# Probing reflection from aerosols with the near-infrared dayside spectrum of
WASP-80b

Bob Jacobs Anton Pannekoek Institute for Astronomy, University of Amsterdam,
Science Park 904, 1098 XH, Amsterdam, the Netherlands  Jean-Michel Désert
Anton Pannekoek Institute for Astronomy, University of Amsterdam, Science Park
904, 1098 XH, Amsterdam, the Netherlands  Peter Gao Earth and Planets
Laboratory, Carnegie Institution for Science, 5241 Broad Branch Road, NW,
Washington, DC 20015, USA  Caroline V. Morley The University of Texas at
Austin, Department of Astronomy, 2515 Speedway, Stop C1400, Austin, Texas
78712-1205  Jacob Arcangeli  Anton Pannekoek Institute for Astronomy,
University of Amsterdam, Science Park 904, 1098 XH, Amsterdam, the Netherlands
Saugata Barat Anton Pannekoek Institute for Astronomy, University of
Amsterdam, Science Park 904, 1098 XH, Amsterdam, the Netherlands  Mark S.
Marley  Lunar and Planetary Laboratory, The University of Arizona, 1629 E.
University Blvd. P.O. Box 210092 Tucson, AZ 85721-0092  Julianne I. Moses
Space Science Institute 4765 Walnut St, Suite B Boulder, CO 80301  Jonathan J.
Fortney  Department of Astronomy and Astrophysics, University of California,
Santa Cruz, 95064, CA, USA  Jacob L. Bean Department of Astronomy &
Astrophysics, University of Chicago, 5640 S. Ellis Avenue, Chicago, IL 60637,
USA  Kevin B. Stevenson  Johns Hopkins APL, 11100 Johns Hopkins Rd, Laurel, MD
20723, USA  Vatsal Panwar  Anton Pannekoek Institute for Astronomy, University
of Amsterdam, Science Park 904, 1098 XH, Amsterdam, the Netherlands
Department of Physics, University of Warwick, Coventry, CV4 7AL, UK

(Received July 26, 2023; Revised September 18, 2023; Accepted September 26,
2023)

###### Abstract

The presence of aerosols is intimately linked to the global energy budget and
the composition of a planet’s atmospheres. Their ability to reflect incoming
light prevents energy from being deposited into the atmosphere, and they shape
spectra of exoplanets. We observed five near-infrared secondary eclipses of
WASP-80b with the Wide Field Camera 3 (WFC3) aboard the Hubble Space Telescope
to provide constraints on the presence and properties of atmospheric aerosols.
We detect a broadband eclipse depth of $34\pm 10$ ppm for WASP-80b. We detect
a higher planetary flux than expected from thermal emission alone at
$1.6\sigma$, which hints toward the presence of reflecting aerosols on this
planet’s dayside, indicating a geometric albedo of $A_{g}<0.33$ at 3$\sigma$.
We paired the WFC3 data with Spitzer data and explored multiple atmospheric
models with and without aerosols to interpret this spectrum. Albeit consistent
with a clear dayside atmosphere, we found a slight preference for near-solar
metallicities and for dayside clouds over hazes. We exclude soot haze
formation rates higher than $10^{-10.7}$ g cm-2s-1 and tholin formation rates
higher than $10^{-12.0}$ g cm-2s-1 at $3\sigma$. We applied the same
atmospheric models to a previously published WFC3/Spitzer transmission
spectrum for this planet and found weak haze formation. A single soot haze
formation rate best fits both the dayside and the transmission spectra
simultaneously. However, we emphasize that no models provide satisfactory fits
in terms of the chi-square of both spectra simultaneously, indicating
longitudinal dissimilarity in the atmosphere’s aerosol composition.

planets and satellites: atmospheres — planets and satellites: gaseous planets

in ApJ Letters, October 20, 2023

##  1 Introduction

Aerosols are thought to be ubiquitous in exoplanet atmospheres (see, e.g. Sing
et al., 2011; Kreidberg et al., 2014; Knutson et al., 2014; Rustamkulov et
al., 2023), although their exact nature remains to be determined. Here, we
follow the definitions of Gao et al. (2021) and consider the two main types of
aerosols in giant exoplanet atmospheres: clouds and hazes. Haze modeling
efforts typically focus on complex hydrocarbon “soot” hazes (Lavvas &
Koskinen, 2017) and the Titan analog “tholin” hazes (Khare et al., 1984).
Clouds form when gas condenses under thermochemical equilibrium, while hazes
are produced photochemically under strong UV irradiation (Ackerman & Marley,
2001; Morley et al., 2012; He et al., 2018; Kawashima & Ikoma, 2018).

Aerosol absorption and reflectivity are wavelength-dependent (Adams et al.,
2019; Feinstein et al., 2023). They therefore modify the thermal structure of
the atmosphere (McKay et al., 1991, 1999; Heng et al., 2012; Keating & Cowan,
2017), which, in turn, affects the formation rate of aerosols (Morley et al.,
2015; Gao et al., 2018). Atmospheric properties such as metallicity, vertical
mixing strength, and longitudinal transport also determine the abundance and
composition of aerosols (Parmentier et al., 2013; Gao et al., 2018; He et al.,
2018).

