# ARES111Ariel Retrieval Exoplanet School V: No Evidence For Molecular
Absorption in the HST WFC3 Spectrum of GJ 1132 b

Lorenzo V. Mugnai La Sapienza Universitá di Roma, Department of Physics,
Piazzale Aldo Moro 2, 00185 Roma, Italy  Darius Modirrousta-Galian INAF –
Osservatorio Astronomico di Palermo, Piazza del Parlamento 1, I-90134 Palermo,
Italy  University of Palermo, Department of Physics and Chemistry, Via
Archirafi 36, Palermo, Italy  Billy Edwards Department of Physics and
Astronomy, University College London, London, United Kingdom  Quentin Changeat
Department of Physics and Astronomy, University College London, London, United
Kingdom  Jeroen Bouwman  Max-Planck-Institut für Astronomie, Königstuhl 17,
69117 Heidelberg, Germany  Giuseppe Morello Instituto de Astrofísica de
Canarias (IAC), 38205 La Laguna, Tenerife, Spain  INAF – Osservatorio
Astronomico di Palermo, Piazza del Parlamento 1, I-90134 Palermo, Italy  Ahmed
Al-Refaie Department of Physics and Astronomy, University College London,
London, United Kingdom  Robin Baeyens  Institute of Astronomy, KU Leuven,
Celestijnenlaan 200D, 3001 Leuven, Belgium  Michelle Fabienne Bieger  College
of Engineering, Mathematics and Physical Sciences, Physics Building,
University of Exeter, Exeter, United Kingdom  Doriann Blain  LESIA,
Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université
de Paris, Meudon, France  Amélie Gressier  Sorbonne Universités, UPMC
Université Paris 6 et CNRS, UMR 7095, Institut d’Astrophysique de Paris,
Paris, France  LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne
Université, Université de Paris, Meudon, France  Gloria Guilluy  Dipartimento
di Fisica, Universitá degli Studi di Torino, via Pietro Giuria 1, I-10125
Torino, Italy  INAF Osservatorio Astrofisico di Torino, Via Osservatorio 20,
I-10025 Pino Torinese, Italy  Yassin Jaziri  Laboratoire d’astrophysique de
Bordeaux, Univ. Bordeaux, CNRS, B18N, allée Geoffroy Saint-Hilaire, 33615
Pessac, France  Flavien Kiefer  LESIA, Observatoire de Paris, Université PSL,
CNRS, Sorbonne Université, Université de Paris, Meudon, France  Mario Morvan
Department of Physics and Astronomy, University College London, London, United
Kingdom  William Pluriel  Laboratoire d’astrophysique de Bordeaux, Univ.
Bordeaux, CNRS, B18N, allée Geoffroy Saint-Hilaire, 33615 Pessac, France
Mathilde Poveda  Laboratoire Interuniversitaire des Systèmes Atmosphériques
(LISA), UMR CNRS 7583, Université Paris-Est-Créteil, Université de Paris,
Institut Pierre Simon Laplace, Créteil, France  Maison de la Simulation, CEA,
CNRS, Univ. Paris-Sud, UVSQ, Université Paris-Saclay, F-91191 Gif-sur-Yvette,
France  Nour Skaf Department of Physics and Astronomy, University College
London, London, United Kingdom  LESIA, Observatoire de Paris, Université PSL,
CNRS, Sorbonne Université, Université de Paris, Meudon, France  Subaru
Telescope, National Astronomical Observatory of Japan, 650 North A’ohoku
Place, Hilo, HI 96720, USA  Niall Whiteford  Institute for Astronomy,
University of Edinburgh, Royal Observatory, Blackford Hill, Edinburgh, EH9
3HJ, UK  Centre for Exoplanet Science, University of Edinburgh, UK  Sam Wright
Department of Physics and Astronomy, University College London, London, United
Kingdom  Kai Hou Yip  Department of Physics and Astronomy, University College
London, London, United Kingdom  Tiziano Zingales  Laboratoire d’astrophysique
de Bordeaux, Univ. Bordeaux, CNRS, B18N, allée Geoffroy Saint-Hilaire, 33615
Pessac, France  Benjamin Charnay  LESIA, Observatoire de Paris, Université
PSL, CNRS, Sorbonne Université, Université de Paris, Meudon, France  Pierre
Drossart  Sorbonne Universités, UPMC Université Paris 6 et CNRS, UMR 7095,
Institut d’Astrophysique de Paris, Paris, France  LESIA, Observatoire de
Paris, Université PSL, CNRS, Sorbonne Université, Université de Paris, Meudon,
France  Jérémy Leconte  Laboratoire d’astrophysique de Bordeaux, Univ.
Bordeaux, CNRS, B18N, allée Geoffroy Saint-Hilaire, 33615 Pessac, France
Olivia Venot  Laboratoire Interuniversitaire des Systèmes Atmosphériques
(LISA), UMR CNRS 7583, Université Paris-Est-Créteil, Université de Paris,
Institut Pierre Simon Laplace, Créteil, France  Ingo Waldmann Department of
Physics and Astronomy, University College London, London, United Kingdom
Jean-Philippe Beaulieu  School of Physical Sciences, University of Tasmania,
Private Bag 37 Hobart, Tasmania 7001 Australia  Sorbonne Universités, UPMC
Université Paris 6 et CNRS, UMR 7095, Institut d’Astrophysique de Paris,
Paris, France

###### Abstract

We present a study on the spatially scanned spectroscopic observations of the
transit of GJ 1132 b, a warm ($\sim$500 K) Super-Earth (1.13 R⊕) that was
obtained with the G141 grism (1.125 - 1.650 $\mu$m) of the Wide Field Camera 3
(WFC3) onboard the Hubble Space Telescope. We used the publicly available
Iraclis pipeline to extract the planetary transmission spectra from the five
visits and produce a precise transmission spectrum. We analysed the spectrum
using the TauREx3 atmospheric retrieval code with which we show that the
measurements do not contain molecular signatures in the investigated
wavelength range and are best-fit with a flat-line model. Our results suggest
that the planet does not have a clear primordial, hydrogen-dominated
atmosphere. Instead, GJ 1132 b could have a cloudy hydrogen-dominated
envelope, a very enriched secondary atmosphere, be airless, or have a tenuous
atmosphere that has not been detected. Due to the narrow wavelength coverage
of WFC3, these scenarios cannot be distinguished yet but the James Webb Space
Telescope may be capable of detecting atmospheric features, although several
observations may be required to provide useful constraints.

##  1 Introduction

One major obstacle that exoplanetary researchers encounter is a general lack
of data. This makes it difficult to determine the composition and internal
structure of exoplanets as there is an inevitable strong degeneracy when one
tries to fit a model to observations. By making use of geophysical and
statistical principles, several studies have determined the degree of
degeneracy in exoplanet compositions (e.g. Adams et al., 2008; Valencia et
al., 2013; Dorn et al., 2017). They found that knowing the mass and radius of
a planet precisely can lead to superior constraints on the ice mass fraction
and size of the inner embryo, but little improvement on the atmospheric
composition. However, they also found that determining the atmospheric
composition (such as from spectroscopy) could lead to a significant
improvement of the interior predictions. Therefore, there is a strong
motivation to characterise exoplanetary atmospheres as this would lead to a
better understanding on the global properties of their host planets.

