# Characterising a World Within the Hot Neptune Desert: Transit Observations
of LTT 9779 b with HST WFC3

Billy Edwards SRON, Netherlands Institute for Space Research, Niels Bohrweg 4,
NL-2333 CA, Leiden, The Netherlands  Quentin Changeat European Space Agency
(ESA), ESA Office, Space Telescope Science Institute (STScI), Baltimore MD
21218, USA  Angelos Tsiaras INAF, Osservatorio Astrofisico di Arcetri, Largo
E. Fermi 5, 50125 Firenze, Italy  Andrew Allan  Leiden Observatory, Leiden
University, PO Box 9513, 2300 RA Leiden, The Netherlands  Patrick Behr
Laboratory for Atmospheric and Space Physics, University of Colorado Boulder,
Boulder, CO 80303  Simone R. Hagey The University of British Columbia, 6224
Agricultural Road Vancouver, BC V6T 1Z1, Canada  Michael D. Himes Planetary
Sciences Group, Department of Physics, University of Central Florida, Orlando,
FL, USA  NASA Postdoctoral Program Fellow, NASA Goddard Space Flight Center,
Greenbelt, MD, USA  Sushuang Ma Department of Physics and Astronomy,
University College London, Gower Street, London, WC1E 6BT, United Kingdom
Keivan G. Stassun Department of Physics and Astronomy, Vanderbilt University,
Nashville, TN 37235, USA  Luis Thomas  Universitäts-Sternwarte München,
Scheinerstr. 1, D-81679 München, Germany  Max-Planck-Institut für
extraterrestrische Physik, Giessenbachstrasse 1, D-85748 Garching, Germany
Department of Physics and Astronomy, University College London, Gower Street,
London, WC1E 6BT, United Kingdom  Alexandra Thompson  Department of Physics
and Astronomy, University College London, Gower Street, London, WC1E 6BT,
United Kingdom  Aaron Boley  The University of British Columbia, 6224
Agricultural Road Vancouver, BC V6T 1Z1, Canada  Luke Booth  Cardiff Hub for
Astrophysics Research and Technology (CHART), School of Physics and Astronomy,
Cardiff University, UK  Jeroen Bouwman  Max-Planck-Institut für Astronomie,
Königstuhl 17, 69117 Heidelberg, Germany  Kevin France  Laboratory for
Atmospheric and Space Physics, University of Colorado Boulder, Boulder, CO
80303  Nataliea Lowson Centre for Astrophysics, University of Southern
Queensland, 499-565 West Street, Toowoomba, QLD 4350, Australia  Annabella
Meech Department of Physics, University of Oxford, Denys Wilkinson Building,
Oxford, OX1 3RH  Caprice L. Phillips Department of Astronomy, The Ohio State
University, 100 W 18th Ave, Columbus, OH 43210 USA  Aline A. Vidotto Leiden
Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands
Kai Hou Yip Department of Physics and Astronomy, University College London,
Gower Street, London, WC1E 6BT, United Kingdom  Michelle Bieger  College of
Engineering, Mathematics and Physical Sciences, University of Exeter, North
Park Road, Exeter, United Kingdom  Amélie Gressier Space Telescope Science
Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA  Estelle Janin
Arizona State University, PO Box 871404, Tempe, 85287-1404, Arizona, USA  Ing-
Guey Jiang Department of Physics and Institute of Astronomy, National Tsing
Hua University, Hsinchu 30013, Taiwan  Pietro Leonardi Dipartimento di Fisica,
Università di Trento, Via Sommarive 14, 38123 Povo, Italy  Dipartimento di
Fisica e Astronomia, Università degli Studi di Padova, Vicolo
dell’Osservatorio 3, 35122 Padova, Italy  Subhajit Sarkar  Cardiff Hub for
Astrophysics Research and Technology (CHART), School of Physics and Astronomy,
Cardiff University, UK  Nour Skaf LESIA, Observatoire de Paris, Univ. Paris
Cité, Univ. PSL, CNRS, Sorbonne Univ., 5 pl. Jules Janssen, 92195 Meudon,
France  National Astronomical Observatory of Japan, Subaru Telescope, 650
North A’ohōkū Place, Hilo, HI 96720, U.S.A.  Department of Physics and
Astronomy, University College London, Gower Street, London, WC1E 6BT, United
Kingdom  Jake Taylor  Department of Physics (Atmospheric, Oceanic and
Planetary Physics), University of Oxford, Parks Rd, Oxford OX1 3PU, UK
Institut Trottier de Recherche sur les Exoplanètes and Département de
Physique, Université de Montréal, 1375 Avenue Thérèse-Lavoie-Roux,
Montréal, QC, H2V 0B3, Canada  Ming Yang College of Surveying and Geo-
Informatics, Tongji University, Shanghai 200092, China  Derek Ward-Thompson
Jeremiah Horrocks Institute, University of Central Lancashire, Preston PR1
2HE, UK

(Received April 28, 2023; Revised June 07, 2023; Accepted June 21, 2023)

###### Abstract

We present an atmospheric analysis of LTT 9779 b, a rare planet situated in
the hot Neptune desert, that has been observed with HST WFC3 G102 and G141.
The combined transmission spectrum, which covers 0.8 - 1.6 $\mu$m, shows a
gradual increase in transit depth with wavelength. Our preferred atmospheric
model shows evidence for H2O, CO2 and FeH with a significance of 3.1 $\sigma$,
2.4 $\sigma$ and 2.1 $\sigma$, respectively. In an attempt to constrain the
rate of atmospheric escape for this planet, we search for the 1.083 $\mu$m
Helium line in the G102 data but find no evidence of excess absorption that
would indicate an escaping atmosphere using this tracer. We refine the orbital
ephemerides of LTT 9779 b using our HST data and observations from TESS,
searching for evidence of orbital decay or apsidal precession, which is not
found. The phase-curve observation of LTT 9779 b with JWST NIRISS should
provide deeper insights into the atmosphere of this planet and the expected
atmospheric escape might be detected with further observations concentrated on
other tracers such as Lyman $\alpha$.

Exoplanet atmospheres (487); Hubble Space Telescope (761);

††journal: AJ

##  1 Introduction

The exoplanet field has rapidly expanded, with thousands of planets currently
known and thousands more anticipated in the coming decade, thanks to dedicated
planet-hunting missions such as Kepler (Borucki et al., 2010) and the
Transiting Exoplanet Survey Satellite (TESS, Ricker et al., 2014). The vast
number of detected worlds enables characterisation of a diverse exoplanet
sample to be further characterised, with low resolution space based
spectroscopy detecting broadband spectral features of molecular species in
exoplanet atmospheres (e.g., Tinetti et al., 2007; Swain et al., 2008).

For over a decade, the Hubble Space Telescope (HST) has been utilised to
conduct observations of the atmospheres of exoplanets. With the spatial
scanning technique allowing for higher signal-to-noise ratio observations
(McCullough & MacKenty, 2012), the characterisation of exoplanetary
atmospheres via the transit (e.g., Kreidberg et al., 2014; Luque et al., 2020;
Murgas et al., 2020; Skaf et al., 2020; Wilson et al., 2020; Yan et al., 2020;
Guilluy et al., 2021; Yip et al., 2021; McGruder et al., 2022; Saba et al.,
2022), eclipse (e.g., Line et al., 2016; Edwards et al., 2020b; Pluriel et
al., 2020; Changeat & Edwards, 2021; Jacobs et al., 2022), and phase-curve
(e.g., Stevenson et al., 2014, 2017; Kreidberg et al., 2018; Arcangeli et al.,
2019; Changeat et al., 2021; Robbins-Blanch et al., 2022; Changeat, 2022)
techniques has rapidly expanded. Indeed, enough planets have now been studied
to facilitate population-style studies (e.g., Sing et al., 2016; Tsiaras et
al., 2018; Fisher & Heng, 2018; Cubillos & Blecic, 2021; Mansfield et al.,
2021; Roudier et al., 2021; Changeat et al., 2022; Edwards et al., 2022).

Figure 1: LTT 9779 b in context with the known population of transiting
planets. In the period-mass and period-radius space, LTT 9779 b occupies a
region which is sparsely populated. The majority of other planets on such a
short orbital period are either stripped rocky cores or Jupiter-sized worlds.

Numerous short-period planets have been discovered and these usually fall into
one of two populations: large, gaseous worlds (i.e. hot-Jupiters) or stripped
rocky cores which are often referred to as ultra-short-period (USP) planets.
Between these two populations, there is a dearth of planets and this area of
the parameter space has been coined the hot Neptune desert (e.g., Szabó &
Kiss, 2011; Beaugé & Nesvorný, 2013; Mazeh et al., 2016). The lack of planets
found in this region cannot be explained by observational biases due to the
large number of Neptunian-sized worlds found on longer orbits. Instead, the
under-population of this regime has been hypothesised to be caused by
photoevaporation whereby planets that spend significant time in these short
orbits either have enough mass to remain a Jupiter-sized world or else have
their primordial atmosphere completely eroded (e.g., Lundkvist et al., 2016;
Lopez, 2017).

LTT 9779 b (Jenkins et al., 2020) is an ultra-hot Neptune discovered using
data from the TESS. With a period of less than a day and a radius of
4.7$\pm$0.23 R⊕, LTT 9779 b lies within the hot Neptune desert, as shown in
Figure 1. Radial velocity measurements have constrained the mass to
29${}^{+0.78}_{-0.81}$ M⊕, yielding a density of 1.536 $\pm$0.123 g/cm3 which
is suggestive of a gas-rich world. Given the rarity of worlds residing within
the hot Neptune desert, LTT 9779 b quickly became a target for atmospheric
studies. Photometric eclipse observations of LTT 9779 b with Spitzer revealed
a spectrum which is best-fitted by a non-inverted atmosphere and evidence was
found for the presence of CO (Dragomir et al., 2020). Phase curve observations
with TESS and Spitzer have also revealed a large ($\sim$1100 K) day-night
temperature contrast and have suggested a super-solar atmospheric metallicity
(Crossfield et al., 2020). However, the transit observations from these phase
curves were not precise enough to constrain molecular composition of the
atmosphere in transmission. As part of a homogeneous population study of 70
gaseous exoplanets, Edwards et al. (2022) presented the HST WFC3 G141
transmission spectrum of LTT 9779 b. They found a spectrum with few obvious
features except a slope of increasing transit depth with wavelength across the
1.1 - 1.6 $\mu$m spectral range, which was best explained by a model with no
molecular absorption, with the slope being instead best fit by Collision
Induced Absorption (CIA) and Rayleigh scattering. Retrievals which included
optical absorbers (TiO, VO, FeH, H-) suggested the presence of TiO, but this
was found to be strongly dependent upon the bluest spectral point and thus it
was noted this could simply be noise.