Aerosols attenuate molecular features in near-infrared (NIR) transmission
spectra of exoplanets (Fortney, 2005). Secondary eclipse spectra are likewise
shaped by aerosols (Demory et al., 2013). Besides probing thermal emission,
secondary eclipse depth measurements can also shine a light on the geometric
albedo of a planet (Sudarsky et al., 2000; Demory et al., 2011; Evans et al.,
2013; Brandeker et al., 2022). Clouds generally create flat NIR reflection
spectra, and soot hazes have a low single-scattering albedo. However, tholin
particles are highly reflective at optical and NIR wavelengths with strong
spectral features while being highly absorbing at blue and UV wavelengths
(Morley et al., 2015). Reflectance spectra can therefore help detect aerosols
and distinguish their composition.

WASP-80b ($M_{p}=0.54\,M_{\rm{Jup}}$, $R_{p}=0.95\,R_{\rm{Jup}}$; Triaud et
al., 2013, 2015) is a warm Jupiter ($T_{\rm{eq}}\approx 800$ K) orbiting a
late-K/early-M dwarf. Its size, proximity to its relatively low-mass host
star, and low equilibrium temperature uniquely allow us to probe its NIR
reflectance. In addition, because of its host star’s high chromospheric
activity (Fossati et al., 2022), WASP-80b is expected to receive a high UV
flux, which potentially enhances haze production. Therefore, WASP-80b is
currently amongst the best targets to investigate NIR reflectance caused by
aerosols.

From a theoretical standpoint, the dayside of WASP-80b is in a peculiar
thermal parameter space in which its atmosphere could be clear, hazy, or
hosting high-pressure silicate clouds (Morley et al., 2015; Gao et al., 2020).
Its equilibrium temperature is also just below the threshold where the
dominating carbon bearer changes from CH4-dominated to CO/CO2-dominated (Moses
et al., 2013; Fortney et al., 2020; Baxter et al., 2021). As tholin particles
become unstable above $\sim$900 K (Morisson et al., 2016), hotter hazes are
expected to be dominated by more-refractory soot particles (Lavvas & Arfaux,
2021). As such, the WASP-80b dayside is also expected to lie in the transitory
region between tholin and soot hazes.

Wong et al. (2022) used the Hubble Space Telescope (HST) and the Spitzer Space
Telescope to measure the WASP-80b transmission spectrum in the range of
$0.4-5.0$ $\mu$m. They observed a muted water feature at $1.4$ $\mu$m and a
steep optical spectral slope. They attribute these features to fine-particle
hazes (${<}0.1$ $\mu$m) and a deep cloud deck on the limbs of the planet.
Their models show a slight preference toward tholins over soots at
metallicities ranging from ${\sim}30$ to $100$ times solar. General
Circulation Models of planets of a similar temperature to WASP-80b predict
efficient heat transport and a low day-to-night contrast resulting in
chemically homogeneous planets (Showman et al., 2015). The dayside of WASP-80b
should therefore also show signs of aerosols.

In this study we present the NIR secondary eclipse spectrum of WASP-80b
observed by the HST Wide Field Camera 3 (WFC3), probing the planet’s dayside.
We use atmospheric models including aerosol feedback to interpret the
spectrum. We also compare the same models to the planet’s transmission
spectrum (Wong et al., 2022), which probes the planet’s limbs.

##  2 Data analysis

###  2.1 Observations

We observed five secondary eclipses of WASP-80b with four HST orbits per
eclipse with WFC3 for Program GO 15131 (PI: J.-M. Désert,
DOI:https://doi.org/10.17909/zr1e-9f27 (catalog 10.17909/zr1e-9f27)). The
observation of one eclipse is called a “visit.” The data were obtained with
the G141 grism, covering $1.1-1.7$ $\mu$m, using the bidirectional spatial
scanning technique. We used the $256\times 256$ subarray and the SPARS10,
NSAMP=14 readout mode. An observation log is provided in Table 1 in Appendix
A.1.

Figure 1: Near-infrared secondary eclipse depth measurements of WASP-80b for
the exponential-ramp method (blue) and the RECTE method (maroon). The right
axis shows the geometric albedo if there were zero thermal emission.
Left: near-infrared secondary eclipse spectrum. The transparent data points in
the background denote the per-visit eclipse depths and the opaque data points
in the foreground are the weighted averages thereof. The data are offset
slightly in wavelength for visibility purposes.
Right: posterior distributions of the “white light” eclipse depth for each
visit. The median and $1\sigma$ levels of the posteriors are marked with a
darker shade. The two methods agree within $1\sigma$, except for the fifth
visit, for which the methods differ by $1.2\sigma$. However, the eclipse
depths measured with the exponential-ramp method are larger for all but one
visit. The mean white light eclipse depth is $34\pm 10$ ppm for the
exponential-ramp method and $22\pm 9$ ppm for the RECTE method.

We used the data reduction pipeline described by Arcangeli et al. (2018) and
updated by Jacobs et al. (2022) to convert the raw data into spectra. For each
visit, we picked the first exposure as our reference exposure.

