allows us to leverage their wavelength-dependent impact on planetary transits
to derive active-region parameters (Sing et al., 2011; Bruno et al.,
2022)—valuable information for correcting transmission spectra for the effects
of stellar activity (see Section 4). Finally, even in cases without obvious
active-region occultations, occultation models can be used to place upper
limits on the impact of low signal-to-noise occulted active regions, which
introduce an uncertainty in the level of stellar-activity contamination
similar to that of unocculted active regions but with an opposite sign
(Ballerini et al., 2012).

####  2.2.3 Our finding

From this analysis, we draw the following finding.

Finding 2.1

Summary: Precise transit observations increasingly reveal occultations of
stellar active regions. Rather than flagging and removing active region
occultations, which results in decreased observing efficiency and possibly
biased transit depth measurements, future observations should move towards
joint inference of the active region and planetary properties.

Capability Needed: Detections of occulted active regions are more common in
precise datasets. From a practical perspective, discarding data impacted by
active region occultations in many interesting systems will result in
continuously lower observing efficiencies as precisions improve. Additionally,
more study is needed to understand the extent to which transit depths may be
biased by active regions that are occulted but undetected.

Capability Today: Many recent studies have included joint inferences of
transit and active region properties using a variety of spot modeling codes.
However, the active regions we can detect in precise transit light curves,
both ground- and space-based, are much larger than those that have been
observed on the Sun. At the same time, data impacted by active region
occultations are commonly discarded in other studies.

Mitigation in Progress: Joint analyses of active region and planetary
properties from impacted light curves have been presented recently.
Additionally, some groups are beginning to look into the impact of heavily
spotted transit chords on inferences.

###  2.3 Theoretical challenges for active region occultations

####  2.3.1 Solar spots and comparison to models of stellar spots

In the context of studying transiting planets occulting starspots, the most
relevant property is the relative brightness of the starspot with respect to
its surroundings. For spots on the Sun, there is a clear connection between
the size of the spot and its umbral intensity: larger spots tend to have
darker umbrae than smaller spots (Mathew et al., 2007; Schad, 2014; Valio et
al., 2020). In the study by Mathew et al. (2007), spots that have an umbral
radius between 5 ′′ (1 $\mbox{${}^{\prime\prime}$}\approx 720$ km) and 15 ′′,
the mean umbral relative intensity drops from 0.5 to 0.3 relative to the
quiet-Sun intensity at the continuum near the Ni i line at 676.8 nm. They also
found a very weak dependence of penumbral intensity on spot size, between 0.84
and 0.81 at the same wavelength.

Another property determining the effective brightness of a spot on a star is
the ratio of penumbral to umbral area. For the Sun, this factor is roughly 4
and generally independent of spot area above a minimal spot area (although
there is some scatter in the literature; e.g., Solanki, 2003).

For starspots, there is a strong connection between the surface temperature of
the star and the spot contrast (Berdyugina, 2005). The spot temperature
contrast is larger for hotter stars, and this seems to be valid for stars of
different surface gravities. Updated summaries of starspot contrasts as a
function of stellar surface temperature can be found in Mancini et al. (2014a)
and Herbst et al. (2021). Interestingly, starspot temperatures inferred from
planetary transits seem to be warmer than temperatures retrieved by other
methods. This may be because the transit method returns the average
temperature of the entire spot while methods like modeling of molecular bands
are mainly sensitive to the umbral temperatures (due to the non-linear
response of molecular lines to temperature).

A particularly useful example for drawing comparisons to solar activity is
that of the active G-dwarf Kepler-71. Both spots and plages have been detected
in its photosphere via occultations by its transiting hot Jupiter (Zaleski et
al., 2019). Despite the higher contrast of Kepler-71 faculae than the solar
counterparts, these plages showed similar properties, such as increasing
contrast towards the limb and larger sizes than sunspots. Assuming a solar-
type differential-rotation profile, the results obtained from independent
modeling of starspots and faculae indicated similar rotational periods at the
transit latitude and the same rotational shear.

####  2.3.2 The importance of MHD simulations for modeling occulted active
regions

Johnson et al. (2021) have used quiet-Sun limb darkening and limb-dependent
facular contrasts derived from MURaM 3D MHD simulations by Beeck et al.
(2015a), together with spot contrasts computed from 1D model atmospheres with
effective temperatures in agreement with 3D MHD results by Panja et al.
(2020), to model rotational light curves of active G2, K0, M0, and M2 stars in
the Kepler band. They found that the spot temperature together with spot
coverage determines the amplitude of the variability, while faculae have a
strong influence on mean brightness levels and the shape of light curves. The
latter might have significant implications for occultation modeling.

Using 3D radiative magnetohydrodynamic simulations, Panja et al. (2020) have
recently confirmed the dependence of spot contrast on stellar surface
temperature for dwarfs within the spectral range G2V–M0V. These authors
simulated the spectral types G2V, K0V and M0V and obtained umbral bolometric
intensities of 0.3, 0.5, and 0.7 relative to the stellar photospheric
intensities. Ongoing work includes simulations of spots with expansive
penumbral filaments, similar to those observed in sunspots for the simulated
G2V starspot, and simulations that allow the calculation of spot contrasts as
a function of wavelength and disk position (Panja et al., in prep).

####  2.3.3 Common degeneracies in the retrieved spot and faculae properties

The main difficulty in accounting for surface inhomogeneities is that these
are essentially never single, isolated features. Thus, dark and bright
features are likely present simultaneously, both occulted and unocculted.
Simultaneous ground-based spectroscopic and space-based photometric
observations of G and K stars show that starspots and plage are often,
although not always, spatially associated, as is true on the Sun (Morris et
al., 2018c). Moreover, it is not always clear whether a bright or dark feature
is being occulted, as models with either type of feature at different times
may offer comparable fits to transit light curves (Kirk et al., 2016; Bruno et
al., 2016). The resulting effect from all features depends on their coverage
(size), location, and the wavelength of observations, and is generally
impossible to separate.

When observing stellar rotation in a single photometric bandpass, both faculae
and starspots can produce rotational modulation signatures. Observing in more
than one bandpass nearly simultaneously can break this degeneracy and suggest
whether spots or faculae dominate. This technique has been applied to
photometry of the planet-hosting M8 dwarf TRAPPIST-1, which shows (1) no clear
spot occultations in transit photometry, (2) strong rotational modulation in
the Kepler bandpass, and (3) very little modulation in Spitzer photometry
(Morris et al., 2018a, e).

####  2.3.4 Our finding

From this analysis, we draw the following finding.

Finding 2.2

Summary: Theoretical advances are needed to understand the limits of what we
can infer about active-region properties from transit light curves and how
best to incorporate prior knowledge from magnetohydrodynamic models into
transit studies.

Capability Needed: More study is needed to understand the limits of inferences
from occultations and how to break degeneracies in retrieved parameters of
occulted active regions, such as size and contrast, with additional
observations, such as spectroscopic transit depths or multiwavelength
monitoring. Additionally, more study is needed to understand best approaches
for propagating information from stellar magnetic activity models into priors
on spot properties, such as typical size and contrast, as a function of
stellar spectral type and activity level.

Capability Today: Uninformative priors on active-region properties are
generally used. Retrieved sizes are generally large and contrasts are
generally small relative to those inferred from other methods, which may point
to biases with the technique or the combined impact of umbral, penumbral, and
facular areas.

Mitigation in Progress: Multiple groups are developing magnetohydrodynamic
models for active regions on stars with differing spectral types and activity
levels.

###  2.4 The availability of well-maintained, open-source tools

Over the years, there have been multiple starspot occultation models developed
both by the eclipsing binary star community (e.g., Wilson-Devinney code:
Wilson & Devinney 1971; Wilson 1979, 1990, 2012; PHEOBE: Prša & Zwitter 2005;
Prša et al. 2016) and the exoplanet community (e.g., ECLIPSE: Silva 2003;
SOAP-T: Oshagh et al. 2013a; PRISM: Tregloan-Reed et al. 2013, 2015, 2018;
SPOTROD: Béky et al. 2014; KSint: Montalto et al. 2014; ellc: Maxted 2016;
StarSim: Herrero et al. 2016; PyTranSpot: Juvan et al. 2018); STSP Morris et
al. 2017; TOSC: Scandariato et al. 2017). Such models require integration over
a 2D grid on the stellar surface or in the projection plane, which is
computationally expensive, with computational time growing as the square of
the grid resolution. The only exceptions to our knowledge are the semi-
analytical SPOTROD and STSP models. At the same time, full 2D integration
(pixelation) has the advantage that it allows individual intensities
(accounting for surface inhomogeneities) to be assigned to every individual
element at specific coordinates.

We summarize some of the most prominent models below.

##### ECLIPSE.

ECLIPSE (Silva, 2003), a code first written in IDL and then translated to
Python, models active-region occultations using a 2D image of a synthetic star
with spots (dark features) or plages (bright features) on the surface of the
limb-darkened stellar disk. The planet, modeled as a circular dark disk, is
positioned in its elliptical orbit every two minutes (or the desired time
interval) and the intensity of all pixels in the image is summed to yield the
light curve intensity at a given time. The spots (or plages) are simulated as
dark (or bright) circles positioned along the transit chord. Spot intensities
vary from 0–1, whereas the plage intensities vary from 1–1.5, where 1 is the
brightness of the activity-free stellar disk center. The temperature of the
spots can be estimated assuming blackbody emission for both the spots/plages
and the stellar photosphere (Valio et al., 2017). Foreshortening of the spots
is taken into account when they are close to the stellar limb. This model was
first applied to HD 209458 (Silva, 2003) and has since been applied to many
targets with high-cadence Kepler data (e.g., Silva-Valio et al., 2010; Valio
et al., 2017; Netto & Valio, 2020; Zaleski et al., 2020; Araújo & Valio,
2021). An example of such modeling is shown in Figure 13 for Kepler-17 with
three spots. ECLIPSE can be found at
GitHub222https://github.com/biaduque/astronomy and was last updated in 2021.

Figure 13:  Top: Simulated star with three spots. Middle: The 100th transit
light curve with a spotless model (blue) and the three spot model (red).
Bottom: Residuals after subtraction of the spotless model from the transit
light curve with the modeled three spots (red curve). Adapted from Valio et
al. (2017).

##### SOAP-T.

Spot Oscillation and Planet Transit (SOAP-T) (Oshagh et al., 2013a) is a SOAP
(Boisse et al., 2012) adaptation that can generate light curves and radial
velocity variations for systems containing a rotating spotted star and a
transiting planet. The stellar disk, active regions on it, and a transiting
exoplanet are simulated numerically using a pixelation approach. This tool has
been used to investigate spot-crossing anomalies within transit light curves
(Oshagh et al., 2013b), as well as to assess their impacts on the estimation
of the transit duration, depth, and timing. SOAP-T was used to study, for the
first time, the impact of the occultation of a stellar spot and plage on the
transmission spectra of transiting exoplanets (Oshagh et al., 2014). SOAP-T
was also used to study the impact of stellar active region occultation on the
Rossiter-McLaughlin effect signal (Oshagh et al., 2016; Boldt et al., 2020),
as well as on the estimation of orbital configuration and properties of
planetary systems (Oshagh et al., 2018) and active regions on their host stars
(Oshagh et al., 2015; Serrano et al., 2020). SOAP-T is available via an online
interface333http://www.astro.up.pt/resources/soap-t/.

##### PRISM.

The Planetary Retrospective Integrated Starspot Model (PRISM) is written in
idl and uses a pixelation approach to model the stellar disc in a 2D array by
subdividing the star into many individual elements. These elements can then be
described by a 2D vector in Cartesian coordinates. Each element is then
assigned an intensity value based on whether a stellar feature is present at
that location and then the quadratic limb darkening law is applied over the
entire stellar disc. The planet is then set to transit the star. For each data
point in the transit light curve, the total received intensity is calculated
based on which elements of the star are visible. The PRISM model has been used
primarily to model starspots found in ground-based transit exoplanetary light
curves (e.g. Tregloan-Reed et al., 2013, 2015; Chen et al., 2017; Mancini et
al., 2017). More recently, PRISM has also been used to simulate spotted
transits observed with 2-min-cadence TESS data (e.g. Tregloan-Reed & Unda-
Sanzana, 2019, 2021). An example of the use of PRISM is provided by Figure 14.
PRISM is available on GitHub444https://github.com/JTregloanReed/PRISM_GEMC and
was last updated in 2019.

Figure 14:  Top: Two consecutive transits of G8 V WASP-19 by the 0.8-d, hot-
Jupiter WASP-19b from ESO NTT, along with the best-fitting PRISM model. The
spot anomalies are clearly visible as upward blips around the midpoints of the
two transits. Bottom: Representation of the stellar disc, starspot and transit
chord for the two datasets, showing the movement of the starspot between the
consecutive nights. The stellar rotation axis lies in the plane of the page
and points upwards. From Tregloan-Reed et al. (2013).

##### SPOTROD.

SPOTROD (Béky et al., 2014) is a semi-analytic tool for modeling planetary
transits of stars having an arbitrary limb-darkening law (being identical for
spots and the stellar photosphere) along with a number of homogeneous,
circular spots on the stellar surface. It can account for both eclipsed and
uneclipsed starspots. The program is written in C and available in Python. The
homogeneous spots are represented by their flux ratio, $f$, which is the ratio
of the flux from a spot (as viewed by the observer) to the flux from an
unocculted stellar surface at the same disc location. Umbra-penumbra
structures of spots can be accounted for by superimposing two concentric spots
of differing intensities, and bright features can be introduced by using
$f>1$. SPOTROD works in polar coordinates, with the advantage being that the
integral over the polar angle can be computed analytically and only the
integral over the radial coordinate requires numerical integration. The
significant reduction of the required computation time is the main advantage
of this model compared to other, typically 2D, models. Thus, SPOTROD can be
used for fitting large numbers of transits with occulted active regions and
also for efficient statistical investigations using MCMC approaches. SPOTROD
is available on GitHub555https://github.com/bencebeky/spotrod and was last
updated in 2015. It has been wrapped into a nested-sampling retrieval
framework, SpotNest (Espinoza et al., 2019), which is also available on
GitHub666https://github.com/nespinoza/spotnest and was last updated in 2018.

