# Hubble Space Telescope transmission spectroscopy for the temperate sub-
Neptune TOI-270d: a possible hydrogen-rich atmosphere containing water vapour

Thomas Mikal-Evans Max Planck Institute for Astronomy, Königstuhl 17, D-69117
Heidelberg, Germany  Nikku Madhusudhan Institute of Astronomy, University of
Cambridge, Madingley Road, Cambridge CB3 0HA, UK  Jason Dittmann  Department
of Astronomy, University of Florida, 211 Bryant Space Science Center,
Gainesville, FL 32611, USA  Maximilian N. Günther European Space Agency (ESA),
European Space Research and Technology Centre (ESTEC), Keplerlaan 1, 2201 AZ
Noordwijk, The Netherlands  Luis Welbanks School of Earth & Space Exploration,
Arizona State University, Tempe, AZ, 85257, USA  Vincent Van Eylen  Mullard
Space Science Laboratory, University College London, Holmbury St Mary,
Dorking, Surrey RH5 6NT, UK  Ian J. M. Crossfield  Department of Physics and
Astronomy, University of Kansas, Lawrence, KS, USA  Tansu Daylan Department of
Astrophysical Sciences, Princeton University, 4 Ivy Lane, Princeton, NJ 08544
Laura Kreidberg  Max Planck Institute for Astronomy, Königstuhl 17, D-69117
Heidelberg, Germany

(Received July 5, 2022; Revised October 30, 2022; Accepted November 22, 2022)

###### Abstract

TOI-270 d is a temperate sub-Neptune discovered by the Transiting Exoplanet
Survey Satellite (TESS) around a bright ($J=9.1$ mag) M3V host star. With an
approximate radius of $2\,R_{\earth}$ and equilibrium temperature of 350 K,
TOI-270 d is one of the most promising small exoplanets for atmospheric
characterisation using transit spectroscopy. Here we present a primary transit
observation of TOI-270 d made with the Hubble Space Telescope (HST) Wide Field
Camera 3 (WFC3) spectrograph across the 1.126-1.644 $\mu\textnormal{m}$
wavelength range, and a 95% credible upper limit of $8.2\times 10^{-14}$ erg
s-1 cm-2 Å-1 arcsec-2 for the stellar Ly$\alpha$ emission obtained using the
Space Telescope Imaging Spectrograph (STIS). The transmission spectrum derived
from the TESS and WFC3 data provides evidence for molecular absorption by a
hydrogen-rich atmosphere at ${4\sigma}$ significance relative to a featureless
spectrum. The strongest evidence for any individual absorber is obtained for
H2O, which is favoured at 3$\sigma$ significance. When retrieving on the WFC3
data alone and allowing for the possibility of a heterogeneous stellar
brightness profile, the detection significance of H2O is reduced to
2.8$\sigma$. Further observations are therefore required to robustly determine
the atmospheric composition of TOI-270 d and assess the impact of stellar
heterogeneity. If confirmed, our findings would make TOI-270 d one of the
smallest and coolest exoplanets to date with detected atmospheric spectral
features.

††journal: AAS Journals††software: NumPy (van der Walt et al., 2011), SciPy
(Virtanen et al., 2020), Matplotlib (Hunter, 2007), emcee (Foreman-Mackey et
al., 2013), batman (Kreidberg, 2015), Astropy (Astropy Collaboration et al.,
2013, 2018), pysynphot (STScI Development Team, 2013), PyMultinest (Buchner et
al., 2014b)††facilities:  HST(WFC3), Spitzer(IRAC), TESS ††thanks: ESA
Research Fellow††thanks: NHFP Sagan Fellow††thanks: LSSTC Catalyst Fellow

##  1 Introduction

Sub-Neptunes are the population of planets with radii smaller than that of
Neptune and larger than approximately $1.8\,R_{\earth}$. The latter
corresponds to the location of the “radius valley” uncovered by the NASA
Kepler survey, which divides small planets between those with volatile-poor
and volatile-rich compositions (Fulton et al., 2017; Van Eylen et al., 2018;
Petigura et al., 2022). Measured densities for the volatile-rich sub-Neptunes
can be explained by a variety of compositions with varying core-mass fractions
and envelopes of volatiles such as hydrogen and water (Figueira et al., 2009;
Rogers & Seager, 2010). The measurement of sub-Neptune atmospheric spectra can
help break this degeneracy by providing a direct probe of the composition of
the uppermost layers of the outer envelope.

The observing strategy employed by the NASA Transiting Exoplanet Survey
Satellite (TESS) (Ricker et al., 2015) since 2018 is well suited for
discovering short-period planets that subsequently make excellent targets for
detailed atmospheric studies (Sullivan et al., 2015; Barclay et al., 2018;
Guerrero et al., 2021; Kunimoto et al., 2022). Most significantly, TESS has
observed around 90% of the sky, meaning that a substantial fraction of all
nearby bright stars have now been monitored for planetary transits with
complete phase coverage out to orbital periods of approximately 10 days. This
includes the majority of nearby M dwarfs, around which smaller planets such as
sub-Neptunes can be more readily detected compared to those orbiting earlier
spectral type hosts, thanks to the relatively deep transit signals that they
produce. As of October 2022, the NASA Exoplanet
Archive111https://exoplanetarchive.ipac.caltech.edu reports that there have
been seventeen transiting exoplanets with radii falling in the
1.8-4$\,R_{\earth}$ sub-Neptune range, validated around bright ($J<10$ mag) M
dwarfs. Of these, TESS has discovered twelve, namely: AU Mic b and AU Mic c
(Plavchan et al., 2020; Martioli et al., 2021); TOI-1634 b (Cloutier et al.,
2021; Hirano et al., 2021); TOI-270 c and TOI-270 d (Günther et al., 2019);
TOI-776 b and TOI-776 c (Luque et al., 2021); TOI-1201 b (Kossakowski et al.,
2021); TOI-1231 b (Burt et al., 2021); TOI-1266 b (Demory et al., 2020;
Stefánsson et al., 2020); LTT3780 c (Cloutier et al., 2020; Nowak et al.,
2020); and GJ 3090 b (Almenara et al., 2022). The other five planets that have
been validated to date around bright M dwarfs and with radii between
approximately 1.8-4$\,R_{\earth}$ are: GJ 436 b (Gillon et al., 2007); GJ 1214
b (Charbonneau et al., 2009); K2-3 b and K2-3 c (Crossfield et al., 2015); and
K2-18 b (Montet et al., 2015). Meanwhile, there are currently 57 additional
sub-Neptune candidates that have been identified by TESS around bright M
dwarfs and that are listed as high priority targets for follow-up
confirmation.222https://exofop.ipac.caltech.edu/tess

This paper presents transmission spectroscopy measurements for the TESS-
discovered sub-Neptune TOI-270 d/L 231-32 d (Günther et al., 2019; Van Eylen
et al., 2021; Kaye et al., 2022), made using the Hubble Space Telescope Wide
Field Camera 3 (HST WFC3). TOI-270 d has a radius of $2.00\pm
0.05\,R_{\earth}$ measured in the TESS red-optical passband and a mass of
$4.20\pm 0.16\,M_{\earth}$, corresponding to a bulk density of $2.90\pm 0.24$
g cm-3 (Kaye et al., 2022). It orbits an M3V host star at a distance of 0.07
AU with an orbital period of $11.4$ days. This places TOI-270 d just inside
the inner edge of the habitable zone, where it has an equilibrium temperature
of around 350 K assuming a Bond albedo of 30% and uniform day-night heat
redistribution.333Earth, Jupiter, Saturn, Uranus, and Neptune all have Bond
albedos close to 30%. There are two other transiting planets known to orbit
the same host star (Günther et al., 2019): TOI-270 b, a $1.3\,R_{\earth}$
super-Earth on a 0.03 AU orbit; and TOI-270 c, a $2.3\,R_{\earth}$ sub-Neptune
on a 0.05 AU orbit. The TOI-270 host star appears to be quiescent, with TESS
photometry showing no evidence for variability, either due to flares or
brightness fluctuations caused by stellar heterogeneities (i.e. faculae and
spots) rotating into and out of view (Günther et al., 2019). Additional
indicators — such as H$\alpha$, the S-index, and a lack of radial velocity
jitter (root-mean-square of $0.16\pm 0.23$ m s-1) — are also consistent with a
low stellar activity level (Van Eylen et al., 2021). To further characterise
the host star, in this study we also present new constraints for the stellar
Ly$\alpha$ emission obtained with the HST Space Telescope Imaging Spectrograph
(STIS).