###  2.2 Systematics correction

Raw WFC3 light curves show an exponential ramp in each HST orbit caused by the
trapping of charges (Zhou et al., 2017). The ramps are strongest in the first
orbit, which we therefore discarded. We removed the ramp in the other orbits
by employing two different techniques: the empirical exponential-ramp method
(e.g. Kreidberg et al., 2014; Arcangeli et al., 2019; Wong et al., 2022) and
the physically motivated RECTE method (Zhou et al., 2017). We provide a
detailed description of both light-curve fitting methods in Appendix A. In
both methods the system parameters are fixed to the values found by Wong et
al. (2022).

We split the WFC3 data into three spectral bins and performed the above
fitting methods on all visits separately for each bin. We display a
compilation of the WFC3 spectroscopic secondary eclipse light-curve fits in
Appendix B.

###  2.3 Observed spectrum

The left panel of Figure 1 shows the fitted eclipse depths for each wavelength
bin, method, and visit. The right panel shows the band-integrated “white
light” eclipse depths for each visit, which are weighted averages of the
spectral eclipse depths. The eclipse depths from the RECTE method are almost
uniformly lower than for the exponential-ramp method. In Appendix C we compare
the RECTE and exponential-ramp methods and conclude that the exponential-ramp
method is slightly more reliable for these data. Using the RECTE-reduced data
does not change the results of this work significantly.

Averaging the eclipse depth over all visits yielded a total average eclipse
depth in the G141 wavelength range of $34\pm 10$ ppm for the exponential-ramp
method, implying a detection of the WASP-80b secondary eclipse at $3.4\sigma$.
This makes WASP-80b the planet with the lowest equilibrium temperature for
which a secondary eclipse has been detected at ${<}2.5$ $\mu$m to date
(Angerhausen et al., 2015; Mansfield et al., 2021; Wong et al., 2021).

The geometric albedo of WASP-80b is

$A_{g}=(a/R_{p})^{2}F_{p}/F_{s}=\frac{F_{p}/F_{s}}{192\rm{\,ppm}}.$

Depending on the fraction of flux originating from thermal emission, we
therefore measure an upper limit $A_{g}<0.33$ at 3$\sigma$ in the G141
wavelength range.

##  3 Atmospheric models and results

###  3.1 Atmospheric model description

To interpret the observations, we generated one-dimensional atmospheric models
that include condensate clouds and photochemical hazes. We first computed
clear-atmosphere models with WASP-80b’s planetary parameters using the
Extrasolar Giant Planet (EGP) radiative-convective-thermochemical equilibrium
code (McKay et al., 1989; Marley et al., 1996; Fortney et al., 2005; Morley et
al., 2012) with atmospheric metallicities of solar, $3{\times}$ solar, and
$10{\times}$ solar. The resulting temperature-pressure (TP) profiles were then
fed into the Community Aerosol and Radiation Model for Atmospheres (CARMA;
Turco et al., 1979; Toon et al., 1988; Ackerman et al., 1995; Gao et al.,
2018) to act as the background atmosphere for simulations of photochemical
hazes, following the setup in Gao et al. (2023). For each metallicity, we ran
soot and tholin haze models for column haze production rates between
$\eta=10^{-14}$ and $\eta=10^{-9}$ g cm-2s-1 with logarithmically spaced
intervals of $10^{0.5}$. We used a constant eddy diffusion coefficient
$K_{\rm{zz}}$ of $10^{8}$ cm2s-1, full day-night heat redistribution and an
internal temperature $T_{\rm{int}}=100$ K. The haze optical properties were
then fed back into the EGP code to calculate their feedback on the TP
profiles. Using the same background atmospheres, we used the EddySed model
(Ackerman & Marley, 2001) to generate cloud distributions self-consistently,
assuming clouds composed of Na2S, MnS, and Cr and sedimentation efficiencies
$f_{\rm sed}$ of 0.5, 1.0, and 2.0. We could not model lower sedimentation
efficiencies as we were unable to make them converge given the clouds’ strong
impact on the TP profiles. We considered spherical haze and cloud particles
and calculated their optical depth per model atmospheric layer, single-
scattering albedo, and asymmetry parameter assuming Mie scattering. We
subsequently used PICASO 3.0 (Batalha et al., 2019; Mukherjee et al., 2023) to
generate reflected light, emission, and transmission spectra from the
atmospheric structure and composition and aerosol optical properties.

###  3.2 Atmospheric model comparison to the data

Figure 2: NIR secondary eclipse spectrum of WASP-80b measured with WFC3 (blue)
and complemented with previously published Spitzer observations (black). A
selection of the atmospheric models from this work are overplotted for a soot
haze (upper panel), tholin haze (middle panel), and clouds (lower panel) using
temperature-pressure profiles presented in Figure 3. The atmospheric models
are separated into three metallicities: $[M/H]=0$ (solid), $[M/H]=0.5$
(dashed), and $[M/H]=1$ (dotted). In each panel, we also provide the clear
atmosphere models in green that are mostly thermal and only contain
discernible reflective features at ${<}0.6$ $\mu$m. The best-fit models in
each scenario are displayed with a bold dash-dotted line. The best-fit tholin
model tracks the clear atmosphere model very closely, as the best-fit tholin
production rate is low. Diamonds denote the band-integrated eclipse depths in
the WFC3/Spitzer wavelength bins for the $[M/H]=0$ clear atmosphere model and
for the best-fit aerosol model. It can be assumed that at ${\lesssim}2.0$
$\mu$m any planetary flux higher than the clear atmosphere model corresponds
to light reflected by aerosols.