##### StarSim2.

StarSim2 (Rosich et al., 2020), an update of the StarSim tool (Herrero et al.,
2016), uses a fine grid of surface elements to model integrated spectral
contributions of a spotted rotating photosphere. It is written in Python and
Fortran 90. The flux intensities and wavelengths of spectral features produced
by active regions are included in the model. The original StarSim tool has
been used to derive stellar surface parameters from light curve inversion as
well as to mitigate their impacts on the transiting planet’s transmission
spectrum (Mallonn et al., 2018). StarSim2 is available on
GitHub777https://github.com/rosich/Starsim-2 and was last updated in 2020.

##### STSP.

STSP is a fast forward model for starspot occultations by transiting
exoplanets and unocculted spot modulation, written in C by L. Hebb and G. Rohn
(Davenport, 2015; Morris et al., 2017; Schutte et al., 2021). It computes the
overlap between the planet, circular starspots with geometric foreshortening,
and concentric nested disks of varying intensity to approximate stellar limb
darkening. The code is highly efficient and coupled to a Markov Chain Monte
Carlo sampler also written in C, making it ideal for studies on high
performance computing facilities. STSP is available on
GitHub888https://github.com/lesliehebb/stsp and was last updated in 2021.

##### ellc.

ellc (Maxted, 2016) is a semi-analytical and semi-numerical model to analyse
the light curves of detached eclipsing binary stars and transiting exoplanet
systems. It can include the effects of both occulted and unocculted starspots
simultaneously. It is implemented as Fortran subroutines called directly from
a user interface written in Python, and is fast enough to enable the use of
modern Monte Carlo methods for data analysis and model testing. The source
code is available at the CDS via anonymous
ftp999http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/591/A111.

####  2.4.1 Our finding

From this analysis, we draw the following finding.

Finding 2.3

Summary: There are several publicly available tools for forward-modeling
active-region occultations. Their maintenance and further development is
necessary to ensure their utility for analyses of precise transit
observations.

Capability Needed: Publicly accessible, well-maintained, and up-to-date tools
for modeling active-region occultations are necessary for analyses of precise
transit observations from current and future facilities.

Capability Today: There are several publicly available forward-modeling tools
for active-region occultations in broad photometric bandpasses today. However,
many are not actively developed or maintained.

Mitigation in Progress: Multiple groups have developed publicly available
codes to aid analyses of active-region crossings.

##  3 Unocculted Active Regions

Chapter Leads: Benjamin T. Montet, Yvonne C. Unruh

Major Contributors: Keivan G. Stassun, Natalie Krivova, Sven Wedemeyer

Other Contributors: Munazza K. Alam, Svetlana V. Berdyugina, Ludmila Carone,
Heather M. Cegla, James R. A. Davenport, Drake Deming, Néstor Espinoza, Heidi
Korhonen, Mayukh Panja, Benjamin V. Rackham

Essential Questions:

  1. 1.

Can we learn about unocculted active regions (UARs) through the study of
transit depth variations in large photometric planet search surveys?

  2. 2.

How well can other signatures of stellar activity in these datasets such as
flares provide information about UARs?

  3. 3.

What are the limitations of what we can learn about UARs from transit
photometry?

  4. 4.

Can additional photometric or spectroscopic data taken simultaneously with
transit data help to better understand the information encoded in light
curves?

  5. 5.

What data can best inform our knowledge of active region filling factors?

  6. 6.

How can we best distinguish between starspots and faculae?

  7. 7.

Can we quantify the noise floor due to granulation as a function of stellar
parameters?

###  3.1 Introduction

####  3.1.1 Motivation

Unocculted active regions on the heterogeneous surface of a star can impact
measured transmission spectra of planets (e.g., Pont et al., 2008; Czesla et
al., 2009; Rackham et al., 2017, 2018, 2019; Zellem et al., 2017). In transit
photometry, the particular configuration of active regions produces a
degenerate signal with an infinite number of different configurations, making
unique identification of unocculted regions challenging. Moreover, while the
most obvious signature of rotational modulation in broadband stellar time-
series photometry is often the signal from starspots, facular regions are
expected to induce a more significant impact on transmission spectra due to
their complicated spectral signatures (e.g., Cauley et al., 2018). In this
chapter, we examine our understanding of unocculted regions and our ability to
infer their presence before and during transmission spectroscopy of active
stars.

####  3.1.2 Scope

We focus on three areas of interest in this chapter, primarily centered around
the measurement and understanding of unocculted active regions rather than
their impacts on atmospheric retrievals, which is instead discussed in the
following chapter. First, in Section 3.2 we investigate what information can
be obtained about unocculted active regions from high-cadence transit
photometry. In Section 3.3 we explore the usefulness of other datasets,
current or planned, in understanding these regions. Finally, in Section 3.4 we
discuss the effects of stellar granulation on transmission spectra.

###  3.2 Information from high-cadence transit photometry

High-cadence and high-precision transit photometry, such as that enabled by
the Kepler and TESS missions (Borucki et al., 2010; Ricker et al., 2015), also
encodes information about the underlying stellar surfaces. Here we investigate
opportunities from these datasets to directly infer properties of unocculted
active regions.

####  3.2.1 Transit depth variations

Transit shapes can be affected by dynamical interactions between multiple
planets or between a planet and its host star, which affects the relative
geometry of the system along our line of sight. Transit shapes can also be
affected by variability on the stellar surface with no change in the geometry
(Agol et al., 2005; Ragozzine & Wolf, 2009; Barros et al., 2013). In this
section, we explore how to disambiguate between the two.

Changes in the observed parameters of transiting planets have provided
significant opportunities to understand planet-planet and star-planet
dynamical interactions. The most dramatic result of a perturbation to a
planet’s orbital parameters is in the measured transit timing, which has been
used to determine orbital configurations and planet masses, as well as to
identify tidal inspiral of hot Jupiter systems (Maciejewski et al., 2016;
Patra et al., 2020). In other systems, transit duration variations have
provided information about orbital precession.

Transit depth variations, in which the magnitude of the depth of the transit
changes over time, are at their most fundamental a change in the relative
brightness of the occulted stellar chord compared to the unocculted starlight
in the atmosphere. This change can be the result of a few different physical
variations. The transit chord geometry itself could be changing as a result of
dynamical interactions (Carter & Winn, 2010; Hamann et al., 2019). The
unocculted stellar surface could also change in brightness due to a change in
the rotational phase of active regions or their emergence or decay. The
occulted stellar surface could change in brightness for the same reason,
producing an equivalent effect in the opposite direction.

The last of these possibilities is discussed more fully in Section 2. Here we
note active regions on the occulted surface produce additional structure in
observed transit photometry (Sanchis-Ojeda & Winn, 2011), while unocculted
active regions do not: sufficiently high-precision photometry can disambiguate
between these cases.

Separating depth variations from dynamical interactions compared to those from
unocculted active regions is also possible. One straightforward consideration
is that a change in the transit chord should also produce a change in the
impact parameter, and thus the transit duration, while brightness variations
should not significantly affect the transit duration as observed in broadband
photometry. Transit duration variations from long-baseline photometry can be
detected at high confidence, with variations of $\approx$1 minute/year
expected to be common (Boley et al., 2020). In most cases, duration variations
should be more significant than depth variations (Holczer et al., 2016).
Careful observations over a long baseline, whether from the same telescope or
others, can provide the evidence needed to separate these cases.

If a system is observed to have transit depth variations and not timing or
duration variations, and there is no evidence for these variations to be
predominantly caused by the growth of active regions along the transit chord,
then it is plausible that this is the result of changes in the unocculted
stellar surface. However, for Kepler and TESS photometry, the primary
hindrance in inferring these changes is in identifying which stellar
surface—that of the target star or another nearby—is changing. The Kepler
telescope point spread function (PSF) is approximately 6 ′′ in size; for TESS,
it is typically 30–50 ′′.101010For both telescopes, the PSF is a strong
function of location on the focal plane and, more weakly, a function of
magnitude and color. A typical photometric aperture used in the Kepler mission
has a diameter of 10–20 pixels; for TESS the typical diameter is more than 1
′. As a result, each aperture is contaminated by the light of multiple nearby
stars, and it is not uncommon for the Exoplanet Follow-up Observing Program
(ExoFOP) database111111https://exofop.ipac.caltech.edu/tess/ to report 50 or
more stars within one arcminute of a TESS Object of Interest (TOI). In
addition, at least 25% of TOIs have unresolved stellar binary companions
(Ziegler et al., 2020), which can equally plausibly be the root of stellar
brightness variations even when all known nearby stars can be ruled out. It is
therefore challenging from transit photometry alone to determine whether a
depth variation is due to a change in brightness of the target star, or a
change in brightness of a background star, which would have an equivalent
effect on the light curve.

This issue can be mitigated at some level by obtaining high-resolution imaging
of these systems to limit the parameter space in which relatively bright
nearby stars can evade seeing-limited detection. Occasional monitoring of
potential candidate transits with ground- or space-based telescopes with
considerably higher pixel scales, in order to remove neighboring stars from
the observed aperture, would also provide a benefit over large photometric
surveys themselves. An even more promising route would be to use the existence
of transit depth variations in concert with other proxies of stellar activity
indicators. For example, spectroscopic surveys that measured chromospheric
activity indicators would be beneficial in enabling inference of whether
potential transit duration variations are due to the target star or chance
brightening of a secondary star in the aperture.

####  3.2.2 Active region distributions

In the context of transmission spectroscopy observations, not all active
regions may be equally important to consider. Cauley et al. (2018) demonstrate
that spectral line contrast absorption decreases dramatically as the
separation between a planet and an active latitude increases, with the most
significant events occurring when the two are within five degrees of each
other. Although not all planets have a low obliquity between their orbital
axis and the stellar spin axis (Winn et al., 2010), for the systems where the
obliquity can be measured, this consideration can impact our interpretation
significantly if we can determine the distribution of active regions on the
surface of the star.

Inferring the two-dimensional distribution of active regions on a stellar
surface from one-dimensional transit photometry is an ill-posed and degenerate
problem, with different stellar surface models able to produce identical light
curves (Vogt et al., 1987; Basri & Shah, 2020; Luger et al., 2021b). This is
the case even if one is trying to recover information on dark (or bright)
features alone. However, the problem is compounded as active regions typically
contain bright (facular or plage-like) features and dark spots. The
contributions from these can add or partially cancel, depending on the
location of the features, the wavelength at which the star is observed, and
the feature size (or magnetic field strength) and the stellar spectral type.
The contribution of faculae is particularly poorly characterised (see Section
1.3.3 and Section 4.3).

In general, longitudinal information is more easily recovered than information
about the latitudes of unocculted active regions (Luger et al., 2021b),
although this is complicated further by the potential of active regions that
manifest at all longitudes, such as a banded region or a polar spot. While
there is some asymmetry even in banded features, their photometric signal is
only representative of the asymmetry rather than the total filling factor,
requiring other techniques to infer their structure.

As discussed in Section 2, significantly more information can be learned about
the size and structure of active regions when they are occulted by a planet.
In the context of transmission spectroscopy, the most promising avenue to use
transit photometry to understand active regions outside of a narrow transit
chord is to consider multi-planet systems with strong dynamical interactions.
Over years to decades, multi-body perturbations can affect neighboring
planets’ inclinations by a few degrees; in some cases, planets can move from
transiting the stellar equator to not transiting.

Figure 15:  Long-term evolution of the (top) inclination and (bottom) observed
impact parameter of the two planets in the K2-146 system. Over timescales of a
decade, the impact parameters from both planets can vary by as much as 10%,
causing previously occulted active regions to become unocculted and vice
versa. From Hamann et al. (2019).

The K2-146 system, described by Hamann et al. (2019) and Lam et al. (2020),
provides an example of these perturbations in action (Figure 15). Over 10
years, the impact parameter for both planets can change by 10%, leading to a
$\sim$10-degree change in the projected latitude of the transit chord on the
surface of the star. Regular monitoring of occulted active regions over many
years can then give a broader understanding of unocculted surfaces at the time
of transmission spectroscopy observations, especially those surfaces within a
few degrees of the transiting planet that are most critical for interpreting
the transmission spectrum.

It is also helpful to know the inclination and rotation period of the star,
and to observe a large number of rotations (Basri & Shah, 2020). This could,
in particular, help to distinguish between the effects of the active regions
on the light curves due to the stellar rotation (change in the projected area
and contrasts) and the evolution of active regions (e.g., redistribution of
the magnetic flux between the dark and bright components leading to a change
in their relative contributions as well as flux decay). Furthermore, a
promising tool to distinguish between the signatures of planets, starspots and
faculae in the light curves is offered by multiband photometry, due to the
different center-to-limb contrasts of the different occulters (see Section
3.3.1 for further details).

####  3.2.3 Stellar flares

The presence of unocculted active regions can also be traced in principle by
measuring the occurrence rate and energy of stellar flares. Kepler and TESS
have been effective flare-finding missions (e.g., Davenport, 2016; Günther et
al., 2020). Flares appear in these light curves as stochastic spikes, which
can be separated from slower and usually weaker variations or sources of noise
(Feinstein et al., 2020). Since flares are distinct events, it can be easier
to unambiguously measure their specific occurrence rate for stars, compared
with the degeneracies in estimating the true filling factor of, e.g.,
starspots, as discussed above.