In spite of this, under most circumstances only the mass and radius of
exoplanets are known, so all that can be done is constrain the internal
compositions from the bulk mean densities (e.g. Zeng & Sasselov, 2013; Zeng et
al., 2016). Recent advances in exoplanetary spectroscopy have allowed for the
atmospheric composition and structure to be constrained enough to attain a
more holistic understanding of the planet. For instance, from the mass and
radius of a planet one cannot tell whether a super-Earth or sub-Neptune is
$\rm H_{2}O$-rich or a silicate embryo with a hydrogen envelope (e.g. Valencia
et al., 2013). However, if one were to constrain the atmospheric composition
of these perplexing bodies, then one could determine whether the planet is icy
(i.e. no atmosphere or a $\rm H_{2}O$-rich one if the temperature is high
enough) or rocky with a hydrogen-rich atmosphere (i.e. collisional absorption
lines of hydrogen are detected with, perhaps, some mineral or volcanic
species).

A number of studies using HST WFC3 have found evidence for molecular
absorption in Sub-Neptunes (e.g. Guo et al., 2020; Guilluy et al., 2021). Of
particular note are the studies of the habitable-zone planet K2-18 b, which
likely has a hydrogen–helium envelope with a high concentration of water vapor
(Tsiaras et al., 2019; Benneke et al., 2019) and possibly $\rm CH_{4}$ (Bézard
et al., 2020; Blain et al., 2021). Meanwhile, GJ 1214 b most probably hosts a
thick cloud layer, with molecular features belonging to cloud-free primary
atmosphere, or one composed of $100\%$ $\rm H_{2}O$ and $100\%$ $\rm CO_{2}$,
having been ruled out (e.g. Kreidberg et al., 2014).

Whilst the atmospheric spectroscopy of small, potentially rocky, exoplanets is
difficult, several analyses have already been made on well-known systems. For
example:

  * •

TRAPPIST-1 b, c, d, e, f and g most probably do not have cloud-free hydrogen
atmospheres (e.g. de Wit et al., 2016).

  * •

The HST WFC3 transmission spectrum of the highly irradiated Super-Earth 55 Cnc
e shows evidence for Hydrogen Cyanide (HCN) (Tsiaras et al., 2016c). However,
the exact nature of its atmosphere, and whether it exists, is still highly
debated (Madhusudhan et al., 2012; Dorn et al., 2019; Modirrousta-Galian et
al., 2020a; Jindal et al., 2020; Zilinskas et al., 2021; Zhang et al., 2021)

  * •

LHS 1140 b, a super-Earth orbiting in the habitable-zone of its star,
potentially hosts an atmosphere containing water vapour but the low SNR, and
narrow wavelength coverage, of the data means this detection is tentative
(Edwards et al., 2021).

Additionally, the Spitzer phase curve of the terrestrial planet LHS 3844 b is
incompatible with a thick atmosphere (Kreidberg et al., 2019). Thus, so far,
there have been no definitive measurements of the atmosphere of a rocky
exoplanet.

In this paper we perform a spectroscopic analysis of GJ 1132 b with the aim of
determining its atmospheric composition. Making use of the mass and radius
measurements from the literature, we then make inferences on the interior
composition and properties of GJ 1132 b. Having a mass, radius, and
equilibrium temperature of $\rm 1.66\pm 0.23\,M_{\oplus}$, $\rm 1.130\pm
0.056\,R_{\oplus}$, and $\rm 500-600~{}K$ (Bonfils et al., 2018) respectively,
GJ 1132 b is a super-Earth that may be an ice planet that migrated inwards, or
a silicate embryo with a hydrogen envelope (see Figure 1). A mixture of these
two compositions or a more exotic make-up may also be possible (Zeng et al.,
2016).

In order to try to overcome this degeneracy we perform a spectroscopic
analysis on the spectral data obtained through Hubble observations. Using five
transit observations, we recover a flat spectrum which shows no sign of
atmospheric features. We rule out a clear hydrogen/helium dominated atmosphere
to $>5\sigma$. Future observations are required to confidently distinguish
between a cloudy primary atmosphere or one with a higher mean molecular
weight.

Figure 1: The mass and radius plot of GJ 1132 b (Bonfils et al., 2018) with
other super-Earths and sub-Neptunes. The Earth-like, $\rm H_{2}O$ and Iron
mass and radius models are from Zeng & Sasselov (2013) and Zeng et al. (2016).
The remnant core model (i.e. a planet that is highly compressed due to once
hosting a large primordial atmosphere that was then subsequently lost) is from
Mocquet et al. (2014). It is important to note that the mass-radius models
shown above are merely illustrative as more complex set-ups are possible (e.g.
Jespersen & Stevenson, 2020; Mousis et al., 2020; Modirrousta-Galian et al.,
2020a). The planets listed are Trappist-1 b,g (Grimm et al., 2018; de Wit et
al., 2016), GJ 357 b (Luque et al., 2019), Kepler-406 c (Marcy et al., 2014),
Kepler-414 b (Hadden & Lithwick, 2014), Kepler-102 d (Marcy et al., 2014), GJ
9827 d (Rice et al., 2019), GJ 1214 b (Harpsøe et al., 2013),CoRoT-7 b (Dai et
al., 2019), HD 97658 b (Van Grootel et al., 2014; Guo et al., 2020), HD 3167 c
(Christiansen et al., 2017; Guilluy et al., 2021; Mikal-Evans et al., 2021),
LHS 1140 b (Ment et al., 2019), and K2-18b (Benneke et al., 2019; Tsiaras et
al., 2019; Bézard et al., 2020; Blain et al., 2021)

.

##  2 Method

###  2.1 Data analysis

Our analysis is based on five transit observations of GJ 1132 b (Table 1)
obtained between April and November 2017 with the G141 infrared grism
($1.125-1.650\;\mu m$) of the Wide Field Camera 3 (WFC3) on board the Hubble
Space Telescope (HST). The observations were part of the HST proposal number
14758 led by Zach Berta-Thompson (Berta-Thompson et al., 2016), and were
downloaded from the public Mikulski Archive for Space Telescope (MAST)
archive222https://archive.stsci.edu/hst/.

Each transit observation required 4 HST orbits and utilised the spatial
scanning technique. The observations were acquired using the 256x256 sub-
array, employing the SPARS10 sampling sequence with 15 up-the-ramp reads which
lead to an exposure time of 103.129 s. The scan speed was 0.2”/s leading to a
total scan length of 170 pixels and a maximum pixel fluence below 24,000
electrons.