In Figure 2 we complement the eclipse depths from this work with data taken by
Spitzer at 3.6 and 4.5 $\mu$m (Wong et al., 2022). We compare them to four
scenarios: a clear atmosphere, an atmosphere with a soot haze, an atmosphere
with a tholin haze, and a cloudy atmosphere. At wavelengths ${\lesssim}2.0$
$\mu$m reflection by aerosols can dominate the spectrum, while these features
are overwhelmed by the thermal emission at longer wavelengths. In Figure 3 we
display the TP profiles that produce the model spectra of Figure 2.

All three WFC3 data eclipse depths are deeper than would be expected from just
thermal emission from a clear atmosphere assuming $T_{\rm{int}}=100$ K and
full day-night heat redistribution (green curves in Figure 2). Higher internal
temperatures do not significantly alter $F_{p}/F_{s}$, but assuming zero day-
night heat redistribution triples $F_{p}/F_{s}$ at WFC3 wavelengths. However,
that would also double the flux at Spitzer wavelengths. The Spitzer data
therefore best fit a reradiation factor (López-Morales & Seager, 2007) of 0.25
(full redistribution), with a 3$\sigma$ upper limit of 0.31. Moreover, planets
near WASP-80b’s $T_{\rm{eq}}$ have been observed and theorized to have near-
full redistribution (Komacek et al., 2017). We therefore assume full
redistribution and interpret the $1.6\sigma$ difference between model and data
as due to reflection from aerosols, though we remain cautious about this model
assumption. Also visible in Figure 2 is how the CO2 absorption feature at 4.3
$\mu$m increases with metallicity for the clear atmosphere model. This is
expected since a higher metallicity moves the balance between
CO2/CH4production toward CO2 (Venot et al., 2014; Soni & Acharyya, 2023).

The higher the haze formation rate, the more the haze model spectra deviate
from the clear atmosphere model. Higher haze formation rates promote larger
particle sizes and densities, leading to stronger optical absorption that
creates a thermal inversion: the upper atmosphere heats up, while the deeper
atmosphere cools down (see Figure 3). Greater haze formation therefore turns
the CO2 absorption feature at 4.3 $\mu$m into an emission feature. The
emission feature appears weak because the optically thick haze prevents us
from probing deeper into the cooler atmospheric layers; as such, the spectrum
resembles a blackbody at shorter wavelengths.

Stronger soot production hardly increases the planet’s reflectivity because
soots have a low single-scattering albedo. Conversely, an increase in tholin
haze production increases the planet’s reflectivity significantly. This
consequently increases the flux at ${<}2.0$ $\mu$m, but decreases the planet’s
flux at longer wavelengths: the heightened reflectivity reduces the total
energy absorbed and cools down the planet, creating a spectral see-saw effect.

If there are clouds on WASP-80b’s dayside, our models indicate they are likely
embedded so deep into the atmosphere that their reflectivity changes the
dayside spectrum only marginally. Higher sedimentation efficiencies result in
a more vertically compact layer of clouds, while lower sedimentation
efficiencies create a more vertically extended cloud layer, causing a slightly
higher albedo.

Figure 3: Temperature-pressure (TP) profiles for a selection of atmospheric
models (described in Section 3.1) for a soot haze (left), tholin haze
(middle), and clouds (right). These TP profiles are used to generate the
spectra in Figure 2. Solid lines denote $[M/H]=0$, dashed lines show
$[M/H]=0.5$ models, and dotted lines denote $[M/H]=1$. As a reference, each
panel also shows in green the TP profiles of the clear atmosphere models
generated with the EGP radiative-convective-thermochemical equilibrium code
(Morley et al., 2012).

###  3.3 Model fits to the spectra

For each scenario, we interpolated over the model grid and used a Markov Chain
Monte Carlo (MCMC) sampler to find the best-fit solution and the uncertainties
on the parameters. We used uniform priors within the parameter ranges
described in Section 3.1 and performed fits on both the dayside spectrum and
the transmission spectrum from Wong et al. (2022) separately. These best-fit
models are plotted in Figure 4 and we show the posterior distributions in
Figure 5. We provide a more detailed accounting of the fits in Appendix D. In
Figure 2 the best-fit models to the dayside spectrum are marked as dash-dotted
lines.

In all scenarios for the dayside spectrum, a near-solar metallicity is
preferred to account for the relatively small CO2 absorption feature at $4.5$
$\mu$m shown in Figure 2. Although the self-consistent clear atmosphere models
fit the Spitzer points well, they predict shallower eclipse depths than
observed for every WFC3 wavelength bin. As such, the best-fit metallicity
($[M/H]=0.24^{+0.20}_{-0.15}$) has $\chi_{\nu}^{2}=1.4$. While this is a
decent fit, the flux surplus at WFC3 wavelengths indicates that the NIR light
detected by HST may not be purely of thermal origin, but also reflective.