The paper is organised into the following sections. Observations are described
in Sections 2. Analyses of the WFC3 and STIS data are presented in Sections 3
and 4, respectively. Atmospheric retrieval analyses are presented in Section
5. Discussion and conclusions are given in Sections 6 and 7, respectively.

##  2 Observations

A transit of TOI-270 d was observed with HST on 2020 October 6 as part of
program GO-15814 (Mikal-Evans et al., 2019b). Data were acquired over three
consecutive HST orbits, with the first and third orbits providing,
respectively, pre-transit and post-transit reference levels for the stellar
brightness. The second HST orbit coincided with the planetary transit, which
has a duration of 2.117 hours (Kaye et al., 2022).

The transit observation was made using the infrared channel of WFC3 with the
G141 grism, covering the 1.126-1.644 $\mu\textnormal{m}$ wavelength range.
During each exposure, the spectral trace was allowed to drift along the cross-
dispersion axis of the detector using the round-trip spatial-scanning
observing mode (Deming et al., 2013; McCullough et al., 2014), with a scan
rate of 0.111 arcsec s-1. A $512\times 512$ pixel subarray containing the
target spectrum was read out for each exposure using the SPARS25 pattern with
seven non-destructive reads per exposure (NSAMP=7), corresponding to
individual exposure times of 138 seconds. With this setup, 15 exposures were
taken during the first HST orbit following target acquisition, and 16
exposures were taken in both the second and third HST orbits. A single shorter
exposure (NSAMP=3) was also taken at the end of the second and third HST
orbits, due to anticipated overrun of the target visibility window (i.e. the
target being lost from view before a full exposure could be completed). These
latter shorter exposures were ultimately discarded from the subsequent
analysis.

To characterise the Ly$\alpha$ emission of the host star, two additional
observations were made with HST on 2020 January 29 and 31 as part of the same
observing program, using HST STIS with the $52\times 0.05$ arcsec slit and the
G140M grating centered at 1,222Å. For each STIS observation, data were
collected for 1,960 seconds using TIME-TAG mode. Both exposures were timed to
avoid transits of the three known planets in the TOI-270 system, as the goal
was to calibrate the absolute emission level of the host star.

##  3 WFC3 analysis: transmission spectroscopy

The WFC3 transit data were reduced using the custom Python code described
previously in Evans et al. (2016) and since used in numerous other studies
(e.g. Mikal-Evans et al., 2019a, 2020). Individual exposures were provided by
the WFC3 pipeline as FITS files with IMA suffixes, for which basic
calibrations have already been applied, such as flat fielding, linearity
correction, and bias subtraction. For a given calibrated IMA exposure,
background counts were determined for each non-destructive read by taking the
median value of a $20\times 120$ pixel box away from the target spectrum. For
each IMA frame, the differences between successive, background-subtracted,
non-destructive reads were computed. These read-differences correspond to
“stripes” of flux that span the cross-dispersion rows scanned between each
read. The flux-weighted cross-dispersion centroids of these stripes were
determined and all rows more than 50 pixels above and below the stripe
centroids were set to zero to mask contaminating contributions, such as
neighbouring stars and cosmic ray strikes. The masked stripes were then summed
together to form reconstructed data frames. For each of these reconstructed
data frames, the final flux-weighted cross-dispersion centroid was determined
and 1D spectra were extracted by summing all pixels along the cross-dispersion
axis within 120 pixels above and below the centroid row. The wavelength
solution was obtained by cross-correlating the 1D spectrum extracted from the
final exposure against a model stellar spectrum multiplied by the G141
throughput profile. The Python package pysynphot (STScI Development Team,
2013) was used to obtain the model stellar spectrum: namely, a Kurucz 1993
model spectrum with properties close to those reported by Günther et al.
(2019) for the TOI-270 host star ($T_{\textnormal{eff}}=3500$ K,
$\log_{10}g=4.88$ cgs, $[{\rm{Fe}/\rm{H}}]=-0.17$ dex).

###  3.1 Broadband transit light curve

A broadband light curve was generated by integrating the flux for each 1D
spectrum across the $0.8$-$1.95\,\mu\textnormal{m}$ wavelength range, to
conservatively encompass the full G141 passband. The light curve was then
fitted by simultaneously modelling the planetary transit signal and
instrumental systematics.

For the planetary transit signal, we used the batman software package
(Kreidberg, 2015). The planetary parameters allowed to vary in the fitting
were: the planet-to-star radius ratio ($R_{p}/R_{\star}$); the deviation of
the transit mid-time ($\Delta T_{c}$) from the mid-time predicted by Kaye et
al. (2022); the normalised semimajor axis ($a/R_{\star}$); and the transit
impact parameter ($b=a\cos i/R_{\star}$, where $i$ is the orbital
inclination). Uniform priors were adopted for $R_{p}/R_{\star}$ and $\Delta
T_{c}$. The posterior distributions for $a/R_{\star}$ and $b$ obtained by Kaye
et al. (2022) were adopted as Gaussian priors in the light curve fitting,
namely: $a/R_{\star}=41.744\pm 0.527$ and $b=0.23\pm 0.08$. The orbital period
was held fixed to $P=11.38194$ based on the value reported by Kaye et al.
(2022).

For the stellar brightness profile, we assumed a quadratic limb darkening law.
Both limb darkening coefficients were allowed to vary during the light curve
fitting, but due to the incomplete phase coverage of the transit, tight
Gaussian priors were adopted. The latter were obtained by providing the
measured values and uncertainties for the stellar properties reported by Van
Eylen et al. (2021) as input to the PyLDTK software package (Parviainen &
Aigrain, 2015), along with the G141 throughput profile. This resulted in
Gaussian priors of the form $u_{1}=0.1611\pm 0.0002$ and $u_{2}=0.1379\pm
0.0008$.

Table 1: TOI-270 d system properties and broadband light curve fit results. Fixed properties have been taken from Günther et al. (2019) and Kaye et al. (2022).  Fixed | Parameter | Value
---|---|---
|  $R_{\star}$ ($R_{\odot}$) | $0.380$
|  $P$ (d) | $11.38014$
| $e$ | $0$
Free | Parameter | Posterior
| $R_{p}/R_{\star}$ | $0.05278_{-0.00118}^{+0.00095}$
| $a/R_{\star}$ | $41.80_{-0.59}^{+0.61}$
| $b$ | $0.233_{-0.085}^{+0.089}$
|  $\Delta T_{1}$ (min) | $-4_{-8}^{+10}$
| $u_{1}$ | $0.1611_{-0.0002}^{+0.0002}$
| $u_{2}$ | $0.1378_{-0.0009}^{+0.0009}$
| $\beta$ | $3.0_{-0.4}^{+0.5}$
Derived | Parameter | Posterior
|  $(R_{p}/R_{\star})^{2}$ (ppm) | $2786_{-124}^{+101}$
|  $R_{p}$ ($R_{\earth}$) | $2.19_{-0.07}^{+0.07}$
| $\cos i$ | $0.0056_{-0.0020}^{+0.0021}$
|  $i$ (∘) | $89.68_{-0.12}^{+0.12}$
|  $T_{1}$ (JD${}_{{\textnormal{{UTC}}}}$) | $2459129.34868_{-0.00544}^{+0.00691}$

We modelled the systematics using a Gaussian process (GP) model, with
covariance described by the sum of two squared-exponential kernels that took
time $t$ and the HST orbital phase $\varphi$ as input variables. For the GP
mean function, the transit signal was multiplied by a deterministic
systematics signal of the form $S_{d}(t,\varphi)=(c_{d}+\gamma
t)\,D(t,\varphi)$, where: $c_{d}$ is a normalisation constant for scan
direction $d$ (i.e. forward or backward); $\gamma$ is the slope of a linear
$t$-dependent baseline trend shared by the two scan directions; and $D$ is an
analytic model for the electron charge-trapping systematics that affect the
WFC3 detector (Zhou et al., 2017). For the latter, the same double-exponential
ramp function described in Mikal-Evans et al. (2022) was adopted, which has
five free parameters ($a_{1}$, $a_{2}$, $a_{3}$, $a_{4}$, $a_{5}$). To allow
for additional high-frequency noise not captured by the systematics model, the
Gaussian measurement uncertainties were allowed to vary in the fitting via a
free parameter $\beta$ that rescaled the photon noise. For further details on
the implementation of this systematics treatment, see Mikal-Evans et al.
(2021).