Table 1: Star and planet parameters used as reference in this paper. Parameter | Value | Source
---|---|---
Stellar parameters
Spectral type | M4.5 V | Berta-Thompson et al. (2015)
$T_{\rm eff}\;[K]$ | $3270\pm 140$ | Bonfils et al. (2018)
$R_{\star}\;[R_{\sun}]$ | $0.2105^{+0.0102}_{-0.0085}$ | Bonfils et al. (2018)
$\log_{10}g\;[cm/s^{2}]$ | $5.05\pm 0.074$ | Bonfils et al. (2018)
$[Fe/H]$ | $-0.12\pm 0.15$ | Berta-Thompson et al. (2015)
Planetary parameters
$M_{p}\;[M_{\earth}]$ | $1.66\pm 0.23$ | Bonfils et al. (2018)
$R_{p}\;[R_{\earth}]$ | $1.130\pm 0.056$ | Bonfils et al. (2018)
$P\;[day]$ | $1.628931\pm 0.000027$ | Bonfils et al. (2018)
$a/R_{\star}$ | $15.6235^{+0.8}_{-0.7}$ |  Bonfils et al. (2018)a
$e$ | $<0.22^{b}$ | Bonfils et al. (2018)
$i\;[deg]$ | $88.68^{+0.40}_{-0.33}$ | Bonfils et al. (2018)
$T_{\text{mid}}\;[BJD-2450000]$ | $7184.55786\pm 0.00031$ | Bonfils et al. (2018)
aderived from (Bonfils et al., 2018) measurements of $a$ and $R_{\star}$
b fixed to zero as in Berta-Thompson et al. (2015)

Following the procedure already described in similar studies (e.g. Edwards et
al., 2020a; Skaf et al., 2020; Anisman et al., 2020; Changeat & Edwards,
2021), we extract white and spectral light-curves from the raw HST/WFC3 images
using the Iraclis software (Tsiaras et al., 2016b). Iraclis is an open-source
software dedicated to the analysis of WFC3 scanning observations and is
publicly available on GitHub333https://github.com/ucl-exoplanets/Iraclis. In
the following we briefly summarise the data analysis steps operated by the
software, but we refer the reader to Tsiaras et al. (2016b) for a complete
discussion.

####  2.1.1 Data reduction and calibration

The Iraclis reduction process included 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 corrections for bad pixels and cosmic rays (Tsiaras
et al., 2016b). In each of the visits, we noted several faint sources which
overlapped with the spectrum for GJ 1132. Hence we split these data into
individual up-the-ramp reads and performed the extraction on these to remove
the signal from these secondary sources which could impact the shorter
wavelengths of the recovered spectrum. Two example reads from the second visit
are shown in Figure 2, with the first order spectrum from faint source visible
below the data from GJ 1132 and the zeroth order of another star also within
the scan’s arc.

Figure 2: Example reads from the beginning (left) and end (right) of a scan
for the second visit. If the data were not extracted from each read
individually, the two faint background sources would contribute to the
spectrum. The colour indicates the count per pixel and is represented with a
log scale.

####  2.1.2 Light curve extraction

We extract the wavelength-dependent light-curves taking into account of the
geometric distortions caused by the tilted detector of the WFC3/IR channel.

We obtain a white light curve, and a set of spectral light curves. The former
is obtained integrating the full wavelength range of WFC3/G141, while the
latter are extracted using narrow band such that the resolving power is 70 at
$1.4\;\mu m$.

####  2.1.3 Limb darkening coefficients

The limb-darkening coefficients are computed using the non-linear formula by
Claret (2000), which scales the intensity emerging from the star as:

$\frac{I(\mu)}{I(1)}=1-\sum_{k=1}^{4}a_{k}(1-\mu^{\frac{k}{2}})$ (1)

where $\mu=\cos(\gamma)$, and $\gamma$ is the angle between the line of sight
and the emergent intensity, and $a_{k}$ are the limb darkening coefficients.

We calculated the $a_{k}$ coefficients using ExoTETHyS (Morello et al., 2020),
with the stellar models from Phoenix 2018 (Claret, 2018) and the parameters in
Table 1. These are given in Table 2.

Table 2: Limb darkening coefficients used here. The first row represents the white light curve while all others are for the spectral light curves. $\lambda\;[\mu m]$ | a1 | a2 | a3 | a4 | $\Delta\lambda\;[\mu m]$
---|---|---|---|---|---
1.3840 | 1.475 | -1.351 | 0.830 | 0.592 |
1.1262 | 1.461 | -1.439 | 0.922 | -0.247 | 0.0219
1.1478 | 1.435 | -1.431 | 0.924 | -0.249 | 0.0211
1.1686 | 1.413 | -1.412 | 0.912 | -0.246 | 0.0206
1.1888 | 1.430 | -1.443 | 0.934 | -0.252 | 0.0198
1.2084 | 1.406 | -1.406 | 0.907 | -0.244 | 0.0193
1.2275 | 1.363 | -1.363 | 0.880 | -0.237 | 0.0190
1.2465 | 1.364 | -1.361 | 0.876 | -0.236 | 0.0189
1.2655 | 1.361 | -1.371 | 0.886 | -0.239 | 0.0192
1.2848 | 1.324 | -1.330 | 0.859 | -0.232 | 0.0193
1.3038 | 1.318 | -1.333 | 0.862 | -0.233 | 0.0188
1.3226 | 1.361 | -1.386 | 0.896 | -0.241 | 0.0188
1.3415 | 1.376 | -1.247 | 0.759 | -0.198 | 0.0189
1.3605 | 1.447 | -1.314 | 0.787 | -0.202 | 0.0192
1.3800 | 1.526 | -1.468 | 0.904 | -0.236 | 0.0199
1.4000 | 1.477 | -1.337 | 0.799 | -0.205 | 0.0200
1.4202 | 1.456 | -1.275 | 0.746 | -0.190 | 0.0203
1.4406 | 1.475 | -1.288 | 0.745 | -0.187 | 0.0206
1.4615 | 1.417 | -1.183 | 0.672 | -0.168 | 0.0212
1.4831 | 1.461 | -1.273 | 0.735 | -0.184 | 0.0220
1.5053 | 1.475 | -1.316 | 0.766 | -0.193 | 0.0224
1.5280 | 1.475 | -1.332 | 0.784 | -0.199 | 0.0230
1.5515 | 1.452 | -1.309 | 0.772 | -0.197 | 0.0241
1.5762 | 1.478 | -1.374 | 0.816 | -0.208 | 0.0253
1.6021 | 1.485 | -1.435 | 0.872 | -0.225 | 0.0264
1.6295 | 1.475 | -1.476 | 0.917 | -0.240 | 0.0283

####  2.1.4 White light-curves fitting

To fit the extracted white and spectral light-curves, we consider the known
time-dependent systematics introduced by HST:

  * •

long-term ‘ramp’, characterised by a linear trend

  * •

short-term ‘ramp’, characterised by an exponential trend.

To remove these systematics, we multiply for a normalisation factor $n_{w}$
and an instrumental corrective factor $R(t)$. The former depend on the
telescope observing scanning mode, $n_{w}^{\text{scan}}$, and when scanning
direction is upwards changes to $n_{w}^{for}$ or to $n_{w}^{\text{rev}}$ when
scanning direction is downwards. $R(t)$ is time dependent and can be derived
as

$R(t)=(1-r_{a}(t-T_{0}))\left(1-r_{b_{1}}e^{-r_{b_{2}}(t-t_{0})}\right)$ (2)

where $t$ is time, $T_{0}$ is the mid-transit time, $t_{0}$ is the starting
time of each HST orbit, $r_{a}$ is the linear systematic trend’s slope,
$r_{b_{1}}$ and $r_{b_{2}}$ are the exponential systematic trend’s
coefficients (Kreidberg et al., 2014; Tsiaras et al., 2016c, b) .