The best-fit haze models tend toward low haze production (soot:
log${}_{10}(\eta)=-13.3\pm 0.5$, tholins:
log${}_{10}(\eta)=-13.2^{+0.7}_{-0.6}$ g cm-2s-1) with $3\sigma$ limits of
log${}_{10}(\eta)<-10.7$ for soots and log${}_{10}(\eta)<-12.0$ g cm-2s-1 for
tholins. The best-fit tholin model has little to no haze formation because of
the strong atmospheric cooling that reflection from tholins create.

The cloudy models have a weak preference for a low $f_{\rm{sed}}$, which
increases the short-wavelength reflectivity. Cloudy models reach a
$\chi^{2}_{\nu}=0.6$. Therefore, they are slightly favored over haze models by
the Bayesian information criterion: $\Delta\rm{BIC}={-}2.3$ compared to a soot
haze and $\Delta\rm{BIC}={-}2.9$ compared to a tholin haze. However, all
aerosol models are consistent with a clear atmosphere model.

The model fits to the transmission spectrum strongly favor a high metallicity,
somewhat hazy atmosphere with log${}_{10}(\eta)=-12.96^{+0.12}_{-0.09}$ g
cm-2s-1 for soots, and log${}_{10}(\eta)=-12.13^{+0.14}_{-0.11}$ g cm-2s-1 for
tholins. Hazes are required to create the optical slope. The large difference
in transit depths of the two Spitzer points indicates a high CO2/CH4ratio and
hence a high metallicity. Both the haze as well as the higher metallicity
subdue the water absorption feature at $1.4$ $\mu$m. The best-fit model is the
soot haze model at $\chi^{2}_{\nu}=1.1$. A clear or purely cloudy atmosphere
is excluded.

###  3.4 Model comparison between dayside and limb

We assess how well our best-fit dayside atmospheric models perform on the limb
spectrum and vice versa in Figure 4 and Appendix D. Here we assumed the
aerosol parameters to be uniform across the planet’s atmosphere. Figure 5
shows the significant overlap of the posterior distributions of all models.
For all aerosol scenarios, the posteriors contain samples with
$\chi^{2}_{\nu}<2.0$ for both the transmission spectrum and the dayside
spectrum, indicating reasonable fits to both parts of the planet. However,
none have $\chi^{2}_{\nu}<1.6$ for both spectra, which shows that no models
fit both spectra well concurrently. Soot hazes generate the lowest combined
$\chi^{2}_{\nu}$. Stellar activity may have steepened/induced an optical
spectral slope or offsets between transmission observation epochs (Rackham et
al., 2018; Wong et al., 2022). Alternatively, the true aerosol composition may
be a mix between the aerosol types discussed in this work, like that found by
Wong et al. (2022), or the composition may be entirely different (He et al.,
2023). The aerosol composition could also differ between the dayside and the
limbs of the planet.

Figure 4: Best-fit models to the WASP-80b dayside (upper panel) and
transmission (lower panel) spectra. Solid lines denote models fit to the
dayside spectrum data. Spectra denoted with dashed lines were fit to the
transmission spectrum data. All data, except for the WFC3 dayside data in
blue, are adopted from Wong et al. (2022). All data in the left panels were
taken with WFC3 and the data in the right panels were taken with Spitzer. We
color the clear atmosphere model green, the soot haze model pink, the tholin
haze model blue, and the cloudy model yellow. Diamonds denote the band-
integrated eclipse/transit depths of the model fits to the dayside spectrum.
Figure 5: Posterior distributions from MCMC fits to the dayside spectrum
(orange) and the transmission spectrum (green). For each model, the x-axis
shows the metallicity distribution. For the cloudy model, we plot the
sedimentation efficiency $f_{\rm{sed}}$ on the y-axis and for the haze models,
we plot the logarithm of the haze formation rate $\eta$ (in g cm-2s-1) on the
y-axis. The three isodensity lines denote the 1$\sigma$, 2$\sigma$, and
3$\sigma$-limits of the posteriors. An extra monochromatic offset parameter
was used to fit transmission spectra. Correlations with that parameter are not
displayed here. None of the posterior samples here have $\chi^{2}_{\nu}<1.6$
for both spectra simultaneously.

##  4 Discussion and conclusion

Although the WFC3 dayside spectrum of WASP-80b shows signs of reflection from
the planet, combining the WFC3 spectrum with the Spitzer data allows us to
reject high haze formation rates $\eta<10^{-10.7}$ for soots and
$\eta<10^{-12.0}$ g cm-2s-1 for tholins. Furthermore, clouds are slightly
favored over hazes.