Figure 1: Circles show the raw WFC3 broadband transit light curve for TOI-270
d as the relative variation of received flux over time. There is an offset in
the flux levels measured for the forward scan and backward scan exposures. Red
lines show the maximum-likelihood light curve model. The root-mean-square
(RMS) of the model fit residuals is printed in the lower right corner of the
axis. Yellow shading indicates the time between transit ingress and egress.
Figure 2: (a) Circles show the measured broadband light curve after dividing
through by the systematics component of the maximum-likelihood model.
Measurement uncertainties are approximately the same size as the circles. Red
line shows the transit component of the maximum-likelihood model. (b) Circles
show residuals of the maximum-likelihood model with $1\sigma$ photon noise
measurement uncertainties. Blue square with errorbar on the right of the axis
indicates the size of the rescaled measurement uncertainties obtained from the
model fit, i.e. the photon noise multiplied by the maximum likelihood $\beta$
value.

Uniform priors were adopted for all transit signal parameters, with the
exception of the Gaussian priors described above for $a/R_{\star}$, $b$,
$u_{1}$, and $u_{2}$. Marginalisation of the posterior distribution was
performed using affine-invariant Markov chain Monte Carlo, as implemented by
the emcee software package (Foreman-Mackey et al., 2013), using 300 walkers
and 1000 steps, with the first 500 steps discarded as burn-in. The maximum-
likelihood model is shown in Figure 1 and the systematics-corrected light
curve with corresponding transit model is shown in Figure 2. The root-mean-
square of residuals for the maximum-likelihood model is 116 ppm, equivalent to
$2.7\times$ the photon noise. Inferred model parameter distributions are
reported in Table 1.

###  3.2 Spectroscopic transit light curves

Following the broadband light curve fitting, spectroscopic light curves were
produced for 28 equal-width channels spanning the
1.126-1.644$\mu\textnormal{m}$ wavelength range using the methodology
described in Mikal-Evans et al. (2021). In brief, a lateral shift in
wavelength and a vertical stretch in flux were applied to the individual 1D
spectra to minimise the residuals relative to a template spectrum. The latter
was chosen to be the 1D spectrum extracted from the final exposure, as it was
used to determine the wavelength solution (Section 3). The resulting residuals
were then binned into the 28 wavelength channels. To produce the final light
curves, transit signals were added to these time series, with the same
properties as those derived from the broadband light curve fit (Section 3.1),
but with limb darkening coefficients fixed to values appropriate for the
wavelength range of each spectroscopic channel, determined in the same manner
described above for the broadband light curve. Using this process, common-mode
systematics were effectively removed from the final spectroscopic light
curves, as well as systematics associated with pointing drifts along the
dispersion axis of the detector.

Fitting of the common-mode-corrected spectroscopic light curves proceeded in a
similar manner to the broadband light curve fitting. The only differences were
that HST orbital phase $\varphi$ was the only input variable provided for the
squared-exponential covariance kernel, and for the mean function the transit
signal was multiplied by a $t$-dependent linear trend to capture the remaining
systematics not removed by the common-mode correction. As for the broadband
light curve fit, white noise rescaling factors $\beta$ were included as free
parameters for each spectroscopic light curve, with uniform priors. The only
transit parameters allowed to vary in the spectroscopic light curve fits were
$R_{p}/R_{\star}$ and the quadratic limb darkening coefficients ($u_{1}$,
$u_{2}$) for each of the separate spectroscopic light curves. Uniform priors
were adopted for the $R_{p}/R_{\star}$ values and tight Gaussian priors
obtained using PyLDTK were adopted for the $u_{1}$ and $u_{2}$ values, as
described in Section 3.1. Alternative treatments of the stellar limb darkening
were found to have a negligible effect on the final results and are described
in Appendix A. Values for $T_{c}$, $a/R_{\star}$, and $b$ were held fixed to
the maximum-likelihood values determined from the broadband light curve fit.

Table 2: Spectroscopic light curve fit results.  Wavelength | $R_{p}/R_{\star}$ | $\left(R_{p}/R_{\star}\right)^{2}$
---|---|---
($\mu$m) |  | (ppm)
1.126-1.144 | $0.05299_{-0.00094}^{+0.00097}$ | $2808_{-99}^{+104}$
1.144-1.163 | $0.05305_{-0.00075}^{+0.00073}$ | $2815_{-79}^{+78}$
1.163-1.181 | $0.05239_{-0.00071}^{+0.00071}$ | $2745_{-74}^{+75}$
1.181-1.200 | $0.05215_{-0.00077}^{+0.00077}$ | $2720_{-80}^{+81}$
1.200-1.218 | $0.05270_{-0.00061}^{+0.00059}$ | $2777_{-64}^{+62}$
1.218-1.237 | $0.05169_{-0.00077}^{+0.00069}$ | $2671_{-79}^{+72}$
1.237-1.255 | $0.05226_{-0.00066}^{+0.00069}$ | $2731_{-69}^{+73}$
1.255-1.274 | $0.05187_{-0.00073}^{+0.00066}$ | $2691_{-75}^{+69}$
1.274-1.292 | $0.05215_{-0.00050}^{+0.00055}$ | $2720_{-51}^{+58}$
1.292-1.311 | $0.05341_{-0.00059}^{+0.00061}$ | $2853_{-63}^{+66}$
1.311-1.329 | $0.05187_{-0.00061}^{+0.00066}$ | $2691_{-63}^{+69}$
1.329-1.348 | $0.05297_{-0.00066}^{+0.00068}$ | $2806_{-70}^{+72}$
1.348-1.366 | $0.05456_{-0.00071}^{+0.00065}$ | $2976_{-77}^{+71}$
1.366-1.385 | $0.05433_{-0.00063}^{+0.00065}$ | $2952_{-68}^{+71}$
1.385-1.403 | $0.05360_{-0.00065}^{+0.00060}$ | $2873_{-69}^{+65}$
1.403-1.422 | $0.05273_{-0.00061}^{+0.00059}$ | $2780_{-64}^{+62}$
1.422-1.440 | $0.05325_{-0.00071}^{+0.00068}$ | $2836_{-75}^{+73}$
1.440-1.459 | $0.05450_{-0.00053}^{+0.00051}$ | $2971_{-58}^{+55}$
1.459-1.477 | $0.05236_{-0.00078}^{+0.00078}$ | $2741_{-81}^{+82}$
1.477-1.496 | $0.05359_{-0.00062}^{+0.00062}$ | $2872_{-66}^{+67}$
1.496-1.514 | $0.05246_{-0.00080}^{+0.00077}$ | $2752_{-83}^{+81}$
1.514-1.533 | $0.05286_{-0.00069}^{+0.00078}$ | $2794_{-73}^{+83}$
1.533-1.551 | $0.05280_{-0.00084}^{+0.00078}$ | $2788_{-88}^{+83}$
1.551-1.570 | $0.05248_{-0.00059}^{+0.00057}$ | $2754_{-61}^{+60}$
1.570-1.588 | $0.05213_{-0.00072}^{+0.00068}$ | $2718_{-74}^{+71}$
1.588-1.607 | $0.05318_{-0.00065}^{+0.00066}$ | $2828_{-69}^{+71}$
1.607-1.625 | $0.05253_{-0.00066}^{+0.00068}$ | $2759_{-69}^{+72}$
1.625-1.644 | $0.05239_{-0.00052}^{+0.00052}$ | $2745_{-54}^{+55}$

Inferred values for $R_{p}/R_{\star}$ and the corresponding transit depths
$(R_{p}/R_{\star})^{2}$ are reported in Table 2. A median precision of 71 ppm
is achieved for the transit depth measurements across all wavelength channels.
Systematics-corrected light curves are shown in Figure 3 and the inferred
white noise rescaling factors are plotted in Figure 4. Posterior distributions
for the limb darkening coefficients are listed in Table 3 and are effectively
identical to the adopted PyLDTK priors (Appendix A).

Figure 3: (Top panels) Spectroscopic light curves after dividing through by
the systematics component of the maximum likelihood light curve models. Data
are plotted using alternating colours for visual clarity. (Bottom panels)
Maximum likelihood model residuals for each spectroscopic light curve, with
corresponding RMS values printed. Note that the plotted error bars are the
$1\sigma$ photon noise uncertainties, but the white noise values were treated
as free parameters in the model fits as described in the text. Figure 4:
Inferred white noise rescaling factors for each spectroscopic light curve. Red
points show median values with errorbars giving the 68% credible intervals.
The black line shows the maximum likelihood values.

