#  LRG-BEASTS: Evidence for clouds in the transmission spectrum of HATS-46 b

E. Ahrer1,2, P. J. Wheatley1,2, S. Gandhi3,1,2, J. Kirk4,5, G. W. King6,1,2,
T. Louden1,2 and L. Welbanks7
1Centre for Exoplanets and Habitability, University of Warwick, Gibbet Hill
Road, CV4 7AL Coventry, UK
2Department of Physics, University of Warwick, Gibbet Hill Road, CV4 7AL
Coventry, UK
3Leiden Observatory, Leiden University, Postbus 9513, 2300 RA Leiden, The
Netherlands
4Center for Astrophysics | Harvard & Smithsonian, 60 Garden Street, Cambridge, MA 02138, USA
5Department of Physics, Imperial College London, Prince Consort Road, London,
SW7 2AZ, UK
6Department of Astronomy, University of Michigan, Ann Arbor, MI 48109, USA
7School of Earth & Space Exploration, Arizona State University, Tempe, AZ,
85257, USA
E-mail<EMAIL_ADDRESS><EMAIL_ADDRESS>Sagan Fellow

(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

We have performed low-resolution ground-based spectroscopy of HATS-46 b in
transmission, using the EFOSC2 instrument on the ESO New Technology Telescope
(NTT). HATS-46 b is a highly-inflated exoplanet that is a prime target for
transmission spectroscopy, having a Jupiter-like radius (0.95
R${}_{\textrm{Jup}}$) but a much lower mass (0.16 M${}_{\textrm{Jup}}$). It
orbits a G-type star with a 4.7 d period, giving an equilibrium temperature of
1100 K. We observed one transit of HATS-46 b with the NTT, with the time-
series spectra covering a wavelength range of 3900 - 9000 Å at a resolution of
$R\sim 380$. We achieved a remarkably precise transmission spectrum of 1.03
$\times$ photon noise, with a median uncertainty of $357$ ppm for $\sim 200$ Å
wide bins, despite the relative faintness of the host star with
$V_{\mathrm{mag}}=13.6$. The transmission spectrum does not show strong
absorption features and retrievals favour a cloudy model, ruling out a clear
atmosphere with $3.0\sigma$ confidence. We also place a conservative upper
limit on the sodium abundance under the alternative scenario of a clear
atmosphere. This is the eighth planet in the LRG-BEASTS survey, which uses 4
m-class telescopes such as the NTT to obtain low-resolution transmission
spectra of hot Jupiters with precisions of around one atmospheric scale
height.

###### keywords:

methods: observational – techniques: spectroscopic – planets and satellites:
atmospheres – planets and satellites: individual: HATS-46 b

††pubyear: 2023††pagerange:  LRG-BEASTS: Evidence for clouds in the
transmission spectrum of HATS-46 b–A

##  1 Introduction

The study of transit depth versus wavelength, or transmission spectroscopy, is
an essential method to characterise the atmospheres of transiting exoplanets
with both ground- and space-based telescopes (e.g. Charbonneau et al., 2002;
Snellen et al., 2008; Bean et al., 2010; Stevenson et al., 2014; Sing et al.,
2016; May et al., 2018; Weaver et al., 2021; Alam et al., 2022; The JWST
Transiting Exoplanet Community Early Release Science Team et al., 2022). Hot
Jupiters, especially those with inflated radii, are prime targets for
transmission spectroscopy as they have large atmospheric scale heights due to
their high temperatures, their hydrogen-dominated atmospheres and their low
surface gravities. The sample of hot Jupiters studied to date exhibit a
diverse range of atmospheric properties that can include: narrow or pressure-
broadened sodium absorption (e.g. Fischer et al., 2016; Nikolov et al., 2018;
Alam et al., 2021; McGruder et al., 2022), detections of other atomic species
and/or broad molecular bands (e.g. Lendl et al., 2017; Carter et al., 2020;
Ahrer et al., 2023; Alderson et al., 2023; Feinstein et al., 2023; Rustamkulov
et al., 2023), Rayleigh scattering (e.g. Kirk et al., 2017; Chen et al., 2021)
and sometimes super-Rayleigh slopes (e.g. Pont et al., 2013; Alderson et al.,
2020; Ahrer et al., 2022), as well as high-altitude clouds muting absorption
features (e.g. Gibson et al., 2013a; Knutson et al., 2014; Kreidberg et al.,
2014; Lendl et al., 2016; Louden et al., 2017; Espinoza et al., 2019; Spyratos
et al., 2021).