In this paper, we present a new set of observations from the HST WFC3 G102,
reduced with the same methodology as in Edwards et al. (2022). The combined
HST WFC3 G102 and G141 transmission spectrum of LTT 9779 b covers the
wavelengths from 0.8$\mu$m to 1.6$\mu$m. Analysing these data, our free
chemistry atmospheric retrievals prefer solutions with high abundances of H2O
and CO2, with a detection significance of 3.11 $\sigma$ and 2.35 $\sigma$,
respectively, as well as the preferring the presence of FeH to 2.12 $\sigma$.
The chemical equilibrium retrievals we conduct do not provide a preferable fit
to the data than the free chemistry retrievals. Nevertheless, the best-fit
solution suggests a carbon-to-oxygen ratio of C/O = 0.56${}^{+0.41}_{-0.34}$
and a very low atmospheric metallicity of log(Z) = -2.74${}^{+0.69}_{-0.56}$.
Furthermore, we search for the 1.083 $\mu$m Helium line, but find no evidence
for it within the HST data. Finally, we use the mid-times from the HST data,
along with literature mid-times, to refine the period of LTT 9779 b and search
for evidence of orbital decay or precession, finding no strong evidence that
the orbital period is changing over the current observational baseline.

##  2 Methodology

HST WFC3 G102 and G141 observations of LTT 9779 b’s transit were taken as part
of proposal GO-16457 (PI: Billy Edwards; Edwards et al., 2020a). These data
were taken using the SPARS10 sequence and the GRISM256 aperture. The total
exposure time was 103.13 seconds, with 16 up-the-ramp samples per exposure.
Each visit consisted of four HST orbits, with the third occurring in-transit.
For wavelength calibration, a direct image with the F132N filter was taken at
the start of the first orbit of each observation sequence. The spatial
scanning technique (McCullough & MacKenty, 2012) was utilised to increase the
duty cycle and, thus, improve the signal-to-noise ratio of the data. The scan
rate employed was 0.18 ”/s, yielding a total scan length of 19.7 ”, which
equated to around 150 pixels.

###  2.1 Data Reduction and Light Curve Fitting

Figure 2: Shifts in the position of the spectrum on the detector in the
spectral (x) and spatial (y) directions for the G102 (top) and G141 (bottom)
visits. In both cases, the pointing across the visit was excellent.

Figure 3: Raw images from the G102 (top) and G141 (bottom) observation
sequences. In each case, the image illustrates the second forward scan of the
second orbit, which is the first dataset used in this analysis. For each
panel, the left image shows the final read while the middle image displays a
non-destructive read. The right image shows the flux levels once the non-
destructive read is subtracted. The regions of negative flux highlight the
persistence effect for these datasets. The colour scale for the right images
differ from the others in this Figure to highlight this negative region.

We carry out the analysis of the transit data using Iraclis, our highly-
specialised software for processing WFC3 spatially scanned spectroscopic
images (Tsiaras et al., 2016b, c, 2018) which has been used in a number of
studies (e.g., Anisman et al., 2020; Changeat et al., 2020; Edwards et al.,
2021; Libby-Roberts et al., 2021; Brande et al., 2022; Garcia et al., 2022).
The reduction process includes the following steps: zero-read subtraction,
reference-pixels correction, non-linearity correction, dark current
subtraction, gain conversion, sky background subtraction, calibration, flat-
field correction and bad-pixels/cosmic-rays correction. Then we extract the
white (1.088-1.680 $\mu$m) and the spectral light curves from the reduced
images, taking into account the geometric distortions caused by the tilted
detector of the WFC3 infrared channel. The pointing performance of HST was
excellent across both visits and Figure 2 shows the shift in the X and Y
position of the spectrum.

In the extraction of the flux from the calibrated images, Iraclis offers two
techniques. The first extracts the flux from the image as it is at the end of
the scan. The second splits the data into the up-the-ramp reads, subtracting
each one sequentially from the next read and extracting the flux from each
resulting image. The splitting extraction is useful for ensuring that there
are no background stars with overlapping contributions to the target star’s
spectrum. However, differences between the flux extracted with each method can
also occur due to persistence. While the level of persistence is dependent
upon the accumulated charge, it is also correlated with the time the charge
has spent on the detector as well as the time since the last read (Anderson et
al., 2014).

In the context of HST WFC3, this means the persistence is dependent upon the
brightness of the host star, the scanning rate, and the readout scheme
employed. We show this effect for the second forward scan of the second orbit
(the first image used in the analysis) in Figure 3. The differences are clear
when comparing the G102 datasets to those taken with the G141 grism: the
persistence effect is greater in the latter case, likely due to the higher
flux levels as the scan rate and readout schemes were identical. As the
extracted flux using the full scan and splitting methods can be different, and
to minimise the impact of persistence, we use the splitting extraction in this
work.

Figure 4: White light curve fits for the HST WFC3 G102 (left) and G141 (right)
data of LTT 9779 b. In each case, the top plot shows the raw light curve (top
panel), corrected light curve and best-fit model (second panel), the residuals
having removed the best-fit model (third panel), and the auto-correlation
function (bottom panel). The lower graphic is the corner plot for the fit. As
with the majority of HST datasets, there is a correlation between the white
light curve depth and the parameters for the systematics (Equation 1), thereby
indicating that achieving absolute transit depths is difficult with this data.
For the data studied here, the G141 data shows the highest correlation.
Nevertheless, no major offset in the transit depth was found between the two
visits.

We fit the light curves using our transit model package PyLightcurve (Tsiaras
et al., 2016a) with the transit parameters from Table 2. The limb-darkening
coefficients are calculated using ExoTETHyS (Morello et al., 2020) and based
on the PHOENIX 2018 models from Allard et al. (2012). The stellar parameters
used are also given in Table 2.

During our fitting of the white light curve, the planet-to-star radius ratio
(Rp/Rs) and the mid-transit time (T0) were the only free parameters, along
with the parameters used to model the systematics (Tsiaras et al., 2016b). It
is common for WFC3 exoplanet observations to be affected by two kinds of time-
dependent systematics: the long-term and short-term ‘ramps’. The first affects
each HST visit and has generally modelled as a linear behaviour, while the
second affects each HST orbit is modelled as having an exponential behaviour
(see e.g., Kreidberg et al., 2014; Tsiaras et al., 2016b). The parametric
model we use for the white light curve systematics (Rw) takes the form:

$R_{w}(t)=n^{scan}_{w}(1-r_{a}(t-T_{0}))(1-r_{b1}e^{-r_{b2}(t-t_{o})}),$ (1)

where t is time, n${}^{\rm scan}_{\rm w}$ is a normalisation factor, T0 is the
mid-transit time, to is the time when each HST orbit starts, ra is the slope
of a linear systematic trend along each HST visit and (r${}_{\rm b1},r_{\rm
b2}$) are the coefficients of an exponential systematic trend along each HST
orbit. The normalisation factor we use (n${}^{\rm scan}_{\rm w}$) is changed
to n${}^{\rm for}_{\rm w}$ for upward scanning directions (forward scanning)
and to n${}^{\rm rev}_{\rm w}$ for downward scanning directions (reverse
scanning). The reason for using separate normalisation factors is the slightly
different effective exposure time due to the known upstream/downstream effect
(McCullough & MacKenty, 2012).

We fit the white light curves using the formulae above, considering the
uncertainties per pixel as propagated through the data reduction process.
However, it is common in HST/WFC3 data to have additional scatter that cannot
be captured by the ramp model. For this reason, we apply a scaling factor to
each of the individual data point uncertainties to match their median to the
standard deviation of the residuals and repeated the fitting (Tsiaras et al.,
2018). The resulting fits for both the G102 and G141 observations are shown in
Figure 4.

Next, we extract spectral light curves using the Iraclis “default_high”
binning for both grisms. We fit these spectral light curves with a transit
model. In this case, the free parameters are the planet-to-star radius ratio
and the parameters for the systematics model. The mid-time was fixed to the
best-fit value from the white light curve fit while other orbital parameters
were again fixed to those in Table 2. The systematics model, ($R_{\lambda}$),
includes the white light curve and a wavelength-dependent, visit-long slope
(Tsiaras et al., 2016b), taking the form:

$R_{\lambda}(t)=n^{scan}_{\lambda}(1-\chi_{\lambda}(t-T_{0}))\frac{LC_{w}}{M_{w}},$
(2)

where $\chi_{\lambda}$ is the slope of a wavelength-dependent linear
systematic trend along each HST visit, LC$w$ is the white light curve and
$M_{w}$ is the best-fit model for the white light curve. Again, the
normalisation factor we use (n${}^{\rm scan}_{\lambda}$) is changed to
n${}^{\rm for}_{\lambda}$ or n${}^{\rm rev}_{\lambda}$ for upward or downward
scanning directions respectively. Also, in the same way as for the white light
curves, we perform an initial fit using the pipeline uncertainties and then
refit while scaling-up these uncertainties, such that their median matches the
standard deviation of the residuals. The spectral light curves fits, for both
visits, are given in Figure 5.

Figure 5: Spectral light curves fitted with Iraclis for the G102 (left) and
G141 (right) observations of LTT 9779 b where, for clarity, an offset has been
applied. Each plots shows the detrended spectral light curves with best-fit
model plotted (left) as well as the residuals from the fitting (right). The
values for the reduced Chi-squared ($\bar{\chi}^{2}$), the standard deviation
of the residuals with respect to the photon noise ($\bar{\sigma}$), and the
auto-correlation (AC) function are also shown.

###  2.2 Atmospheric Retrievals

We explore the nature of LTT 9779 b’s lower atmosphere using Bayesian
retrievals. These atmospheric retrievals are performed on the extracted
transmission spectrum using the publicly available retrieval suite TauREx 3.1
(Al-Refaie et al., 2021, 2022)111https://github.com/ucl-
exoplanets/TauREx3_public. In our retrievals, we assume that LTT 9779 b
possesses a primary atmosphere with a solar ratio of helium to hydrogen (He/H2
= 0.17). The atmosphere of LTT 9779 b is simulated to range from 10-4 to 106
Pa (10-9 to 10 Bar) and sampled uniformly in log-space by 100 atmospheric
layers. The retrieved radius is, therefore, the 10 Bar radius. We include
Collision Induced Absorption (CIA) from H2-H2 (Abel et al., 2011; Fletcher et
al., 2018) and H2-He (Abel et al., 2012) as well as Rayleigh scattering for
all molecules. We model clouds as a uniform opaque deck, fitting only the
cloud-top pressure (i.e. grey clouds). We then perform two main types of
retrievals, those which fit each molecular species independently (i.e. free
chemistry) and those which assume molecules to be in chemical equilibrium.

For the free chemistry retrievals, we include the molecular opacities from the
ExoMol (Tennyson et al., 2016), HITRAN (Gordon et al., 2016) and HITEMP
(Rothman & Gordon, 2014) databases. Based on the expected chemical species of
such a hot planet, we include the opacities of H2O (Polyansky et al., 2018),
CO (Li et al., 2015), CO2 (Rothman et al., 2010), HCN (Barber et al., 2013),
TiO (McKemmish et al., 2019), VO (McKemmish et al., 2016), FeH (Wende et al.,
2010) and H- (John, 1988). To implement the last of these, we use the
methodology described in Edwards et al. (2020b), fixing the neutral hydrogen
volume mixing ratio and thus only fitting for e- volume mixing ratio. We note
that Himes & Harrington (2022) showed that Equation 3 from John (1988) does
not replicate the table of coefficients in that same paper. Himes & Harrington
(2022) recommend using Table 1 from John (1988), which is what is implemented
here.