##  4 STIS analysis: stellar Ly$\alpha$

The STIS G140M data were reduced using the standard STIS pipeline (CALSTIS
version 3.4.2). Figure 5 shows the reduced and calibrated two-dimensional
spectra. The geocoronal Ly$\alpha$ emission is clearly visible as a strong
vertical stripe (the horizontal axis is the dispersion direction). Emission
from TOI-270 would lie adjacent to the geocoronal emission due to the Doppler
shift between HST and TOI-270. However, no evidence is visible in either
exposure for emission from TOI-270.

Figure 5: Calibrated HST STIS Ly$\alpha$ observations of TOI-270. (Top)
Calibrated spectrum taken on 2020 January 31. Wavelength dispersion direction
is along the horizontal axis. The bright stripe down the middle is the Earth’s
Ly$\alpha$ geocoronal emission. Ly$\alpha$ emission from TOI-270 would be
visible alongside this line at the Doppler shift corresponding to the velocity
difference between HST and the target. We find no significant evidence of
Ly$\alpha$ emission in this exposure. (Bottom) Identical as above, but for a
second exposure taken on 2020 January 29.

To assess the sensitivity of the STIS data to Ly$\alpha$ emission from
TOI-270, a spectrum was extracted (including the geocoronal emission) at the
target location for each exposure. These data are shown in Figure 6. We note
that during the second observation (2020 January 31), there is an apparent
flux excess redwards of the geocoronal emission line. However, there is no
evidence for this excess in the first observation (2020 January 29).
Furthermore, the derived error bar at this wavelength is $0.6\times 10^{-13}$
erg cm-2 sec-1 Å-1 arcsec-2. Given that the amplitude of the excess is only
about $10^{-13}$ erg cm-2 sec-1 Å-1 arcsec-2, this translates to a $<2\sigma$
detection significance. Therefore we do not believe this feature in the data
to be due to significant emission from TOI-270.

We derive a conservative upper-limit for the stellar Ly$\alpha$ emission from
the data errorbars close to where confusion with the Earth’s emission becomes
significant, and estimate that we could have detected line emission peaking
approximately twice as high as these error bars, and spread over the resolving
power of the instrument. Using this approach, we place a $95\%$ credible upper
limit of $8.2\times 10^{-14}$ erg s-1 cm2 Å-1 arcsec-2 on the Ly$\alpha$
emission of TOI-270.

Figure 6: Ly$\alpha$ emission of TOI-270 for the exposure on 2020-01-29 (red)
and 2020-01-31 (blue). The large emission line is due to the Earth’s
geocoronal emission. The slight bump redwards of this line on the 2020-01-31
data set is suggestive of brief Ly$\alpha$ emission of TOI-270. However, we do
not recover this emission on the other observation. Additionally, we see
comparable noise bursts in other areas of our 2-D spectrum (Figure 5), and
therefore we suggest that we have not detected Ly$\alpha$ emission from
TOI-270.

##  5 Atmospheric retrieval analysis

We use the transmission spectrum of TOI-270 d to retrieve the atmospheric
properties at the day-night terminator region of the planet using the AURA
atmospheric retrieval framework for transmission spectra (Pinhas et al.,
2018). The model assumes a plane-parallel atmosphere in hydrostatic
equilibrium. The temperature structure, chemical composition, and the
properties of clouds/hazes are free parameters in the model. We consider
opacity contributions due to prominent chemical species expected in temperate
hydrogen-rich atmospheres in chemical equilibrium and disequilibrium, which
include H2O, CH4, NH3, CO, CO2, and HCN (e.g. Madhusudhan & Seager, 2011;
Moses et al., 2013; Yu et al., 2021; Hu et al., 2021; Tsai et al., 2021). The
opacities of the molecules were obtained using corresponding line lists from
the HITRAN and Exomol databases: H2O (Rothman et al., 2010), CH4 (Yurchenko &
Tennyson, 2014), NH3 (Yurchenko et al., 2011), CO (Rothman et al., 2010), CO2
(Rothman et al., 2010), and HCN (Barber et al., 2014), and collision-induced
absorption (CIA) due to H2-H2 and H2-He (Richard et al., 2012). The absorption
cross sections are computed from the line lists following Gandhi & Madhusudhan
(2017). Besides molecular absorption, we also consider Rayleigh scattering due
to H2 and parametric contributions from clouds/hazes and stellar heterogeneity
as described in Pinhas et al. (2018). The Bayesian inference and parameter
estimation in the retrievals are conducted using the Nested Sampling algorithm
(Feroz et al., 2009) implemented with the PyMultiNest package (Buchner et al.,
2014a).

Figure 7: Observations and retrieval of the transmission spectrum of TOI-270
d. Top: Retrieval with baseline planetary atmosphere model and no stellar
heterogeneity. Bottom: Retrieval including stellar heterogeneity. Both
retrievals included the TESS (photometric point at 0.8 $\mu$m) and WFC3
(spectrum between 1.1-1.7 $\mu$m) data, shown in red. The blue curve shows the
median-fit model spectrum and the light blue shaded regions show the $1\sigma$
and $2\sigma$ credible ranges. The binned model points for the median-fit
spectrum are shown as yellow circles. Figure 8: Posterior probability
distributions for the atmospheric model parameters of TOI-270 d obtained from
the retrieval without stellar heterogeneity and including both the TESS and
WFC3 data. The inset at the bottom left shows the retrieved values, for the
volume mixing ratios of the molecules ($X_{\rm i}$), isothermal temperature
($T_{0}$), reference pressure in bar ($P_{\rm ref}$), haze amplitude and slope
($a$ and $\gamma$), cloud-top pressure in bar ($P_{c}$) and cloud/haze
covering fraction ($\bar{\phi}$). The retrievals show moderate evidence for
H2O at 3.0 $\sigma$ significance. No other molecules are individually detected
above 2 $\sigma$, and the model does not show any evidence for clouds/hazes in
the observed slant photosphere. The retrieved parameters are reported in Table
4.

###  5.1 Baseline retrieval assuming uniform stellar brightness

We follow a similar approach to the retrieval conducted using AURA for the
temperate sub-Neptune K2-18 b (Madhusudhan et al., 2020). We consider an
isothermal pressure-temperature ($P$-$T$) profile with the temperature as a
free parameter. Assuming a non-isothermal profile does not significantly
influence the results and is not warranted given the data quality (also see
e.g. Constantinou & Madhusudhan, 2022). Our baseline model, therefore,
includes twelve free parameters: volume mixing ratios of the six molecules
noted above ($X_{\rm i}$ for $i\ =$ H2O, CH4, NH3, CO, CO2, HCN); the
isothermal temperature ($T_{0}$); the reference pressure ($P_{\rm ref}$)
corresponding to the planet radius of 2.19 R⊕ derived from the broadband light
curve (Table 1); and four cloud/haze parameters, including the haze amplitude
and slope ($a$ and $\gamma$), cloud-top pressure ($P_{c}$) and cloud/haze
covering fraction ($\phi$). The model fit to the observed spectrum is shown in
Figure 7 and the posterior probability distributions for the model parameters
are shown in Figure 8.

For this baseline model, we find a preference for absorption by a combination
of the molecular species listed above in a hydrogen-rich atmosphere at
4$\sigma$ significance. The significance is derived by comparing the Bayesian
evidence (e.g., Benneke & Seager, 2013; Welbanks & Madhusudhan, 2021) for the
baseline model relative to that obtained for a featureless spectrum, i.e., a
flat line. When considered individually, the evidence in favour of a given
molecule being present in the atmosphere is lower, with the strongest evidence
being obtained for H2O at $3\sigma$ significance. We do not find significant
evidence ($>2\sigma$) for absorption due to any other individual molecules.
The retrieved parameters are reported in Table 4.

Using the baseline model we retrieve the H2O abundance to be
$\log(X_{\rm{H}_{2}\rm{O}})=-1.77^{+0.69}_{-0.93}$. We do not obtain strong
constraints on the volume mixing ratios for any of the other molecules, as
shown in Figure 8. The cloud/haze properties are also poorly constrained, with
the cloud-top pressure retrieved as $\log(P_{\rm c}/{\rm
bar})=-0.77^{+1.63}_{-2.47}$ and a cloud/haze covering fraction of
$0.38^{+0.33}_{-0.23}$, i.e. consistent with a cloud-free slant photosphere at
$2\sigma$. The isothermal temperature is constrained to $247^{+80}_{-68}$ K.

To investigate the extent to which the results described above are driven by
the relative transit depth levels of the TESS and WFC3 passbands, a second
retrieval was performed using only the WFC3 data, with the TESS data point
excluded. Similar to the above case, we still find evidence for H2O in the
planetary atmosphere at 3$\sigma$ significance, with no significant
constraints on any other absorber or clouds/hazes. An H2O abundance of
$\log(X_{\rm{H}_{2}\rm{O}})=-1.92^{+0.74}_{-0.97}$ is obtained, which is fully
consistent with the constraint obtained from the original analysis that
included the TESS data point.