Detailed statistical analyses of flares on Sun-like stars (e.g. Maehara et
al., 2015; Notsu et al., 2019; Okamoto et al., 2021) are limited in their
ability to compare directly to the Sun itself: the smallest flares on Sun-like
stars observed by Kepler are still more energetic than the largest flares
observed on the Sun or even than the upper limit on the possible solar flare
energy (Schrijver et al., 2012; Aulanier et al., 2013). Yet these so-called
“superflares” seem to follow the same relationship between occurrence and
emitted energy as smaller flares, suggesting a common physical origin. There
is clear and convincing evidence that the energies of solar flares are
correlated with the magnetic energy in active regions on the Sun (Mayfield &
Lawrence, 1985). For example, flare rates on the Sun are ${\sim}10\times$
higher during activity cycle maximum, when the largest number of sunspots and
active regions are present (Aschwanden & Freeland, 2012). Three potential
extreme solar particle events, identified by Brehm et al. (2021) in the newest
radiocarbon data with annual resolution, all occurred close to solar activity
maxima (Usoskin et al., 2021). Notsu et al. (2013) similarly demonstrate that
the energies of superflares observed on solar-type stars trace the total
starspot coverage on these stars. Yet the occurrence of strongest flares or
flare candidates on the Sun does not seem to be closely correlated with the
strength of the cycle, and strong events can happen even during relatively
weak cycles (Bazilevskaya et al., 2014; Omodei et al., 2018; Usoskin et al.,
2021). From an analysis of main-sequence stars, Roettenbacher & Vida (2018)
found that only low-amplitude flares were correlated with observed starspot
phase.

For stars that are different from the Sun, there are more uncertainties about
the relationship between active region coverage and flare frequency, making
flares a more difficult proxy to interpret for transmission spectroscopy
analyses.

Tracing flare energies on stars provides us with key information about the
overall active region coverage on these stars. However, locating these active
regions on the stellar surface is not possible from observing the flares
alone, somewhat limiting our ability to infer the impact of these active
regions on exoplanet transmission spectra.

Doyle et al. (2018) find no correlation with rotational phase for any flares
on M dwarfs, an interpretation matched by Feinstein et al. (2020) in an
analysis of stars in young moving groups. These observations may suggest very
large ($\approx$80%) active-region filling factors are typical for M dwarfs
and young stars, consistent with values inferred via spectroscopic methods of
the young star LkCa4 (Gully-Santiago et al., 2017), or may suggest variations
in the underlying relations between active-region size and flares on non-Sun-
like stars. For M dwarfs, flares may primarily occur from smaller active
regions spread across the entire photosphere, while the starspot modulations
observed by Kepler and TESS may be tracing larger and more stable active
regions or “spot caps” (Hawley et al., 2014a). There is an opportunity for
continued theoretical modeling of active regions on these stars to be combined
with the additional photometry for young and low-mass stars that will be
collected over the coming years with TESS to more fully understand the
relations between flares and active regions on stars different from the Sun.

####  3.2.4 The potential for improved data analysis methods

While some features of active regions, such as the overall latitude
distribution, can demonstrably not be uniquely inferred from transit
photometry, here we consider what limitations may be due to current data
processing practices.

The Kepler and TESS data analysis pipelines are motivated by the search for
exoplanets. While they do try to preserve stellar signals when possible,
attempting to maintain those signals is sometimes at odds with the goal of
planet detection.

Planet transits are relatively small signals (hundreds of ppm) with sharp
features, few-hour timescales, and characteristic shapes, and are mostly
achromatic. Therefore, relative precision is only needed on timescales of
hours to a few days, while slow variability can be effectively removed by data
processing pipelines. Since the signals are nearly achromatic, single-bandpass
broadband photometry is acceptable for finding transits.

Significant effort has been made towards increasing the photometric precision
achievable by analyzing these data for transits, though there is clear
evidence that additional information can be recovered to better understand the
observed stars themselves. For example, Montet et al. (2017) used the Kepler
full-frame images, a set of calibration data obtained approximately monthly
over the Kepler mission, to calibrate photometry from that telescope and
measure absolute brightness variations over multi-year timescales. That data
product provides the opportunity to probe the relative contributions of
facular and spot regions on the surface of the star as they grow and decay due
to changing activity levels.

Similarly, Hedges et al. (2021) characterized the color dependence of the
Kepler point spread function, enabling identification of changing average
stellar temperatures (and thus colors) over the course of the mission. This
technique has the potential to further our knowledge of large active regions,
possibly breaking some degeneracies between starspot size and temperature by
providing effective multi-wavelength photometry over a four-year baseline. It
also could enable improved inference of temperatures of stellar flares
observed by Kepler.

Further development of new data analysis methods for Kepler and TESS data can
help understand unocculted active regions in spaces where information may be
quashed by the instrument pipeline or otherwise overwhelmed by systematic
effects. Possible opportunities where significant progress may be both
achievable and particularly beneficial include the improved recoverability of
low-amplitude or long-period rotational modulation, the characterization of
the smallest flares, and the development of machine learning methods to
separate astrophysical and instrumental signals.

####  3.2.5 Our finding

From this analysis, we draw the following finding.

Finding 3.1

Summary: High-cadence light curves provide the potential to understand
unocculted active regions, but the information is not comprehensive enough to
make unambiguous measurements at present. Theoretical advances are needed to
make full use of these light curves.

Capability Needed: Significant theoretical work is needed to understand the
relations between observational signatures of stellar activity in light
curves, and continued advances in data analysis methods developed to re-
analyze archival data sets can provide major improvements in our ability to
leverage information from these missions.

Capability Today: The large data sets needed to develop a data-driven
methodology, such as the NASA Kepler and TESS missions, are producing
opportunities for improved data analysis tools. These can be supported by
programs such as NASA ADAP.

Mitigation in Progress: The NASA-NSF EPRV initiative enabled opportunities for
the development of theoretical work to improve our understanding of the
effects of stellar activity on time-series spectroscopy, which is a parallel
need to the theoretical work outlined here.

###  3.3 Information from other datasets

In characterizing the effects of unocculted active regions on transmission
spectra, the high-cadence photometry obtained to discover these systems does
not exist in a vacuum. Here we consider other observations, whether or not
they are obtained simultaneously with the transmission spectrum, and their
ability to understand active regions. Solar observations show that the
absolute as well as the relative surface coverage of spots and faculae (or
plage) varies as a function of time. As the transmission spectrum
“contamination” depends on the feature contrasts in the given spectral band, a
single active-region tracer is generally insufficient and ideally two active
region tracers should be combined, ideally with very distinct sensitivity
levels to bright and dark active region components.

####  3.3.1 Multiband photometry

Both Kepler and TESS observe with a single broadband filter. With simultaneous
observations at multiple wavelengths, the changing color of an active stellar
surface over time can be inferred. This strategy has been used to determine
temperatures of stellar flares (Howard et al., 2020), and there is a long
tradition of using multiband photometric light curve modeling to infer spot
temperatures and covering fractions on active stars (see Section 1.4.2 and
Berdyugina (2005) for a review on starspot properties and observations). While
multiband photometry can lift some of the degeneracies between filling factors
and active region temperatures (e.g. Rosich et al., 2020), spot contrasts only
vary slowly as a function of wavelength, meaning that spot temperature
determinations remain very uncertain. Recovering active-region filling factors
becomes even more of a problem when trying to map spots and faculae
simultaneously using broad-band photometry. However, as facular regions have a
much stronger spectral signature than starspot regions (Shapiro et al., 2014),
narrow-band photometry focused on particular spectral regions (e.g., Ca ii H &
K and molecular bands such as CN bands, the CH G-band, or the TiO band in the
red optical; Zellem et al. 2010) could provide an outsized benefit in
understanding the distributions of faculae, motivating future theoretical
modeling. These spectral regions are also discussed more fully in Section
3.3.4.

Figure 16: Spot (top), facular (middle), and network (bottom) filling factors
as obtained from SDO (black dots; obtained using segmentation) and
reconstructed using TSI and Ca S-index time series. Blue symbols are for a
machine-learning algorithm, orange symbols are from linear fitting. From
Milbourne et al. (2021).

Work by Milbourne et al. (2021) suggests that for solar twins, where spot and
facular contrasts are relatively well constrained by theory and solar
observations, it should be possible to recover spot and facular filling
factors using a combination of high-fidelity broadband photometry and a
magnetic-activity tracer such as the Ca S-index (which can either be obtained
using high-resolution spectroscopy or narrow-band photometry). The first
results are promising (Figure 16), though they rely on accurate knowledge of
the spot and facular contrasts. There is also both theoretical and
observational evidence that spot and facular contrasts are affected by stellar
metallicity, but the effects have not been fully explored in detail for a
large population (Karoff et al., 2018; Witzke et al., 2018). Thus, more
information on active-region contrasts for different spectral types and
metallicities is needed before this can be extended to stars with non-solar
spectral types. Further work will also be needed to explore how the location
and relative importance of spots and faculae affects such reconstructions.

To map and understand the distribution of faculae, their spectral signatures
should be further explored. Faculae have strong UV contrasts, though this has
as yet been not fully explored, mainly due to a lack of time-resolved UV
photometry. Broadly, optical photometry has been traditionally considered to
retrieve stellar heterogeneities from long-term photometry, with the Strömgren
$b$ and $y$ filters commonly considered (e.g. Gray, 2005). FUV photometry may
provide a promising addition to this set, though current capabilities may
enable only a limited benefit compared to monitoring of stellar calcium
emission features (Findeisen et al., 2011). In the near-IR, there is some
evidence that signatures of stellar activity may be even smaller than
anticipated for some young stars (Miyakawa et al., 2021), making them a sub-
optimal choice to measure long-term photometric variability. However,
Stefansson et al. (2018) highlight a promising custom filter, 30-nm wide and
centered at 857 nm. This filter spans the Ca ii infrared triplet and minimises
the effects of telluric absorption. These authors suggest this filter offers
an inexpensive opportunity to study stellar activity in the near-IR; further
work should be undertaken to determine the usefulness of this or other
potential bandpasses in the context of identifying and quantifying the extent
of stellar surface heterogeneities.

####  3.3.2 Very-long-baseline photometry

For many bright stars, additional photometry exists from ground-based surveys
with time baselines extending ten years or more before the present day. These
data are often leveraged by the exoplanet community to great effect in the
confirmation and characterization of planetary systems, demonstrating their
utility in combination with high-cadence transit photometry. In particular,
the WASP (Pollacco et al., 2006), KELT (Pepper et al., 2007), and ASAS-SN
(Kochanek et al., 2017) surveys often have the precision to separate planet
candidates from background eclipsing binaries and infer stellar rotation
periods through starspot modulation. On much longer timescales, the DASCH
survey provides photometry with 0.1 magnitude precision over 100 years through
the digitization of a photographic survey that began in 1885. These data have
been used to study long-term variability in the Kepler field (Tang et al.,
2013).

These datasets offer a tradeoff between time baseline and photometric
precision, with a century of data available at $\approx 10$% precision or a
decade at $\approx 1$% precision. These offer the opportunity to potentially
measure changes in large photometric variability, such as photometric
variations from activity cycles or the growth and decay of large polar spots.

While these data have information about unocculted active regions that can be
used to understand the overall activity level of the star, they are collected
years or decades before the transmission spectra are obtained. Long-baseline
observations do provide data on the relative overall activity of the star at
the current time, through spectroscopic tracers such as a single measurement
of chromospheric activity from the Ca ii H and K lines can provide a similar
level of information contemporaneously with the transmission spectrum. There
is currently a paucity of theoretical motivation suggesting that these
observations can provide useful information in interpreting a transmission
spectrum. The converse has even been suggested: Iyer & Line (2020) suggest
that prior knowledge of stellar heterogeneities does not improve precision in
planetary parameters achievable from an atmospheric retrieval if the
heterogeneities are appropriately marginalized. Expanded theoretical work
highlighting benefits of this long-term photometry specifically in the context
of transmission spectroscopy would help to motivate the future utility of
these data in this context.

####  3.3.3 Interferometry

The nearby active star $\zeta$ And is among the so far few stars for which a
global surface temperature map has been successfully constructed via aperture
synthesis imaging (Roettenbacher et al., 2016). The data, which were obtained
with the interferometric CHARA Array at a wavelength of 1600 nm and an angular
resolution of 0.5 mas, reveal variations in the surface temperature that are
related to starspots.

Interferometric observations are possible with present technology only for
bright stars with large angular sizes; these are typically red giants. Recent
work has enabled constraints on the spot locations for the K2V exoplanet host
$\epsilon$ Eridani through a combination of RV spectroscopy, TESS photometry,
and CHARA and MIRC-X interferometry (Roettenbacher et al., 2022), though the
spot detections are marginal with this dataset, underscoring the challenge of
imaging exoplanet hosts. Thus, the primary utility of optical interferometry
at present is in enabling a better understanding of possible configurations of
active regions on stellar surfaces, which can be compared to theoretical
models to provide constraints on the stellar dynamo. In the context of
transmission spectroscopy, an important step is theoretical modeling of the
differences between the dynamo and resultant magnetic fields between typical
planet-hosting stars and the giants that are observable with optical
interferometry.

####  3.3.4 Low- and medium-resolution spectroscopy

Photometric observations of active stars can be used to identify active
regions, especially starspots. However, they typically produce a degeneracy
between filling factors and active region temperature: a given amount of
photometric modulation could be produced by a relatively small but very dark
starspot or a larger spot with a relatively small differential between its
temperature and the unocculted stellar surface. Low- and medium-resolution
spectroscopy can offer a more detailed view than photometry, provided the
instrumental stability is sufficient to monitor relatively subtle spectral
changes. An example of (facular-dominated) solar cycle variability observed at
mid-resolution ($R\sim 1000$) with the Aura/OMI instrument is shown in Figure
17 (Marchenko et al., 2019). The blue and UV wavelength regions are of
particular use here as facular contrasts are much larger at shorter
wavelengths. A number of relatively broad spectral features stand out, such as
the Ca ii H & K lines, the CH G-band, and the CN violet system (see Section
3.3.1).