In each free chemistry case, all molecular abundances are allowed to vary from
log(VMR) = -1 to log(VMR) = -15. Higher mixing are not expected in the
hydrogen-dominated atmosphere of LTT 9779 b and, in any case, these would also
necessitate accounting for self-broadening of the molecular lines (Anisman et
al., 2022a, b). We explore using both an isothermal temperature profile and an
Npoint profile. For the former, we fit only the temperature. For the later, we
fit the temperature at the “surface” (10 Bar) and the temperature at the “top”
of the atmosphere (10-9 Bar) as well as two intermediary points. For these
intermediary points, we also fit the pressure at which these points occur.
Therefore, the isothermal profile adds only a single free parameter to the
retrieval while the NPoint adds six. For the free chemistry retrievals, we
explore both chemical profiles which were constant with altitude and more
complex, varying with altitude, two-layer profiles (Changeat et al., 2019).

Additionally, we conduct equilibrium chemistry retrievals using the code
GGchem (Woitke et al., 2018) via the TauREx plugin system (Al-Refaie et al.,
2022). As with the free chemistry retrievals, we include Rayleigh scattering
and CIA as well as simple grey clouds. For these retrievals, the free chemical
parameters are the atmospheric metallicity and C/O ratio. For the equilibrium
chemistry retrievals, the metallicity is allowed to vary from 1e-4 to 1e4 and
the C/O ratio has bounds of 1e-3 and 2.

Recovering absolute transit depths is difficult, particularly given the strong
systematics present within HST observations (e.g., Guo et al., 2020; Changeat
et al., 2020). Therefore, one can induce offsets in the transit depth between
datasets from different instruments222Offsets are also found between different
observations with the same instrument, see e.g., Edwards et al. (2022). which,
if left uncorrected, could bias the retrieved atmospheric composition. Hence,
we also conduct retrievals where we allow the G141 dataset to be shifted
relative to the G102 data, with this offset being a free parameter in the
retrieval (e.g., Luque et al., 2020; Yip et al., 2021). We allow the G141 data
to be shifted due to the strong correlations between the transit depth and
systematics model (see Figure 4). To allow for this possibility to be fully
explored, the bounds for this offset are set to be extremely broad: $\pm$1e-2
(10000 ppm).

Stellar activity, in the form of photospheric heterogeneities (i.e., spots and
faculae), can contaminate the transmission spectrum of an exoplanet (e.g.,
Ballerini et al., 2012; McCullough et al., 2014; Rackham et al., 2018; Barclay
et al., 2021). The contamination introduced is strongly chromatic with the
strongest effects seen at shorter, optical wavelengths. As such, the
possibility of stellar contamination is particularly important to consider for
the G102 observations. Hence, we conduct retrievals using the ASteRA (Active
Stellar Retrieval Algorithm) plugin for TauREx, outlined in Thompson et al.
(2023), to explore potential contamination in the case of LTT 9779 b. In our
setup, we allow for possible contamination effects due to both unocculted
spots and unocculted faculae. ASteRA requires 4 additional fitting parameters
which are the spot and faculae temperatures, TSpot and TFac respectively, and
their respective filling factors, FSpot and FFac. We again use intentionally
nonrestrictive priors, with FSpot and FFac bounds of 0 and 0.99, TSpot bounds
of 4000K and 5440K and TFac bounds of 5450K to 6000K.

Finally, we explore the parameter space using the nested sampling algorithm
Multinest (Feroz et al., 2009; Buchner et al., 2014) with 1000 live points and
an evidence tolerance of 0.5. We then utilise the Bayesian evidence derived by
Multinest as a means of selecting the preferred atmospheric model and for
judging the significance of molecular detections.

###  2.3 Probing Atmospheric Mass Loss via the Helium Line at 1.083 $\mu$m

Close-in gaseous planets are expected to be undergoing atmospheric escape due
to the high levels of stellar irradiation. Indeed, hydrodynamic escape has
been proposed as the cause of the dearth of hot Neptunes, with planets either
being completely stripped or having a high-enough starting mass to retain the
majority of their primordial envelope (e.g., Lundkvist et al., 2016; Mazeh et
al., 2016).

Observational studies have been undertaken in an attempt to detect atmospheric
escape and constrain the rate of mass loss. Many of these have focused on
using the Ly$\alpha$ line, but despite these successes, attenuation by neutral
hydrogen in the interstellar medium removes the majority of the Ly$\alpha$
line profile and so other tracers of mass-loss have also been proposed. One
such alternative line is that of metastable Helium which occurs at 1.083$\mu$m
(Oklopčić & Hirata, 2018). Ground-based observations have had notable success
in detecting escape via this observable (e.g., Allart et al., 2018; Nortmann
et al., 2018; Zhang et al., 2023), but the first detection of Helium came via
observations with HST. The G102 grism of WFC3 was used to observed WASP-107 b
(Anderson et al., 2017), with an excess absorption being detected around 1.083
$\mu$m (Spake et al., 2018). These data suggested a mass-loss rate of
$10^{10}$ \- $3\times 10^{11}$ g s-1. Similarly, HST WFC3 G102 data of
HAT-P-11 b found evidence for a mass-loss rate of 109 \- 1011 g s-1 (Mansfield
et al., 2018) although high-resolution ground-based observations suggested a
lower mass-loss rate (Allart et al., 2018). Observations of the Helium triplet
have also been undertaken for planets on the edge of the hot Neptune desert,
with the resulting mass-rates suggesting that the upper-edge (i.e., the higher
mass planets) of the desert is impervious to atmospheric escape (Vissapragada
et al., 2022).

As LTT 9779 b lies within the rarely populated hot Neptune desert it is
expected that atmospheric loss should be ongoing, despite the old age of the
system. Therefore, as well as using the HST WFC3 G102 data to constrain the
atmospheric composition via a low-resolution spectrum, we also extract a
higher-resolution spectrum to search for evidence of mass-loss via the Helium
line. Using the excellent wavelength calibration offered by Iraclis, we
extract overlapping bins with a bandwidth of 3 nm (30 Å) and a separation of
0.1 Å across the entire G102 range and perform fits to each of these light
curves in the same way as discussed in Section 2.1. We then use the transit
depths recovered in these overlapping bins to search for excess absorption
around 1.083$\mu$m.

Separately, we estimate the expected atmospheric escape rate using a photo-
evaporation model (Allan et al. 2023, submm.). In our model, the high-energy
stellar radiation ionises hydrogen and helium atoms, and the excess energy
released after the ionisation heats the planet’s upper atmosphere, which more
easily evaporate. We construct the incoming high-energy stellar spectrum of
LTT 9779 using HST STIS NUV/Optical observations (G230L and G430L) that were
taken as part of the MUSCLES Extension for Atmospheric Transmission
Spectroscopy programme (GO-16166; PI: Kevin France; France et al., 2020). As
LTT 9779 is a Sun-like star (Jenkins et al., 2020), the FUV portion of the
spectrum (1170 - 2200 Å) is assumed to be the spectrum of the quiet Sun (Woods
et al., 2009), scaled to the HST STIS G230L spectrum of LTT 9779; the adopted
scaling factor was 9.0519$\times 10^{-16}$. Meanwhile, the HST STIS G140M data
is utilised to reconstruct the Ly$\alpha$ using the methodology described in
Youngblood et al. (2022). The Ly$\alpha$ flux is then used to compute the EUV
(100 - 1170 Å) flux of LTT 9779 using the scaling relations from Linsky et al.
(2014). Finally, as X-ray observations with Chandra led to a non-detection, we
also use a scaled solar X-ray spectrum (5 - 100 Å).

Our atmospheric escape model requires as input the incident flux at four
energy bins, X-ray (0.517-1.24 nm), hard EUV (10-36nm), soft-EUV (36-92 nm)
and FUV+NUV (91.2-320 nm). By integrating the spectrum above, the luminosities
at each of these bins are 3.35$\times 10^{26}$, 3.02$\times 10^{27}$,
2.30$\times 10^{27}$, and 2.22$\times 10^{31}$ erg s-1, respectively. Our
model then solves for the hydrodynamics equations (conservation of mass,
momentum and energy) and ionisation balance of hydrogen (Allan & Vidotto,
2019). In our most recent model version (Allan et al, submm.), we also self-
consistently compute the helium population (neutral helium in the singlet and
triplet states, as well as ionised helium), and their corresponding
energetics. The helium abundance is an input parameter of our model and we run
two models, the first assuming an abundance by number of $2\%$ and a second at
10%.

###  2.4 Updated Ephemeris and Search for Orbital Decay or Precession

Maintaining exoplanet ephemerides is crucial for ensuring that atmospheric
studies of exoplanets can be undertaken. Therefore, we utilise the mid-times
from our HST light curve fits, as well as literature observations, to refine
the period of LTT 9779 b. Data from TESS Sector 2 led to the discovery of LTT
9779 b and it has since re-observed the host star in Sector 29.333We note that
LTT 9779 will also be studied in TESS Sector 69 (Aug-Sep 2023). These TESS
data were analysed by Kokori et al. (2022a) as part of the ExoClock project
(Kokori et al., 2021, 2022b), which aims to refine the ephemerides of planets
which will be studied by the Ariel mission (Tinetti et al., 2018; Edwards et
al., 2019; Tinetti et al., 2021). In our work, we took the TESS mid-times from
this previous study and incorporated new unpublished TESS eclipses. As with
Kokori et al. (2022a), we utilise the 2 minute cadence Pre-search Data
Conditioning (PDC) light curves (Smith et al., 2012; Stumpe et al., 2012,
2014). Due to the poor signal-to-noise ratio of the TESS eclipses, we fit them
in groups of four eclipses to achieve eclipse mid-time uncertainties that were
of a similar precision to the transit measurements. Furthermore, before the
end of operations, Spitzer observed eclipses and phase-curves of LTT 9779 b
(Crossfield et al., 2020; Dragomir et al., 2020). We combine the mid-times
from these studies with our data to extend the number of epochs during which
LTT 9779 b has been observed. A full list of the mid-times utilised here are
given in the Appendix in Tables LABEL:tab:tr_mt & LABEL:tab:ec_mt.

To further constrain the orbital period, we utilise the radial velocity data
taken of LTT 9779 by CORALIE and HARPS which were presented in the detection
paper of the planet (Jenkins et al., 2020). To model the radial velocity
profile, we use RadVel (Fulton et al., 2018). The radial velocity data and the
transit mid-times are fitted under one likelihood using Multinest (Feroz et
al., 2009; Buchner et al., 2014) to explore the parameter space. For the
linear ephemeris model, we assume a circular orbit (e = 0) following the
conclusions in Jenkins et al. (2020).