To extract the white transit light curve, $F_{w}^{v}(t)$, for each visit, $v$,
we both fit the transit model multiplied by the instrumental systematics,
$n_{w}^{\text{scan}}R(t)F_{w}^{v}(t)$ and we fit the systematic model $R(t)$
on the out of transit data, correcting the light curve and then fitting again
$n_{w}^{\text{scan}}F_{w}^{v}(t)$.

To fit the light curves we use the data presented in Table 1, leaving as free
parameters the radii ratio, $R_{p}/R_{\star}$, and the mid transit time,
$T_{\text{mid}}$. For the fit we used a Monte-Carlo Markov chain of 350000
steps with 200 walkers and 200000 burned iterations, using the emcee Python
package (Foreman-Mackey et al., 2013). Each light curve has been fitted
individually and so we obtained the white light curve squared radii ratio for
each transit $(R_{p}/R_{\star})^{2}_{w,v}$. Initially, we fitted the white
light curves using the formulae above and 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 explained by the ramp
model. For this reason, we scaled up the uncertainties in the individual data
points, for their median to match the standard deviation of the residuals, and
repeated the fitting Tsiaras et al. (2018) The resulted detrended white light
curves are reported in Figure 3 and the fit results are in Table 3. The Table
shows that the $(R_{p}/R_{\star})^{2}_{w,v}$ are compatible under $2\,\sigma$
and that the standard deviation of the fitting residuals for the white light
curves are significantly higher than the photon noise. The ratio between the
standard deviation of the fitting residuals and the photon noise is reported
in Table 3 as $\bar{\sigma}$.

Figure 3: In the top panel are reported the detrended white light curves from each visit along with the best-fit transit model. In the bottom panel, the residuals are reported.  Table 3: Derived parameters from the white light curves and fitting metrics: 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). Parameter | 1st visit | 2nd visit | 3rd visit | 4th visit | 5th visit
---|---|---|---|---|---
$\left(R_{p}/R_{\star}\right)^{2}_{w,v}$ | $0.002430^{+0.000039}_{-0.000030}$ | $0.002430^{+0.000024}_{-0.000017}$ | $0.002440^{+0.000040}_{-0.000030}$ | $0.002632^{+0.000011}_{-0.000017}$ | $0.002352^{+0.000029}_{-0.000029}$
$T_{\text{mid}}\;[BJD-2450000]$ | $7862.19152^{+0.00008}_{-0.00009}$ | $8020.19899^{+0.00004}_{-0.00004}$ | $8077.21035^{+0.00008}_{-0.00007}$ | $8080.46887^{+0.00007}_{-0.00007}$ | $8083.72719^{+0.00008}_{-0.00005}$
$\bar{\chi}$ | 1.18 | 1.16 | 1.17 | 1.20 | 1.17
$\bar{\sigma}$ | 1.43 | 1.03 | 1.50 | 2.42 | 1.45
AC | 0.13 | 0.32 | 0.15 | 0.11 | 0.22

####  2.1.5 Spectral light-curves fitting

To correct for the systematics present in the spectral light-curves of each
visit, $F_{\lambda}^{v}(t)$, we fit each curve with a model that includes the
white light curve associated, $F_{w}^{v}(t)$:

$n^{\text{scan}}_{\lambda}\left[1-r_{a}(t-T_{0})\right]\frac{F_{\lambda}^{v}(t)}{F_{w}^{v}(t)}$
(3)

where $r_{a}$ is the coefficient of a wavelength-dependent linear slope along
each HST visit and $n^{\text{scan}}_{\lambda}$ is the normalisation factor,
that changes to $n^{\text{for}}_{\lambda}$, when the scanning direction is
upwards, and to $n^{\text{rev}}_{\lambda}$ when it is downwards. In the
spectral light-curve fitting, the only free parameter is Rp/R⋆, while the
other parameters are the same as we used for the white light-curve fitting.
For the fit we used a Monte-Carlo Markov chain of 150000 steps with 100
walkers and 100000 burned iterations, using again the emcee package (Foreman-
Mackey et al., 2013).

To check the quality of our fits, we use the auto-correlation of the residuals
for each light curve using the numpy correlate package. To determine a ‘good’
value of the auto-correlation, we generated a thousand instances of random
Gaussian noise and computed the auto-correlation. For the number of data
points in our light curves ($\sim$70), 85% of the time the auto-correlation of
Gaussian noise is below 0.35. For each of our spectra, the auto-correlation is
smaller than 0.32 (see Table 3) and thus any correlations found are consistent
with those found in Gaussian noise.

We also check the success of our fit by computing the reduced Chi-squared from
the comparison between the data and the model ($\bar{\chi}$) as well as the
standard deviation of the residuals with respect to the photon noise
($\bar{\sigma}$). The reduced Chi-square between the spectral light curves for
each visit is between 1.16 (second visit) and 1.2 (fourth visit). The averaged
standard deviation of the residuals with respect to the formal photon noise is
between 1.03 (second visit) and 2.42 (fourth visit), and therefore the
resulted post-processing total noise is between $6\%$ and $142\%$ greater than
the photon noise.

Then, to compare light curves obtained from different visits,
$F_{\lambda}^{v}(t)$, we correct for offsets by subtracting each spectrum by
the corresponding white light curve depth, $(R_{p}/R_{\star})^{2}_{w,v}$, and
adding the weighted average transit depth of all white light-curves,
$(R_{p}/R_{\star})^{2}_{w}$. Finally, we compute the weighted average from all
the transit observations, $(R_{p}/R_{\star})^{2}_{\lambda}$, reported in Table
4. The spectral light curve fits are shown in Figure 4 while the spectrum
obtained from each visit, and the final average spectrum, are shown in Figure
5.

We notice that in each spectral bin, the measurements in each observation are
generally compatible within $1\sigma$ of the mean, as shown in Figure 5. Where
data points are not within $1\sigma$, there are no obvious trends with the
observation number or wavelength. To assess if the five transmission spectra
obtained are statistically consistent, we perform a Kolmogorov-Smirnov test.
We perform this test by comparing the transmission spectra two at a time, in
every possible combination, to test the null hypothesis that they come from
the same distribution. We use the SciPy package (Virtanen et al., 2020) for
the computation. We conclude that we cannot reject the null hypothesis for any
of the couples because the minimum resulting p-value is $28\%$.