###  5.2 Retrievals allowing for stellar heterogeneity

We also investigate the possibility of a heterogeneous stellar brightness
profile influencing the observed transmission spectrum, as has been suggested
for other temperate sub-Neptune atmospheres (e.g. Rackham et al., 2018;
Barclay et al., 2021). We include the effect of stellar heterogeneity
following Pinhas et al. (2018), by adding three parameters to the baseline
retrieval described in the previous section: the average stellar photospheric
temperature ($T_{\rm phot}$); the average temperature of the heterogeneity
($T_{\rm het}$); and the covering fraction of the heterogeneity ($\delta$).
When considering the WFC3 and TESS data together and allowing for stellar
heterogeneity, we find that the retrieved planetary atmosphere properties do
not change significantly, and the quality of the fit to the data is similar to
that obtained for the retrievals that assumed a homogeneous stellar brightness
profile. With stellar heterogeneity included, we obtain evidence for H2O
absorption in the planetary atmosphere at 3$\sigma$ significance, with a
derived abundance of $\log(X_{\rm{H}_{2}\rm{O}})=-1.91^{+0.74}_{-0.98}$, fully
consistent with the abundances obtained for the retrievals without stellar
heterogeneity. Again, we find no significance evidence for any other chemical
species in the planetary atmosphere. For the star spots, we infer a covering
fraction of $\delta=0.06^{+0.05}_{-0.03}$ and temperature of $T_{\rm
het}=2446^{+1120}_{-988}$ K. The resulting model fit is shown in Figure 7.

When considering the combined TESS and WFC3 dataset, the baseline model
without stellar heterogeneity is favoured over the model with stellar
heterogeneity at $2\sigma$ significance. In both cases, the fit to the data is
primarily driven by the H2O absorption in the planetary atmosphere. The model
with stellar heterogeneity is marginally disfavored due to the larger number
of free parameters that do not contribute significantly to the fit. In
particular, a substantial contamination by stellar heterogeneities would
produce a larger offset between the TESS and WFC3 transit depth levels than
that which is observed (Pinhas et al., 2018).

To determine the information content of the WFC3 data alone, we performed an
additional retrieval including stellar heterogeneity but with the TESS data
point excluded. The resulting model fit is shown in Figure 9. In this case, we
find that the detection significance of H2O is reduced to 2.8$\sigma$ with an
abundance constraint of $\log(X_{\rm{H}_{2}\rm{O}})=-2.09^{+0.89}_{-1.21}$,
which remains consistent with the abundance constraints obtained from the
retrievals that included the TESS data point. Comparing the Bayesian evidences
for WFC3-only retrievals with and without stellar heterogeneity, we find that
there is still no strong preference for contamination by stellar
heterogeneity; the evidence remains marginally higher for the baseline model
without stellar heterogeneity. As an additional check, we performed a
retrieval on the WFC3 data alone assuming a model with a featureless planetary
spectrum and a heterogeneous stellar brightness profile. We find that this
scenario is also disfavored at over $3\sigma$ significance relative to the
baseline retrieval allowing for a planetary atmosphere and not including
stellar heterogeneity. Nevertheless, the marginal detection significance
(2.8$\sigma$) obtained for H2O when allowing for stellar heterogeneity and
considering the WFC3 data alone, and our current inability to definitively
rule out contamination by stellar heterogeneity, implies that more
observations are required to robustly establish the presence of H2O in the
planetary atmosphere.

Figure 9: Retrieved transmission spectrum considering WFC3 data alone and a
model including stellar heterogeneity. The blue curve shows the median-fit
model spectrum and the light blue shaded regions show the $1\sigma$ and
$2\sigma$ credible ranges. The binned model points for the median-fit spectrum
are shown as yellow circles. The TESS data point at 0.8 $\mu$m is not included
in the retrieval but is shown here for comparison.

##  6 Discussion

Although we cannot yet definitively discount the possibility that the measured
transmission spectrum is contaminated by stellar heterogeneity, various
indicators point to the TOI-270 host star being a particularly quiet M dwarf,
likely with an age of at least a billion years. For example, Günther et al.
(2019) report two measurements that are suggestive of a very low stellar
activity level. First, they find an absence of fast rotational modulation,
transit spot crossings, and flares in existing TESS photometry, which spans
nearly three years (non-continuous; see also Kaye et al., 2022). Second, the
same authors detected a shallow H$\alpha$ absorption feature and reported an
absence of Ca H/K emission lines in their reconnaissance spectra. Both
findings are common signs for less active M dwarfs, while active stars would
show H$\alpha$ and Ca H/K in emission (e.g. Cram & Mullan, 1985; Stauffer &
Hartmann, 1986; Robertson et al., 2013). A subsequent study by Van Eylen et
al. (2021) reports a tentative stellar rotation period of $\sim 57$ days
derived from a periodogram analysis of TESS photometry, matching the
expectations for an old, quiet M dwarf (Newton et al., 2016). Van Eylen et al.
additionally analyse HARPS and ESPRESSO radial velocity measurements, which
independently confirm very low stellar activity. For example, the ESPRESSO
radial velocity jitter is constrained to $0.16\pm 0.23$ m s-1, consistent with
zero. Additionally, the lack of Ly$\alpha$ emission detected in the present
study (Section 4) is consistent with a low activity level for the host star.
The low stellar activity level suggested by these various auxiliary indicators
are in line with the preference we obtain for the measured transmission
spectrum being minimally contaminated by stellar heterogeneity (Section 5).

Pending further observations, if we assume for now that the measured WFC3
signal is caused by the atmosphere of TOI-270 d rather than unocculted star
spots, then the retrieved chemical abundances provide initial constraints on
the bulk planetary composition and surface conditions. TOI-270 d has been
predicted to be a candidate Hycean world (Madhusudhan et al., 2021), i.e. an
ocean world with a hydrogen-rich atmosphere capable of hosting a habitable
ocean. The mass ($4.20\pm 0.16M_{\earth}$), broadband radius ($2.17\pm
0.05\,R_{\earth}$), and equilibrium temperature (350 K) of the planet together
allow for a range of internal structures, including (a) a gas dwarf with a
rocky core overlaid by a thick hydrogen-rich atmosphere, (b) a water world
with a steamy atmosphere ($\sim$80-100% H2O volume mixing ratio), and (c) a
Hycean world composed of a water-rich interior and a hydrogen-rich atmosphere.
In this study, we obtain a 99% credible upper limit of 30% for the H2O volume
mixing ratio, thereby precluding a water world with a steamy atmosphere
composed of $>80\%$ H2O. However, more stringent constraints on the
atmospheric molecular abundances will be needed to robustly distinguish
between the gas dwarf versus Hycean world scenarios.

The retrieved H2O abundance provides a tentative constraint on the atmospheric
metallicity of the planet. The H2O abundance we retrieve for TOI-270 d,
$\log(X_{\rm{H}_{2}\rm{O}})=-1.77^{+0.69}_{-0.93}$, is similar to that
reported previously for the sub-Neptune K2-18 b (Madhusudhan et al., 2020),
$\log(X_{\rm{H}_{2}\rm{O}})=-2.11^{+1.06}_{-1.19}$. Assuming all the oxygen in
the atmosphere is in H2O, the retrieved H2O abundance of TOI-270 d corresponds
to an O/H ratio spanning 2-99$\times$ solar, with a median value of $20\times$
solar. This estimate is consistent with the mass-metallicity trend observed
for close-in exoplanets using oxygen as a metallicity indicator (Welbanks et
al., 2019) as well as with theoretical predictions of atmospheric metal
enrichment in low-mass exoplanets, albeit at the lower-end of the
theoretically predicted range (e.g. Fortney et al., 2013).

The derived atmospheric abundances also potentially provide insights into
chemical processes in the atmosphere, which in turn could constrain the
surface conditions. In chemical equilibrium, given the low temperature
($\sim$300-350 K) of the atmosphere, CH4 and NH3 are expected to be the
prominent carbon and nitrogen bearing species, respectively (Madhusudhan &
Seager, 2011; Moses et al., 2013), similar to that seen in the solar system
giant planets. Assuming solar elemental ratios of C/O and N/O, the abundances
of CH4 and NH3 are expected to be $\sim$0.5$\times$ and $\sim$0.2$\times$ the
H2O abundance, respectively. However, while H2O is retrieved in abundance, as
discussed above, we do not retrieve comparable constraints for CH4 and NH3.
The lack of significant evidence for CH4 and NH3 may indicate chemical
disequilibrium in the atmosphere, as also noted for K2-18 b (Madhusudhan et
al., 2020).