Figure 17: Spectral solar-cycle variability for cycle 24 as observed by Ozone
Monitoring Instrument (OMI) on Aura (black line; the blue line shows the cycle
21 and 22 variability below 400 nm scaled to match the cycle 24 variability
for Mg ii). Enhanced variability is clearly seen in the Ca ii H & K lines as
well as the CN violet band (between $\sim$ 380 nm and 390 nm), and the CH
G-band (at 430 nm). From Marchenko et al. (2019).

Currently very little is known about contrasts of active regions on stars of
spectral types other than the Sun and more theoretical work is needed to
understand and model bright features (see Section 4.3). Magnetoconvection
simulations show that faculae will become less bright for later spectral
types, in particular for M stars (Beeck et al., 2015a). Preliminary
calculations suggest variability in the CN and CH bands will decrease, while
TiO bands become more important; at the same time, facular UV contrasts remain
comparable to those observed for Sun-like stars (Norris, 2018).

####  3.3.5 High-resolution spectroscopy

Much as in the low/medium resolution spectroscopy discussed in the previous
section, high-resolution spectroscopy can be used to better understand active-
region filling factors. With sufficiently high resolution, molecular bands can
be detected at high significance. Spectroscopic signatures of molecular
features are strong functions of temperature and pressure, so these features
provide an ideal laboratory to understand the stellar surface as the sum of
multiple components at different temperatures (e.g., Berdyugina et al., 2003).
For example, O’Neal et al. (1998b) demonstrated that the active K star II Peg
had a coverage fraction of ${\sim}$50% from observations of TiO molecular
bands. Gully-Santiago et al. (2017) showed an even higher filling factor for
the young star Lk Ca 4 using the same molecular features. In fact, the most
studied active K stars II Peg and IM Peg were never observed in their
unspotted states, as evidenced by the continued presence of variable TiO bands
in their spectra (Neff et al., 1995; Berdyugina et al., 1998, 1999). Thus, the
disappearance of the TiO bands forming only in cool spots can provide the
reference for the unspotted stellar atmosphere and brightness (Berdyugina et
al., 1998). Similar observations of other stars at different levels of
activity remain critical to understanding overall active-region filling
factors and thus the underlying sizes, atmospheric parameters, and
distributions of active regions.

Additionally, molecular features trace the stellar magnetic field through
their polarization (Berdyugina, 2011). High-resolution spectropolarimetry of
these lines provide estimates of magnetic fields on active stars, also
directly within spatially unresolved spots (Berdyugina, 2002; Berdyugina et
al., 2006). In particular, Afram & Berdyugina (2015) highlight that high-
resolution spectropolarimetry of TiO on M dwarfs, CaH on K dwarfs, and MgH and
FeH on G dwarfs provide particularly promising avenues to understand stellar
magnetic fields. This has been demonstrated for M dwarfs by studying atomic
and molecular spectropolarimetric signatures, revealing variations of the
magnetic field complexity on stellar surfaces, with the height in the
atmosphere and depending on the stellar effective temperature (Berdyugina,
2011; Afram & Berdyugina, 2019).

Extreme precision radial velocity (EPRV) observations to measure planet masses
and orbits also require care to mitigate the effects of active regions on
stellar spectra. Considerable effort has been expended to attempt to separate
the effects of stellar active regions from planetary signals. These efforts
have been successful in developing methods that can effectively predict the RV
signal from active regions from observed photometric variability (e.g. Aigrain
et al., 2012) and to model the surfaces of very active stars to measure the
masses of their planets (e.g. Barragán et al., 2019). Observations of the Sun
with the HARPS-N spectrograph also demonstrate that RVs can effectively be
modeled in the face of known active region distributions (Milbourne et al.,
2021).

A common finding in EPRV studies of active regions is the importance of
simultaneous photometry and spectroscopy to condition data-driven models.
Having both data sets is critical in many cases to measure planet masses
(Oshagh et al., 2017); it is likely that in many cases simultaneous
observations will also provide a benefit to uniquely characterise unocculted
active regions in transmission spectroscopy data.

####  3.3.6 Conclusion

Each of the methods described in this section holds the potential to improve
our understanding of unocculted active regions for transmission spectroscopy.
While there is evidence from EPRV observations that simultaneous photometry is
highly important for active stars, it is not as obvious for stars with lower
activity levels. An important step forward is not just understanding what data
additional sets are important, but to what level the answer is a function of
spectral type, age, and/or activity level. Theoretical work that can
effectively predict the effects of stellar activity on transmission spectra
would be beneficial in answering this question.

####  3.3.7 Our finding

From this analysis, we draw the following finding.

Finding 3.2

Summary: Simultaneous multi-band photometry and contemporaneous spectroscopy
provide critical information towards understanding the potential effects of
active regions on transmission spectroscopy observations. While other data
sets can provide information on filling factors, theoretical work is needed to
maximise the utility of these data for transmission spectroscopy.

Capability Needed: A better understanding of the emergent flux from stellar
active regions, including both photometric (SED) and spectral signatures
(e.g., Na D line, He 10830 Å, Ca infrared triplet, etc.), especially for
spectral types and metallicities other than the Sun, is essential to robustly
interpret transmission spectra.

Capability Today: There is a relatively good understanding of active-region
contrasts for solar twins from solar observations and modeling.

Mitigation in Progress: Ab-initio modelling of emergent fluxes from spots and
faculae for different spectral types is being developed by multiple research
groups.

###  3.4 Stellar granulation

One of the ultimate sources of an astrophysical “noise floor” in stellar light
curves is stellar surface granulation. Because it is a fundamental feature of
stars with convective envelopes (i.e., $T_{\rm eff}\lesssim 6700$ K), it
represents a true lower limit to the photometric variability that any star can
attain. This is summarized in Figure 9, where the lower “granulation flicker
floor” shows the lowest possible photometric variability amplitude for
otherwise inactive stars, as a function principally of the stellar surface
gravity, $\log g$. On the timescale of typical planet transits (i.e.,
$\lesssim$8 hr), in the Kepler bandpass (i.e., visible light), the
“granulation flicker” noise ranges from $\sim$0.02 ppt for the least active
dwarfs to $\gtrsim$0.4 ppt for the least active giants.

The amplitude of the “granulation flicker” noise scales with the
granule/inter-granule brightness contrast, which is minimized at longer
wavelengths. For example, the granular brightness contrast for a solar-type
star is $\sim 100\times$ lower at 10 $\mu$m than in visible light. Thus, for
inactive dwarfs, the “granulation flicker” noise at 10 $\mu$m should be as low
as $\sim$0.2 ppm on planet-transit timescales.

While these are relatively small contributions to the overall stellar
photometric noise, from the standpoint of a planet transit spectrum, the
impact can become the dominant source of uncertainty, particularly for
transits around larger stars and at shorter wavelengths. That is because a
larger star of a given mass will have a lower surface gravity, hence a
stronger granulation signal, and as noted above, that signal is strongest in
the visible. Indeed, as shown by the simulations of Morris et al. (2017);
Sulis et al. (2020), for planets transiting Sun-like stars observed in the
visible, the absolute error on the retrieved planet radius due to granulation
noise can be as large as $\sim$2% and $\sim$10% for super-Earth and Earth-
sized planets, respectively.

In practice, stellar granulation can impact the transit spectrum thus in two
ways. The first and most obvious one is the one related to the extra noise
this granulation adds to light curves, effectively setting a lower limit to
the possible precision attainable on the retrieved transit depths as a
function of wavelength. This source of noise, however, should be minor in most
cases. While studying this, Sarkar et al. (2018) considered the relative and
absolute contributions to the error budget for atmosphere retrieval of the
planets HD 209458b (a hot Jupiter orbiting a G0V-type star) and GJ 1214b (a
super-Earth orbiting an M4.5V-type star). The results are summarized in Figure
18 and Figure 19, where we see that in the worst case (HD 209458b in the
visible), where the stellar noise from granulation dominates over the photon
noise, the impact on the transit-depth measurement for atmospheric retrieval
is at most $\sim$0.05%.

Figure 18: Simulations of the relative noise contributions to planet-transit
depth due to stellar granulation (yellow) and photon noise (blue) as a
function of transit duration, for the cases of a hot Jupiter orbiting a
G0V-type star (HD 209458b) and a super-Earth orbiting an M4.5V-type star (GJ
1214b), in the visible (left) and near-IR (right). For each planet, compare
the large yellow dot to the large blue dot; this is the relative contribution
of stellar granulation noise to photon noise for atmospheric retrieval. Note
that in the left panel (visible light), the yellow and blue dots overlap for
HD 209458b, meaning that the stellar granulation noise begins to dominate the
error budget. From Sarkar et al. (2018).  Figure 19: Tabular summary of Figure
18. Relative uncertainty in planet transit depth for the two representative
cases (in ppm), and the resulting absolute uncertainty on the planet radius
for atmospheric retrieval (in percent) for different wavelength regimes of
observation. From Sarkar et al. (2018).

The second way in which granulation could impact on the transit spectrum,
however, is through the transit light source effect, similar to the impact
caused by unnoculted spots and faculae described by Rackham et al. (2018,
2019), but produced by the effectively different granulation pattern in
different parts of the stellar surface. This is an effect that Chiavassa et
al. (2017) studied through 3D simulations using the STAGGER grid and synthetic
images computed with the radiative transfer code OPTIM3D Chiavassa et al.
(2009). The study concluded that the impact of this contamination could be as
large as a few percent in the transit depth of small, terrestrial exoplanets
orbiting Sun-like stars at $0.7\mu$m. While Chiavassa et al. (2017) did this
experiment with simulations for both a Sun-like star and a K-dwarf star, it is
unclear how big this impact is in reality, and how realistic those simulations
are both as a function of wavelength and granulation amplitudes. This latter
effect is one that should be studied in detail, especially given missions such
as the ones proposed in the Astro2020 Decadal Survey, which could perform
precise optical spectrophotometry.

####  3.4.1 Our finding

From this analysis, we draw the following finding.

Finding 3.3

Summary: Stellar “granulation flicker” constitutes a fundamental “noise floor”
on stellar light curves that increases with decreasing stellar surface gravity
and at shorter wavelengths. The impact of this stellar granulation can enter
as a source of noise and/or contamination for transmission spectroscopy in two
ways. The first is through extra light curve scatter, whose impact is minimal
in most cases (at most $\sim$0.05% error on the transit depth in the visible
and even less at longer wavelengths). The second is through a contamination
source similar to that of spots and faculae, albeit at a much lower amplitude
($\sim 1\%$ of the transit depth at about 0.7 $\mu$m). This second source is
significant at short wavelengths for smaller exoplanets around Sun-like stars,
but decreases strongly as a function of wavelength.

Capability Needed: 3D granulation simulations need to be validated against
observed light curves as a function of spectral type and wavelengths relevant
for future space-based observatories ($\sim$0.3–5 $\mu$m). Simulations of
exoplanets crossing those simulated stellar surfaces should be studied in more
detail as to study the full impact of these features as a contamination source
in the transmission spectrum of high-profile exoplanet systems.

Capability Today: Granulation is well understood in large optical bandpasses
from space-based missions such as CoRoT, Kepler and TESS. Methodology is in
place in order to understand and analyze its amplitude given an observed
precise light curve. 3D stellar models can be used to model granulation as a
function of wavelength for different spectral types.

Mitigation in Progress: All-sky missions such as TESS can retrieve the
properties of the granulation signal for high-profile exoplanet host stars.

##  4 Stellar & Planetary Retrievals

Chapter Leads: Ryan J. MacDonald, Benjamin V. Rackham

Major Contributors: Joanna K. Barstow, Natalie Krivova, Aishwarya Iyer, Chima
McGruder, Luis Welbanks

Other Contributors: Heather M. Cegla, Serena Criscuoli, Chuanfei Dong, Néstor
Espinoza, Chloe Fisher, Emily Gilbert, Veselin Kostov, Mike Line, Mercedes
López-Morales, Karan Molaverdikhani, Rishi R. Paudel, Kevin Reardon, Alexander
I. Shapiro, Kevin B. Stevenson, Jeff A. Valenti, Sven Wedemeyer

Essential Questions:

  1. 1.

What is the state of the art for stellar and planetary retrievals of
transmission spectra?

  2. 2.

What wavelengths and resolutions are necessary for useful constraints on
active-region contrasts and coverages? Do these requirements vary with
spectral type?

  3. 3.

What are the best practices for propagating stellar spectral information into
atmospheric retrievals of transit observations?

  4. 4.

What additional information is necessary to uniquely disentangle stellar and
planetary signals via retrievals?

  5. 5.

What are the limitations of using retrievals to disentangle stellar and
planetary features?

  6. 6.

What future work should be pursued in this context?

###  4.1 Introduction

As noted in Section C, a primary concern with transmission spectroscopy is the
potential of unocculted active regions (including, e.g., spots or faculae) to
alter transit depths through the transit light source effect (TLSE, see Figure
20) and, thus, bias inferences of the properties of the exoplanetary
atmosphere. Here we examine the state of the art for Bayesian frameworks that
jointly fit for the properties of a planetary atmosphere and a heterogeneous
stellar photosphere, i.e., one with magnetic active regions. We begin by
defining more precisely these retrieval frameworks and outlining the scope of
our analysis.

Figure 20:  Illustration of the transit light source effect. Unocculted
heterogeneities (i.e., magnetic active regions) can mask or mimic spectral
features in transmission spectra by introducing a difference between the
spectrum of the light source illuminating an exoplanet’s atmosphere—the
emergent spectrum of the transit chord—and the light source necessarily used
as a reference for the transit depth measurement—the disk-averaged spectrum of
the star. From Rackham et al. (2018).