Figure 4: Spectral light curves fitted with Iraclis for the transmission spectra where, for clarity, an offset has been applied. Left: the detrended spectral light curves with best-fit model plotted. Right: residuals from the fitting with mean 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) across the five transits. Figure 5: In the top panel are reported the transmission spectral data collected in each visit with their uncertainties (coloured data points) and the average transmission spectrum (black) obtained from their combination. The middle panel shows the uncertainty of each data point while the bottom panel shows the divergence from the mean, in sigma, of each data point. Table 4: This table reports for every spectral bin the averaged transmission spectra measured with combined the spectral light curves obtained with Iraclis, $(R_{p}/R_{\star})^{2}_{\lambda}$ . $\lambda\;[\mu m]$ | $(R_{p}/R_{\star})^{2}_{\lambda}$ | Uncertainty | $\Delta\lambda\;[\mu m]$
---|---|---|---
1.1263 | 0.002325 | 0.000034 | 0.0219
1.1478 | 0.002402 | 0.000033 | 0.0211
1.1686 | 0.002376 | 0.000035 | 0.0206
1.1888 | 0.002412 | 0.000030 | 0.0198
1.2084 | 0.002453 | 0.000031 | 0.0193
1.2275 | 0.002441 | 0.000031 | 0.0190
1.2465 | 0.002418 | 0.000030 | 0.0189
1.2655 | 0.002428 | 0.000031 | 0.0192
1.2848 | 0.002425 | 0.000028 | 0.0193
1.3038 | 0.002481 | 0.000028 | 0.0188
1.3226 | 0.002478 | 0.000028 | 0.0188
1.3415 | 0.002428 | 0.000030 | 0.0189
1.3605 | 0.002408 | 0.000028 | 0.0192
1.3801 | 0.002444 | 0.000029 | 0.0199
1.4000 | 0.002439 | 0.000030 | 0.0200
1.4202 | 0.002398 | 0.000031 | 0.0203
1.4406 | 0.002388 | 0.000029 | 0.0206
1.4615 | 0.002377 | 0.000028 | 0.0212
1.4831 | 0.002457 | 0.000029 | 0.0220
1.5053 | 0.002404 | 0.000029 | 0.0224
1.5280 | 0.002438 | 0.000029 | 0.0230
1.5516 | 0.002435 | 0.000030 | 0.0241
1.5763 | 0.002388 | 0.000027 | 0.0253
1.6021 | 0.002416 | 0.000027 | 0.0264
1.6295 | 0.002418 | 0.000028 | 0.0283

###  2.2 Atmospheric characterisation

To characterise the planetary atmosphere we use the retrieval code
TauREx3444https://github.com/ucl-exoplanets/TauREx_public (Al-Refaie et al.,
2019), the new version of TauREx (Waldmann et al., 2015a, b). The code maps
the atmospheric forward model parameter space to find the best fit to the
observed spectra. TauREx allow us to identify absorbers in the spectrum using
line-lists from ExoMol (Tennyson et al., 2016), HITEMP (Rothman et al., 2010a)
and HITRAN (Rothman et al., 1987). To perform the retrieval we use Multinest
algorithm (Feroz et al., 2011; Buchner et al., 2014) to sample the parameter
space through 1500 live points and we set the algorithm evidence tolerance to
0.5.

####  2.2.1 Temperature-pressure profile

We simulate the planetary atmosphere assuming an isothermal temperature-
pressure profile with constant molecular abundances as a function of altitude.
This assumption is driven by the narrow wavelength range investigated in the
data, that results in restricted probed range of the planetary
temperature–pressure profile (Rocchetto et al., 2016). We calculated the
equilibrium temperatures as:

$T_{\text{eq}}=T_{\star}\left(\frac{R_{\star}}{2\,a}\right)^{1/2}(1-A)^{1/4}$
(4)

where $R_{\star}$ is the stellar radius, $a$ is the semi-major axis, $A$ is
the Bond albedo. To keep in line with other studies, we adopt a standard Bond
albedo of $A=0.3$ (Bonfils et al., 2018), although we are aware that the
albedo is highly sensitive to the planetary properties and could therefore
vary significantly (e.g. Marley et al., 1999; Modirrousta-Galian et al.,
2021). For the equilibrium temperature we use $T_{\text{eq}}=520\pm 44\;K$,
where the uncertainty comes from the error propagation on the stellar
parameters and the planet’s semi-major axis from Table 1. Then for the
atmospheric retrievals we use a wide range of temperature priors from
$0.5\;T_{\text{eq}}$ to $1.5\;T_{\text{eq}}$ (i.e. 260 - 780 K).

####  2.2.2 Atmosphere composition

For the atmosphere we use the plane-parallel approximation, building 100
plane-parallel layers to uniformly sample in log-space the pressure range from
$10^{-4}$ to $10^{6}\;\rm{Pa}$. We assumed a primary atmosphere of He and H2
with a fixed ratio between the two molecules of 0.17, then we introduce the
trace gases: H2O (Barton et al., 2017; Polyansky et al., 2018), CH4 (Hill et
al., 2013; Yurchenko & Tennyson, 2014), CO (Li et al., 2015), CO2 (Rothman et
al., 2010b), HCN (Barber et al., 2014) and NH3 (Yurchenko et al., 2011). To
perform the atmospheric fit we use as boundaries for each molecule $10^{-12}$
and $10^{-1}$ in volume mixing ratios (log-uniform prior). To fit the planet
atmosphere we used two models: one with all the molecules listed above
molecules and a second which also included N2 (Western et al., 2018). In fact
N2 is a largely inactive gas over the spectral range considered and its only
contribution is to the atmospheric mean molecular weight. Using such
distinction between the two models we are considering a light, primary
atmosphere while also exploring the potential for heavy, secondary atmosphere.
We note that, as the abundances of all molecules was allowed to extend to 1
(i.e. 100%), the retrieval without N2 is also capable of resulting in a high
mean molecular weight atmosphere.

Additionally, we include in all our models Rayleigh scattering and collision
induced absorption of H2–H2 (Abel et al., 2011; Fletcher et al., 2018) and
H2–He (Abel et al., 2012). Clouds are modeled assuming a grey opacity model
and cloud top pressure bounds are set between $10^{-2}$ and $10^{6}$ Pa. We
also set a large range of priors for the planetary radius, from $0.5\;R_{p}$
to $1.4\;R_{p}$ referring to the literature value reported in Table 1. The
planetary radius is assumed to be equivalent at $10^{6}\;$Pa pressure.

To assign a significance to our detection, we use the Bayes Factor between the
nominal atmospheric model and a model which contains no active trace gases,
Rayleigh scattering or collision induced absorption. We perform a retrieval
where no molecular absorbers are active which provides a flat line model to
test the significance of retrievals including molecular opacities.

##  3 Results

The final spectrum recovered is extremely flat, with few deviations from a
flat line. Nevertheless, we conducted retrievals to explore the possibility
that any of these minor features could be attributed to molecular species.
While formation and evolution theories suggest a hydrogen dominated atmosphere
is unlikely for this planet, we started by exploring this possibility. Our
initial retrieval, conducted with a hydrogen-dominated atmosphere containing
clouds and the molecules discussed in Section 2.2, found no evidence of
features. The retrieval including N2 came to similar results, with the
spectrum essentially being fitted by a grey cloud deck alone in both cases.
The Bayesian evidence for each retrieval, log(E) = 218.44 and log(E) = 218.38
for retrievals with and without N2 respectively, shows that the cloud only
model (log(E) = 218.52) provides the best fit to the data.