Given the short period of LTT 9779 b, one might expect that the planet’s orbit
should be shrinking gradually over time due to a transfer of angular momentum
from the planet to the host star, eventually leading to planetary engulfment.
It may occur when the orbital period of a planet is shorter than the
rotational period of its host star, as is the case for LTT 9779 b (Jenkins et
al., 2020). In this scenario the star’s tidal bulge lags behind the tidal
bulge of the planet, generating a net torque that spins up the star and causes
the planet to spiral inwards (Levrard et al., 2009; Matsumura et al., 2010).
For a given arrangement, the rate of the decay of the orbital period is
dependent on the efficiency of tidal energy dissipation within the star,
parameterised by the modified stellar tidal quality factor $Q^{\prime}_{*}$
(Penev et al., 2018). Directly measuring the orbital decay rate via long-term
transit timing measurements provides an estimate of $Q^{\prime}_{*}$, with a
larger value being associated with less efficient dissipation and therefore a
slower decay rate. While many studies have searched for evidence of orbital
decay (e.g., Patra et al., 2020; Hagey et al., 2022), the only highly
convincing detection so far has been for WASP-12 b (e.g., Maciejewski et al.,
2016; Patra et al., 2017; Yee et al., 2019; Turner et al., 2020; Wong et al.,
2022).

Therefore, in addition to fitting the timing data with a constant-period
model, we fit an orbital decay model to the mid-times and radial velocity data
of LTT 9779 b. For a planet on a Keplerian circular orbit with a constant
orbital period $P$, we expect the central time of the transits $t_{tra}$ and
the occultations $t_{occ}$ to increase linearly. Therefore, these can be
described by,

$\displaystyle t_{tra}$ $\displaystyle=$ $\displaystyle t_{0}+PE\rm~{}and$ (3)
$\displaystyle t_{occ}$ $\displaystyle=$ $\displaystyle
t_{0}+\frac{P}{2}+PE\rm,$ (4)

where $t_{0}$ is the mid-transit time of the reference epoch and $E$ is the
orbit number. In the case of orbital decay, the gradual shrinking of the
orbital period gives rise to nonlinear drift in the observable transit and
eclipse mid times. The simplest way to represent this behaviour is to include
a quadratic term in the expected transit and eclipse centre times. The model
is given by,

$\displaystyle t_{tra}$ $\displaystyle=$ $\displaystyle
t_{0}+PE+\frac{1}{2}\frac{dP}{dE}E^{2}\rm~{}and$ (5) $\displaystyle t_{occ}$
$\displaystyle=$ $\displaystyle
t_{0}+\frac{P}{2}+PE+\frac{1}{2}\frac{dP}{dE}E^{2}\rm.$ (6)

where $\frac{dP}{dE}$ is the period derivative, which we assume to be
constant. If negative, it signifies that the orbit of the planet is decaying.
We again sample the parameter space using Multinest and compare the Bayesian
evidence between each fit to determine the preferred model. The constant
period model has two free parameters: the reference epoch $t_{0}$ and the
period $P$. The decay model has three parameters, adding the $dP/dE$ term. As
we fit the mid-times and radial velocity data simultaneously, each model has
the additional RV model parameters of the velocity semi-amplitude ($K$) and
systemic velocities of HARPS (VH) and Coralie (VC).

On the other hand, if the orbit of LTT 9779 b is slightly eccentric, one may
expect the argument of periapse to precess over time due to a number of
effects (see Section 4.2) which would induce sinusoidal variations in the
transit and eclipse timing. Hence, we also attempt to fit an apsidal
precession model to the timing data. In this case, the transit and eclipse
times can be expressed as:

$\displaystyle t_{tra}$ $\displaystyle=$ $\displaystyle
t_{0}+P_{s}E-\frac{eP_{a}}{\pi}\cos{\omega}\rm,$ (7) $\displaystyle t_{occ}$
$\displaystyle=$ $\displaystyle
t_{0}+\frac{P_{a}}{2}+P_{s}E+\frac{eP_{a}}{\pi}\cos{\omega}\rm,$ (8)
$\displaystyle\omega(E)$ $\displaystyle=$
$\displaystyle\omega_{0}+\frac{d\omega}{dE}E\rm,~{}and$ (9) $\displaystyle
P_{s}$ $\displaystyle=$ $\displaystyle
P_{a}\left(1-\frac{d\omega/{dE}}{2\pi}\right)\rm,$ (10)

for argument of pericentre $\omega$, phase $\omega_{0}$, and precession rate
$d\omega/dE$. In these equations, $P_{s}$ represents the planet’s sidereal
period, which is assumed to be fixed, while $P_{a}$ is the “anomalistic”
period. This latter period is also fixed, but accounts for the additional
period signal due to precession. We note that this approach is an
approximation and is only valid for e$<<$0.1 (Ragozzine & Wolf, 2009), but,
given the very short period of LTT 9779 b and an upper limit of $e<0.058$ at
95% confidence from Jenkins et al. (2020), this assumption is valid in this
scenario. For the precession model there are a total of eight free parameters
($t_{0}$, $P$, $\omega_{0}$, $d\omega/dE$, $e$, $K$, VH, & VC).

##  3 Results

###  3.1 Atmospheric Composition

We conduct a number of atmospheric retrievals using TauREx 3.1 using both free
chemistry and chemical equilibrium models. Based on the Bayesian evidence, the
preferred model is a free chemistry retrieval which assumed an isothermal
atmosphere and for abundances of H2O and CO2 that changed with altitude. The
model is preferred to that with constant chemical abundances by 2.41 $\sigma$.
The preference between this free model and the chemical equilibrium retrieval
with a non-isothermal temperature profile is 2.40 $\sigma$. The non-isothermal
chemical equilibrium retrieval is preferred to its isothermal counterpart by
2.48 $\sigma$. We show the best-fit spectra for the preferred free and
chemical equilibrium models in Figure 6.

Our preferred free chemistry retrieval favour the presence of H2O, CO2 and FeH
while also placing upper limits of the presence of TiO and VO. The retrieved
abundances for our preferred free and chemical equilibrium retrievals are
compared in Figure 7. While many of the abundances agree across these two
models, the CO2 abundance is far higher in the free chemistry case, with the
H2O abundance in the lower half of the atmosphere also being noticeably
higher. While our models preferred the presence of CO2, WFC3 data only has
limited sensitivity to carbon-bearing species and this can mean that the
molecules retrieved is very dependent upon how the retrieval is setup (e.g.,
Changeat et al., 2020).

Our preferred chemical equilibrium retrieval is that which uses a non-
isothermal profile. It is likely that this allows for the model to have more
flexibility in the dissociation of molecules with altitude compared to when an
isothermal profile is used. However, when comparing the retrieved metallicity
and C/O ratio we find that the temperature profile did not overly impact the
results. We note again that the HST WFC3 range does not give a strong
sensitivity to carbon-bearing species and so the C/O ratio is not only poorly
constrained but also not likely to be trustworthy (Rocchetto et al., 2016).

Figure 6: The obtained spectrum from HST WFC3 G102 and G141. Over-plotted are
the preferred free chemistry (orange) and chemical equilibrium (purple)
models. Based on the Bayesian evidence, the free chemistry model is preferred
to 2.4 $\sigma$. Figure 7: Retrieved molecular abundances from free chemistry
(orange) and chemical equilibrium (purple) retrievals. Our free chemistry
retrievals suggest the presence of H2O, CO2 and FeH. They also place upper
limits on the abundances of TiO and VO but could not constrain CO or e-. The
preferred abundance of CO2 is very different between the models, as is the H2O
abundance in the lower atmosphere. The retrieved temperature profiles also
slightly differ, but are generally within 1 $\sigma$.

Spectral data from different instruments and epochs cannot be automatically
assumed to be compatible. Recovering absolute transit depths is extremely
difficult and the corner plots of the white light curve fit for the HST WFC3
G141 observations (Figure 4) show a clear correlation between the transit
depth and the systematics model. Therefore, despite the datasets seemingly
being compatible when plotted together, we also perform retrievals which allow
a global offset to be applied to the G141 data. For these, we utilise the
setups from our preferred free chemistry and chemical equilibrium retrievals,
with the only change being the addition of this offset parameter.

We find that, in the free chemistry case, the retrieval converges to a
solution with a slight offset. However, given the 1 $\sigma$ uncertainties on
this parameter, it is also consistent with there being no offset
(-10${}^{+33}_{-38}$ ppm). Meanwhile, the chemical equilibrium retrieval
prefers a more significant offset (-60$\pm$26 ppm) and we show the preferred
solution, including the offset to the HST WFC3 G141 data, in Figure 8.
However, in both cases, the Bayesian evidence shows that the models without
offsets were preferred to 3.96 and 3.4 $\sigma$ for the free and chemical
equilibrium cases respectively.

Figure 8: Spectrum from the chemical equilibrium retrieval which included an
offset for the HST WFC3 G141 data. The retrieval preferred to reduce the depth
of the G141 data by 60 ppm but the solution is not preferred over a retrieval
without an offset.

Figure 9: Probability distributions for the carbon-to-oxygen ratio (C/O, top)
and atmospheric metallicity (log10(Z), bottom) from the different chemical
equilibrium retrievals conducted here. The constraints placed on these
proprieties are poor in each case, but all three prefer solution with very low
atmospheric metallicities.

Due to the slope of the spectrum, we investigate the possibility that
unocculted spots and faculae are the cause of the modulation seen. Unocculted
faculae in particular are capable of reproducing the observed negative
bluewards slope. Our free-chemistry retrievals in which this effect was
accounted for lead to a fit which has a highly similar Bayesian evidence to
that of the free-chemistry model alone but requires 4 additional fitting
parameters. The inclusion of the modelling of stellar heterogeneities removes
any strong constraints on the atmosphere, with no molecules being conclusively
detected. However, the retrieval converges to an extremely high faculae
filling factor (65% $\pm$ 12 of the unocculted stellar surface). Given that
the star is known to be slowly rotating and therefore inactive (Jenkins et
al., 2020), and that there have been no indications of occulted faculae in any
transit observations taken of the LTT 9779 b, this value is likely
unrealistic.

We provide an overview of our retrieval setups, as well as the associated
evidence and reduced chi-square values, in Table 1.

###  3.2 Search for the 1.083 $\mu$m Helium Line

As well as the low-resolution spectrum used for our atmospheric retrievals, we
also extract a higher-resolution spectrum for the G102 data with the aim of
searching for the Helium line at 1.083 $\mu$m that would be indicative of
ongoing mass-loss. However, despite sampling this spectral range with
overlapping spectral bins which had a spacing of only 0.1 Å and a bandwidth of
3 nm (30 Å), we find no obvious evidence of excess absorption at, or around,
this wavelength (see top panel of Figure 10). The variations that are seen in
this spectrum are likely due to correlated noise.