####  4.1.1 Retrievals

Atmospheric retrieval refers to a broad class of techniques used to extract
constraints on properties of a planetary atmosphere (e.g., composition,
temperature, clouds) from an observed spectrum. Retrieval codes start with a
set of spectral observations, such as HST transmission spectra, and compute
the range of models consistent with the data, as illustrated in Figure 21. A
retrieval model describes an atmosphere by a set of free parameters (e.g.,
molecular abundances, planetary radius) and uses a Bayesian sampling algorithm
(typically MCMC or nested sampling) to explore the posterior distribution of
the model. A retrieval typically computes $\gtrsim 10^{5}$ spectra to map the
parameter space defining a model, with nested models then compared to identify
the statistical significance of each model component (e.g., whether a given
molecule is supported by the data).

Figure 21:  Schematic illustration of a retrieval framework. Retrievals start
with an observed (or simulated) spectrum. A forward model is called repeatedly
to compare model spectra for a wide range of atmospheric properties to the
observations. A Bayesian sampling algorithm (here, nested sampling) guides the
parameter space exploration, producing the posterior distribution for each
parameter and detection significances for each model component (e.g.,
molecular species, presence of stellar heterogeneities). From MacDonald &
Madhusudhan (2017).

####  4.1.2 The scope of this analysis

Extracting the most information from transmission spectra requires inference
frameworks that allow us to constrain the properties of stars and planets
simultaneously. In this context, the analysis presented here considers how we
can best use the information we receive on both stars and planets in transit
observations from space-based facilities. We focus on three areas of interest:
the utility of joint stellar and planetary retrievals generally (Section 4.2);
the known limitations of the approach, with a focus on the availability of
suitable model spectra for stellar active regions (Section 4.3); and the
complementarity of short-wavelength observations to HST and JWST NIR
observations for inferring stellar photospheric properties (Section 4.4). In
the following sections, we summarize the analysis that leads to our top-level
findings in these three areas.

###  4.2 The utility of joint stellar and planetary retrievals

We first consider the general utility of employing joint stellar and planetary
retrievals over other, simpler approaches. In reaching our finding, we
considered how unocculted stellar heterogeneities modify transmission spectra,
approaches for directly correcting for stellar spottedness without using
retrievals, the current state of the art for modeling stellar photospheric
heterogeneity in retrievals, and recent studies that suggest direct approaches
for corrections may underestimate the actual level of stellar heterogeneity
and thus underscore the utility of retrievals.

####  4.2.1 Unocculted stellar heterogeneities modify transmission spectra

When a stellar surface contains heterogeneities residing outside the transit
chord (i.e., unocculted spots and faculae), the transmission spectrum of a
transiting planet can accrue a wavelength dependence not caused by the
planetary atmosphere. The origin of this effect is a mismatch between the
stellar intensity incident on the planetary atmosphere and the average
intensity of the full stellar surface (see Figure 20). The TLSE can be
expressed by the following functional form:

$D_{\lambda,\,\rm{obs}}=D_{\lambda,\,\rm{atm}}\,\epsilon_{\lambda,\,\rm{het}}$
(3)

where $D_{\lambda,\,\rm{obs}}$ is the observed transmission spectrum,
$D_{\lambda,\,\rm{atm}}=(R_{p,\lambda}/R_{s})^{2}$ is the intrinsic
transmission spectrum of the planetary atmosphere (i.e., the square of the
wavelength-dependent planet-to-star radius ratio), and
$\epsilon_{\lambda,\,\rm{het}}$ is the wavelength-dependent “contamination
factor” introduced by the TLSE. For a stellar surface with a single type of
unocculted heterogeneity (i.e., a population of similar spots or,
alternatively, faculae), the contamination factor can be written as (e.g.,
Rackham et al., 2018)

$\epsilon_{\lambda,\,\rm{het}}=\frac{1}{1-f_{\rm
het}\left(1-\frac{S_{\lambda,\,\rm{het}}(T_{*,\,\rm{het}})}{S_{\lambda,\,\rm{phot}}(T_{*,\,\rm{phot}})}\right)}$
(4)

where $f_{\rm het}$ is the fractional coverage area of the heterogeneous
regions, $S_{\lambda,\,\rm{het}}$ and $S_{\lambda,\,\rm{phot}}$ are the
specific intensities of the heterogeneity and background photosphere,
respectively, with $T_{*,\,\rm{het}}$ and $T_{*,\,\rm{phot}}$ being their
corresponding temperatures. Figure 22 shows example model spectra of
$S_{\lambda,\,\rm{het}}$ (left panel) and the contamination spectra
$\epsilon_{\lambda,\,\rm{het}}$ (right panel). We see that the contamination
factor deviates from unity significantly at short wavelengths ($\lesssim
1\,\mbox{$\mu$m}$), with transit depths enhanced by unocculted spots and
lowered by unocculted faculae.

Figure 22:  Stellar spectral components and their impacts on transmission
spectra. The left panel shows example model spectra of three primary stellar
photospheric components. The right panel illustrates the multiplicative change
in transit depth introduced by unocculted spots and faculae, assuming a 10%
coverage fraction. From Pinhas et al. (2018).

####  4.2.2 Non-retrieval approaches for correcting for stellar spottedness

Without even turning to retrievals, a rich body of work exists on mitigating
the impact of stellar heterogeneities on transmission spectra (see review by
Bruno & Deleuil, 2021). In the transmission spectroscopy literature, the
primary non-retrieval approach used to account for a heterogeneous stellar
photosphere is to apply a direct correction for stellar heterogeneity based on
the photometric variability of the star. Modeling the stellar flux as a linear
combination of the flux from the quiescent photosphere
$F_{\mathrm{phot},\lambda}$ and spots $F_{\mathrm{spot},\lambda}$, which cause
a total dimming of $\Delta f(\lambda_{0},t)$ at a nominal wavelength
$\lambda_{0}$, Sing et al. (2011) derive an expression for the correction
required for the transit depth $D_{\lambda}$, given by

$\frac{\Delta D_{\lambda}}{D_{\lambda}}=\Delta
f(\lambda_{0},t)\left(1-\frac{F_{\mathrm{spot},\lambda}}{F_{\mathrm{phot},\lambda}}\right)/\left(1-\frac{F_{\mathrm{spot},\lambda_{0}}}{F_{\mathrm{phot},\lambda_{0}}}\right).$
(5)

This implies a concomitant correction to the planet-to-star radius ratio of

$\Delta(R_{p,\lambda}/R_{s})\simeq\frac{1}{2}\frac{\Delta
D_{\lambda}}{D_{\lambda}}(R_{p,\lambda}/R_{s}).$ (6)

Zellem et al. (2017) present a similar approach, relying on the variability of
the out-of-transit stellar spectra, which are used to establish the baseline
for transmission spectroscopy studies, to infer a per-visit stellar activity
correction.

However, as noted by Berta et al. (2011), who derived a correction similar to
that of Sing et al. (2011), this approach (whether photometric or
spectroscopic) relies on the assumption that the maximum brightness in a light
curve corresponds to an unspotted photosphere. This is an increasingly poorer
assumption for active stars, which can have many active regions that
contribute to a persistent level of spottedness as the star rotates.

These highly spotted stars are those for which corrections for stellar
heterogeneity are most important to consider. McCullough et al. (2014), for
example, note that the strongly sloped transmission spectrum of HD 189733 b
could be explained by spots alone (without any contribution from haze in the
planetary atmosphere) if the total covering fraction of unocculted spots were
5.6%, not the 1–1.7% coverage that had been inferred through variability
monitoring and previously taken into account (Pont et al., 2008, 2013; Sing et
al., 2009, 2011). From this example and others, we conclude that rotational
variability provides a lower limit on the heterogeneity of a stellar
photosphere. Thus, applying a direct correction based on the stellar
variability may underestimate the actual correction required.

####  4.2.3 Including stellar heterogeneities in retrievals

Figure 23:  The impact of unocculted spots in a retrieval analysis. A
simulated hot Jupiter transmission spectrum contaminated by unocculted spots
(orange data) is subjected to two retrievals: (i) simultaneous modeling of the
planetary atmosphere and unocculted spots (top panels); and (ii) the planetary
atmosphere only (bottom panels). The posterior distributions (right panels)
compare the true planetary atmosphere and stellar properties (red dashed
lines) to the $1\,\sigma$ confidence regions for each parameter (blue error
bars). The model without spots attempts to compensate by adding a haze slope
and a cloud deck, resulting in a similar fit but significantly biased
($\gtrsim 3\,\sigma$) composition inferences. The model including unocculted
spots within the retrieval achieves a better fit to the data and successfully
recovers the input planetary atmosphere and stellar properties.

By constraining the impact of stellar contamination directly from transmission
spectra, retrievals can identify photospheric heterogeneity that is not
evident in variability monitoring. These analyses can fit simultaneously for
the properties of the planetary atmosphere and any heterogeneities and
appropriately marginalize over the contamination signal while estimating
planetary parameters. Retrieval codes typically accomplish this by adding
three additional free parameters encoding the heterogeneous regions (e.g.,
Pinhas et al., 2018; Rathcke et al., 2021): $f_{\rm het}$, $T_{*,\,\rm{het}}$,
and $T_{*,\,\rm{phot}}$. During parameter space exploration, each pair of
$T_{*,\,\rm{het}}$ and $T_{*,\,\rm{phot}}$ are used to compute spectra of the
heterogeneity and the photosphere by interpolating grids of stellar models,
e.g., the PHOENIX (Husser et al., 2013) or Castelli-Kurucz grids (Castelli &
Kurucz, 2003). Given the interpolated stellar spectra and $f_{\rm het}$, the
contamination factor is computed using Equation 4 and combined with the
atmospheric spectrum as in Equation 3. The combined transmission spectrum is
then compared with the observations at each point in the parameter space.

We provide an example retrieval analysis in Figure 23. We generated a
simulated transmission spectrum of a hot Jupiter (with planet properties based
on HD 209458b) transiting a star with unocculted spots. For this example, we
assumed 5% spot coverage with a spot temperature 900 K colder than the
photosphere. The unocculted spots produce a steep slope at visible wavelengths
and secondary features imprinted by stellar absorption. The simulated data
cover 0.34–1.80 $\mu$m, roughly corresponding to the range of HST/STIS+WFC3,
at a precision of 30 ppm. We subjected this dataset to two retrievals with the
POSEIDON code (MacDonald & Madhusudhan, 2017) under different assumptions: (i)
unocculted spots are included within the retrieval; and (ii) no spots are
considered, only the planetary atmosphere shapes the spectrum. We find that
the atmosphere-only retrieval attempts to account for the lack of spots by
adding a haze (producing a similar optical slope) and a cloud deck. While both
models result in an acceptable fit, the atmospheric properties are
significantly biased when unocculted spots are not considered: the Na and K
abundances are biased by $\sim$5$\sigma$, the H2O abundance is biased by
$\sim$3$\sigma$, and one would incorrectly conclude that the atmosphere has
potent aerosols. Conversely, the retrieval including unocculted spots
correctly recovers all input parameters within the 1–2$\,\sigma$ expected from
Gaussian scatter. The Bayesian evidence also prefers the model including spots
($\Delta\ln Z=11.6$), showing that a retrieval code can differentiate between
these scenarios. This exercise demonstrates that biases in atmospheric
properties can be mitigated by including stellar heterogeneities in
retrievals.

Figure 24: The statistical preference for including the TLSE in retrievals of
synthetic JWST/NIRISS data as a function of spot covering fraction. In this
exercise, Iyer & Line (2020) performed retrievals on the transmission spectrum
of a sub-Neptune orbiting an M-dwarf with unocculted spots, varying the data
precision from 15 to 120 ppm (point colors) and the spot covering fractions
from 0.6$\%$ to 12$\%$. The black dashed lines indicate the degree of
statistical preference for the TLSE-correction-included retrieval model
(Trotta, 2008). The overall trend is that the model including the TLSE is
increasingly preferred for better precision and for spot covering fractions
above 1$\%$. Below 1$\%$ spot coverage, the biases from ignoring the
correction are not as noteworthy (except for 15 ppm precision, where the TLSE
model is still strongly preferred). Such small spot coverage (a low evidence
regime) also incurs inaccuracies in computing Bayes factors, causing the
crossing over of the 30 ppm point (e.g., Lupu et al., 2014). From Iyer & Line
(2020).

The confidence with which unocculted stellar spots or faculae can be
identified is a function of spectral precision, coverage fraction, and
wavelength range. Using simulated JWST/NIRISS data and Bayesian model
comparisons, Iyer & Line (2020) show how the level of preference for stellar
contamination varies with these factors for typical sub-Neptunes orbiting
M-dwarfs. For large covering fractions of unocculted spots (above 1$\%$, see
Figure 24), the Bayes factor increasingly favors a model including the proper
TLSE correction across spectrophotometric precisions from 15 to 120 ppm. For
small spot covering fractions (below 1$\%$), the TLSE signal is evident in
high-fidelity JWST/NIRISS data (${\sim}$15 ppm precision). However, it may be
harder to identify stellar contamination for small spot coverage at more
typical precisions ($\gtrsim$ 30 ppm). Iyer & Line (2020) draw consistent
conclusions for including the TLSE in retrievals—in their case, for
JWST/NIRISS data of sub-Neptunes transiting M-dwarfs—compared to those we draw
from the analysis of simulated HST/STIS+WFC3 data of a hot Jupiter transiting
a G dwarf in Figure 23. Notwithstanding these analyses, there is considerable
scope for future work to further quantify when the inclusion of stellar
contamination within a retrieval framework is necessary, e.g., considering the
sensitivity of such inferences to other instruments with different precisions,
wavelength coverage, and spectral resolutions.