Figure 6: Comparison of the log evidence for a cloudy atmosphere to that of
single molecule retrievals where the abundance of said molecule was fixed and
no clouds were included. In each case, the cloudy model is preferred to
$>$5$\sigma$. Figure 7: Best-fit spectra for the secondary atmosphere models.
The cloud only model (i.e. a flat line) still provides the best-fit to the
spectrum obtained. Figure 8: Inset top right: reported the transmission
spectra extracted with Iraclis software from the 5 HST visits of GJ 1132 b. In
black is reported the average transmission spectra while the green line is the
spectrum retrieved with TauREx and the shaded region represents the $3\sigma$
confidence level. Left: the retrieval posteriors for GJ 1132 b which show no
evidence for molecular species.

To better show the noncompliance of our data with molecular features, we
performed retrievals for clear hydrogen-dominated atmospheres with only one
molecule which was forced to mixing ratios from $10^{-6}$ to $10^{-1}$. The
latter is set as a rough boundary between primary and secondary atmospheres
(i.e. a mean molecular weight $>>$ 2.3). We use the Bayesian evidence from
these retrievals, given in Figure 6, to rule them out to a given significance.
We ran these for H2O, NH3, CO, CO2, CH4 and HCN and, in every case, the cloud
only model provided a better fit to the data to $>$5$\sigma$. Hence, our
results suggest we can rule out a clear, primary atmosphere with high
confidence: if GJ 1132 b hosts a primary atmosphere (i.e. one dominated by
hydrogen and helium), according to our spectrum, the planet must be completely
overcast.

We also attempted to fit several models with secondary atmospheric
compositions. These were atmospheres composed entirely of H$2$O and CO2 (i.e.
VMR${}_{\rm H_{2}O}$ = 1 and VMR${}_{\rm CO_{2}}$ = 1), as well as an
atmosphere similar to that of Venus (with volume mixing ratios of VMR${}_{\rm
CO_{2}}$ = 0.965, VMR${}_{\rm H_{2}O}$ = 2e-5, VMRCO = 1.7e-5, VMR${}_{\rm
SO_{2}}$ = 1.5e-4). For each of these, a cloud-free atmosphere was assumed and
the molecular abundances were again fixed. Thus, the only free parameters were
the planet radius and the temperature. The best-fit spectrum in each case is
given in Figure 7 although with the Bayesian evidence for each setup. Again,
the best fitting model is that of a flat line, with a cloud free, 100% H2O
atmosphere being ruled out to $>$3 sigma. However, while providing worse fits
to the data than the cloud-only model, the clear, 100% CO2 and Venusian
atmosphere models cannot be definitively ruled out with the current dataset.

Hence, no evidence for molecular features could be extracted from this
dataset. For completeness we include the posterior distribution for our
baseline retrieval in Figure 8. Our results suggest that the atmosphere of GJ
1132 b is likely to be cloudy but that certain enriched atmospheres, with
small scale-heights that led to only minor features over the HST WFC3 range,
could also explain the data. A final possibility, which is compatible with our
spectrum, is that the planet hosts an atmosphere too thin to be detected and
that we are measuring the transit depth caused by the planet’s solid surface.

##  4 Discussion

###  4.1 Statistical goodness of fit analysis

Due to the absence of molecular features in the measured spectrum, we
statistically compare the data reported in Table 4 with a constant value
defined as the weighted average of the planetary-to-stellar radii ratios. By
using chi squared statistics, we obtain $\chi^{2}=26$ with $\nu=25-1=24$
degrees of freedom. The obtained reduced chi squared value is
$\chi_{\nu}^{2}=26/24=1.08$, with an uncertainty of
$\sigma_{\chi_{\nu}^{2}}=0.29$. Because $\chi_{\nu}^{2}\sim 1$, we cannot
exclude the possibility that the measured data comes from a constant
distribution as the flat line is a good model to describe the data. Therefore,
the collected data does indeed show no detectable molecular features.

Because we compare different observations to obtain the spectrum in Table 4,
we perform a Jack-knife analysis (Quenouille, 1949, 1956; Tukey, 1958). This
consists of taking the original dataset, $X$, which is composed of $n$
samples, and creating $n$ new datasets, $x_{i}$. Each new dataset is like the
original except that it has $n-1$ samples. The removed sample is different for
each new dataset so that no two are identical. In our case we have 5
observations so $n=5$. For each of these new samples we compute the average
spectrum, as described in sec 2.1.5, and then we compare it with its weighted
average value, $\hat{x_{i}}$. In an identical manner as before, we make use of
the reduced chi squared value $\chi_{\nu}^{2}$ as a metric for the goodness of
the fit. The results are reported in Tab. 5. All of our $\chi_{\nu}^{2}$ are
$\sim 1$ indicating a very good fit. This confirms our results and
demonstrates that we are not biased in our analysis.

Table 5: Reduced chi squared ($\chi_{\nu}^{2}$) from Jack-knife analysis. The first column reports the observation that has been remove to the data set before computing the chi squared. The second column reports the resulted reduced chi squared of the comparison between the dataset average spectrum and its weighted average value, for the data set without the removed observation. Rem. obs. | $\chi_{\nu}^{2}$
---|---
1 | 1.3
2 | 0.6
3 | 1.6
4 | 1.0
5 | 1.2

We also computed the Jack-knife bias as $bias=(n-1)(\hat{X}-\hat{x})=3e-7$,
where $\hat{X}$ is the average radii ratio computed from the $X$ sample, and
$\hat{x}$ is the average of the mean radii ratios $\hat{x_{i}}$. The measured
bias is two orders of magnitude smaller than the uncertainties and can
therefore be neglected.

###  4.2 The Physical Implications of our Results

As explained previously, from mass and radius measurements it is not always
possible to accurately determine the bulk composition of an exoplanet.
However, there are a few clues that could help us evaluate whether GJ 1132 b
could have a hydrogen atmosphere or not. Specifically, one could consider the
effects of X-ray and ultraviolet (XUV) irradiation from the host star and its
effects on a primordial atmosphere. Performing a backwards reconstruction of
the maximum amount of hydrogen that could be lost by XUV irradiation is beyond
the scope of this study, but it is worth discussing.

Consider for example the super-Earth GJ 357 b. Having a mass, radius, and
temperature of $\rm\simeq 1.84M_{\oplus}$, $\rm\simeq 1.22R_{\oplus}$, and
$\rm\simeq 500~{}K$ (Luque et al., 2019), respectively, its properties are
relatively similar to those of GJ 1132 b. However, what makes GJ 357 b unique
is that it orbits a very low active M-type star (Modirrousta-Galian et al.,
2020b). In spite of the abnormally low XUV levels, a careful backwards
evaporation reconstruction model shows that up to $\sim$ 38 M⊕ of hydrogen
could have been lost (Modirrousta-Galian et al., 2020b). Although GJ 357 b was
probably born with a hydrogen envelope significantly smaller than this
(perhaps M${}_{atm}\lesssim 0.02~{}M_{\oplus}$ Ikoma & Hori (2012); Chachan &
Stevenson (2018)), this calculation shows that even stars with very low
activity levels could completely strip off the primordial atmosphere of a
planet. While the activity level of GJ 1132 is not known, statistically
speaking it is most probably higher than that of GJ 357 b (e.g. Penz & Micela,
2008; Sanz-Forcada et al., 2011), so by comparison one can infer that GJ 1132
b most probably lost its hydrogen envelope. Of course, other effects such as
magnetism (e.g. Matsakos et al., 2015), magma-atmosphere exchanges (e.g.
Chachan & Stevenson, 2018), and migration (e.g. Nayakshin & Lodato, 2012) may
have lowered the evaporation rates, but large mass-losses would be expected
nonetheless. Therefore, based on the mass-radius of GJ 1132 b, our current
understanding of XUV-induced evaporation, and our spectroscopic results, a
strong argument can be made that GJ 1132 b is a telluric body lacking a
primordial envelope that instead might host a secondary atmosphere. However,
we do acknowledge that other setups are plausible. For instance, GJ 1132 b
could be an airless rocky planet (e.g. Modirrousta-Galian et al., 2021) or a
rocky planet without clouds but an atmosphere that is too thin to be detected
in these data. Notwithstanding, these configurations may be less probable
given that geological outgassing is expected to generate thick secondary
atmospheres with clouds (Kite et al., 2009; Noack et al., 2017; Dorn et al.,
2018).