Transmission spectroscopy of hot Jupiters provides crucial information about
the composition and chemistry of these exoplanets to understand their
formation and migration process (e.g. Öberg et al., 2011; Madhusudhan et al.,
2014; Booth et al., 2017), as well as what processes play a role in cloud and
haze formation at these hot temperatures. The processes and parameters
governing the presence or absence of clouds and hazes in the atmospheres of
gas giants are still debated (e.g. Heng, 2016; Fu et al., 2017; Fisher & Heng,
2018; Pinhas et al., 2019; Gao et al., 2020).

A larger sample size is needed to explore this parameter space, and the aim of
the Low-Resolution Ground-Based Exoplanet Atmosphere Survey using Transmission
Spectroscopy (LRG-BEASTS; ‘large beasts’) is to contribute to that by
characterising a large number of gaseous exoplanets in transmission at optical
wavelengths. This includes the detection of hazes, Rayleigh scattering and
grey clouds in the atmospheres of WASP-52 b (Kirk et al., 2016; Louden et al.,
2017), HAT-P-18 b (Kirk et al., 2017), WASP-80 b (Kirk et al., 2018), WASP-21
b (Alderson et al., 2020) and WASP-94A b (Ahrer et al., 2022), as well as
detections of sodium absorption in the atmospheres of WASP-21 b (Alderson et
al., 2020) and WASP-94A b (Ahrer et al., 2022). In addition, within LRG-BEASTS
Kirk et al. (2019) analysed the atmosphere of WASP-39 b revealing a supersolar
metallicity and Kirk et al. (2021) found tentative evidence for TiO in the
atmosphere of the ultrahot Jupiter WASP-103 b.

In this paper we present the first transmission spectrum of the exoplanet
HATS-46 b. Our observations were made using the EFOSC2 instrument on the New
Technology Telescope (NTT) as part of the LRG-BEASTS survey. HATS-46 b was
discovered within the HATSouth survey (Bakos et al., 2013) by Brahm et al.
(2018). Their photometric observations, together with follow-up radial
velocity measurements, confirm HATS-46 b, which orbits its G type host star in
$4.74$ days. Using TESS and Gaia data, HATS-46 b has been re-characterised by
Louden & Hartman (2021) who provided revised planetary and orbital parameters:
HATS-46 b has a mass of $0.158\pm 0.042$ M${}_{\textrm{Jup}}$ and a radius of
$0.951\pm 0.029$ R${}_{\textrm{Jup}}$, orbiting at a distance of $0.05272\pm
0.00045$ au; the equilibrium temperature was determined to $1082.1\pm 8.2$ K.
Stellar and planet parameters are summarised in Table 1. The star HATS-46 does
not appear to be very active as the RV measurements by Brahm et al. (2018) did
not show any evidence for periodic modulation on a rotation period.
Unfortunately, the signal-to-noise of the RV spectra was not sufficient to
place constraints on the chromospheric activity from the Ca II H&K lines
(Brahm et al., 2018). The TESS light curves showed evidence for variability,
with a possible period at around 15 d, but if real this signal would also have
been expected to be detected in the HATSouth light curve (Louden & Hartman,
2021).

This paper is divided into the following sections. First, we describe the
observations in Section 2, then discuss the data reduction and analysis in
Sections 3 & 4. This is followed by our discussion and conclusions in Section
5.

Table 1: Parameters for the star HATS-46 and its planet HATS-46 b, with $V_{\textrm{mag}}$ and spectral type as determined by Brahm et al. (2018) and all other parameters as revised by Louden & Hartman (2021). Parameter | Value
---|---
Stellar parameters
$V_{\textrm{mag}}$ | $13.634\pm 0.050$
Spectral type | G
Temperature $T_{\textrm{eff}}$ (K) | $5451\pm 19$
Age (Gyr) | $8.4\pm 1.9$
Surface gravity log $g$ (log10(cm s-2)) | $4.474\pm 0.019$
Metallicity $[$Fe/H$]$ | $-0.029\pm 0.039$
Mass ($M_{\odot}$) | $0.869\pm 0.023$
Radius ($R_{\odot}$) | $0.894\pm 0.010$
Planetary parameters
Period (d) | $4.7423749\pm 0.0000043$
Mass ($M_{\textrm{Jup}}$) | $0.158\pm 0.042$
Radius ($R_{\textrm{Jup}}$) | $0.951\pm 0.029$
Semi-major axis (au) | $0.05272\pm 0.00045$
Equilibrium temperature $T_{\textrm{eq}}$ (K) | $1082.1\pm 8.2$
Inclination (∘) | $86.97\pm 0.10$
Surface gravity log g (log10(cm s-2)) | $2.64\pm 0.14$

##  2 Observations

We observed HATS-46 with the NTT using the EFOSC2 instrument (Buzzoni et al.,
1984) on the night of 17 August 2017111Based on observations collected at the
European Southern Observatory under ESO programme 099.C-0390(A) (PI: Kirk)..
EFOSC2 is mounted at the Nasmyth B focus of the ESO NTT in La Silla, Chile,
which has a Loral/Lesser CCD detector with a size of 2048 $\times$ 2048
pixels. The overall field of view is 4.1 arcmin with a resolution of 0.12
arcseconds per pixel and a pixel binning of $2\times 2$ was applied.