The inclusion of unocculted stellar heterogeneities within retrievals is a
relatively new addition to the literature. Consequently, approaches can vary
between different studies and a “best practice” consensus has yet to emerge.
Four of the main differences are as follows.

  1. 1.

Free parameters: A single heterogeneity can be described by three free
parameters ($f_{\rm het}$, $T_{*,\,\rm{het}}$, and $T_{*,\,\rm{phot}}$, see
Pinhas et al. 2018), or a subset can be fixed (e.g., Bruno & Deleuil, 2021).
Additional parameters could be added for multiple heterogeneities. When such
models (e.g., including both spots and faculae; Zhang et al., 2018) are
necessary is unclear and worthy of future study.

  2. 2.

Out-of-transit stellar spectra: Recent studies have leveraged baseline, out-
of-transit stellar spectra in real and simulated datasets to fit for stellar
heterogeneity parameters, either while simultaneously modeling their impact on
transmission spectra or simply gathering prior information for analyses of
transmission spectra (Zhang et al., 2018; Wakeford et al., 2019; Iyer & Line,
2020; Cracchiolo et al., 2021). It is unclear whether this approach provides
an additional advantage over analyses of transmission spectra alone.

  3. 3.

Priors: Some studies ascribe Gaussian priors to $T_{*,\,\rm{phot}}$ (e.g.,
Pinhas et al., 2018; Rathcke et al., 2021), encoding a priori knowledge on the
stellar $T_{\rm eff}$, while others use uniform priors (e.g., Iyer & Line,
2020).

  4. 4.

Stellar grids: Many model stellar grids are available, with different grids
implemented in different retrieval codes. We consider the impact of this
further in Section 4.3.

Alongside these differences, other common assumptions include: fixing the
metallicity and surface gravity of any heterogeneities to those of the
photosphere (both set to a priori values) and, as noted previously, the
consideration of only one heterogeneity. The variety of approaches in the
literature to date serves to illustrate that more work on retrievals including
stellar heterogeneities will be beneficial.

####  4.2.4 Existing spectra are impacted

Recent studies employing retrievals have found mounting evidence for
unocculted heterogeneities impacting transmission spectra, in many cases at a
level beyond what was previously inferred via variability measurements. Pinhas
et al. (2018) reanalyzed nine hot Jupiter transmission spectra from HST and
Spitzer (Sing et al., 2016), finding moderate evidence (3.1$\sigma$) for
stellar heterogeneity in the spectrum of WASP-6b, beyond that previously
estimated to be present from variability measurements (Jordán et al., 2013;
Nikolov et al., 2015). Another three hot Jupiters show moderate to weak
suggestions of stellar heterogeneity: WASP-39b (2.5$\sigma$), HD 209458b
(1.6$\sigma$), and HAT-P-12b (1.4$\sigma$). Rathcke et al. (2021) studied the
optical and NIR transmission spectrum of the hot Jupiter WASP-79b and inferred
the presence of unocculted faculae (4.7$\sigma$) covering $\sim$15% of the
disk of the F5V host star with a temperature contrast of $\sim$500 K.
Similarly, Kirk et al. (2021) studied the optical and NIR transmission
spectrum of the ultrahot Jupiter WASP-103b, notably using 11 optical transits
that paint a consistent picture between epochs and across four instruments.
From this spectrum, which shows a marked decrease in transit depth at blue-
optical wavelengths, they inferred the presence of unocculted faculae
(4.1$\sigma$) covering $\sim$20% of the stellar disk with a temperature
contrast of $\sim$400 K. In these examples, the impact of stellar
heterogeneity on the transmission spectra was either underestimated in
previous studies applying direct corrections or may have been missed if not
for the use of retrievals, which points to the utility of this approach for
identifying and disentangling signals from stellar heterogeneity and planetary
atmospheres in transmission spectra.

####  4.2.5 Our finding

From this analysis, we draw the following finding.

Finding 4.1

Summary: Retrievals of transmission spectra that include the effects of
unocculted active regions can guard against biases. More work is needed to
understand when these retrievals are necessary and what are the limitations
and best practices of this approach.

Capability Needed: A detailed understanding is needed of when to marginalize
over stellar heterogeneity in retrievals of planetary atmospheric parameters
and the best practices for doing so.

Capability Today: Multiple groups have developed retrievals that use simple
parameterizations of unocculted heterogeneities and rely on stellar spectral
models.

Mitigation in Progress: This is an active area of research in the retrievals
community.

###  4.3 Limitations of the approach

We next consider the known limitations of the retrieval approach, focusing on
the availability of suitable model spectra for stellar magnetic active
regions. In reaching our finding, we considered the disagreement among current
model stellar spectra and the related impact of employing different stellar
spectra on retrieved planetary properties as well as recent advances in
modeling spectra of stellar magnetic active regions.

####  4.3.1 Disagreement among model stellar spectra and its impact on
retrievals

Figure 25:  Disagreements among model stellar spectra and their resulting
contamination factors. Left: Spectra from popular stellar model grids of an M
dwarf with $T_{\mathrm{eff}}=3000$ K, $\log g=5.0$, and [Fe/H]$=0.0$. Right:
The stellar contamination factor that influences planetary spectra via the
TLSE (Equation 4) constructed from these stellar models, assuming a fractional
coverage of unocculted spots on the photosphere of $f_{s}=5\%$ and a spot
temperature of $T_{\mathrm{s}}=2700$ K. From Iyer et al. (in prep.).

A primary limitation of retrieval approaches for handling stellar
contamination is their reliance on stellar models, which vary substantially in
their predictions of the spectra of cool stars. Substantial variations in
spectral shape among widely used stellar models (Figure 25, left panel) owe to
a variety of factors, including the choice of opacity data included and
spectral line list completeness; treatment of line-broadening effects; and
physical assumptions, such as plane-parallel vs. spherical geometry and LTE
vs. non-LTE chemistry conditions. The variation is more pronounced for mid-to-
late M stars ($<$3500 K) than for FGK stars due to molecular opacities
dominating such atmospheres and photospheric surface heterogeneities that are
common in active cool stars (Hawley & Pettersen, 1991; Hawley et al., 2014b;
Schmidt et al., 2014). As a result, the choice of stellar models used while
correcting for TLSE signals can impact planetary properties retrieved from
transmission spectra.

This impact has been explored quantitatively in a recent study by Iyer & Line
(2020, Figure 26). These authors used the PHOENIX-ACES model grid (Husser et
al., 2013) to mimic a “true” disk-integrated stellar spectrum of an M dwarf
($T_{\mathrm{phot}}=3300$ K) contaminated by unocculted spots ($T_{s}=2838$ K)
covering a fractional area fs of 12$\%$. They performed a retrieval on a
simulated transmission spectrum with this contamination, using the PHOENIX
model grid (Allard et al., 2003) to calculate the TLSE contribution to the
transmission spectrum. They find the fit reasonably explains the shape of the
transmission spectrum. However, the induced variations in the best-fit
spectrum are probably due to false opacity signatures or incorrect estimates
of the thermal profile—evident in the form of bias in the posterior
probability distributions of the planetary irradiation temperature Tirr,
metallicity [M/H], and carbon-to-oxygen ratio $\log$ (C/O) (Figure 26, right
panel). This exercise highlights that, despite an appropriate implementation
of the TLSE, our ability to correct for the contribution of stellar
contamination heavily depends on the accuracy of the stellar models used to
represent the contaminated stellar photosphere—particularly for cooler host
stars (K- and M-type)—thereby emphasizing the need for improved stellar
atmosphere models.

Figure 26:  The impact of disagreements between stellar models on retrievals.
Here Iyer & Line (2020) simulated a dataset contaminated by unocculted spots
using the PHOENIX-ACES model grid (Husser et al., 2013) but retrieved it using
the PHOENIX model grid (Allard et al., 2003). They find significant biases in
the retrieved values of the atmospheric irradiation temperature
$T_{\mathrm{irr}}$, metallicity [M/H], and carbon-to-oxygen ratio $\log$
(C/O). Top Left: disk-integrated stellar spectra from both model grids and
their residuals. Bottom Left: contaminated transmission spectra in both cases
and the retrieved spectrum. Right: posterior distributions of the atmospheric
parameters compared to the true model inputs (dashed lines). From Iyer & Line
(2020).

####  4.3.2 Advances in modeling spectra of active regions

Figure 27:  Simulations of faculae with the 3D radiation-magnetohydrodynamics
code MURaM (Vögler et al., 2005) and their derived contrast spectra. Left:
normalized emergent intensities from a simulated G2 atmosphere at different
viewing angles, wavelengths, and for two average magnetic field strengths (400
G and 500 G). Faculae have markedly higher contrasts near the limb and at
shorter wavelengths. Right: average facular contrast spectra for G2 simulated
atmospheres with differing field strengths, both at disk center (top right)
and nearer to the limb (bottom right). The spectra show different structures
than what are currently captured by approximations of facular spectra with
disk-integrated stellar spectra. The center-to-limb variations shown here are
also not captured by current approximations of faculae in retrievals. From
Norris et al. (2017).

Facular and sunspot contrasts employed by retrieval models are typically
derived from 1D, plane-parallel, semi-empirical model atmospheres (e.g.,
Vernazza et al., 1981; Kurucz, 1992a, b, c; Fontenla et al., 1993, 1999, 2002,
2006). For faculae in particular, such models are adjusted to agree with solar
observations (Vernazza et al., 1981). However, for stars other than the Sun,
such observations are not available, and thus adjustment of the models is not
possible. Furthermore, while such semi-empirical models capture the overall
disc-integrated properties of faculae reasonably well, they do not recover the
observed center-to-limb variation (CLV) of the facular contrast (e.g., Yeo et
al., 2013).

More realistic CLV of facular contrasts is provided by 3D magneto-hydrodynamic
(MHD) simulations, as discussed in Section 1. The first 3D radiative
hydrodynamic (HD) simulations for stars were reported by Nordlund & Dravins
(1990). The magnetic field was introduced in such simulations more recently,
and by now a series of models for stars of spectral types F to M with
different mean vertical magnetic fields is available (Beeck et al., 2011;
Beeck, 2014; Beeck et al., 2015a; Wedemeyer et al., 2013; Steiner et al.,
2014; Salhab et al., 2018). Norris et al. (2017) and Johnson et al. (2021)
used the 3D MURaM atmospheres from Beeck et al. (2015a) to calculate the CLV
of the facular contrast for G2 (see Figure 27), K0, M0, and M2 stars with the
mean vertical magnetic field ranging between 100 G and 500 G. Norris et al.
(2017) found the computed CLV profiles of a G2 star to be in good agreement
with solar observations (Neckel & Labs, 1994). More recently, simulations by
Johnson et al. (2021) have clearly demonstrated a strong effect of faculae on
the mean brightness and shape of stellar light curves, pointing to the need
for more accurate facular models. Using a self-consistent approach and 1D
model atmospheres, Witzke et al. (2018) have additionally shown that facular
contrast increases with stellar metallicity, underscoring the importance of
accurate fundamental stellar parameters when modeling stellar magnetic
activity.

In the case of spots, 3D MHD simulations using the MURaM code have been
largely successful in reproducing the fundamental observed features of spots,
both on the Sun and other stars. Rempel et al. (2009a, b) have produced MURaM
simulations of sunspots and found good agreement with observations. Recently,
Panja et al. (2020) have used the MURaM code to perform the first ab initio
simulations of spots on cool main-sequence stars other than the Sun. Their
simulations for G2V, K0V, and M0V stars provide umbral and penumbral effective
temperatures for these stars, along with other fundamental parameters of
starspots, such as the brightness relative to the stellar surface and magnetic
field strength. They conclude that the trend of increasing temperature
difference with photospheric temperature that they observe is consistent with
observations of starspots.

Taken together, these studies highlight recent advances in modeling spectra of
magnetic active regions and underscore the existing limitations. While 1D
models, such as those used to derive template spectra for state-of-the-art
retrievals of transmission spectra, generally reproduce well the observed
features of spots, they fail to capture aspects of facular contrasts that can
impact transit observations. In particular, the CLV of the facular contrast
and the dependence of facular contrast on stellar metallicity are important in
this context but not addressed in modern retrievals. Recent work with 3D MHD
simulations can be leveraged to improve template spectra for spots and
faculae, though the output of these realistic stellar models has yet to be
incorporated into exoplanetary retrieval analyses.

####  4.3.3 Our finding

From this analysis, we draw the following finding.

Finding 4.2

Summary: Retrieval approaches rely on stellar models, and thus their accuracy
is limited by model fidelity. Further efforts to develop model spectra for
spots and faculae and incorporate them into exoplanetary atmospheric
retrievals are needed.

Capability Needed: More work is needed to (1) further test and develop models
for cool stars, (2) assess the impact of using stellar spectra to approximate
active regions, and (3) develop model spectra for active regions, particularly
faculae, for different spectral types.

Capability Today: Retrieval analyses today rely on stellar spectra derived
from 1D models as templates for spot and faculae spectra.

Mitigation in Progress: Recent studies have produced ab initio spot and
faculae spectra from 3D MHD models for a few FGKM spectral types. These
studies reveal spectral differences with respect to spectra from 1D stellar
spectral models that underscore the limitation of this approach, particularly
for faculae.

###  4.4 The complementarity of short-wavelength observations

The third and final general aspect we considered is the complementarity of
short-wavelength observations to HST and JWST NIR observations for inferring
stellar photospheric properties. In reaching our finding, we considered
forward-modeling efforts that suggest the impacts of heterogeneous stellar
photospheres are largest at UV and blue-optical wavelengths and recent studies
that either point to stellar contamination in short-wavelength transit data or
increase the model preference for a heterogeneous stellar photosphere by
including optical data.