###  4.3 Comparison with previous works

To compare our measurements with previous works we adopt the radii ratios
published in recent papers. We use the measurements from Table 3 of Dittmann
et al. (2017) and Table 6 of Diamond-Lowe et al. (2018), and we compute the
$(R_{p}/R_{\star})^{2}$ from them, where needed. Additionally, GJ 1132 b has
also been studied by TESS and we used the pipeline from Edwards et al. (2020b)
to download, clean and fit the 2 minute cadence Pre-search Data Conditioning
(PDC) light curves (Smith et al., 2012; Stumpe et al., 2012, 2014). Then we
report all the data in Table 6 and in Figure 9.

Figure 9: Transit depths from various studies on GJ 1132 b, as listed in Table
6, and the spectrum recovered in this work. Also plotted are forward models
which assume a clear H/He atmosphere with various molecules, each at an
abundance of volume mixing ratios of $10^{-3}$. We note that we do not
directly compare the models to the combined dataset due to the possibility of
incompatibilities between them.

While it has become common to combine data from different instruments there
may be an offset between the datasets. These offsets can occur due to
imperfect correction of instrument systematics, from the use of different
orbital parameters or limb darkening coefficients during the light curve
fitting or from stellar variability or activity (e.g. Stevenson et al., 2014a;
Morello et al., 2017; Stevenson et al., 2014b; Tsiaras et al., 2018; Yip et
al., 2020; Bruno et al., 2020; Pluriel et al., 2020; Murgas et al., 2020;
Changeat et al., 2020; Yip et al., 2021; Schlawin et al., 2021). As there is
no wavelength overlap between our HST observations and the ground-based data
we cannot be certain of the compatibility of the observations.

The transit depth from the TESS data agrees with the data from Diamond-Lowe et
al. (2018) (see Figure 9). Nevertheless, while the datasets could potentially
be compatible, we err on the side of caution and do not perform a joint fit.
We note that the study by Diamond-Lowe et al. (2018) also concluded that GJ
1132 b could not have a clear, primordial envelope and thus the studies are in
agreement on this conclusion. Additionally, the Spitzer transit from Dittmann
et al. (2017) exhibits a similar transit depth to ours, but again we do not
include it in a joint fit. Finally, we note that Southworth et al. (2017)
claimed the detection of an atmosphere due to the modulation of several
ground-based photometric measurements but, given the precision obtained in
Diamond-Lowe et al. (2018) was higher than in said study, we do not include it
in our plots.

Table 6: Collection of transit depths of GJ 1132 b from other instruments. Data from Dittmann et al. (2017) are from Table 3 and for Diamond-Lowe et al. (2018) we use data from Table 6. Instrument | $\lambda\;[\mu m]$ | $(R_{p}/R_{\star})^{2}$ | Reference
---|---|---|---
Spitzer | 4.50 | $0.00242\pm 0.00008$ | D17
MEarth | 2.19 | $0.00207\pm 0.00005$ | D17
LDSS3C | 0.71 | $0.00240\pm 0.00010$ | DL18
LDSS3C | 0.73 | $0.00206\pm 0.00010$ | DL18
LDSS3C | 0.75 | $0.00219\pm 0.00009$ | DL18
LDSS3C | 0.77 | $0.00233\pm 0.00009$ | DL18
LDSS3C | 0.79 | $0.00214\pm 0.00009$ | DL18
LDSS3C | 0.81 | $0.00234\pm 0.00009$ | DL18
LDSS3C | 0.83 | $0.00212\pm 0.00009$ | DL18
LDSS3C | 0.85 | $0.00229\pm 0.00009$ | DL18
LDSS3C | 0.87 | $0.00229\pm 0.00009$ | DL18
LDSS3C | 0.89 | $0.00233\pm 0.00009$ | DL18
LDSS3C | 0.91 | $0.00218\pm 0.00008$ | DL18
LDSS3C | 0.93 | $0.00222\pm 0.00009$ | DL18
LDSS3C | 0.95 | $0.00206\pm 0.00010$ | DL18
LDSS3C | 0.97 | $0.00220\pm 0.00010$ | DL18
LDSS3C | 0.99 | $0.00210\pm 0.00010$ | DL18
LDSS3C | 1.01 | $0.00223\pm 0.00012$ | DL18
LDSS3C | 1.03 | $0.00228\pm 0.00016$ | DL18
TESS | 0.8 | $0.002312\pm 0.000093$ | This Work
D17: Dittmann et al. (2017)
DL18 : Diamond-Lowe et al. (2018)

During the review process of this paper, an independent study also analysed
the same HST WFC3 data of GJ 1132 b. Swain et al. (2021) found evidence for a
slope over this wavelength region, attributed to an H2 dominated atmosphere
with hazes, as well as spectral features that were proposed to be due to
absorption by CH4 and HCN. Their work suggested GJ 1132 b had lost its
primordial envelope and gained a second atmosphere through volcanic processes
that released H2 captured in the early age.

As our extracted spectrum differs greatly from that of Swain et al. (2021), we
conducted an independent analysis of the datasets with an additional open-
source pipeline: the Calibration of trAnsit Spectroscopy using CAusal Data
(CASCADe555https://jbouwman.gitlab.io/CASCADe/). While Iraclis has been
developed specifically for analysing HST WFC3, CASCADe is an instrument
independent reduction pipeline and has been applied to both Hubble and Spitzer
datasets. The CASCADe pipeline starts the data reduction with the ima
intermediate data product, which were produced by the CALWFC3 data reduction
pipeline (note that Iralcis takes the raw data and applies calibration steps
itself). CASCADe implements a novel data driven method, pioneered by Schölkopf
et al. (2016), utilising the causal connections within a data set to calibrate
the spectral time-series data. For a full description of the pipeline steps,
we refer the reader to (Carone et al., 2021).