At our request, a slit with a width of 27 arcsec was custom-built, with the
aim of avoiding differential slit losses between target and comparison star.
Grism #13 was used for our spectroscopic measurements, providing a low-
resolution ($R\sim 380$) spectrum from $3900-9000$ Å.

In total, 93 spectral frames were acquired, each with a relatively long
exposure time of $240$ s due to the relatively faint magnitude of both target
and comparison star. The readout time was 22 seconds. The observations were
taken at an airmass ranging from 1.60 to 1.12 to 1.26. The illumination of the
moon was at $16\%$ and it only rose towards the very end of the observation
night at a distance to the target of $108^{\circ}$.

For calibration, 67 bias frames were acquired, as well as 112 flat frames (54
lamp, 53 sky, 5 dome) and 3 HeAr arc frames, taken at the beginning of the
night. While we experimented with using flat frames in our data reduction, we
did not use any in our final reduction as we found it to increase the noise in
our data. This is in line with previous reports of similar analyses, both by
the LRG-BEASTS and ACCESS surveys (e.g. Rackham et al., 2017; Bixel et al.,
2019; Weaver et al., 2020; Kirk et al., 2021).

A nearby star (UCAC4 169-000364) at a distance of 1 arcmin to the target star
HATS-46 served as a comparison star and is not known to be a variable star.
The two stars are a good match in both magnitude ($\Delta V_{\textrm{mag}}$ =
0.87) and colour ($\Delta(B-V)=0.09$), thus well-suited for differential
spectro-photometry.

##  3 Data Reduction

LRG-BEASTS observations are commonly reduced using a custom-built Python
pipeline, which is described in detail by Kirk et al. (2018). The data for
HATS-46 have been reduced following this pipeline, but with modifications to
the cosmic ray removal and wavelength calibration, introduced in Ahrer et al.
(2022). In the following we summarise the reduction steps.

First, the biases were median-combined to produce a master bias. When
executing the Python script for extracting the spectra from each science frame
the master bias is subtracted from each science frame. However, before
extracting the spectra from the individual frames, pixels affected by cosmic
rays were identified and replaced with the median of the surrounding pixels.

An aperture width of 32 pixels was applied to extract the spectral counts from
each star. To fit the sky background we used a second order polynomial, which
was fitted to regions of 50 pixels either side of the stars at a distance of 5
pixels from the edge of the aperture. Outliers of more than three standard
deviations were masked from the fit. Extracted properties such as airmass,
pixel shift along the slit, Full Width Half Maximum (FWHM), normalised sky
background and differential white-light flux and their changes throughout the
night are displayed in Fig. 1. Example spectra are plotted in Fig. 2.

Figure 1: From top to bottom: variations of airmass, pixel shift along the X
axis, FWHM, sky background and differential flux across the night. In the
middle panels, the target is indicated with dark blue X symbols, and the
comparison star with orange + symbols.

Wavelength calibration follows the spectral extractions and is a two-step
process. First, RASCAL (Veitch-Michaelis & Lam, 2019) was utilised to find a
wavelength solution using the HeAr arc frames. The second step is to optimise
the wavelength calibration by fitting the positions of the stellar absorption
lines in each frame, adjusting the solution, and then saving the wavelength
solution for each frame individually. This allowed us to account for
wavelength drifts between the frames throughout the night, which were of the
order of $\sim 5$ pixels or $\sim 20$ Å.

Lastly, the spectra were binned into 26 wavelength bins, computed by summing
the flux within the corresponding wavelength range of each frame and dividing
by the comparison star’s flux in the same wavelength bin to correct for the
affects of the Earth’s atmosphere. Similarly, a white-light light curve was
computed by defining one single bin across the whole wavelength range. Bin
widths of $\sim 200$ Å (avoiding edges of strong stellar absorption lines)
were applied across the whole spectral range, with the exception of two small
ranges where we searched for absorption by sodium and potassium, see Fig. 2.

Figure 2: Normalised spectra of comparison star (orange) and target star (dark
blue), as well as the expected strong telluric lines (black) in the redder
part of the wavelength range. Wavelength bin edges are indicated with dashed
black lines. Green lines indicate the position of the sodium doublet
($5890,5895$ Å) and potassium doublet ($7665,7699$ Å).

Observations with EFOSC2 at wavelengths $>7200$ Å are subject to fringing
effects (see Fig. 2). We found that correcting for these effects in the
individual spectra using flat fields was not possible as the fringing changed
in amplitude and phase during the night and the acquired flat frames were
taken before the observations started.