We also model the predicted atmospheric evaporation using the methods of Allan
& Vidotto (2019) and the reconstructed high-energy spectrum of LTT 9779
presented in Section 2.3. We find that assuming either a 2/98% or 10/90%
helium to hydrogen number abundance, the evaporation rate is expected to be
$\sim 10^{11}$ g/s, reaching velocities of up to $\sim 50$ km/s. However, even
though the planet is anticipated to have a substantial evaporation rate driven
by photoionisation, the expected signature of the evaporation in the triplet
lines is very small, particularly in the 2/98% case. The middle panels of
Figure 10 show the anticipated transmission spectrum in the helium triplet,
where we derive a peak transit depth of 0.29%. Due to the width of the
spectral bins (3 nm/30 Å), the Helium triplet would not appear as a sharp peak
but as a plateau in the data: multiple bins would completely contain the
excess absorption. In the bottom panel of Figure 10 we show the magnitude of
this plateau when our 10/90% He/H model is convolved with these spectral bins.
Even in the 10/90% case, the expected signature strength is far smaller than
the uncertainties on the G102 spectra data ($\sim$20 ppm versus $\sim$135
ppm). Therefore, we conclude the data is not sufficient to detect this tracer
as even though we expect LTT 9779 b has a significant evaporation rate, its
evaporation is barely seen in the helium triplet.

Figure 10: Search for the 1.083 $\mu$m Helium triplet. While it is expected
that the planet is undergoing mass loss, little evidence could be found via
this tracer with the data collected with HST WFC3 G102. Top: the higher-
resolution HST WFC3 G102 spectrum extracted in this work. The bins are spaced
by 0.1 Å but have a bandwidth of 3 nm and, therefore, are overlapping. The
location of the peak of the Helium triplet signature is indicated by the
purple dashed line. The best-fit atmospheric model from Section 3.1 is also
shown (red) for context, as are a set of bins which are not overlapping
(green). Middle: expected signal of the Helium triplet derived from
simulations of atmospheric escape driven by photoevaporation (Allan et al,
submm.). The line is formed of three segments (dotted, dashed, dot-dash) which
together produce the final signal (solid). The expected triplet signature is
shown for two He/H ratios. The HST WFC3 G102 data is also shown, with no
excess absorption seen in these bins. Bottom: our simulated Helium signature
when convolved with the bins extracted. As the spectral bins are overlapping,
the expected signal in these bins from the triplet appears as a plateau. The
size of the signal ($\sim$20 ppm) is much smaller than the uncertainties on
each data point ($\sim$ 135 ppm), even in the 10/90 He/H case. Thus we
conclude that the data is not sensitive enough to detect the expected triplet
signature.

###  3.3 Updated Ephemeris and Search for Long-Term Timing Variations

We fit the transit and eclipse mid-times with three models: linear ephemeris,
orbital decay, and apsidal precession. We find no statistical evidence to
prefer orbital decay over a linear ephemeris: the linear model has a Bayesian
log evidence of ln(E) = -225.1 while the decay yielded ln(E) = -224.9. The
apsidal precession model, however, is highly favoured with a Bayesian evidence
of ln(E) = -201.2. Examination of the data shows that the Spitzer transits
have a significant observed minus calculated (O-C) residual compared to the
uncertainties on the mid-time (see Figure 11). These were taken from fits
conducted by Crossfield et al. (2020) to the phase curves of LTT 9779 b. The
eclipse mid-times from these phase curves (which were taken from the same data
but independently fitted by, Dragomir et al., 2020) do not show, in contrast,
the same magnitude of deviation, thereby suggesting these points may be
outliers rather than an actual detection of a significant deviation from the
expected time.

Due to the shape of the decay and precession models within an O-C plot (i.e.,
a parabola and a sin curve), we surmise that these Spitzer transit mid-times
could be driving the model towards a solution that favours precession, with
the large gaps in the transit coverage also enabling such a solution.
Therefore, we also explore fits to the data without the Spitzer transit mid-
times. In this case, the linear model is preferred with ln(E) = -181.0 versus
ln(E) = -185.8 and ln(E) = -181.7 for the orbital decay and apsidal precession
models, respectively. Though the evidence against apsidal precession versus a
linear ephemeris is only marginal, the best-fit solution for the precession
model is linear within the uncertainty (see Table 6). The inclusion or
exclusion of the Spitzer transit mid-times has a minimal impact on the best-
fit linear period but, given the potentially spurious nature of the mid-times,
we report the recovered period without these points in Table 2. For
completeness, the best-fit parameters for all fits are given in the Appendix.

Figure 11: Plots from our ephemeris fitting for LTT 9779 b. Top: Observed-
minus-calculated (O-C) plots for all transit and eclipse mid-times. The
reference epoch is set to be halfway between the first and last transit used
in this work. Traces from all three models, linear (grey), decay (red), and
precession (turquoise), are also shown. Middle: O-C plots once the Spitzer
transits have been discarded. In doing so, all evidence for non-linear
ephemerides is also removed. Bottom: fit to the literature radial velocity
data. For brevity, we only show the best-fit model to this data when
considering a constant period and when the Spitzer transit mid-times have been
discarded, which we adopt as our favoured model. However, these data are used
in all our fits.

##  4 Discussion

###  4.1 The Atmosphere of LTT 9779 b

We have presented transmission observations of the hot Neptune LTT 9779 b,
extracting a spectrum from 0.8-1.6 $\mu$m. Our best-fit free chemistry model
shows evidence for high abundances of H2O and CO2. To test the strength of
each of these detections, we run additional retrievals. Without H2O in the
model, the best-fit model provides a worse fit to the data with the Bayesian
evidence suggesting that the presence of H2O is preferred to 3.12 $\sigma$. In
this model without H2O, the retrieved CO2 abundance is even higher than in our
preferred model as shown in Figure 12. We also run a retrieval without CO2,
finding that the Bayesian evidence was reduced in this case: the inclusion of
CO2 was preferred to 2.01 $\sigma$. The lower significance of this detection
is likely due to the fact that WFC3 data only has limited sensitivity to
carbon-bearing species. Furthermore, it has been shown that carbon-bearing
species identified within a preferred model can be dependent upon how the
retrieval is setup (e.g., Changeat et al., 2020). Interestingly, the removal
of CO2 from the model does not lead to the detection of CO or HCN. Instead,
the H2O abundance is affected with a slightly higher volume mixing ratio being
preferred (see Figure 12). The other molecular species that was constrained in
the free-chemistry case was FeH and we found that our retrievals preferred its
presence to 2.13 $\sigma$. Hence, for all these species we find a relatively
weak detection significance.

Figure 12: Changes to the retrieved abundances of H2O, CO2 and FeH when one of
the other molecules is removed from the retrieval. In all three cases, the
model without the molecule is not preferred to the full setup. Comparing the
Bayesian evidence suggests the presence of H2O is preferred to 3.11 $\sigma$
while there is a 2.35 $\sigma$ preference for the inclusion of CO2 and a 2.12
$\sigma$ preference for FeH. All these retrievals were conducted with an
isothermal temperature-pressure profile.

Our retrievals with ASteRA prefer models with a high spot coverage. Such
coverages are unrealistic, but could potentially be caused by assuming the
wrong star temperature in our models. As the spots in the model are hotter
than the rest of the stellar surface, the unrealistic coverage might indicate
that our assumed stellar temperature is too low. We explore this possibility
by independently determining the basic stellar parameters. We perform an
analysis of the broadband spectral energy distribution (SED) of the star
together with the Gaia DR3 parallax (with no systematic offset applied; see,
e.g., Stassun & Torres, 2021), in order to determine an empirical measurement
of the stellar radius, following the procedures described in Stassun & Torres
(2016); Stassun et al. (2017, 2018). We pull the $B_{T}V_{T}$ magnitudes from
Tycho-2, the $JHK_{S}$ magnitudes from 2MASS, the W1–W4 magnitudes from WISE,
the $G_{\rm BP}G_{\rm RP}$ magnitudes from Gaia, as well as the NUV flux from
GALEX. Together, the available photometry spans the full stellar SED over the
wavelength range 0.2–20 $\mu$m (see Figure 13).

We perform a fit using PHOENIX stellar atmosphere models, with the free
parameters being the effective temperature ($T_{\rm eff}$) and metallicity
([Fe/H]); we set the extinction $A_{V}\equiv 0$, due to the close proximity of
the system, and we assume a surface gravity $\log g\approx 4.5$ as appropriate
for a main-sequence dwarf. Finally, we use the Gaia spectrum as a consistency
check for the overall absolute flux calibration.

The resulting fit (Figure 13) has a best-fit $T_{\rm eff}=5450\pm 75$ K and
[Fe/H] = $0.0\pm 0.3$, with a reduced $\chi^{2}$ of 1.4. Integrating the model
SED gives the bolometric flux at Earth, $F_{\rm bol}=3.503\pm 0.041\times
10^{-9}$ erg s-1 cm-2. Taking the $F_{\rm bol}$ and together with the Gaia
parallax directly gives the bolometric luminosity, $L_{\rm bol}=0.7173\pm
0.0084$ L⊙, which with the $T_{\rm eff}$ gives the stellar radius,
$R_{\star}=0.951\pm 0.018$ R⊙. In addition, we can estimate the stellar mass
from the empirical eclipsing-binary based relations of Torres et al. (2010),
giving $M_{\star}=0.96\pm 0.06$ M⊙. Finally, the mass and radius together give
the mean stellar density, $\rho_{\star}=1.58\pm 0.13$ g cm-3.

These values are consistent with those from (Jenkins et al., 2020), which we
use for all the analyses here. In particular, the recovered temperature is not
higher than assumed: it is, in fact, slightly lower ($T_{\rm eff}=5450\pm 75$
K vs $5480\pm 42$ K). Therefore, it seems that this is not the cause of the
high spot coverage preferred in our retrievals with ASteRA.

Figure 13: Spectral energy distribution of LTT 9779. Red symbols represent the observed photometric measurements, where the horizontal bars represent the effective width of the passband. Blue symbols are the model fluxes from the best-fit PHOENIX atmosphere model (black). The Gaia spectrum is also shown as a grey swathe; the inset plot shows a close-up. Table 1: Summary of atmospheric retrievals conducted in this work. Chemistry | TP Profile | Molecules Removed† | 2-layer Molecules | Offset | Spots/Fac | ln(E) | $\bar{\chi}^{2}$
---|---|---|---|---|---|---|---
Free | Isothermal | None | H2O & CO2 | False | False | 299.10 | 1.57
Free | Isothermal | H2O | CO2 | False | False | 295.64 | 1.74
Free | Isothermal | CO2 | H2O | False | False | 297.51 | 1.62
Free | Isothermal | FeH | H2O & CO2 | False | False | 297.93 | 1.73
Free | Isothermal | None | None | False | False | 297.77 | 1.46
Free | Isothermal | None | H2O & CO2 | False | True | 299.31 | 2.43
Free | Isothermal | None | H2O & CO2 | True | False | 293.76 | 1.68
Free | NPoint | None | H2O & CO2 | False | False | 298.32 | 2.15
Free | NPoint | None | H2O & CO2 | True | False | 294.98 | 2.27
Free | NPoint | None | None | False | False | 297.61 | 1.87
Chem Eq | Isothermal | N/A | N/A | False | False | 295.74 | 1.57
Chem Eq | NPoint | N/A | N/A | False | False | 297.62 | 1.77
Chem Eq | NPoint | N/A | N/A | True | False | 293.30 | 1.90
$\dagger$ Compared to standard setup of H2O, CO2, CO, HCN, TiO, VO, FeH, H-
Figure 14: High-resolution ($\delta\lambda$ = 30 Å, spaced by 0.1 Å) HST WFC3
G102 data for LTT 9779 b (top) and WASP-107 b (bottom). In the latter case,
the excess absopriotn due to the Helium triplet is clearly apparent.