Such disequilibrium may result if the base of the outer atmospheric envelope
occurs at a pressure of less than $\sim$ 100 bar and interfaces with an
interior layer of different composition (Yu et al., 2021; Hu et al., 2021;
Tsai et al., 2021). For example, a water ocean below a shallow hydrogen-
dominated envelope can deplete CH4 and NH3 in the observable atmosphere. The
chemical composition inferred for TOI-270 d may, therefore, be consistent with
the presence of a water ocean below the outer hydrogen-rich envelope, similar
to the constraints inferred for the habitable-zone sub-Neptune K2-18 b
(Madhusudhan et al., 2020). However, more precise abundance constraints from
future observations will be required to further elucidate the interior and
surface conditions of TOI-270 d.

##  7 Conclusion

We have presented an atmospheric transmission spectrum for the temperate sub-
Neptune TOI-270 d measured using the HST WFC3 spectrograph, spanning near-
infrared wavelengths 1.126-1.644$\mu\textnormal{m}$. We also used observations
made with the HST STIS spectrograph to place a 95% credible upper limit of
$8.2\times 10^{-14}$ erg s-1 cm2 Å-1 arcsec-2 on the Ly$\alpha$ emission of
the host star. Assuming a homogeneous brightness profile for the stellar disc,
the combined TESS and WFC3 transmission spectrum provides strong ($4\sigma$)
evidence for infrared absorption by the planetary atmosphere. Although the
present data precision make it challenging to uniquely identify the molecules
present, the strongest evidence is obtained for H2O at $3\sigma$ significance.
If we allow for the possibility of a heterogeneous stellar brightness profile
and exclude the TESS point from our analysis, the detection significance of
H2O in the planetary atmosphere is reduced to $2.8\sigma$, but the model is
disfavoured at the $2\sigma$ level relative to the model assuming a
homogeneous stellar brightness profile. Furthermore, even when we allow for
stellar heterogeneity and the TESS point is excluded, the detection of a
planetary atmosphere is still preferred over a featureless planetary spectrum
at more than $3\sigma$ significance.

While the current data broadly favour the detection of a planetary atmosphere
and a homogeneous stellar brightness profile, further observations will be
required to increase the robustness of the H2O detection and to firmly rule
out contamination of the measured signal by stellar heterogeneity. If
verified, the inferred atmospheric H2O abundance of
$\log(X_{\rm{H}_{2}\rm{O}})=-1.77^{+0.69}_{-0.93}$ would imply that TOI-270 d
has a hydrogen-rich outer envelope and is a not water world with a steam-
dominated atmosphere. The constraints obtained for the atmospheric composition
remain compatible with TOI-270 d being a Hycean planet with a water ocean
layer below a hydrogen-rich outer envelope.