##  4 Data Analysis

###  4.1 Transit model

Each transit light curve was described using the batman Python package
(Kreidberg, 2015) in combination with the analytic light curves from Mandel &
Agol (2002) and fitted using the nested sampling algorithm PolyChord (Handley
et al., 2015). First, the white-light light curve was fitted using the ratio
of planet to star radius $R_{p}/R_{*}$, the inclination of the system $i$, the
scaled stellar radius $a/R_{*}$, the time of mid-transit $T_{C}$ and the two
quadratic limb-darkening coefficients $u1$ and $u2$. We computed the limb-
darkening coefficients with the Limb-Darkening Toolkit (LDTk) package
(Parviainen & Aigrain, 2015), which uses phoenix models (Husser et al., 2013)
based on the stellar parameters to determine $u1$ and $u2$ and their errors.
One of them ($u2$) was held fixed to the generated value to avoid degeneracy,
while the other one was fitted for ($u1$) using a uniform prior with four
times the generated error (see Table 2) to allow for small inconsistencies
between the stellar model and the observation. This quadratic limb-darkening
law provides a good fit to the data, see Section 4.2, and the fitted values
for $u1$ were consistent with the model prediction. The Kipping
parameterisation (Kipping, 2013) was also tested to check for potential
effects in the transmission spectrum due to the chosen limb-darkening
parameterisation, but we can confirm that this is not the case.

All priors for the system parameters can be found in Table 2, which were
chosen to be uniform and wide ($\pm 5\sigma$) centred on the previously
reported literature values (Table 1; Louden & Hartman, 2021). Depending on the
detrending method, additional parameters were added to the fitting (introduced
in the following section).

Table 2: Parameter values obtained from the white-light curve fitting and the respective priors. Values for semi-major axis $a$, radius of the star $R_{*}$ and radius of the planet $R_{p}$ and inclination $i$ are listed in Table 1. The retrieved values for the parameters $a/R_{*}$, $i$ and $T_{C}$ listed here were fixed for the spectroscopic light curve fitting.  Parameter | Prior distribution and range | Fitted values
---|---|---
Scaled stellar radius $a/R_{*}$ | Uniform | $a/R_{*}\pm 5\sigma_{a/R_{*}}$ | $13.94^{+0.24}_{-0.65}$
Inclination $i$ (∘) | Uniform |  $i$ $\pm$ 5$\sigma_{i}$ | $87.60^{+0.12}_{-0.33}$
Time of mid-transit $T_{C}$ (BJD) | Uniform |  $0.9\times\ T_{C}$, $1.1\times\ T_{C}$ | $2457983.70725^{+0.00046}_{-0.00033}$
Transit depth $R_{p}/R_{*}$ | Uniform |  $R_{p}/R_{*}$ $\pm$ 5$\sigma_{R_{p}/R_{*}}$ | $0.11250^{+0.0.0018}_{-0.00083}$
Limb-darkening coefficient $u1$ | Uniform | $u1\pm 4\sigma_{u1}$ | $0.547\pm 0.014$
Limb-darkening coefficient $u2$ | Fixed | – | 0.1171

The determined values for $a/R_{*}$, $i$ and $T_{C}$ from the white-light
light curve fitting (Table 2) were then held fixed for the spectroscopic light
curve fitting, which allowed us to fit for relative changes in transit depths
over the wavelength range. Thus the fitting parameters for each of the 26
binned light curves were transit depth $R_{p}/R_{*}$, limb-darkening
coefficient $u1$ and additional noise modelling parameters.

###  4.2 Light curve fitting

For detrending the white-light light curve, various different approaches were
investigated e.g. different combinations of kernels and kernel inputs for a
Gaussian Process (GP), 1st and 2nd order polynomials using airmass, FWHM,
derotator angle, etc. However, all of these models retrieved very low
amplitudes for their respective noise modelling, e.g. see amplitude of the
best-fitting GP model in top panel in Fig. 3 which is $0.062$ % compared to
the transit depth of $1.287\,$%. In addition, the Bayesian evidence values for
each of these fits did not statistically favour a particular GP model or
parametric fitting model. The differences across all wavelengths in Bayesian
evidences averaged at $0.5$ ($0.67\sigma$) and never exceeded $1$
($<1.15\sigma$). Consequently, we opted to use only a linear dependence on the
FWHM for detrending the white-light light curve, see bottom panel in Fig. 3.

(a) Gaussian Process (b) Linear function of FWHM

Figure 3:  The white-light light curve fitted with a transit and two different
models to account for systematics. The best-fit model is plotted in green,
while the individual components of the model are plotted in dashed turquoise
for the transit model and dark blue for the respective systematics models. In
the top panels, labelled (a), we use a GP model for systematics. In the lower
panels, labelled (b), we use a linear function of FWHM.