Hazes are formed after the dissociation of, e.g. CH4, HCN, CO, CO2 and C2H2
molecules under strong UV irradiation in the upper atmosphere
(${\gtrsim}10^{-4}$ bar) (Kawashima & Ikoma, 2018; He et al., 2018). CH4 has
been detected on the limbs and the dayside of WASP-80b with JWST (Bell et al.,
2023), and with high-resolution spectroscopy (Carleo et al., 2022); the latter
report an HCN detection but remained inconclusive regarding C2H2. Fortney et
al. (2013) show with thermochemical equilibrium models that the haze
production rate is approximately highest for planets with the equilibrium
temperature of WASP-80b. Given the host star’s strong UV flux, the ingredients
for strong haze formation are present at WASP-80b. Haze production on WASP-80b
could be suppressed if there is a relative lack of CH4 in the upper atmosphere
due to, for example, increased eddy mixing in the deep atmosphere (Baxter et
al., 2021).

In addition to the UV flux, haze production may increase with increasing
temperatures (He et al., 2020). The dayside receives both higher UV fluxes and
hosts higher temperatures than the limbs. Yet, the inferred dayside haze
production is similar to, or possibly even lower than, the limb haze
production, which we probe with the transmission spectrum. Hazes produced on
the dayside may be rapidly advected to the evening terminator by an eastward
jet. The evening limb could therefore show a higher haze mass than the dayside
(Steinrueck et al., 2021).

Wong et al. (2022) infer a ${\sim}30$–$100$ times solar metallicity from low-
resolution transit spectroscopy because of a weak water feature and a large
$4.5$ $\mu$m transit depth that may be indicative of strong CO2 absorption.
Conversely, Carleo et al. (2022) suggest an atmosphere that is consistent with
a solar composition from high-resolution transit spectroscopy. In line with
Wong et al. (2022), our transmission spectrum fits tend toward high
metallicities. However, our dayside spectrum fits tend toward solar
metallicities because the relative flux in the Spitzer bandpasses does not
indicate a strong CO2 feature. As Wong et al. (2022) note, a possibly
anomalous 4.5 $\mu$m Spitzer transmission data point may cause this
difference. Excluding this point would allow for solar compositions with both
the models from Wong et al. (2022) and our models. The best-fit aerosol
composition is not significantly different at solar metallicities.

Wong et al. (2022) analyzed the WASP-80b transmission spectrum with a free-
retrieval. They inferred a fine-particle (${\lesssim}0.1$ $\mu$m) haze with a
deep cloud deck at $\chi^{2}_{\nu}=0.88$. Our grid-retrieval over atmospheric
models was able to find almost equally good fits ($\chi^{2}_{\nu}=1.1$) with
only a haze. The average particle size in our CARMA models matches that
inferred by Wong et al. (2022).

Although the modeled sedimentation efficiency of clouds has a marginal impact
on the dayside spectrum, the results show a slight preference for low
sedimentation efficiencies ($f_{\rm{sed}}<1$), in line with previous works
(Morley et al., 2013; Adams et al., 2022). Those works find even lower values
for $f_{\rm{sed}}$ than we could self-consistently model here. Theoretically,
lower values of $f_{\rm{sed}}$ would increase the albedo, potentially
improving the fit to the WFC3 data.

Comparing the retrieved aerosol composition from WASP-80b’s dayside and
transmission spectra shows a possible difference in aerosol composition and/or
abundance between the dayside and limbs of the planet. Alternatively, the data
can be interpreted with a uniform soot haze model, which fits both spectra at
$\chi_{\nu}^{2}=1.6$. A comprehensive joint analysis of both the transmission
and the secondary eclipse spectra can significantly help disentangle
degenerate solutions to the data (Griffith, 2014; Zhang et al., 2020).
However, such analysis is outside the scope of this paper due to the one-
dimensional nature of the atmospheric models and the limited precision and
spectroscopic abilities of WFC3 and Spitzer. The GTO observations that are
being taken by JWST for WASP-80b are well suited to such combined analysis.

J.M.D acknowledges support from the Amsterdam Academic Alliance (AAA) Program,
and the European Research Council (ERC) European Union’s Horizon 2020 research
and innovation program (grant agreement No. 679633; Exo-Atmos). This work is
part of the research program VIDI New Frontiers in Exoplanetary Climatology
with project number 614.001.601, which is (partly) financed by the Dutch
Research Council (NWO). Support for program HST-GO-15131 was provided by NASA
through a grant from the Space Telescope Science Institute, which is operated
by the Associations of Universities for Research in Astronomy, Incorporated,
under NASA contract NAS5-26555.

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##  Appendix A Light-curve fitting methods

To remove the telescope systematics, we employ two different methods: the
exponential-ramp method (e.g. Kreidberg et al., 2014; Arcangeli et al., 2019),
and the RECTE method (Zhou et al., 2017). An exponential-ramp method was also
used for the transmission spectroscopy measurements of WASP-80b by Wong et al.
(2022).