## References

  * Almenara et al. (2022) Almenara, J. M., Bonfils, X., Otegi, J. F., et al. 2022, A&A, 665, A91
  * Astropy Collaboration et al. (2013) Astropy Collaboration, Robitaille, T. P., Tollerud, E. J., et al. 2013, A&A, 558, A33
  * Astropy Collaboration et al. (2018) Astropy Collaboration, Price-Whelan, A. M., Sipőcz, B. M., et al. 2018, AJ, 156, 123
  * Barber et al. (2014) Barber, R. J., Strange, J. K., Hill, C., et al. 2014, MNRAS, 437, 1828
  * Barclay et al. (2021) Barclay, T., Kostov, V. B., Colón, K. D., et al. 2021, AJ, 162, 300
  * Barclay et al. (2018) Barclay, T., Pepper, J., & Quintana, E. V. 2018, ApJS, 239, 2
  * Benneke & Seager (2013) Benneke, B., & Seager, S. 2013, ApJ, 778, 153
  * Buchner et al. (2014a) Buchner, J., Georgakakis, A., Nandra, K., et al. 2014a, A&A, 564, A125
  * Buchner et al. (2014b) —. 2014b, A&A, 564, A125
  * Burt et al. (2021) Burt, J. A., Dragomir, D., Mollière, P., et al. 2021, AJ, 162, 87
  * Castelli & Kurucz (2003) Castelli, F., & Kurucz, R. L. 2003, in Modelling of Stellar Atmospheres, ed. N. Piskunov, W. W. Weiss, & D. F. Gray, Vol. 210, A20
  * Charbonneau et al. (2009) Charbonneau, D., Berta, Z. K., Irwin, J., et al. 2009, Nature, 462, 891
  * Cloutier et al. (2020) Cloutier, R., Eastman, J. D., Rodriguez, J. E., et al. 2020, AJ, 160, 3
  * Cloutier et al. (2021) Cloutier, R., Charbonneau, D., Stassun, K. G., et al. 2021, AJ, 162, 79
  * Constantinou & Madhusudhan (2022) Constantinou, S., & Madhusudhan, N. 2022, MNRAS, 514, 2073
  * Cram & Mullan (1985) Cram, L. E., & Mullan, D. J. 1985, ApJ, 294, 626
  * Crossfield et al. (2015) Crossfield, I. J. M., Petigura, E., Schlieder, J. E., et al. 2015, ApJ, 804, 10
  * Deming et al. (2013) Deming, D., Wilkins, A., McCullough, P., et al. 2013, ApJ, 774, 95
  * Demory et al. (2020) Demory, B. O., Pozuelos, F. J., Gómez Maqueo Chew, Y., et al. 2020, A&A, 642, A49
  * Evans et al. (2016) Evans, T. M., Sing, D. K., Wakeford, H. R., et al. 2016, ApJ, 822, L4
  * Feroz et al. (2009) Feroz, F., Hobson, M. P., & Bridges, M. 2009, MNRAS, 398, 1601
  * Figueira et al. (2009) Figueira, P., Pont, F., Mordasini, C., et al. 2009, A&A, 493, 671
  * Foreman-Mackey et al. (2013) Foreman-Mackey, D., Hogg, D. W., Lang, D., & Goodman, J. 2013, PASP, 125, 306
  * Fortney et al. (2013) Fortney, J. J., Mordasini, C., Nettelmann, N., et al. 2013, ApJ, 775, 80
  * Fulton et al. (2017) Fulton, B. J., Petigura, E. A., Howard, A. W., et al. 2017, AJ, 154, 109
  * Gandhi & Madhusudhan (2017) Gandhi, S., & Madhusudhan, N. 2017, MNRAS, 472, 2334
  * Gillon et al. (2007) Gillon, M., Pont, F., Demory, B. O., et al. 2007, A&A, 472, L13
  * Guerrero et al. (2021) Guerrero, N. M., Seager, S., Huang, C. X., et al. 2021, ApJS, 254, 39
  * Günther et al. (2019) Günther, M. N., Pozuelos, F. J., Dittmann, J. A., et al. 2019, Nature Astronomy, 3, 1099
  * Hirano et al. (2021) Hirano, T., Livingston, J. H., Fukui, A., et al. 2021, AJ, 162, 161
  * Hu et al. (2021) Hu, R., Damiano, M., Scheucher, M., et al. 2021, ApJ, 921, L8
  * Hunter (2007) Hunter, J. D. 2007, Computing in Science and Engineering, 9, 90
  * Husser et al. (2013) Husser, T.-O., Wende-von Berg, S., Dreizler, S., et al. 2013, A&A, 553, A6
  * Kaye et al. (2022) Kaye, L., Vissapragada, S., Günther, M. N., et al. 2022, MNRAS, 510, 5464
  * Kossakowski et al. (2021) Kossakowski, D., Kemmer, J., Bluhm, P., et al. 2021, A&A, 656, A124
  * Kreidberg (2015) Kreidberg, L. 2015, PASP, 127, 1161
  * Kunimoto et al. (2022) Kunimoto, M., Winn, J., Ricker, G. R., & Vanderspek, R. K. 2022, AJ, 163, 290
  * Kurucz (1993) Kurucz, R. 1993, ATLAS9 Stellar Atmosphere Programs and 2 km/s grid. Kurucz CD-ROM No. 13. Cambridge, Mass.: Smithsonian Astrophysical Observatory
  * Luque et al. (2021) Luque, R., Serrano, L. M., Molaverdikhani, K., et al. 2021, A&A, 645, A41
  * Madhusudhan et al. (2020) Madhusudhan, N., Nixon, M. C., Welbanks, L., Piette, A. A. A., & Booth, R. A. 2020, ApJ, 891, L7
  * Madhusudhan et al. (2021) Madhusudhan, N., Piette, A. A. A., & Constantinou, S. 2021, ApJ, 918, 1
  * Madhusudhan & Seager (2011) Madhusudhan, N., & Seager, S. 2011, ApJ, 729, 41
  * Martioli et al. (2021) Martioli, E., Hébrard, G., Correia, A. C. M., Laskar, J., & Lecavelier des Etangs, A. 2021, A&A, 649, A177
  * McCullough et al. (2014) McCullough, P. R., Crouzet, N., Deming, D., & Madhusudhan, N. 2014, ApJ, 791, 55
  * Mikal-Evans et al. (2020) Mikal-Evans, T., Sing, D. K., Kataria, T., et al. 2020, MNRAS, 496, 1638
  * Mikal-Evans et al. (2019a) Mikal-Evans, T., Sing, D. K., Goyal, J. M., et al. 2019a, MNRAS, 488, 2222
  * Mikal-Evans et al. (2019b) Mikal-Evans, T., Crossfield, I., Daylan, T., et al. 2019b, Atmospheric characterization of two temperate mini-Neptunes formed in the same protoplanetary nebula, HST Proposal
  * Mikal-Evans et al. (2021) Mikal-Evans, T., Crossfield, I. J. M., Benneke, B., et al. 2021, AJ, 161, 18
  * Mikal-Evans et al. (2022) Mikal-Evans, T., Sing, D. K., Barstow, J. K., et al. 2022, Nature Astronomy, 6, 471
  * Montet et al. (2015) Montet, B. T., Morton, T. D., Foreman-Mackey, D., et al. 2015, ApJ, 809, 25
  * Moses et al. (2013) Moses, J. I., Line, M. R., Visscher, C., et al. 2013, ApJ, 777, 34
  * Newton et al. (2016) Newton, E. R., Irwin, J., Charbonneau, D., et al. 2016, ApJ, 821, 93
  * Nowak et al. (2020) Nowak, G., Luque, R., Parviainen, H., et al. 2020, A&A, 642, A173
  * Parviainen & Aigrain (2015) Parviainen, H., & Aigrain, S. 2015, MNRAS, 453, 3821
  * Petigura et al. (2022) Petigura, E. A., Rogers, J. G., Isaacson, H., et al. 2022, AJ, 163, 179
  * Pinhas et al. (2018) Pinhas, A., Rackham, B. V., Madhusudhan, N., & Apai, D. 2018, MNRAS, 480, 5314
  * Plavchan et al. (2020) Plavchan, P., Barclay, T., Gagné, J., et al. 2020, Nature, 582, 497
  * Rackham et al. (2018) Rackham, B. V., Apai, D., & Giampapa, M. S. 2018, ApJ, 853, 122
  * Richard et al. (2012) Richard, C., Gordon, I. E., Rothman, L. S., et al. 2012, J. Quant. Spec. Radiat. Transf., 113, 1276
  * Ricker et al. (2015) Ricker, G. R., Winn, J. N., Vanderspek, R., et al. 2015, Journal of Astronomical Telescopes, Instruments, and Systems, 1, 014003
  * Robertson et al. (2013) Robertson, P., Endl, M., Cochran, W. D., & Dodson-Robinson, S. E. 2013, The Astrophysical Journal, 764, 3
  * Rogers & Seager (2010) Rogers, L. A., & Seager, S. 2010, ApJ, 716, 1208
  * Rothman et al. (2010) Rothman, L. S., Gordon, I. E., Barber, R. J., et al. 2010, J. Quant. Spec. Radiat. Transf., 111, 2139
  * Stauffer & Hartmann (1986) Stauffer, J. R., & Hartmann, L. W. 1986, ApJS, 61, 531
  * Stefánsson et al. (2020) Stefánsson, G., Kopparapu, R., Lin, A., et al. 2020, AJ, 160, 259
  * STScI Development Team (2013) STScI Development Team. 2013, pysynphot: Synthetic photometry software package, ascl:1303.023
  * Sullivan et al. (2015) Sullivan, P. W., Winn, J. N., Berta-Thompson, Z. K., et al. 2015, ApJ, 809, 77
  * Tsai et al. (2021) Tsai, S.-M., Innes, H., Lichtenberg, T., et al. 2021, ApJ, 922, L27
  * van der Walt et al. (2011) van der Walt, S., Colbert, S. C., & Varoquaux, G. 2011, Computing in Science Engineering, 13, 22
  * Van Eylen et al. (2018) Van Eylen, V., Agentoft, C., Lundkvist, M. S., et al. 2018, MNRAS, 479, 4786
  * Van Eylen et al. (2021) Van Eylen, V., Astudillo-Defru, N., Bonfils, X., et al. 2021, MNRAS, 507, 2154
  * Virtanen et al. (2020) Virtanen, P., Gommers, R., Oliphant, T. E., et al. 2020, Nature Methods, 17, 261
  * Welbanks & Madhusudhan (2021) Welbanks, L., & Madhusudhan, N. 2021, arXiv e-prints, arXiv:2103.08600
  * Welbanks et al. (2019) Welbanks, L., Madhusudhan, N., Allard, N. F., et al. 2019, ApJ, 887, L20
  * Yu et al. (2021) Yu, X., Moses, J. I., Fortney, J. J., & Zhang, X. 2021, ApJ, 914, 38
  * Yurchenko et al. (2011) Yurchenko, S. N., Barber, R. J., & Tennyson, J. 2011, MNRAS, 413, 1828
  * Yurchenko & Tennyson (2014) Yurchenko, S. N., & Tennyson, J. 2014, MNRAS, 440, 1649
  * Zhou et al. (2017) Zhou, Y., Apai, D., Lew, B. W. P., & Schneider, G. 2017, AJ, 153, 243

The authors are grateful for constructive feedback provided by the anonymous
referee. Support for HST program GO-15814 was provided by NASA through a grant
from the Space Telescope Science Institute, which is operated by the
Association of Universities for Research in Astronomy, Inc., under NASA
contract NAS 5-26555. This research has made use of the SIMBAD database,
operated at CDS, Strasbourg, France. Some of the data presented in this paper
were obtained from the Mikulski Archive for Space Telescopes (MAST). STScI is
operated by the Association of Universities for Research in Astronomy, Inc.,
under NASA contract NAS5-26555. Support for MAST for non-HST data is provided
by the NASA Office of Space Science via grant NNX13AC07G and by other grants
and contracts. MNG acknowledges support from the European Space Agency (ESA)
as an ESA Research Fellow. NM thanks Savvas Constantinou for helpful
discussions. All the HST data used in this paper can be found in MAST:
http://dx.doi.org/10.17909/2h3r-t275 (catalog 10.17909/2h3r-t275)

##  Appendix A Stellar limb darkening

Figure 10: Coefficients ($u_{1}$, $u_{2}$) for a quadratic stellar limb
darkening law obtained using ExoCTK and PyLDTK. Separate sets of ExoCTK
coefficients were computed assuming an ATLAS 9 (blue circles) and Phoenix ACES
(red circles) stellar model. The PyLDTK coefficients (black points) assume a
Phoenix ACES stellar model. Posterior distributions obtained from the light
curve fits are shown as orange diamonds, with $1\sigma$ credible intervals
that are smaller than the marker symbols.

For the fiducial light curve analyses, a quadratic stellar limb darkening law
was adopted with coefficients that were allowed to vary as free parameters. As
described in Sections 3.1 and 3.2, tight Gaussian priors obtained using PyLDTK
were adopted for these light curve fits. The limb darkening coefficiet priors
and resulting posteriors are listed in Table 3 for the spectroscopic light
curves. Due to the limited phase coverage of the transit, the limb darkening
coefficients are effectively unconstrained by the data and consequently the
posteriors are indistinguishable from the priors (Figure 10).

To investigate the sensitivity of the final results to the stellar limb
darkening treatment, the spectroscopic light curve fits were repeated with
$u_{1}$ and $u_{2}$ held fixed to values computed using the online ExoCTK
tool.444https://exoctk.stsci.edu Specifically, ExoCTK provides the option of
computing limb darkening coefficients using both Phoenix ACES (Husser et al.,
2013) and ATLAS9 (Kurucz, 1993; Castelli & Kurucz, 2003) stellar models. As
shown in Figure 10, there are clear differences in the limb darkening
coefficients computed by ExoCTK using these two stellar models, and compared
to those obtained with PyLDTK, which also uses the Phoenix ACES models.
However, as can be seen in Figure 11, the final transmission spectrum is found
to be robust to the choice of limb darkening treatment.

