center}
  \caption{An image of Venus acquired by the {\it Akatsuki} mission,
    shown in its original high-resolution format (left), and a
    convolved 5$\times$5 pixel format (right) to simulate a direct
    imaging exoplanet observation.}
  \label{fig:imaging}
\end{figure*}

Alternatively, a collaborative approach to exoplanet characterization
between direct and indirect detection techniques may aid in resolving
potential atmospheric model degeneracies. In addition to planetary
mass, radius, and spectroscopy of the upper atmosphere, additional
parameters of rotation, obliquity, atmospheric dynamics, and surface
topography are needed to fully constrain surface conditions. In
particular, Venus atmospheric dynamics serve as a warning with regards
to confusing solid planet with atmospheric rotation, and the
interaction between atmosphere and topography. Shown in the left panel
of Figure~\ref{fig:imaging} is a high-resolution image of Venus
acquired by the {\it Akatsuki} mission. By contrast, the right panel
shows the same data that have been convolved to a 5$\times$5 pixel
image, where a noise model has been included to incorporate systematic
instrumentation effects. Even this image resolution is optimistic for
exoplanet imaging in the short term, and yet the task of extracting
reliable planetary parameters is challenging
\cite{stark2020}. However, the trajectory of future exoplanet mission
planning lies in solving such challenges and directly detecting
terrestrial exoplanets \cite{kopparapu2018}, the vast majority of
which are invisible to the the transit method of detection and
characterization. The Nancy Grace Roman Space Telescope equipped with
a coronagraph will serve as a path-finder and technology demonstration
for achieving exoplanet direct imaging goals
\cite{kasdin2020}. Mission concepts, such as {\it LUVOIR}
\cite{reportluvoir} and the Habitable Exoplanet Observatory (HabEx)
Mission Concept Study \cite{reporthabex}, will be crucial next steps
toward a full terrestrial characterization. The expected limited
signal-to-noise of these data must be convolved with the important
lessons learned from the Venusian atmosphere in order to properly
interpret the dynamics of the plethora of tidally locked planets that
await observation.


\section{Conclusions}
\label{conclusions}

With the dramatic rise in exoplanet discoveries, particularly within
the terrestrial regime, the need to fully characterize the limited
inventory of terrestrial atmospheres within the Solar System is more
important than ever \cite{horner2020b,kane2021d}. Exoplanetary science
is now investing in the task of detecting and interpreting exoplanet
atmospheres, which is a substantial observational and modeling
undertaking. In the near term, many of the exoplanets studied in this
fashion will have been detected via the transit technique. The
consequence of this detection source is a strong bias toward
short-period planets, that will generally have a high chance of both
being tidally locked and pushed into a post runaway greenhouse state,
provided the atmosphere has not been significantly desiccated. As
such, many of the climate simulations conducted for terrestrial
planets have explored the effects of high incident flux and tidal
locking on the possible climate dynamics.

Whilst the exoplanet focus is on Earth-size planets around other
stars, within the Solar System we have an ideal example of an
Earth-sized near tidally locked planet. Venus offers the promise of
in-situ data that we will never have for an exoplanet, and the
possibility of a fully-resolved study of climate dynamics for an
atmosphere that is significantly different from that of the
Earth. Even so, the complexity of the Venusian atmosphere retains many
unanswered questions, such as the composition and chemistry of the
middle and deep atmosphere, and the interaction with the surface. The
opportunity to answer these questions and apply a detailed model of
the Venus climate to other worlds is not only appealing, it is a
necessary step in the quest to characterize the analogs of Earth's
twin around other stars.


\section*{Acknowledgements}

This research has made use of the NASA Exoplanet Archive, which is
operated by the California Institute of Technology under contract with
the National Aeronautics and Space Administration under the Exoplanet
Exploration Program. The results reported herein benefited from
collaborations and/or information exchange within NASA's Nexus for
Exoplanet System Science (NExSS) research coordination network, which
is sponsored by NASA's Science Mission Directorate.


\section*{Data Availability}

Figure~\ref{fig:radii} used data from the NASA Exoplanet Archive,
available here:\\
https://exoplanetarchive.ipac.caltech.edu/ \\
Figure~\ref{fig:rocke3d}
used output data from ROCKE-3D simulations in netCDF format
\cite{kane2018d}. Figure~\ref{fig:imaging} used data from the Akatsuki
Science Data Archive, available here:\\
https://darts.isas.jaxa.jp/planet/project/akatsuki/ \\
The data from figures \ref{fig:radii}, \ref{fig:rocke3d}, and
\ref{fig:imaging} are available
here:\\
http://stephenkane.net/tidalvenus/