We ran CASCADe using the same planet parameters and limb darkening
coefficients as discussed in Section 2.1. A comparison between these spectra,
and to that obtained by Swain et al. (2021), is given in Figure 10. We
immediately notice a vertical offset in the spectra obtained by Iraclis and
CASCADe. The offset is likely to be caused by differences in the correction of
the systematics and such offsets between different pipelines has been seen
before, for example for WASP-117 b (Anisman et al., 2020; Carone et al., 2021)
and KELT-11 b (Changeat et al., 2020; Colón et al., 2020). The finding of this
offset provides further evidence that combining instruments without wavelength
overlap is dangerous (Yip et al., 2020, 2021)

Figure 10: Comparison of the results from the data reduction and spectrum
extraction undertaken here using Iraclis and CASCADe. While there is an offset
between the spectra, normalising them by their mean transit depth shows they
are consistent to within 1$\sigma$. However, the spectra recovered with both
pipelines here differs significantly to that from Swain et al. (2021).

Despite this offset, we note that the spectral features in the CASCADe
spectrum, or lack thereof, are highly similar to those obtained with Iraclis.
By subtracting the mean from each spectrum, we show that the recovered data
points are all within 1$\sigma$. Comparing these to Swain et al. (2021), we
clearly highlight the disparity between our study and theirs: whereas they
uncover spectral variations of $\pm$200 ppm from the mean transit depth, both
our pipelines yield spectra where 21 of the 25 data points (84%) lie within
$\pm$50 ppm of the mean transit depth, with no data points being more than 75
ppm from the mean.

The exact cause of the difference in the recovered transmission spectra
between this study and that of Swain et al. (2021) is hard to discern without
detailed one to one comparisons of the pipelines utilised. Iraclis and CASCADe
are both open-source, well-used and have been validated against other results
within the literature. Additionally, their approach to the data calibration
and reduction, especially in the fitting of the systematic trends that are
encountered within HST WFC3 data, are utterly different and so achieving
almost identical spectra with these pipelines leads us to have confidence in
our results. Our team is working closely with those from Swain et al. (2021)
to resolve the discrepancy between our work and theirs.

Figure 11: Simulated JWST observations for various atmospheric types which are
consistent with current data. The coloured regions show the 1$\sigma$ errors
on the observation which has been binned to R$\sim$50.

###  4.4 Future missions

Future missions will offer increased sensitivity and wider spectral coverage.
This will be key in the hunt for atmospheric features on smaller planets.
While Ariel will be able to characterise H/He dominated atmospheres (Edwards
et al., 2019), or rule out their presence on small worlds, it may struggle to
provide additional constraints on GJ 1132 b given its lack of a clear H/He
atmosphere and spectral features. Hence, we focus on JWST and show in Figure
11 the data that could be obtained from 1 single transit with either NIRISS
GR700XD or NIRSpec G395M, modelled using ExoWebb, an adapted version of the
Terminus tool described in Edwards & Stotesbury (2021) which uses the Pandeia
engine (Pontoppidan et al., 2016). The coloured regions show the 1$\sigma$
errors on the observation which has been binned to R$\sim$50 and, as they can
rarely be distinguished, this suggests that even JWST may struggle to
disentangle different atmospheric types or provide significant evidence for
molecular features. With the exception of the Venus-like case, the forward
models assume a H/He envelope with the addition of the stated molecule. The
cloud deck for the 0.1% H2O and CO2 atmospheres was set to 100 Pa (0.001 Bar),
while 10 Pa (0.0001 Bar) was included for the 50% H2O case.

##  5 Conclusion

We present the data analysis of five spectroscopic observations of GJ 1132 b
obtained with the G141 grism of the WFC3 onboard of the HST. We extracted the
planetary transmission spectra with Iraclis pipeline and we attempted to
retrieve the atmospheric composition using TauREx3. Our findings agree with
those of Diamond-Lowe et al. (2018) and the transmission spectrum we obtain
from our data shows no molecular features in the investigated wavelength
range. We compared the spectrum with different atmospheric types to verify the
non compliance with any molecular content at the data precision and we
concluded that is compatible with a flat transmission spectrum only. Future
astronomical missions, such as JWST, will help further constrain the
atmospheric properties of GJ 1132 b although multiple observations may be
required for spectral features to be discerned. While it may be difficult to
understand its true nature, GJ 1132 b remains an interesting candidate for
future atmospheric studies.

Acknowledgments:

We thank our anonymous referee for their insightful comments which have
improved the quality of our work. Additionally, we thank Mark Swain and his
team for open and constructive talks surrounding the analysis of these
datasets.

This work was realised as part of “ARES Ariel School” in Biarritz in 2019. The
school was organised by JPB, AT and IW with the financial support of CNES. JPB
acknowledges the support of the University of Tasmania through the UTAS
Foundation and the endowed Warren Chair in Astronomy, Rodolphe Cledassou,
Pascale Danto and Michel Viso (CNES). WP, TZ, and AYJ have received funding
from the European Research Council (ERC) under the European Union’s Horizon
2020 research and innovation programme (grant agreement n∘ 679030/WHIPLASH and
n∘ 758892/ExoAI). SW was supported through the STFC UCL CDT in Data Intensive
Science (grant number ST/P006736/1). LVM and DMG acknowledge the financial
support of the ARIEL ASI grant n. 2018-22-HH.0. BE, QC, MM, AT and IW
acknowledge funding from the European Research Council (ERC) under the
European Union’s Horizon 2020 research and innovation programme grant ExoAI
(GA No. 758892) and the STFC grants ST/P000282/1, ST/P002153/1, ST/S002634/1
and ST/T001836/1. GG acknowledges the financial support of the 2017 PhD
fellowship programme of INAF. RB is a PhD fellow of the Research Foundation –
Flanders (FWO). DB acknowledges financial support from the ANR project
”e-PYTHEAS” (ANR-16-CE31-0005-01). NS acknowledges the support of the IRIS-
OCAV, PSL. MP acknowledges support by the European Research Council under
Grant Agreement ATMO 757858 and by the CNES. OV thanks the CNRS/INSU Programme
National de Planétologie (PNP) and CNES for funding support. JB acknowledges
support from the European Research Council under the European Union’s Horizon
2020 research and innovation program ExoplANETS-A (GA No. 776403). GM has
received funding from the European Union’s Horizon 2020 research and
innovation programme under the Marie Skłodowska-Curie grant agreement No.
895525.

Data: This work is based upon observations with the NASA/ESA Hubble Space
Telescope, obtained at the Space Telescope Science Institute (STScI) operated
by AURA, Inc. The publicly available HST observations presented here were
taken for proposal 14758, led by Zach Berta-Thompson (Berta-Thompson et al.,
2016). These were obtained from the Hubble Archive which is part of the
Mikulski Archive for Space Telescopes. This paper also includes data collected
by the TESS mission which is funded by the NASA Explorer Program. TESS data is
also publicly available via the Mikulski Archive for Space Telescopes (MAST).

Software: Iraclis (Tsiaras et al., 2016b), TauREx3 (Al-Refaie et al., 2019),
pylightcurve (Tsiaras et al., 2016a), ExoTETHyS (Morello et al., 2020),
Astropy (Astropy Collaboration et al., 2018), h5py (Collette, 2013), emcee
(Foreman-Mackey et al., 2013), Matplotlib (Hunter, 2007), Multinest (Feroz et
al., 2009; Buchner et al., 2014), Pandas (pandas development team, 2020),
Numpy (Oliphant, 2006), SciPy (Virtanen et al., 2020).

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