Given its high irradiation, it was anticipated that LTT 9779 b would be
undergoing significant mass loss. Hence, it might be expected that this escape
could be observed using tracers of atmospheric escape such as the Helium
triplet at 1.083 $\mu$m and thus that the non-detection within the HST WFC3
G102 is surprising. However, it is important to consider that the
observability of the atmospheric escape via this particular tracer is not only
dependant on the level of atmospheric escape. The population of helium in the
triplet state also plays a critical role and this has been shown to depend on
the nature of the stellar irradiance. The triplet state is more readily
populated for K-dwarf hosts with their relatively low mid-UV flux (which can
photoionise helium out of the triplet state) to EUV flux (which is both a
significant contributor to driving the escape itself and populating the
triplet via recombinations) compared to warmer G-type stars (Oklopčić, 2019).
Our work shows that LTT 9779 b indeed receives a high mid-UV flux, with our
model finding that mid-UV photoionisations is the main depopulating source for
triplet-state helium and hence largely responsible for lack of a clear
detection of Helium at 1.083 $\mu$m. To further cement this non-detection, we
apply the same fitting procedure to the HST WFC3 G102 data of WASP-107 b,
which is shown in Figure 14 and highlights the strength of the signal seen in
that case.

Alternative tracers, such as the commonly used hydrogen Lyman-$\alpha$ line
may allow the predicted strong escape of LTT 9779 b to be observed. Again
utilising the model of Allan & Vidotto (2019), we predict significant
absorption in the non-contaminated Lyman-$\alpha$ line wings and show the
resulting profile in Figure 15. However, we note that three dimensional
modeling considering the interaction with the stellar wind is required for a
realistic Lyman-$\alpha$ prediction, given that high velocity blue-shifted
absorption originates due to the interaction with the stellar wind (Carolan et
al., 2021). We leave such a detailed analysis for further work.

Figure 15: Anticipated Lyman-$\alpha$ signature for LTT 9779 b assuming 2/98%
He/H (dotted) and 10/90% He/H (solid). While no trace of atmospheric escape
was found with the Helium triplet, this tracer may offer another chance to
detect and/or constrain the escape rate of LTT 9779 b’s atmosphere.

In their study of Helium escape for planets close to the Neptune desert,
Vissapragada et al. (2022) derived a boundary below which a planet could not
have lost more than 50% of its initial mass to photoevaporation. As LTT 9779 b
is situated below this region, they noted that is was unlikely to be the
photoevaporated core of a giant gaseous planet, with high-eccentricity orbital
migration being the more likely explanation for the planet’s current
characteristics as the planet could have been delivered to its current
location relatively late. Further evidence for this could present in the
planet’s atmospheric composition (e.g., a high C/O ratio) or via the detection
of a remaining eccentricity i the orbit of LTT 9779 b. However, the data
analysed here, and in previous studies (e.g., Dragomir et al., 2020;
Crossfield et al., 2020), is not able to provide such evidence.

Hence, it is hard to conclude a great deal about the nature of the atmosphere
of LTT 9779 b. We expect that far better constraints on the nature of LTT 9779
b’s atmosphere from the JWST NIRISS (Doyon et al., 2012) phase-curve
observations, which have already been taken as part of Cycle 1. The transit
portion of the JWST phase-curve may also shed light on spectral variability
when compared to the data presented here. Given the wider spectral coverage
and higher SNR, the NIRISS transmission data should also be able to more
easily disentangle atmospheric features from stellar contamination. An
analysis of the global temperature and chemistry will test the implications
made in this study, and those from the Spitzer data, and provide a more
accurate interpretation of both. While we do not detect the signature of
atmospheric escape from the Helium triplet in this work, the JWST NIRISS
observations may provide a detection. Additionally, observations with HST of
the Ly$\alpha$ line may provide better constrains on the current escape rate
pf LTT 9779 b’s atmosphere and thus on the nature of the hot Neptune desert.

Furthermore, eclipses observations of LTT 9779 b with CHEOPS have found
evidence for variability (AO2-013; PI: James Jenkins), with additional
observations being taken to confirm this (AO3-022; PI: James Jenkins). HST
WFC3 UVIS is also being used to study the eclipse spectrum of LTT 9779 b
(GO-16915; PI: Michael Radica; Radica et al., 2022) and these data may further
constrain the eclipse-depth variability as well as helping to determine the
albedo. Given the HST observations used here were taken roughly a year apart,
the conclusions of these eclipse studies may indicate that, while the G102 and
G141 data have similar transit depths in their overlapping spectral region,
dynamic changes to the planet may mean the spectra are not compatible.

###  4.2 The Orbit of LTT 9779 b

Figure 16: The orbital period derivative in milliseconds per year expected for
LTT 9779 b given different values of the modified stellar tidal quality factor
$Q^{{}^{\prime}}_{*}$. The right-hand vertical axis shows the expected O–C
signal over the current observational baseline and the grey shaded region
represents the average timing uncertainty in the data. Three values of
$Q^{{}^{\prime}}_{*}$ are highlighted: (1) derived with Eq. 11 from the best-
fit orbital decay rate when the Spitzer transit timings were included, (2)
predicted with Eq. 13 from the tidal forcing period of the system, and (3) the
value for WASP-12 from Wong et al. (2022).

While we do not find compelling evidence in the data to suggest that LTT 9779
b is undergoing orbital decay, we explore the magnitude of tidal dissipation
of energy within the star necessary to yield an observable signal. Assuming
the constant-phase lag model for tidal evolution suggested by Goldreich &
Soter (1966), the expected decay rate is given by:

$\displaystyle\frac{dP}{dt}$ $\displaystyle=$
$\displaystyle-\frac{27\pi}{2Q^{\prime}_{*}}\left(\frac{M_{p}}{M_{*}}\right)\left(\frac{R_{*}}{a}\right)^{5}\rm$
(11)

where $M_{p}$ is the planet’s mass, $M_{*}$ is the star’s mass, $R_{*}$ is the
star’s radius, $a$ is the semi-major axis of the planet’s orbit and
$Q^{{}^{\prime}}_{*}$ is the modified tidal quality factor. From our fit of
the orbital decay model this yields a $Q^{{}^{\prime}}_{*}$ of $1.5\times
10^{4}$ (without Spitzer transits) or $2.1\times 10^{3}$ (with Spitzer
transits), both far outside the range of $10^{5}<Q^{{}^{\prime}}_{*}<10^{8}$
expected given the current theory of energy dissipation within the convective
envelopes of cool stars (Penev et al., 2018) and two orders of magnitude
smaller than the value of $1.5\times 10^{5}$ derived for WASP-12 (Patra et
al., 2017; Yee et al., 2019; Wong et al., 2022). Based on this analysis and
the strong preference of the Bayes factor for a linear ephemeris, we conclude
that the best-fit orbital decay rates from the data do not warrant further
consideration.

Penev et al. (2018) derived an empirical model for $Q^{{}^{\prime}}_{*}$ given
the tidal forcing period of the star-planet system $P_{\text{tide}}$ from an
analysis of all known exoplanet systems with $M_{p}>0.1M_{\text{Jup}}$,
$P<3.5$ days, and $T_{eff,*}<6100$ K, the parameter space in which the LTT
9779 system resides. They found,

$\displaystyle Q^{{}^{\prime}}_{*}$ $\displaystyle=$
$\displaystyle\max\left[{\frac{10^{6}}{(P_{\text{tide}}/\text{days})^{3.1}}},{10^{5}}\right]\rm~{}where$
(12) $\displaystyle P_{\text{tide}}$ $\displaystyle=$ $\displaystyle
1/{2\left(\frac{1}{P_{\text{orb}}}-\frac{1}{P_{\text{spin}}}\right)}\rm.$ (13)

Based on this result, we predict $Q^{{}^{\prime}}_{*}$ for LTT 9779 by
adopting a stellar rotation period of 45 days, as found in Jenkins et al.
(2020). Taking this rotation period at face value requires the assumption that
the orbit of LTT 9779 b is aligned with the stellar rotation axis and so this
is, in effect, an upper limit. With this model and assumption, we predict that
$Q^{{}^{\prime}}_{*}=1.7\times 10^{7}$ for LTT 9779 which corresponds to an
orbital decay rate of $-0.0085$ ms$\text{yr}^{-1}$ for LTT 9779 b. Figure 16
shows that if orbital decay were occurring at this rate, the O–C expected
within the current observational baseline would be far below the average
uncertainty of the mid-transit times. In the near-future, more data will be
available from CHEOPS, HST, JWST and TESS observations. By time the next TESS
data for this planet is taken in Sector 69, LTT 9779 b will have orbited its
host star around 2300 times since the first detection of a transit. If we
assume the $Q^{{}^{\prime}}_{*}$ predicted from the tidal forcing period, the
O–C would be a mere $-0.05$ seconds by that time. Thus, despite the very short
orbital period of LTT 9779b it is unlikely that, if occurring, tidal orbital
decay could be detected.

Likewise, our fit to the timing data suggests that there is only evidence for
orbital precession when the Spitzer data is included and that the best-fit
apsidal precession model seems to be exploiting the large gaps in the coverage
of the transit and eclipse data. Nevertheless, we explore the potential
magnitude of precession we might expect for this world, comparing it to
preferred value from our fit. We estimate a maximum theoretical apsidal
precession rate by summing the contributions of general relativistic effects
and tidal and rotational bulges of both the planet and star, using Equations
(6), (10), and (12) from Ragozzine & Wolf (2009). The magnitude of apsidal
precession raised by tidal and rotational bulges depends on the Love number
$k_{2}$ of the perturbing body, thus we assume a value of $k_{2*}=0.03$ for
LTT 9779, typical of sun-like main sequence stars (Ragozzine & Wolf, 2009),
and $k_{2p}=0.3$ for LTT 9779 b. We chose the latter as a generous value for a
hot Neptune with a core mass fraction of $\sim$0.9 (Jenkins et al., 2020)
given the results of the case study of the Hot Neptune GJ 436 b by Kramm et
al. (2011), noting that lower values would reduce the predicted rates of
precession. Given that we additionally assume the upper limit of orbital
eccentricity ($e<0.058$) from Jenkins et al. (2020), we effectively calculate
the maximum possible precession rate from the aforementioned effects. Our
calculations yield:

$\displaystyle\dot{\omega}_{\text{tot}}$ $\displaystyle=$
$\displaystyle\dot{\omega}_{\text{tide},p}+\dot{\omega}_{\text{tide},*}+\dot{\omega}_{\text{rot},p}+\dot{\omega}_{\text{rot},*}+\dot{\omega}_{\text{GR}}$
(14) $\displaystyle=$ $\displaystyle(4.0\times 10^{-5}+1.5\times
10^{-7}+2.6\times 10^{-6}$ $\displaystyle+$ $\displaystyle 3.6\times
10^{-8}+1.1\times 10^{-5})\,rad/E$ $\displaystyle\approx$ $\displaystyle
5.4\times 10^{-5}rad/E$

where $\dot{\omega}_{\text{tide}}$ and $\dot{\omega}_{\text{rot}}$ refer to
the contribution from the tidal and rotational bulges, and
$\dot{\omega}_{\text{GR}}$ being from general relativistic effects. The
cumulative precession rate of $5.4\times 10^{-5}$ rad/E is two orders of
magnitude below our best-fit model ($d\omega/dE=3.1\times 10^{-3}$ rad/E).
Given that we have assumed characteristics that would maximise the theoretical
apisdal precession rate, we conclude that none of the above effects could be
the source of the timing variation seen in Figure 11.