To determine the transit depths for each wavelength bin, we fitted the
individual light curves of the 26 bins with a transit model and a detrending
model. We conducted an investigation of the systematics modelling, similar to
the one done for the white-light light curve fit. This was to ensure that our
transmission spectrum is independent of the choice of noise modelling, and to
provide the best estimate of the uncertainties.

The light curves show very little evidence for systematic trends such as
drifts or correlated noise, see left panel in Fig. 4 for the raw light curves.
We experimented with simple models to account for the small noise amplitudes,
as well as using a transit model without any systematic modelling at all.
First, linear models in time, airmass and FWHM were investigated, with the
linear in FWHM performing the best according to the Bayesian evidence value of
each spectroscopic light curve fit and an average fitted noise amplitude of
$0.06\%$ or $600$ ppm. In addition, we looked into GP models and sampled
different types of kernels and kernel input, out of which the a exponential-
squared model with FWHM as input resulted in the best choice, with an average
fitted GP amplitude of $0.03\%$ or $300$ ppm. As both the linear in FWHM and
GP model resulted in similar transit depths and small noise amplitudes, we
chose the first, parametric model over the GP model due to its lower
uncertainties in the transit depths. This results in an average precision of
transit depth error equal to 1.03 $\times$ photon noise. The light curves and
respective fits are shown in Fig. 4, as well as the residual scatter of the
fits and their respective Root Mean Square (RMS) values.

Figure 4: Left: Our fits (red) of the undetrended spectroscopic light curves
(black) using a transit model and a linear in FWHM for detrending to the data
with their respective centre wavelengths (blue end at the top) displayed on
the right vertical axis. Right: Residuals of the corresponding light curve
fitting. The scatter is quantified in the form of the RMS on the right
vertical axis.

The previously described models all favoured only small variations and FHWM as
the detrending source for all spectroscopic bins. This led us to investigate
using a common noise model (e.g. as used in Sing et al., 2012; Gibson et al.,
2013b; Lendl et al., 2016; Nikolov et al., 2016; Nortmann et al., 2016;
Huitson et al., 2017; Todorov et al., 2019; Wilson et al., 2020; Kirk et al.,
2021; McGruder et al., 2022) in the hope of reducing our uncertainties and
getting rid of common noise structures potentially dominating the systematics.
In this method the GP component from the white-light light curve fit is
subtracted from the spectroscopic light curves before fitting them
individually. However, this did not have the desired effect of improving the
noise modelling and on average resulted in larger uncertainties. Therefore we
did not pursue this method further.

All computed transmission spectra using the GP model, the polynomial model,
the common noise model and one without any detrending at all i.e. solely a
transit model, are shown in Fig. 5. This demonstrates that our resulting
transmission spectrum is independent of our choice of noise modelling.
Following the points made above about each detrending approach, we selected a
simple polynomial model, ‘Linear in FWHM’, as the preferred detrending method.
The final transmission spectrum in tabular form is displayed in Table 3. Note
that for our final spectrum we chose to dismiss the relatively large transit
depth of the bin centred on the potassium doublet due the high chance of it
being affected by the nearby strong telluric signal (O2 A-band). Other studies
in the past have come to similar conclusions when probing for potassium
absorption with ground-based instruments (e.g. Kirk et al., 2017; McGruder et
al., 2022).