####  4.4.1 Projected impacts are strongest at short wavelengths

Many studies in the past decade have considered the impact of unocculted
active regions on transit observations. Usually, these studies focus on
interpretations of transmission spectra from individual systems with active
host stars, such as HD 189733 (Pont et al., 2008, 2013; Sing et al., 2009,
2011; McCullough et al., 2014; Oshagh et al., 2014), WASP-6 (Jordán et al.,
2013; Nikolov et al., 2015), and GJ 1214 (Berta et al., 2011, 2012; Rackham et
al., 2017). Despite the different spectral types and activity levels of these
host stars, studies of individual targets like these consistently find that
the projected impacts of unocculted active regions are most evident at blue-
optical and shorter wavelengths, where the contrasts between active regions
(whether spots or faculae) and the quiescent photosphere are greatest.

This finding is borne out as well by studies of unocculted active regions for
less-active stars, like the Sun. Llama & Shkolnik (2015) studied the impact of
solar-like photospheric heterogeneity on transits by injecting a hot Jupiter
transit into resolved observations of Solar Cycle 24 from NASA’s Solar
Dynamics Observatory. While they recovered accurate planetary radii in the
optical (4500 Å), they found that solar-like unocculted active regions biased
their recovered $R_{p}/R_{s}$ values in $\sim$20% of their simulated soft
X-ray (94 Å) and UV (131–1700 Å) light curves. At these wavelengths,
unocculted active regions generally led to a mean underestimate of 10% of the
planetary radius, with up to 25% underestimates occurring during high-activity
periods.

Turning to stars other than the Sun, Rackham et al. (2018, 2019) estimated the
impact of unocculted active regions for FGKM stars with typical activity
levels. Using a suite of Monte Carlo simulations, they estimated the spot and
faculae covering fractions that correspond to the observed variabilities of
FGKM dwarfs by spectral type. They found that spot covering fractions, in
particular, increase from $\sim$0.1% for F dwarfs to 2–4% for late-K dwarfs to
$\sim$10% for M dwarfs. If present on the unocculted stellar disk, spots and
faculae alter transit depths in the 0.3–5.5 $\mu$m wavelength range by a few
to tens of percent, depending on assumptions about spot size and spot-to-
faculae areal ratio (Figure 28). Along with the other studies summarized here,
these studies of exoplanet host stars with typical activity levels agree that
impacts should be most evident at blue-optical and UV wavelengths.

Figure 28:  Estimated contamination spectra due to spots and faculae on FGKM
dwarfs. Using spot and faculae covering fractions inferred from rotational
variabilities, forward modeling suggests that typical impacts of stellar
contamination will be larger for cooler stars, though considerable uncertainty
exists as to the relative impacts of spots and faculae. In any case, spectral
contamination due to stellar photospheric heterogeneity is predicted to be
largest at short wavelengths (${<}0.6$ $\mu$m). From left to right, the
columns show the spectral contamination from unocculted spots on FGK dwarfs,
spots and faculae on FGK dwarfs, spots and faculae on M dwarfs, and spots on M
dwarfs. From Rackham et al. (2018, 2019).

####  4.4.2 Short-wavelength observations reveal stellar contamination

Many existing exoplanet transmission spectra are assembled piece-wise via
observations with various instruments covering different wavelength ranges
(e.g., HST/STIS, HST/WFC3, Spitzer/IRAC; Sing et al., 2016). Consequently, the
atmospheric interpretations inferred from a given planet’s spectrum can change
over time as the spectral wavelength range becomes more complete. Given that
the impact of unocculted stellar heterogeneities is most pronounced at short
wavelengths, one may anticipate that initial atmospheric reconnaissance using
only infrared observations can miss signatures of stellar contamination. Here
we focus on one recent case study demonstrating the utility of short-
wavelength transmission spectra to reveal unocculted stellar heterogeneities.

The hot Jupiter WASP-79b (Smalley et al., 2012) has been considered a strong
candidate for the JWST Early Release science (ERS) program (Bean et al.,
2018). Sotzen et al. (2020) presented initial observations of WASP-79b
obtained with HST/WFC3, Spitzer/IRAC, TESS, and Magellan/LDSS3. They inferred
the presence of H2O absorption from the infrared observations and attributed a
blue downward slope from the ground-based LDSS3 data to FeH. An independent
analysis by Skaf et al. (2020), using only HST/WFC3 data, reached similar
conclusions. However, neither of these studies considered unocculted stellar
heterogeneities in their retrievals. Recently, Rathcke et al. (2021) presented
additional HST/STIS observations of WASP-79b, which extended the transmission
spectrum down to 0.3 $\mu$m and confirmed the lower transit depths at short
wavelengths suggested by LDSS3 (see Figure 29). Their retrieval analysis
identified a strong preference for unocculted faculae (4.7$\sigma$), covering
$\sim$15% of the stellar disk with a temperature contrast of $\sim$500 K, but
without the need for FeH. This provides another demonstration that, in the
presence of informative data, atmospheric interpretations can be biased if
stellar contamination is not considered (see Section 4.2.3).

Since JWST observations will be confined to wavelengths longer than 0.6
$\mu$m, we assessed the information content provided by optical transmission
spectra in the context of WASP-79b. Figure 29 shows how the inferred stellar
properties alter when only the infrared ($>1.0\,\mbox{$\mu$m}$) observations
are considered. We see that the retrieval does not identify unocculted faculae
when the optical data is omitted ($T_{*,\,\rm{het}}$ is consistent with
$T_{*,\,\rm{phot}}$ and $f_{\rm het}$ is consistent with 0). This suggests
that complementary blue-UV observations, at shorter wavelengths than JWST can
observe, may aid the identification of unocculted stellar heterogeneities.
However, additional work would be beneficial to explore whether the
conclusions from this case study apply more broadly.

Figure 29:  Top: the optical and near-infrared transmission spectrum of the
hot Jupiter WASP-79b. The decreasing transit depth towards blue wavelengths is
a characteristic signature of unocculted faculae (detected at 4.7$\sigma$).
Three distinct retrieval codes independently inferred the necessity of faculae
to explain WASP-79b’s transmission spectrum, demonstrating the robustness of
this interpretation. Bottom: retrieved stellar heterogeneity parameters from
the full optical + near-infrared dataset (left panel) and from the near-
infrared data alone (right panel). The identification of faculae for WASP-79b
crucially hinges on data at wavelengths $<1.0\,\mbox{$\mu$m}$. From Rathcke et
al. (2021).

####  4.4.3 Combining visible and NIR spectra improves physical inferences

The inclusion of visible wavelength observations provides an additional
quantitative benefit: better inferences for both the planetary atmospheric
properties and any unocculted stellar heterogeneities. Kirk et al. (2021)
recently demonstrated this with a retrieval analysis of the ultrahot Jupiter
WASP-103b. Similar to the case of WASP-79b, they found the transit depth of
WASP-103b to decrease towards blue wavelengths (Figure 30). They showed that
retrievals including only infrared HST and Spitzer observations can infer
unocculted faculae (2.4$\sigma$) from a slope in the WFC3 observations, but
the addition of precise ground-based observations helps confirm this inference
(4.3$\sigma$). At the same time, the detection significance of the planetary
atmosphere increased marginally from 1.9$\sigma$ to 2.8$\sigma$. This provides
a quantitative example of how short-wavelength observations can increase our
confidence in a given interpretation of an exoplanet’s transmission spectrum.

Figure 30:  The panchromatic transmission spectrum of ultrahot Jupiter
WASP-103b. The spectral impact of unocculted faculae is more pronounced at
shorter wavelengths. Retrievals on the NIR HST and Spitzer data favor the
inclusion of faculae at 2.4$\sigma$. Including the optical data, combined from
11 ground-based transits with four different facilities, boosts the detection
significance of unocculted faculae to 4.3$\sigma$. The optical data also boost
the detection significance for a planetary atmosphere, inferred by suggestions
of TiO, H2O, and HCN, to 2.8$\sigma$ from 1.9$\sigma$ with the NIR data alone.
From Kirk et al. (2021).

####  4.4.4 Our finding

From this analysis, we draw the following finding.

Finding 4.3

Summary: For low-resolution transmission spectra, the impact of unocculted
active regions is larger at shorter wavelengths. More work is needed to
quantify the complementary nature of such spectra for JWST observations.

Capability Needed: Future retrieval work will benefit from a general
understanding of when short-wavelength data are necessary to complement NIR
transmission spectra from HST and JWST. Similarly, an understanding of what
biases may be introduced by studying NIR spectra alone—even in the context of
joint stellar and planetary retrievals.

Capability Today: Recent studies have shown that supplementing space-based NIR
observations with optical observations (either ground- or space-based) boosts
the detection significance of stellar contamination in transmission spectra
and alters interpretations of planetary atmospheric properties.

Mitigation in Progress: The general utility of ${<}0.6\,\mbox{$\mu$m}$
observations for complementing JWST transmission spectra is an active area of
research.

##  5 Future Complementary Observations

Chapter Leads: Elisa V. Quintana, Robert T. Zellem

Major Contributors: Thomas Barclay, Serena Criscuoli, Helen Giles, Aishwarya
Iyer, Heidi Korhonen, Elisabeth R. Newton, Sarah Peacock, Benjamin V. Rackham,
Kevin Reardon, Rachael M. Roettenbacher, Keivan G. Stassun, Kevin B. Stevenson

Other Contributors: Sarah L. Casewell, Heather M. Cegla, Elsa Ducrot, Emily
Gilbert, Veselin Kostov, Natalie Krivova, Susan Mullally, Rishi R. Paudel,
Sven Wedemeyer

Essential Questions:

  1. 1.

What datasets and/or techniques can help to unveil stellar photospheres?

  2. 2.

What strategies would optimize transit spectroscopy given the findings of the
SAG?

###  5.1 Introduction

Exoplanet transmission spectroscopy is a key science case for the James Webb
Space Telescope (e.g., Barstow & Irwin, 2016; Greene et al., 2016; Morley et
al., 2017) and the focus for the upcoming Ariel/CASE mission, both of which
will have unprecedented precision to probe exoplanet atmospheres. Guided by
the findings from Section 1 through Section 4, the goal of this chapter is to
identify current capabilities and future complementary observations that could
provide datasets and techniques to constrain stellar heterogeneities in aid of
exoplanet transmission spectroscopy studies. Here we describe the current
landscape for ground- and space-based facilities, and identify gaps in
observations and capabilities that are needed to mitigate or correct for
stellar contamination. We focus first on observations of the Sun and second on
observations of exoplanetary host stars.

###  5.2 Observations of the Sun

Observations of our nearest star provide the best opportunity to resolve and
characterize stellar active regions over time. Here we describe two lines of
research that leverage solar observations to inform our understanding of
exoplanetary transits: studying the Sun as a resolved star, and studying the
Sun as a resolved planetary host. In each context, we discuss the parameters
of useful observations and current or future facilities for gathering these
data.

####  5.2.1 Studying the Sun as a resolved star

As described in Section 1, the brightness of the Sun (total and over selected
spectral ranges) has been monitored from space since 1978. The Sun’s
brightness varies on all timescales accessible to observations, from minutes
to decades (e.g., Kopp, 2016). Despite the wealth of solar observations
collected to date, resolved observations of the Sun in the visible and IR are
still needed to study spectral variations of active regions on minute-to-year
timescales, as noted in Finding 1.1. These are the relevant timescales
spanning single-transit observations and observational campaigns that stack
ten or more transits to build up the necessary signal-to-noise ratio to probe
atmospheric features for smaller, cooler exoplanets (e.g., Kreidberg et al.,
2014; Benneke et al., 2019a, b).

To understand and model the effect of stellar active regions on these
timescales, it is important to combine information obtained from both long-
term, full-disk (i.e., disk-integrated) observations and high-spatial-
resolution (sub-arcsecond) observations. The former allows an estimate of the
temporal evolution of the areal coverage by the different features and an
analysis of their properties (both individual and statistical), such as
typical sizes, magnetic field, and photometric contrast in specific spectral
bands. These quantities are fundamental ingredients of irradiance models and
are the main observables for the validation of global dynamo models.

##### Full-disk observations.

A number of existing facilities provide systematic full-disk observations of
the Sun. Ground-based facilities targeted to investigate solar variability are
typically furnished with broadband Ca ii K filters (see Petrie et al. 2021 for
a recent review on Ca ii K solar observations), and other broadband
photospheric filters and/or H-alpha filters. Examples of current facilities
include the Precision Solar Photometric Telescopes in Rome (Ermolli et al.,
1998) and Hawaii (Rast et al., 1999), and the Solar Observatories of
Kanzelhöhe, Tenerife, San Fernando, Kodaikanal and Mitaka. Furthermore,
multiple historical Ca ii K archives have been compiled, together providing
more than a century of solar full-disk observations (Chatzistergos et al.,
2019a, 2020b). Full-disk observations in the UV and EUV, fundamental to
understanding and modelling the variability at the shortest wavelengths, are
currently provided by AIA aboard the Solar Dynamic Observatory (SDO) and SUVI
aboard the GOES 16 and 17 satellites These will be complemented in the near
future with observations acquired in the UV by the SUIT instrument on the
Indian Aditya-L1 mission (Ghosh et al., 2016). Full-disk continuum images,
such as those provided SoHO/MDI or SDO/HMI, have been used to study brightness
and other properties of sunspots and their changes over the solar cycle (e.g.,
Mathew et al., 2007; Watson et al., 2014; Kiess et al., 2014). Full-disk
magnetograms acquired in both the photosphere (e.g., SoHO/MDI, SDO/HMI, ISS)
and chromosphere (e.g., GONG, ISS) allow studies of the evolution of the
magnetic field over the activity cycle. A combination of full-disk
magnetograms and broad-band imagery allows understanding of the relation
between the magnetic field and the radiative properties of different features
(e.g., Yeo et al., 2013; Criscuoli et al., 2017), and are assimilated in some
irradiance reconstruction models (e.g., Krivova et al., 2003).