We also consider the possibility that apsidal precession may be induced by an
additional body within the system. Before the confirmation of LTT 9779 b by
Jenkins et al. (2020), there were suggestions of other planets within the LTT
9779 system (Pearson, 2019), the best solutions being a 39.4$\pm$9.5 M⊕ planet
on a 1.516 day orbit and a 73.4$\pm$28.1 M⊕ planet on a 1.65 day orbit. Using
Equation (8) from Heyl & Gladman (2007), we calculate the expected apsidal
precession rate raised by these proposed companions. However, we again find
that the predicted precession rate(s) would be far below the best-fit value
from our timing models (see Figure 17), and note that any companion inducing
such a strong precession rate would be easily detectable in the radial
velocity data. Hence, we find no reasonable way to explain the precession rate
fit when including the Spitzer transits, concluding that it is not a viable
orbital solution and that it is likely due to poor sampling of the transit and
eclipse epochs since the discovery of LTT 9779 b. The combination of current
and future transit and eclipse data from CHEOPS, HST WFC3 UVIS, JWST, and TESS
should be capable of providing definitive evidence against the precession
model, as highlighted in Figure 18.

Figure 17: One source of orbital precession could be other planets within the
system. We show the possible parameter space for the mass and orbital
separation of a companion planet (LTT 9779 c) for three possible precession
rates: the best-fit value from our model fit (black) and those of the two
candidate solutions identified in Pearson (2019) (blue and orange). The blue
and orange dashed lines are the same as the latter but corrected for the
expected precession from other effects calculated in Equation 14. The solid
part of the black line represents the possible mass-separation solutions for a
companion planet that would provide the best-fit apsidal precession rate from
the timing data while remaining undetected in the radial velocity data (K$<$5
m/s) given the residuals of our fit (see Figure 11). Figure 18: Epochs covered
by existing data with CHEOPS, JWST and HST WFC3 UVIS, as well as those that
will be covered in TESS Sector 69. Over-plotted are our best-fit models when
the Spitzer transit timings are included in the analysis. With these data, the
apsidal precession model is likely to be conclusively ruled out while the
decay model will still be harder to distinguish from the linear period,
although stronger constraints on the maximum decay rate could be placed.

##  5 Conclusions

We use open-source codes to reduce and analyse the HST WFC3 G102 & G141
transmission spectrum of the ultra-hot Neptune LTT 9779 b. However, the
constraints placed on the atmospheric parameters from these data are poor,
with the best-fit value of many parameters sometimes simply being the centre
of the prior. Nevertheless, our retrievals on these data prefer the presence
of H2O, CO2 and FeH and the significance of these detections varies from
2-3$\sigma$. On the other hand, the best-fit values for the molecular
abundances are higher than expected from chemical equilibrium models. While we
find no evidence for excess absorption around the Helium triplet, our
modelling shows this is expected given the stellar irradiation. We find little
evidence to suggest that LTT 9779 b’s orbit is decaying, but this is
unsurprising given the expected magnitude of the orbital decay and its small
effect on the transit times. While a model for apsidal precession can
preferably fit the timing data, it yields a solution which cannot be
physically explained and the detection hinges purely on two transit timings
from Spitzer. Therefore, while these HST data shed further light on the nature
of LTT 9779 b, much remains to be discovered and many questions are left
unanswered. Analysis of data from CHEOPS, HST WFC3 UVIS, and JWST NIRISS
should begin to resolve some of these outstanding queries to help us
understand this rare and intriguing world.

## Acknowledgements

BE is grateful to Wilson Joy Skipper for coordinating the HST programme
GO-16457, under which these HST WFC3 observations were acquired. QC is funded
by the European Space Agency under the 2022 ESA Research Fellowship Program.
We acknowledge support from ESA through the Science Faculty - Funding
reference ESA-SCI-SC-LE-117. NS acknowledges support from the PSL Iris-OCAV
project, and from NASA (Grant #80NSSC19K0336). This project has also received
funding from the European Research Council (ERC) under the European Union’s
Horizon 2020 research and innovation programme (grant agreements No 758892,
ExoAI, and No 817540, ASTROFLOW) and from the Science and Technology Funding
Council (STFC) grant ST/S002634/1 and ST/T001836/1 and from the UK Space
Agency grant ST/W00254X/1.

Software: Iraclis (Tsiaras et al., 2016b), TauREx3 (Al-Refaie et al., 2021),
TauREx GGChem (Woitke et al., 2018; Al-Refaie et al., 2022), ASteRA (Thompson
et al., 2023), ExoTETHyS (Morello et al., 2020), PyLightcurve (Tsiaras et al.,
2016a), RadVel (Fulton et al., 2018), Multinest (Feroz et al., 2009; Buchner
et al., 2014), Astropy (Astropy Collaboration et al., 2018), h5py (Collette,
2013), emcee (Foreman-Mackey et al., 2013), Matplotlib (Hunter, 2007), Pandas
(McKinney, 2011), Numpy (Oliphant, 2006), SciPy (Virtanen et al., 2020),
corner (Foreman-Mackey, 2016).

Data: This work is based upon publicly-available observations taken with the
NASA/ESA Hubble Space Telescope as part of proposals GO-16457 (PI: Billy
Edwards; Edwards et al., 2020a) and GO-16166 (PI: Kevin France; France et al.,
2020). These observations were facilitated by the Space Telescope Science
Institute, which is operated by the Association of Universities for Research
in Astronomy, Inc., under NASA contract NAS 5–26555. The data were obtained
from the Mikulski Archive for Space Telescopes (MAST) at the Space Telescope
Science Institute. The specific observations analyzed can be accessed via
https://doi.org/10.17909/dr7t-g194 (catalog DOI: 10.17909/dr7t-g194). We are
thankful to those who operate the Hubble Space Telescope and the corresponding
archive, the public nature of which increases scientific productivity and
accessibility (Peek et al., 2019).

## Appendix

Here, we provide the posteriors for several of the retrievals conducted in
this study. Figure 19 shows the posteriors for our preferred free chemistry
retrieval while the free chemistry retrieval with an offset between the HST
WFC3 G102 and G141 datasets is shown in Figure 20. Likewise, Figures 21 and 22
show the posteriors from the chemical equilibrium retrievals with and without
an offset, respectively. Finally, in Figure 23 we shown the posteriors from
our retrieval which included the effects of spots and faculae.

Table 2 gives the stellar and planetary parameters used in this study while
the HST WFC3 G102 and G141 spectra are given in Table 3. We also provide the
transit and eclipse mid-times used in this study in Tables LABEL:tab:tr_mt and
LABEL:tab:ec_mt, respectively. We also provide the best-fit parameters from
the linear, decay, and precession models in Table 6.

Figure 19: Posterior distributions for our preferred free chemistry retrieval
which included an isothermal temperature profile and two-layer abundances for
H2O and CO2. We note that, for many parameters, the best-fit value is simply
the mean of the prior. Figure 20: Posterior distributions for the free
chemistry retrieval which included an offset in the HST WFC3 G141 data. The
retrieval converges to a solution which has a slight offset, but the ”no
offset” solution is well within the 1 $\sigma$ uncertainties. Furthermore, the
Bayesian evidence for this retrieval is significantly less than that of the
same retrieval minus an offset parameter. The difference in the Bayesian
evidence suggests an offset between the datasets is rejected at the 3.7
$\sigma$ level. Figure 21: Posterior distributions for our preferred chemical
equilibrium retrieval which included a non-isothermal temperature profile. We
note that this retrieval was not preferred over the free chemistry model given
in Figure 19, with the Bayesian evidence preferring the latter to 2.4
$\sigma$. Additionally, while the non-isothermal temperature profile led to a
preferable fit, it did not led to a well-constrained TP profile. Figure 22:
Posterior distributions for the chemical equilibrium retrieval which included
an offset in the HST WFC3 G141 data. The retrieval converges to a solution
which has a significant offset. However, the Bayesian evidence for this
retrieval is significantly less than that of the same retrieval minus an
offset parameter. The difference in the Bayesian evidence suggests an offset
between the datasets is rejected at the 3.4 $\sigma$ level, the same degree to
which the free chemistry retrievals prefer a lack of offset. Figure 23:
Posterior distributions for our free chemistry retrieval which accounted for
spots and faculae. The retrieval prefers a solution without an atmospheric
detection for LTT 9779 b and instead favours a very large, and unlikely,
faculae covering fraction.