Figure 5:  Transmission spectra of HATS-46 b using NTT/EFOSC2 observations. Median precisions of transit depths for $\sim 200$ Å wide bins are quoted in brackets in the description respectively. The orange and blue colours represent the resulting transmission spectrum using Gaussian Process (387 ppm) and a linear in FWHM (357 ppm) to account for systematics modelling, respectively. The black represents the case for when not using any noise modelling i.e. solely a transit model (326 ppm). The green indicates a model where the GP component fitted to the white-light light curve was subtracted (common noise model) from the spectroscopic light curves and then a linear in FWHM was used to fit residual systematics (358 ppm). The ‘Linear in FWHM’ transmission spectrum is used for the retrieval analysis (see text for further details), but note that the bin centred on the potassium doublet (7665, 7699 Å) is not included as it is affected by the close-by strong telluric O2 line.  Table 3: Retrieved transmission spectrum of HATS-46 b in tabulated form using the ’Linear in FWHM’ detrending approach, as plotted in Fig. 5, excluding the bin centred on the K doublet. Bins (Å) | $R_{p}/R_{*}$ | u1 | u2 (fixed)
---|---|---|---
3900 - 4200 | $0.1137^{+0.0018}_{-0.0017}$ | $0.92\pm 0.02$ | -0.0737
4200 - 4440 | $0.1157\pm 0.0017$ | $0.87\pm 0.02$ | -0.0523
4420 - 4680 | $0.1130\pm 0.0015$ | $0.79\pm 0.02$ | 0.0380
4680 - 4910 | $0.1134^{+0.0014}_{-0.0013}$ | $0.73\pm 0.02$ | 0.0726
4910 - 5120 | $0.1115^{+0.0014}_{-0.0015}$ | $0.71\pm 0.02$ | 0.0721
5120 - 5350 | $0.1154\pm 0.0014$ | $0.67\pm 0.02$ | 0.0837
5350 - 5570 | $0.1117^{+0.0014}_{-0.0015}$ | $0.63\pm 0.01$ | 0.1050
5570 - 5818 | $0.1139\pm 0.0013$ | $0.59\pm 0.01$ | 0.1241
5818 - 5868 | $0.1155^{+0.0029}_{-0.0030}$ | $0.58\pm 0.01$ | 0.1330
5868 - 5918 | $0.1117\pm 0.0029$ | $0.58\pm 0.01$ | 0.1209
5918 - 5968 | $0.1156^{+0.0028}_{-0.0029}$ | $0.58\pm 0.01$ | 0.1295
5968 - 6190 | $0.1121^{+0.0018}_{-0.0016}$ | $0.55\pm 0.01$ | 0.1336
6190 - 6400 | $0.1136^{+0.0014}_{-0.0015}$ | $0.53\pm 0.01$ | 0.1364
6400 - 6610 | $0.1128\pm 0.0015$ | $0.50\pm 0.01$ | 0.1512
6610 - 6820 | $0.1146\pm 0.0015$ | $0.50\pm 0.01$ | 0.1433
6820 - 7040 | $0.1136\pm 0.0015$ | $0.48\pm 0.01$ | 0.1446
7040 - 7240 | $0.1146^{+0.0017}_{-0.0018}$ | $0.47\pm 0.01$ | 0.1449
7240 - 7440 | $0.1130^{+0.0018}_{-0.0019}$ | $0.45\pm 0.01$ | 0.1452
7440 - 7649 | $0.1157^{+0.0020}_{-0.0021}$ | $0.44\pm 0.01$ | 0.1464
7749 - 7950 | $0.1127\pm 0.0023$ | $0.42\pm 0.01$ | 0.147
7950 - 8150 | $0.1111\pm 0.0026$ | $0.42\pm 0.01$ | 0.1476
8150 - 8350 | $0.1128\pm 0.0029$ | $0.40\pm 0.01$ | 0.1482
8350 - 8550 | $0.1120^{+0.0030}_{-0.0031}$ | $0.38\pm 0.01$ | 0.1474
8550 - 8770 | $0.1111\pm 0.0033$ | $0.37\pm 0.01$ | 0.1488
8770 - 9000 | $0.1177\pm 0.0035$ | $0.37\pm 0.01$ | 0.1494

###  4.3 Atmospheric Retrieval

We retrieve the transmission spectrum of HATS-46 b using the HyDRA (Gandhi &
Madhusudhan, 2018) and Aurora (Welbanks & Madhusudhan, 2021) atmospheric
retrieval codes. Our model uses 14 free parameters which describe the
atmospheric composition, thermal profile and cloud/haze properties (shown in
Table 4) to generate spectra of HATS-46 b to compare against the observations.
We use high temperature molecular line lists to compute the cross sections and
hence opacity for the spectrally active species, utilising the Kurucz line
list for the atomic species Na and K (Kurucz & Bell, 1995), and the ExoMol
POKAZATEL line list for H2O (Tennyson et al., 2016; Polyansky et al., 2018).
We spectrally broaden each line in the line list with both pressure and
temperature, resulting in a Voigt profile (see e.g. Gandhi et al., 2020). We
also include collisionally induced absorption from H2-H2 and H2-He
interactions (Richard et al., 2012), as well as Rayleigh scattering due to H2.

In addition to these sources of opacity we also include 4 free parameters to
model and fit for a partially cloudy and/or hazy atmosphere, as any
clouds/hazes can have a strong influence on the overall spectrum. We include a
grey (wavelength independent) cloud deck, Pcl, and two parameters which
determine a wavelength dependent haze, with $\alpha_{\mathrm{haze}}$ the
strength and $\gamma_{\mathrm{haze}}$ the wavelength dependence of the haze
(see e.g., Pinhas et al., 2018). Finally, we include the cloud/haze fraction,
$\phi_{\mathrm{cl}}$, as a free parameter, with the prior ranging from 0,
representing a clear atmosphere, to 1, a fully cloudy/hazy atmosphere (see
Table 4).