###  A.1 Exponential-ramp method

In the exponential-ramp method one fits an analytical model, to the light
curve of each visit. The model has the form:

$\displaystyle F(\mathbf{t})$ $\displaystyle=$ $\displaystyle
M_{\lambda,v}(\mathbf{t})\,\Theta_{\lambda,v,s}(\mathbf{t})\,T_{\lambda,v,o}(\mathbf{t})$
(A1) $\displaystyle\Theta_{\lambda,v,s}(\mathbf{t})$ $\displaystyle=$
$\displaystyle C_{\lambda,v,s}+V_{\lambda,v,s}(\mathbf{t}-t_{\rm{ecl}})$ (A2)
$\displaystyle T_{\lambda,v,o}(\mathbf{t})$ $\displaystyle=$ $\displaystyle
1-R_{\lambda,v,o}e^{-(\mathbf{t}-t_{b})/\tau_{\lambda,v}}$ (A3)

where $M(\mathbf{t})$ is the secondary eclipse model from batman (Kreidberg,
2015), $\mathbf{t}$ is a vector of observation times, $C$ is a normalization
constant, $V$ is a visit-long linear slope, $R$ is the WFC3 ramp amplitude,
$\tau$ is the ramp timescale, $t_{b}$ is the time of the first exposure in the
orbit, and $t_{\rm{ecl}}$ is the mid-eclipse time. The subscripts
$\lambda,v,s$ and $o$ denote whether a parameter is a function of wavelength,
telescope visit, scan direction, and orbit number respectively. In this work,
the telescope systematics were not shared between visits because the
observational orientation and the number of subexposures per exposure varies
per visit (see Table 1). We set the ramp amplitude of the last orbit equal to
the amplitude of the penultimate orbit.

Table 1:  Observation Log

Visit | UT start date |  $n_{\rm{sub}}$ aa Number of subexposures per exposure. |  $\phi$ bb Position angle of V3-axis of HST (deg).
---|---|---|---
1 | 17 June 2019 | 13 | 40
2 | 5 July 2019 | 12 | 40
3 | 11 July 2019 | 12 | 31
4 | 8 August 2019 | 12 | 330
5 | 11 August 2019 | 13 | 330

Notes.

There is no variation of the measured eclipse depths with the position angle
of the telescope. However, eclipses measured in the 13-subexposure mode are
$1.5\sigma$ shallower than the eclipses measured in the 12-subexposure mode.
We removed the 13-th subexposure from the first and fifth visits and reran the
fits. This did not change the eclipse depths significantly (${<}5$ ppm). The
variations in eclipse depth may, therefore, originate from the variability of
the host star.

The exponential-ramp method is often unable to correctly fit for the first
exposure of each orbit (e.g. Changeat & Edwards, 2021; Gressier et al., 2022)
as it often deviates from the ramp model. We therefore removed them for this
method.

###  A.2 RECTE method

In the RECTE method, we swap $T(t)$ in Equation A1 for the system of
differential equations from Zhou et al. (2017) that govern the filling and
emptying of the charge traps. This requires the fitting of four other
parameters: the number of initially filled fast/slow charge traps
($E_{f/s,0_{v,\lambda}}$) and the number of fast/slow charge traps that are
filled in between orbits ($\Delta E_{f/s_{v,\lambda}}$). These parameters are
the same for each scan direction, but different for each visit and wavelength.
Contrary to the exponential-ramp model, the RECTE method is able to cope with
the low flux values of the first exposure of each orbit. For this method, we
therefore leave these exposures in our fits.

The RECTE modeling approach may enable the use of the first orbit of every
visit that would otherwise be discarded (Zhou et al., 2017). We experimented
with maintaining this extra orbit in our analysis as that could decrease the
measurement uncertainty. However, we found this particular data set to be ill-
suited to such analysis with RECTE. The orbit-long ramp of the first orbit is
so strong that any good fit with RECTE requires negative initially filled
charge traps, which are unphysical. Limiting $E_{f/s,0_{v,\lambda}}\geq 0$
yields bad fits (on average 115% above photon noise) and strongly negative
eclipse depths at a mean white light eclipse depth of $-125\pm 7$ ppm. We
therefore decided to remove the first orbit of each visit from our RECTE
analysis and work with the three remaining orbits, analogous to the
exponential-ramp method.

###  A.3 Estimation of errors

In order to estimate the errors on our fitted parameters and identify the
degeneracies in the model, we used an MCMC approach using the open-source
emcee code (Foreman-Mackey et al., 2013). Each chain has 25,000 steps with 70
walkers and a burn-in period of 2000 steps. Our average final precision on the
spectroscopic eclipse depths per visit with the exponential-ramp and RECTE
methods were 41 ppm and 31 ppm, respectively, per wavelength bin. We reached
an average spectrophotometric precision on the best fits of 4% and 6% above
photon noise, respectively.

###  A.4 Spectral drift on the detector

Some WFC3 light-curve fits may benefit from adding an additional term $(1+c\
\delta_{\lambda})$ to equation A2 (e.g. Haynes et al., 2015; Wakeford et al.,
2016), where $c$ is an additional fit parameter and $\delta_{\lambda}$ is the
band-integrated drift of the spectrum on the detector in the dispersion
direction. We measured $\delta_{\lambda}$ by cross-correlating the observed
spectral flux of each exposure to the reference exposure. However, including
fit parameter $c$ did not improve the Bayesian information criterion. We
therefore did not use this term.

##  Appendix B Light curves

Figures 6 and 7 show the secondary eclipse light curves for the exponential-
ramp method and the RECTE method, respectively. We fit the light curves in the
three wavelength bins and for each visit separately.