Table 2: Stellar and planetary parameters used or derived in this study. Parameter | Unit | Value | Source
---|---|---|---
R∗ | R⊙ | 0.949 $\pm$ 0.006 | J20
M∗ | M⊙ | 1.02${}^{+0.02}_{-0.03}$ | J20
T∗ | K | 5480$\pm$42 | J20
log(g) | log10(cms-2) | 4.47$\pm$0.11 | J20
Fe/H | dex | 0.25$\pm$0.04 | J20
Age | Gyr | 2.0 ${}^{+1.3}_{-0.9}$ |
P${}_{\text{rot}}$ | days | $<45$ | J20
Rp | R⊕ | 4.72$\pm$0.23 | J20
Mp | M⊕ | 29.32${}^{+0.78}_{-0.81}$ | J20
a/R∗ |  | 3.877${}^{+0.090}_{-0.091}$ | J20
i | deg | 76.39$\pm$0.43 | J20
e |  | $<0.058$ | J20
Teq | K | 1978$\pm$19 | J20
T0 | BJDTDB | 2459043.310602$\pm$0.000090 | TW
P | days | 0.79206410$\pm$0.00000014 | TW
J20: Jenkins et al. (2020); TW: This Work
Table 3: The HST WFC3 G102 spectrum extracted in this work and the HST WFC3 G141 spectrum from Edwards et al. (2022). Wavelength | Transit Depth | Uncertainty | Bandwidth
---|---|---|---
[$\mu$m] | [% ] | [%] | [$\mu$m]
0.83750 | 0.1810 | 0.0077 | 0.0250
0.86250 | 0.1772 | 0.0087 | 0.0250
0.88750 | 0.1986 | 0.0071 | 0.0250
0.91250 | 0.1921 | 0.0066 | 0.0250
0.93750 | 0.1938 | 0.0060 | 0.0250
0.96250 | 0.1975 | 0.0060 | 0.0250
0.98750 | 0.2099 | 0.0054 | 0.0250
1.01250 | 0.2081 | 0.0051 | 0.0250
1.03750 | 0.2024 | 0.0051 | 0.0250
1.06250 | 0.1951 | 0.0041 | 0.0250
1.08750 | 0.1919 | 0.0056 | 0.0250
1.11250 | 0.2051 | 0.0066 | 0.0250
1.13750 | 0.1997 | 0.0051 | 0.0250
1.12625 | 0.2175 | 0.0064 | 0.0219
1.14775 | 0.1970 | 0.0060 | 0.0211
1.16860 | 0.1963 | 0.0087 | 0.0206
1.18880 | 0.1917 | 0.0071 | 0.0198
1.20835 | 0.2002 | 0.0062 | 0.0193
1.22750 | 0.1956 | 0.0065 | 0.0190
1.24645 | 0.1953 | 0.0071 | 0.0189
1.26550 | 0.2163 | 0.0056 | 0.0192
1.28475 | 0.1921 | 0.0062 | 0.0193
1.30380 | 0.2013 | 0.0060 | 0.0188
1.32260 | 0.2036 | 0.0073 | 0.0188
1.34145 | 0.2054 | 0.0076 | 0.0189
1.36050 | 0.2090 | 0.0071 | 0.0192
1.38005 | 0.2136 | 0.0073 | 0.0199
1.40000 | 0.2093 | 0.0065 | 0.0200
1.42015 | 0.2006 | 0.0062 | 0.0203
1.44060 | 0.2112 | 0.0063 | 0.0206
1.46150 | 0.2097 | 0.0058 | 0.0212
1.48310 | 0.2103 | 0.0052 | 0.0220
1.50530 | 0.2180 | 0.0070 | 0.0224
1.52800 | 0.2149 | 0.0051 | 0.0230
1.55155 | 0.2074 | 0.0060 | 0.0241
1.57625 | 0.2116 | 0.0063 | 0.0253
1.60210 | 0.2143 | 0.0060 | 0.0264
1.62945 | 0.2203 | 0.0061 | 0.0283
Table 4: Transit mid-times utilised in this work. Transit Mid-Time | Uncertainty | Epoch | Source
---|---|---|---
[BJDTDB] | [days] |  |
2458354.21580 | 0.00120 | -870 | TESS (K22)
2458355.00840 | 0.00160 | -869 | TESS (K22)
2458355.79800 | 0.00110 | -868 | TESS (K22)
2458357.38318 | 0.00099 | -866 | TESS (K22)
2458358.17580 | 0.00110 | -865 | TESS (K22)
2458358.96760 | 0.00200 | -864 | TESS (K22)
2458359.75890 | 0.00110 | -863 | TESS (K22)
2458360.55100 | 0.00130 | -862 | TESS (K22)
2458361.34230 | 0.00140 | -861 | TESS (K22)
2458362.13651 | 0.00100 | -860 | TESS (K22)
2458362.92650 | 0.00130 | -859 | TESS (K22)
2458363.71870 | 0.00100 | -858 | TESS (K22)
2458364.51130 | 0.00120 | -857 | TESS (K22)
2458365.30484 | 0.00077 | -856 | TESS (K22)
2458366.09510 | 0.00100 | -855 | TESS (K22)
2458366.88765 | 0.00100 | -854 | TESS (K22)
2458369.26457 | 0.00074 | -851 | TESS (K22)
2458370.05550 | 0.00100 | -850 | TESS (K22)
2458370.84950 | 0.00180 | -849 | TESS (K22)
2458371.63979 | 0.00074 | -848 | TESS (K22)
2458372.43220 | 0.00210 | -847 | TESS (K22)
2458373.22520 | 0.00170 | -846 | TESS (K22)
2458374.01730 | 0.00130 | -845 | TESS (K22)
2458374.80930 | 0.00130 | -844 | TESS (K22)
2458375.60121 | 0.00092 | -843 | TESS (K22)
2458376.39385 | 0.00076 | -842 | TESS (K22)
2458377.18376 | 0.00077 | -841 | TESS (K22)
2458377.97850 | 0.00170 | -840 | TESS (K22)
2458378.76838 | 0.00080 | -839 | TESS (K22)
2458379.56140 | 0.00150 | -838 | TESS (K22)
2458380.35167 | 0.00099 | -837 | TESS (K22)
2458381.14590 | 0.00140 | -836 | TESS (K22)
2458781.13997 | 0.00032 | -331 | Spitzer (C20)
2458783.51684 | 0.00053 | -328 | Spitzer (C20)
2459088.45768 | 0.00090 | 57 | TESS (K22)
2459089.25123 | 0.00093 | 58 | TESS (K22)
2459090.04391 | 0.00078 | 59 | TESS (K22)
2459090.83570 | 0.00110 | 60 | TESS (K22)
2459091.62575 | 0.00087 | 61 | TESS (K22)
2459092.41940 | 0.00100 | 62 | TESS (K22)
2459093.21130 | 0.00120 | 63 | TESS (K22)
2459094.00276 | 0.00100 | 64 | TESS (K22)
2459094.79610 | 0.00074 | 65 | TESS (K22)
2459095.58610 | 0.00170 | 66 | TESS (K22)
2459096.37986 | 0.00079 | 67 | TESS (K22)
2459097.16960 | 0.00260 | 68 | TESS (K22)
2459097.96335 | 0.00095 | 69 | TESS (K22)
2459102.71480 | 0.00130 | 75 | TESS (K22)
2459103.50590 | 0.00100 | 76 | TESS (K22)
2459104.29951 | 0.00077 | 77 | TESS (K22)
2459105.09100 | 0.00100 | 78 | TESS (K22)
2459105.88175 | 0.00080 | 79 | TESS (K22)
2459106.67610 | 0.00150 | 80 | TESS (K22)
2459107.46860 | 0.00180 | 81 | TESS (K22)
2459108.25930 | 0.00084 | 82 | TESS (K22)
2459109.05020 | 0.00100 | 83 | TESS (K22)
2459109.84550 | 0.00120 | 84 | TESS (K22)
2459110.63740 | 0.00140 | 85 | TESS (K22)
2459111.42907 | 0.00086 | 86 | TESS (K22)
2459112.22229 | 0.00092 | 87 | TESS (K22)
2459377.56157 | 0.00018 | 422 | HST (TW)
2459733.19839 | 0.00019 | 871 | HST (TW)
C20: Crossfield et al. (2020); K22: Kokori et al. (2022a)
TW: This Work
Table 5: Eclipse mid-times utilised in this work. Eclipse Mid-Time | Uncertainty | Epoch | Source
---|---|---|---
[BJDTDB] | [days] |  |
2458354.61092 | 0.00205 | -870 | TESS (TW)
2458358.57127 | 0.00115 | -865 | TESS (TW)
2458360.94750 | 0.00123 | -862 | TESS (TW)
2458364.11575 | 0.00150 | -858 | TESS (TW)
2458368.86808 | 0.00102 | -852 | TESS (TW)
2458372.03640 | 0.00164 | -848 | TESS (TW)
2458375.20465 | 0.00234 | -844 | TESS (TW)
2458378.37286 | 0.00111 | -840 | TESS (TW)
2458541.53740 | 0.00110 | -634 | Spitzer (D20)
2458544.70430 | 0.00200 | -630 | Spitzer (D20)
2458550.24910 | 0.00260 | -623 | Spitzer (D20)
2458555.00240 | 0.00130 | -617 | Spitzer (D20)
2458562.13080 | 0.00200 | -608 | Spitzer (D20)
2458563.71590 | 0.00170 | -606 | Spitzer (D20)
2458569.25990 | 0.00280 | -599 | Spitzer (D20)
2458574.80220 | 0.00290 | -592 | Spitzer (D20)
2458780.73960 | 0.00670 | -332 | Spitzer (D20)
2458781.53340 | 0.00130 | -331 | Spitzer (D20)
2458783.11600 | 0.00350 | -329 | Spitzer (D20)
2458783.90490 | 0.00400 | -328 | Spitzer (D20)
2459088.85451 | 0.00153 | 57 | TESS (TW)
2459092.02276 | 0.00118 | 61 | TESS (TW)
2459095.19103 | 0.00125 | 65 | TESS (TW)
2459098.35925 | 0.00155 | 69 | TESS (TW)
2459104.69580 | 0.00132 | 77 | TESS (TW)
2459107.86407 | 0.00136 | 81 | TESS (TW)
D20: Dragomir et al. (2020); TW: This Work
Table 6: Best-fit parameters from our linear, decay, and precession model fits to the transit and eclipse mid-times and radial velocity data of LTT 9779 b. Due to the significant O-C seen in the Spitzer transit mid-times, but not the Spitzer eclipse mid-times, we show the results for fits with and without these transit mid-times, preferring the latter as discussed in Section 3.3. Model | Parameter | Unit | Without Spitzer Transits | With Spitzer Transits
---|---|---|---|---
Linear | P | [days] | 0.79206406 $\pm$ $0.00000014^{\dagger}$ | 0.79206380 $\pm$ 0.00000014
$t_{0}$ | [BJDTDB] | 2459043.310621 $\pm$ $0.000088^{\dagger}$ | 2459043.310895 $\pm$ 0.000086
Decay | P | [days] | 0.79206404 $\pm$ 0.00000014 | 0.79206376 $\pm$ 0.00000014
$t_{0}$ | [BJDTDB] | 2459043.31067 $\pm$ 0.00015 | 2459043.31122 $\pm$ 0.00014
dP/dE | [days epoch-1] |  $-2.4\times 10^{-10}$ $\pm$ $5.6\times 10^{-10}$ |  $-1.71\times 10^{-9}$ $\pm$ $0.54\times 10^{-9}$
dP/dt | [ms yr-1] |  $-9$ $\pm$ 22 |  $-68$ $\pm$ 21
Precession | P | [days] | 0.79206409 $\pm$ 0.00000015 | 0.79206476 $\pm$ 0.00000023
$t_{0}$ | [BJDTDB] | 2459043.310601 $\pm$ 0.000093 | 2459043.311163 $\pm$ 0.000092
$\omega_{0}$ | [rad] | 3.8 $\pm$ 2.1 | 4.358 $\pm$ 0.070
d$\omega$/dE | [rad epoch-1] | 0.0030 $\pm$ 0.0023 | 0.00313 $\pm$ 0.00015
| e |  | 0.00018 $\pm$ 0.00042 | 0.00623 $\pm$ 0.00082
†Preferred ephemeris solution

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