Table 3:  Posterior distributions for stellar limb darkening coefficients inferred from the spectroscopic light curve fits.  Wavelength | $u_{1}$ | $u_{2}$
---|---|---
($\mu$m) |  |
1.126-1.144 | $0.17411_{-0.00015}^{+0.00017}$ | $0.14986_{-0.00049}^{+0.00049}$
1.144-1.163 | $0.17069_{-0.00017}^{+0.00016}$ | $0.14954_{-0.00055}^{+0.00058}$
1.163-1.181 | $0.16853_{-0.00017}^{+0.00016}$ | $0.14873_{-0.00053}^{+0.00050}$
1.181-1.200 | $0.16550_{-0.00016}^{+0.00016}$ | $0.14536_{-0.00053}^{+0.00051}$
1.200-1.218 | $0.16563_{-0.00016}^{+0.00016}$ | $0.14539_{-0.00053}^{+0.00051}$
1.218-1.237 | $0.16187_{-0.00017}^{+0.00017}$ | $0.14692_{-0.00053}^{+0.00052}$
1.237-1.255 | $0.16173_{-0.00017}^{+0.00017}$ | $0.14545_{-0.00055}^{+0.00052}$
1.255-1.274 | $0.15879_{-0.00018}^{+0.00019}$ | $0.14405_{-0.00060}^{+0.00062}$
1.274-1.292 | $0.15610_{-0.00020}^{+0.00020}$ | $0.14629_{-0.00063}^{+0.00062}$
1.292-1.311 | $0.15446_{-0.00019}^{+0.00017}$ | $0.14377_{-0.00059}^{+0.00059}$
1.311-1.329 | $0.15106_{-0.00019}^{+0.00017}$ | $0.14106_{-0.00055}^{+0.00056}$
1.329-1.348 | $0.16933_{-0.00017}^{+0.00017}$ | $0.13147_{-0.00072}^{+0.00068}$
1.348-1.366 | $0.16980_{-0.00021}^{+0.00020}$ | $0.13276_{-0.00084}^{+0.00082}$
1.366-1.385 | $0.16661_{-0.00019}^{+0.00020}$ | $0.12976_{-0.00090}^{+0.00077}$
1.385-1.403 | $0.17225_{-0.00021}^{+0.00022}$ | $0.13419_{-0.00093}^{+0.00094}$
1.403-1.422 | $0.17482_{-0.00027}^{+0.00027}$ | $0.14076_{-0.00107}^{+0.00115}$
1.422-1.440 | $0.16906_{-0.00028}^{+0.00029}$ | $0.16630_{-0.00120}^{+0.00123}$
1.440-1.459 | $0.16990_{-0.00028}^{+0.00030}$ | $0.15845_{-0.00131}^{+0.00129}$
1.459-1.477 | $0.17439_{-0.00032}^{+0.00030}$ | $0.16207_{-0.00121}^{+0.00125}$
1.477-1.496 | $0.16697_{-0.00027}^{+0.00031}$ | $0.15601_{-0.00115}^{+0.00116}$
1.496-1.514 | $0.16053_{-0.00030}^{+0.00028}$ | $0.15220_{-0.00126}^{+0.00130}$
1.514-1.533 | $0.16335_{-0.00029}^{+0.00026}$ | $0.14715_{-0.00110}^{+0.00113}$
1.533-1.551 | $0.16388_{-0.00029}^{+0.00028}$ | $0.15854_{-0.00119}^{+0.00117}$
1.551-1.570 | $0.15884_{-0.00027}^{+0.00030}$ | $0.16827_{-0.00108}^{+0.00115}$
1.570-1.588 | $0.15116_{-0.00028}^{+0.00024}$ | $0.13940_{-0.00111}^{+0.00114}$
1.588-1.607 | $0.14712_{-0.00027}^{+0.00028}$ | $0.16774_{-0.00113}^{+0.00111}$
1.607-1.625 | $0.14538_{-0.00019}^{+0.00018}$ | $0.13665_{-0.00086}^{+0.00077}$
1.625-1.644 | $0.14406_{-0.00023}^{+0.00024}$ | $0.14131_{-0.00090}^{+0.00097}$
Figure 11: Derived transmission spectra for the different stellar limb
darkening treatments described in Appendix A. Free coefficients with PyLDTK
priors (black circles), coefficients held fixed to the PyLDTK values (orange
squares), and coefficients held fixed to the ExoCTK values assuming ATLAS9
(red triangles) and Phoenix ACES (blue triangles) stellar models. A high level
of consistency is obtained for all limb darkening treatments. Table 4: Priors
and Retrieved Parameters for the Models in this Work

Parameter | Prior Distribution | Baseline ModelT,W | Stellar HeterogeneityT,W | Stellar HeterogeneityW
---|---|---|---|---
$\log_{10}(X_{\text{H}_{2}\text{O}})$ | $\mathcal{U}(-12,-0.3)$ | $-1.77^{+0.69}_{-0.93}$ | $-1.91^{+0.74}_{-0.98}$ | $-2.09^{+0.89}_{-1.21}$
$\log_{10}(X_{\text{CH}_{4}})$ | $\mathcal{U}(-12,-0.3)$ | $-7.78^{+2.67}_{-2.49}$ | $-7.71^{+2.60}_{-2.57}$ | $-7.35^{+2.54}_{-2.57}$
$\log_{10}(X_{\text{NH}_{3}})$ | $\mathcal{U}(-12,-0.3)$ | $-8.04^{+2.42}_{-2.37}$ | $-7.72^{+2.25}_{-2.41}$ | $-8.02^{+2.25}_{-2.29}$
$\log_{10}(X_{\text{CO}})$ | $\mathcal{U}(-12,-0.3)$ | $-6.60^{+3.37}_{-3.31}$ | $-6.15^{+3.10}_{-3.33}$ | $-6.36^{+3.13}_{-3.28}$
$\log_{10}(X_{\text{CO}_{2}})$ | $\mathcal{U}(-12,-0.3)$ | $-5.81^{+3.22}_{-3.79}$ | $-5.62^{+3.11}_{-3.77}$ | $-5.73^{+3.04}_{-3.67}$
$\log_{10}(X_{\text{HCN}})$ | $\mathcal{U}(-12,-0.3)$ | $-6.53^{+2.93}_{-3.27}$ | $-6.58^{+2.87}_{-3.16}$ | $-6.70^{+2.82}_{-3.06}$
$\text{T}_{0}$ [K] | $\mathcal{U}(0,400)$ | $247^{+80}_{-68}$ | $257^{+72}_{-69}$ | $232^{+76}_{-65}$
$\log_{10}(\text{P}_{\rm ref})$[bar] | $\mathcal{U}(-6,2)$ | $-1.04^{+0.46}_{-0.54}$ | $-2.35^{+1.47}_{-1.78}$ | $-3.34^{+1.56}_{-1.47}$
$\log_{10}(a)$ | $\mathcal{U}(-4,10)$ | $0.71^{+4.04}_{-2.90}$ | $0.49^{+3.39}_{-2.70}$ | $1.36^{+3.95}_{-3.13}$
$\gamma$ | $\mathcal{U}(-20,2)$ | $-10.83^{+7.20}_{-5.80}$ | $-10.84^{+6.99}_{-5.59}$ | $-10.52^{+6.97}_{-5.75}$
$\log_{10}(\text{P}_{\rm c})$ [bar] | $\mathcal{U}(-6,2)$ | $-0.77^{+1.63}_{-2.47}$ | $-0.88^{+1.68}_{-2.45}$ | $-1.53^{+1.91}_{-2.22}$
$\phi$ | $\mathcal{U}(0,1)$ | $0.34^{+0.36}_{-0.22}$ | $0.38^{+0.33}_{-0.23}$ | $0.37^{+0.31}_{-0.23}$
$\delta$ | $\mathcal{U}(0.0,0.5)$ | N/A | $0.06^{+0.05}_{-0.03}$ | $0.08^{+0.05}_{-0.04}$
$\text{T}_{\rm het}$ [K] | $\mathcal{U}(701,5259)$ | N/A | $2446^{+1120}_{-988}$ | $2202^{+855}_{-866}$
$\text{T}_{\rm phot}$ [K] | $\mathcal{N}(3506,100)$ | N/A | $3512^{+81}_{-84}$ | $3505^{+84}_{-82}$

Note. — The superscript in the model name indicates the data included in the
retrieval: T for TESS and W for HST-WFC3. N/A means that the parameter was not
considered in the model by construction.