We model the temperature profile of the atmosphere using the method described
in Madhusudhan & Seager (2009). This parametrisation breaks the atmosphere
into three distinct layers, with the temperature at the top of the model
atmosphere included as a free parameter. We also retrieve the transition
pressures P1 between the top layers 1 and 2 and P3 between layers 2 and 3. The
top two layers have temperature-pressure gradients $\alpha_{1}$ and
$\alpha_{2}$ as free parameters. The final deepest layer of the atmosphere is
fixed to an isotherm, and continuity of the temperature between these layers
results in 6 free parameters for the temperature profile. We restrict our
parametrisation to only allow non-inverted or isothermal temperature profiles
given that we do not expect stratospheres for planets with such temperatures
(e.g. Fortney et al., 2008), similar to previous work with transmission
retrievals (e.g. Pinhas et al., 2019). We also include an additional free
parameter for the reference pressure, Pref, the point in the atmosphere where
the radius of the planet is set. We model the atmosphere between 100-10-6 bar
with 100 layers evenly spaced in log pressure, and model the spectrum with
4000 wavelength points between 0.39-0.9 $\mu$m. Our Bayesian analysis is
carried out using the Nested Sampling algorithm MultiNest (Feroz & Hobson,
2008; Feroz et al., 2009; Buchner et al., 2014).

The retrieved constraints are shown in Table 4, and the posterior distribution
is shown in the Appendix, Fig. 7. For our retrievals we considered two
competing scenarios: a cloudy/hazy atmosphere and a relatively-clear
atmosphere. The first case, where clouds mask atomic and molecular species in
the transmission spectrum of HATS-46 b, is statistically preferred to
3.0$\sigma$ due to the relatively featureless spectrum, when using Bayesian
model evidence comparisons (e.g., Benneke & Seager, 2013; Welbanks &
Madhusudhan, 2021). In the alternative, less statistically preferred scenario
of a clear atmosphere, where clouds do not mask the atomic and molecular
species, we can place constraints on the abundance of K and Na. There is no
visible feature of Na in the spectrum, hence we place an upper limit on Na
abundance of $\log(\rm{Na})<-4.45$ to 3$\sigma$, i.e., less than
$20\times$solar Na abundance for this cloud-free scenario. This is a
conservative upper limit, since the lack of features in the transmission
spectrum drives the atmospheric temperatures in the model to the lower end of
the prior, which decreases the atmospheric scale height and thereby the
strength of features. There is therefore a degeneracy between temperature and
abundance, and an atmospheric temperature closer to the equilibrium
temperature would give a tighter limit on abundance.

Additionally, we assess the impact of unnoculted star spots and faculae in the
transmission spectrum of HATS-46 b using Aurora (Welbanks & Madhusudhan,
2021). We allow for the possibility of a contaminated stellar photosphere and
retrieve for three additional parameters to the fiducial model described
above. These are, the photospheric temperature (Gaussian prior centred at
effective temperature of the star and a width of 100 K), the fraction of
unnoculted spots or faculae (uniform prior between 0 and 50 %), and the
temperature of these inhomogeneities (uniform prior from 0.5 to 1.5 times the
effective temperature of the star). Priors are in line with what is
recommended by Pinhas et al. (2018). The retrieved properties stellar
properties are in agreement with the possibility of a spotless star. The
retrieved photospheric temperature of HATS-46 is consistent with the reported
value in Table 1, with a relatively low fraction of spots (i.e., $2\sigma$
upper limit of $\lesssim 22\%$) with temperatures consistent with the
photospheric stellar temperature at $2\sigma$. The presence of stellar
heterogeneities is not preferred since its Bayesian evidence value is lower
relative to our fiducial model. Based on these observations and the models
considered here, we find no evidence for stellar contamination affecting our
observations.