##### High-spatial-resolution observations.

High-spatial-resolution observations are fundamental to understanding the
physical processes that generate, sustain, and dissipate magnetic structures,
and that determine their radiative properties. These, in turn, are fundamental
for the development and validation of models. Current ground-based facilities
(e.g., Dunn Solar Telescope, Swedish Solar Tower, Phil Goode Solar Telescope,
GREGOR Solar Telescope) and space-based facilities (e.g., HINODE, IRIS) allow
the Sun to be observed at sub-arcsecond spatial resolution (corresponding to a
few hundred kilometers on the Solar surface), at high temporal cadence, and at
moderate-to-high spectral resolution. These facilities also typically support
spectropolarimetric observations to infer properties of the magnetic fields.
The five first-light instruments of the upcoming NSF Daniel K. Inouye Solar
Telescope (DKIST, Rimmele et al., 2020) will provide solar observations at
unprecedented spatial and temporal resolution, at high spectropolarimetric
sensitivity, and in a wide spectral range (380–5000 nm) that will allow
observations of the Sun from the base of the photosphere to the corona.
Synergistic observations in the millimeter spectral range with ALMA and in the
UV with IRIS will provide essential information to validate and improve
modeling, especially of the chromosphere and corona. Finally, the recently
launched Solar Orbiter (Müller et al., 2020) will observe for the first time
polar magnetic fields at sub-arcsecond spatial resolution, thus providing
essential information to improve our understanding of the global dynamo and of
the radiative emission of faculae at high latitude.

Although breakthrough discoveries are expected in the understanding of the
multi-scale, dynamical processes occurring in the solar atmosphere, it should
be noted that, because detailed information about physical and magnetic
properties of plasma are derived from the analysis of spectral and
spectropolarimetric observations, current and future solar facilities
typically acquire data at high spectral resolution in relatively narrow
spectral ranges (usually not more than $\sim$1 nm). For the purposes of
studying the impact of stellar variability on both planetary atmospheres
themselves and our observations of them, however, we are often interested in
variability over wider—and sometimes poorly studied—spectral ranges (e.g.,
Ermolli et al., 2013; Matthes et al., 2017). UV variability, in particular, is
known to affect planetary atmospheres and their habitability (Linsky, 2017),
but unfortunately, this is also the region in which models present the largest
discrepancies. Additionally, with the exception of IRIS, which has been
providing solar spectra in three UV regions since 2012, spatially and
spectrally resolved observations in the UV and shorter wavelength ranges,
necessary to validate and improve models are scarce (Criscuoli, 2019). Most of
spatially and spectrally resolved observations in the UV/EUV ranges have been
so far rocket- or balloon-born, such as the recently launched (2015)
Chromospheric Lyman-Alpha Spectro-Polarimeter (CLASP) or the 2019
Chromospheric Layer Spectropolarimeter (CLASP2), which have collected
spectropolarimetric data in the Mg ii h & k range (Narukage et al., 2016). The
Sunrise UV Spectropolarimeter and Imager (Feller et al., 2020) aboard the
SUNRISE III balloon, scheduled for launch in 2022, will provide for the first
time sub-arcsecond, spectropolarimetric observations of the Sun in the near-UV
(300–400 nm) at a spectral resolution of $\sim$2 nm. The SUIT instrument on
the Indian Aditya-L1 space mission to be launched early 2022 will, for the
first time, image the Sun in both broad and narrow spectral bands in the UV
range from 200 to 400 nm (Ghosh et al., 2016).

####  5.2.2 Studying the Sun as a resolved planetary host

In addition to using the Sun to learn about other stars, the planets in our
Solar System provide opportunities to learn about exoplanets. Several “Earth
as an exoplanet” studies have discussed the potential of using observations of
the Earth from past planetary science missions (fly-bys) or current Earth
science missions (e.g., EPOXI/DISCOVR) to identify key features that are
observable for exoplanets (e.g., Cowan et al., 2009; Llama & Shkolnik, 2015,
2016; Berdyugina & Kuhn, 2019). Recently, Mayorga et al. (2021) proposed that
a small spacecraft at Earth-Sun L2 could potentially observe transits of the
Earth and Moon across the Sun during periods of high activity. These
observations would provide several means towards understanding the biases
imparted on transmission spectra from active regions. For example, knowing a
priori that a planet transits a star with numerous active regions and has a
flat transmission spectrum (because the planet has no atmosphere, a high mean-
molecular-weight atmosphere, or high gravity) would provide a testing ground
for understanding the effects of occulted and unocculted active regions on the
planet’s measured transmission spectrum. Such an experiment would benefit from
our knowledge of the properties of active regions from ground-based solar
telescopes, thus providing quantitative points of comparison with the ground
truth for active regions of various temperatures and sizes.

####  5.2.3 Our finding

From this analysis, we draw the following finding.

Finding 5.1

Summary: Our understanding of stellar photospheric heterogeneity and its
impact on observations of transiting exoplanets is informed greatly by studies
of the Sun. While many suitable facilities exist to study the Sun as a star,
the field would benefit from additional capabilities to study planetary
transits of the Sun.

Capability Needed: Resolved observations of the Sun in the visible and IR are
needed to study spectral variations of active regions on minute-to-year
timescales. Observations of planetary bodies transiting the Sun, either
resolved or unresolved, are needed to provide the ground-truth for
exoplanetary transits.

Capability Today: Many ground- and space-based facilities exist to study the
Sun as a resolved star. No dedicated facilities exist to study planetary
transits of the Sun.

Mitigation in Progress: DKIST will provide sensitive solar observations with
unprecedented spatial and temporal resolution and across a wide spectral range
of interest to exoplanetary transit observations (380–5000 nm).

###  5.3 Observations of exoplanetary host stars

Understanding stellar activity, both the observations and the theory behind
what physical processes drive the observations, requires a multiwavelength,
multi-facility approach. Here we describe useful avenues to better constrain
exoplanet host stars in upcoming years in the context of photometry, UV
observations, and advances in interferometry.

####  5.3.1 Photometric approaches to constrain active-region parameters

##### Long-baseline photometry.

Precise, time-domain photometric surveys (e.g., CoRoT, Kepler, K2, and TESS)
have revolutionized our understanding of stellar activity by enabling the
measurements of stellar flares and stellar rotation for a wide range of
spectral types. As discussed in Section 3.3.2, long-baseline photometry of
exoplanet host stars can be used effectively to monitor for epoch-to-epoch
stellar variability (e.g., Knutson et al., 2012; Sing et al., 2015; Mallonn &
Strassmeier, 2016; Mallonn et al., 2018; Zellem et al., 2017; Mansfield et
al., 2018; Kilpatrick et al., 2020; Rosich et al., 2020). Complementary
observations from the ground allow us to place comparatively temporally-
limited observations with space-based observatories into a larger baseline to
explore whether any observed variations can be attributed to the variability
of the host star. These observations can be conducted on a variety of
platforms, from automatic robotic telescopes (e.g., Dukes, 1992) to even
6-inch-class telescopes, which have the potential to observe even a relatively
dim 11.3 V-mag host star with a per-minute precision of 0.67% (Zellem et al.,
2020). From space, the recently selected Pandora SmallSat Mission (Quintana et
al., 2021) will explore the potential of small telescopes (0.45 m) to reliably
constrain stellar photospheres and exoplanetary atmospheres by collecting
multi-epoch, long-baseline transit observations of active K- and M-type
exoplanet hosts with simultaneous visible photometry and NIR spectroscopy.

##### Multiband photometry.

While photometric monitoring of exoplanet host stars can give insights into
their epoch-to-epoch variability, detailed modeling of the stellar activity is
generally limited by degeneracies between the spot temperature and spot size.
For instance, a small, cool spot can produce the same amount of flux to first
order as a large, comparatively warm/bright spot. As discussed in Section
3.3.1, however, multiband photometry can provide the necessary constraints to
resolve this degeneracy and better understand the impact of active regions on
stellar spectral contamination in exoplanetary transmission spectra. For
example, TiO forms in cooler spots but dissociates at hotter temperatures
(Mirtorabi et al., 2003; Berdyugina et al., 2003). Therefore, one can perform
simultaneous observations of the host star both inside the TiO band and just
outside to provide measurements of the starspot temperature and, thus, its
size (e.g., Zellem et al., 2010). Such a study was done of the
chromospherically active star IM Peg using the relatively small 0.75-m Four
College Consortium telescope (Dukes, 1992) as well as spectroscopy with the
2.5-m Nordic Optical Telescope (Berdyugina et al., 1999). This study and
others like it show that, while these observations can be time-consuming, they
potentially could be shifted to smaller telescopes, alleviating the need for
larger telescopes (Zellem et al., 2020). Here too the Pandora SmallSat Mission
(Quintana et al., 2021) will provide a relevant space-based counterpart with
its simultaneous visible photometry and NIR spectroscopy designed to uniquely
identify the properties of heterogeneous photospheres with absolutely
calibrated, multi-epoch observations.

##### Existing datasets and underutilized avenues for photometry.

Existing single- or multi-band photometry may be available for a given
exoplanet host, given the abundance of existing time-domain photometric
surveys, including those searching for transiting exoplanets, such as Kepler
(Borucki et al., 2010), TESS (Ricker et al., 2014), HAT-P (Bakos et al.,
2004), WASP (Pollacco et al., 2006), HATS (Bakos et al., 2013), MEarth
(Nutzman & Charbonneau, 2008), NGTS (Wheatley et al., 2018), SPECULOOS (Delrez
et al., 2018), EDEN (Gibbs et al., 2020), and more. If data is not already
available from a targeted or wide-field survey, monitoring the star over
multiple rotation periods could be time-consuming. Spun-down M dwarfs, for
example, can have periods as long as 140 days (Newton et al., 2018). However,
while monitoring exoplanet host stars over multiple rotation periods is
challenging due to the oversubscription of professional observatories, there
is the opportunity for amateur astronomers to contribute. For example, the
American Association of Variable Star Observers (AAVSO) has been observing
variable stars for $\sim$100 years and has over 2 million stars in its
Variable Star Index (VSX, Watson et al., 2006).

##### High-cadence photometry.

Finally, obtaining high-cadence photometry will help in a number of areas.
TESS recently introduced a 20-sec cadence mode, which can be used to resolved
short-duration activity such as flares, but the number of stars observed at
short cadence is typically limited. High-cadence observations which fully
resolve the ingress and egress of the transit can independently constrain the
planetary radius even when the transit is contaminated by significant spot
occultation events (Morris et al., 2018b).

####  5.3.2 UV observations to inform models of host-star atmospheres

With the wealth and quality of existing solar observations, highly
sophisticated semi-empirical models of the Sun have been developed, including
complex models of spots, flares, and other magnetic phenomena (See Section 1).
Extensive modeling efforts have furthered our understanding of the solar
interior, the detailed structure in the upper atmosphere, and the solar
activity cycle and associated energetic events. Due to the disparity in the
quality and quantity of X-ray–NUV spectra of lower-mass, planet-host stars,
including K and M dwarfs, the current state-of-the-art for stellar atmosphere
models is not at the same level as solar models. Stellar modeling efforts
would greatly benefit from a future EUV/FUV/NUV dedicated mission with time-
dependent measurements to improve our understanding of active-region coverage
and temperature, and flare frequency, size, and color on these low-mass,
planet-host stars. With this knowledge, composite semi-empirical models of
stellar atmospheres could be developed, complete with accurate precision
modeling of photospheric and chromospheric heterogeneities that would, amongst
other things, advance the general understanding of stellar atmospheres and
improve our ability to disentangle the stellar and planetary contributions
from UV transit spectra.

####  5.3.3 Constraining host-star surface inhomogeneities through
interferometric imaging

##### Global surface temperature maps.

Stellar surfaces have been indirectly imaged for decades using Doppler imaging
(e.g., Berdyugina, 2005; Strassmeier, 2009; Korhonen et al., 2021) and light-
curve imaging (e.g., Lanza et al., 1998; Berdyugina et al., 2002;
Roettenbacher et al., 2013) in order to detect surface inhomogeneities, such
as starspots and faculae (see also Section 1). In these methods, either high-
resolution spectra or photometric observations are used to obtain maps of the
stellar surface with inversion methods. Light-curve inversion imaging
reconstructs the stellar surface based upon the observed brightness
fluctuations. Doppler imaging utilizes the evolution of distortions of
absorption lines caused by surface features rotating in and out of view to
reconstruct the features of the stellar surface. Both methods suffer from
degeneracies, especially for the latitudinal information of the spots. The
determination of starspot latitudes is constrained in light-curve inversion
with limb-darkening laws and estimated coefficients, while in Doppler imaging
with the location of the spot feature within absorption line profiles and the
speed at which it crosses the profile as the star rotates. While the light-
curve method cannot provide starspot latitudes, the Doppler imaging can locate
spot latitudes and longitudes within the stellar hemisphere that is best
visible to the observer with respect to the equator, as was demonstrated by
modeling various spots (e.g., Vogt & Penrod, 1983; Piskunov et al., 1990;
Berdyugina, 1998).

In recent years, advances in long-baseline optical/near-infrared
interferometry have enabled the direct-imaging of starspots on stellar
surfaces (Roettenbacher et al., 2016, 2017; Parks et al., 2021; Martinez et
al., 2021). This is the only method that can obtain reliable, unambiguous
information of the spot locations in latitude and longitude within both
stellar hemispheres relative to the equator. However, the targets currently
accessible with present interferometric resources are limited, as this
technique requires very bright targets with spots that appear large enough on
the sky. Additionally, obtaining a complete image of the stellar surface
requires repeated observations with phase coverage across a rotation. This can
require large amounts of dedicated observing time. The relative rate of
evolution of the surface structure compared to the stellar rotation must also
be considered.