Parameter | Prior Range | Retrieval Constraint
---|---|---
$\log(X_{\mathrm{H_{2}O}})$ | -15 $\rightarrow$ -1 | $-8.4^{+4.8}_{-4.2}$
$\log(X_{\mathrm{Na}})$ | -15 $\rightarrow$ -1 | $-10.1^{+3.5}_{-3.0}$
$\log(X_{\mathrm{K}})$ | -15 $\rightarrow$ -1 | $-8.6^{+3.3}_{-4.0}$
$T_{\mathrm{top}}$ / K | 750 $\rightarrow$ 2500 | $1167^{+530}_{-300}$
$\alpha_{1}\,/\,\mathrm{K}^{-\frac{1}{2}}$ | 0 $\rightarrow$ 1 | $0.67^{+0.21}_{-0.23}$
$\alpha_{2}\,/\,\mathrm{K}^{-\frac{1}{2}}$ | 0 $\rightarrow$ 1 | $0.61^{+0.25}_{-0.27}$
$\log(P_{1}/\mathrm{bar})$ | -6 $\rightarrow$ 2 | $-1.7\pm 1.7$
$\log(P_{2}/\mathrm{bar})$ | -6 $\rightarrow$ 2 | $-4.1^{+1.6}_{-1.3}$
$\log(P_{3}/\mathrm{bar})$ | -2 $\rightarrow$ 2 | $0.60^{+0.90}_{-1.35}$
$\log(P_{\mathrm{ref}}/\mathrm{bar})$ | -4 $\rightarrow$ 2 | $-2.51^{+1.02}_{-0.86}$
$\log(\alpha_{\mathrm{haze}})$ | -4 $\rightarrow$ 6 | $-0.0^{+2.8}_{-2.5}$
$\gamma_{\mathrm{haze}}$ | -20 $\rightarrow$ -1 | $-11.3^{+6.3}_{-5.5}$
$\log(P_{\mathrm{cl}}/\mathrm{bar})$ | -6 $\rightarrow$ 2 | $-4.42^{+1.24}_{-0.94}$
$\phi_{\mathrm{cl}}$ | 0 $\rightarrow$ 1 | $0.79^{+0.13}_{-0.19}$
Table 4: Parameters and uniform prior ranges for our retrieval. We retrieve
the Na, K and H2O abundances, temperature profile, and partial cloud/haze
parameters. Our temperature profile includes 6 free parameters, and our
cloud/haze parametrisation includes 4 free parameters (see Section 4.3).
Figure 6: Transmission spectrum of HATS-46 b as observed by NTT/EFOSC2 and
using linear in FWHM detrending (black), and the median retrieved atmospheric
model (red), including the respective $1\sigma$ and $2\sigma$ confidence
intervals. It is shown that the retrieved transmission spectrum is relatively
featureless, suggesting high-altitude clouds in the atmosphere. Note that
narrower bins around the Na doublet ($5890,5895$ Å) are used to probe for
absorption and the bin centred on the K doublet ($7665,7699$ Å) was
disregarded due to the close strong O2 telluric line.

##  5 Discussion & Conclusions

We presented the analysis and results of spectroscopic NTT/EFOSC2 data of
HATS-46 b in transmission. The inflated, Jupiter-sized exoplanet orbits its
relatively faint (V${}_{\textrm{mag}}$ = 13.6) G type host star in a 4.7-day
period and has an equilibrium temperature of 1100 K (Louden & Hartman, 2021).

One transit was observed with NTT/EFOSC2 using the method of long-slit
spectroscopy and a comparison star was used to conduct differential
spectroscopy. A total of 93 spectral frames with exposure times of $240$ s
were acquired. The resulting light curves did not show noise structures beyond
a weak dependence on seeing, with fitted average amplitudes of $600$ ppm for
our best noise model, which included a linear detrend against FWHM.

We extracted the transmission spectrum in 26 bins, covering the wavelength
range of $3900-9000$ Å with a median transit depth uncertainty of $357$ ppm
for the $\sim 200$Å wide bins. The measured transmission spectrum is
relatively featureless, it does not show a sodium feature or a scattering
slope. The fitted, relatively large transit depth at the wavelength of the
potassium doublet was dismissed as an effect of the nearby strong telluric
signal due to the O2 A-band. Our atmospheric retrieval analysis of the
transmission spectrum of HATS-46 b favours a cloudy atmosphere with
$3.0\sigma$ confidence. In an alternative cloud-free model we place a
conservative upper limit on the Na abundance of $20\times$solar ($3\sigma$
confidence). Including stellar activity in our retrievals results in lower
Bayesian evidence and no meaningful constraints on the additional parameters.
If activity were to play a role in the shape in our transmission spectrum, we
would expect to retrieve constraints on the spot coverage fraction or
temperature of the spots. Thus the cloudy atmosphere model without the
additional stellar activity parameters is favoured.

## Acknowledgements

This research has made use of the NASA Exoplanet Archive, which is operated by
the California Institute of Technology, under contract with the National
Aeronautics and Space Administration under the Exoplanet Exploration Program.
PJW acknowledges support from STFC under consolidated grants ST/P000495/1 and
ST/T000406/1. SG is grateful to Leiden Observatory at Leiden University for
the award of the Oort Fellowship. JK acknowledges financial support from
Imperial College London through an Imperial College Research Fellowship grant.

## Data Availability

The raw data used in our analysis are available from the ESO data archive
under ESO programme 099.C-0390(A) (PI: Kirk). The reduced light curves
presented in this article will be available via VizieR at CDS (Ochsenbein et
al., 2000).

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##  Appendix A Posterior distributions

Figure 7: Posterior distribution of HATS-46 b from the retrieval of the
NTT/EFOSC2 observations of HATS-46 b. We retrieved three chemical species,
H2O, Na and K, and parametrised the atmospheric temperature profile with six
parameters, as discussed in Section 4.3. We also include additional parameters
for the reference pressure and partial clouds/hazes.