We note that the scatter around the mean of the per-visit eclipse depths is
25% smaller than the average uncertainty. For a sample size of 15 normally
distributed measurements, there is a 13% probability that their standard
deviation is ${>}25$% smaller than their uncertainty. This could be an
indication that the uncertainties are overestimated.

Figure 6: Measured light curves of the WASP-80b secondary eclipse divided into
three wavelength bins (columns) over five visits (rows) for the exponential-
ramp method. In each cell, we show the normalized, telescope systematics-
reduced data and split them into forward-scanned (dark), and reverse-scanned
(light) data. We determined a unique eclipse depth for each bin and each
visit. The fitted light curve is shown as a solid line and we denote the times
of first, second, third, and fourth contact with vertical dashed lines. For
each fit, we provide a residual histogram to the right of the light curve. We
compare them to the expected photon noise (solid line). The residuals satisfy
a Shapiro-Wilks test at the $\alpha=0.1$ level and they can thus be considered
gaussian. In Figure 7 we display the equivalent of this figure for the RECTE
method. Note that for the exponential-ramp method, the first exposure of each
orbit has been removed, whereas this exposure is kept for the RECTE method.
Figure 7: The same as Figure 6 but for the RECTE method. The residuals satisfy
a Shapiro-Wilks test at the $\alpha=0.15$ level and they can thus be
considered gaussian.

##  Appendix C Comparing fitting methods

It is noticeable from Figure 1 that the RECTE method measures shallower
eclipses than the exponential-ramp method across all three wavelength bins and
for most visits. The averaged white light eclipse depth is slightly more than
$1\sigma$ larger for the exponential-ramp method. In this section, we dive
deeper into the performance of both methods.

Contrary to the RECTE method, the exponential-ramp method (see Appendix A) has
one parameter, $R_{\lambda,v,1}$, that acts only on the first orbit, hence on
fewer data points than all the RECTE parameters act on. The uncertainty on
$R_{\lambda,v,1}$ is therefore relatively large and some degeneracies arise
between it and the eclipse depth parameter. The exponential-ramp method
therefore has a ${\sim}10$% lower precision on the eclipse depth. This effect
is exacerbated for visits 3 and 4. Those visits have a shorter preeclipse
baseline (see Figures 6 and 7) and therefore have even larger degeneracies
between eclipse depths and $R_{\lambda,v,1}$. This results in ${\sim}30$%
larger uncertainties for these two visits than for the other visits (see
Figure 1). However, the RECTE method having a higher precision does not
necessarily mean it has a higher accuracy.

In Figure 8 we explored the residual structure for both light-curve fitting
methods (exponential-ramp, blue; RECTE, maroon). We did this by averaging the
first seven exposures of the first orbit over all visits into a single data
point, averaging the middle six exposures, and averaging the last six
exposures into a single data point. We performed this averaging for each orbit
and each wavelength bin to obtain the upper panel of Figure 8. The standard
deviation of all the residuals in the upper panel of Figure 8 is 12 ppm for
the exponential-ramp method and 16 ppm for the RECTE method. This signifies
that the RECTE method creates a larger residual structure. This is
corroborated by the lower right panel, where we averaged over wavelength and
over the three orbits to obtain a residual blueprint for an orbit with both
methods. This is the average residual structure for an orbit. Once again, we
see that the RECTE method creates a significantly larger intraorbit residual
structure than the exponential-ramp method. The standard deviation of the
residuals in the lower right panel of Figure 8 is 10 ppm for the RECTE method
and 4 ppm for the exponential-ramp method.

Because of the above arguments and the fact that the exponential-ramp method’s
light curves are also closer to photon noise (4% above it versus 6% above
photon noise), we opt to work with the exponential-ramp method as our main
result.

Figure 8: An investigation into the residual structures of the exponential-
ramp method (blue) and the RECTE method (maroon).
Upper panels: residuals of the exponential-ramp light curves (from Figure 6)
and the RECTE light curves (from Figure 7) averaged over all visits. We
combined the first seven exposures, middle six exposures, and the last six
exposures of each orbit into three separate data points per orbit.
Lower left: residuals of the upper panels averaged over wavelength.
Lower right: averaged residual structure for an orbit. That is, to obtain the
first data point we averaged over the first data point, of each orbit in the
lower left panel; to obtain the second data point we averaged over the second
data point of each orbit the lower left panel; and for the third, we averaged
over the third data point of each orbit. The lower level of scatter in this
diagram for the exponential-ramp method shows that that method is more capable
of capturing the shape of the orbit-long telescope systematics for this
particular set of observations.

##  Appendix D Details of the model fits

Table 2 shows a detailed accounting of the model fits. These model fits are
the results of fits to the dayside spectrum as well as fits to the
transmission spectrum. We computed the $\chi^{2}_{\nu}$ on both the dayside
spectrum as well as the transmission spectrum for both types of fits.

Table 2: Summary of model fits.

Model | $\chi^{2}_{\nu}$ |  $\Delta$BIC aa The difference in Bayesian information criterion with respect to the clear atmosphere model. This is performed on the spectrum to which the model was fit. A lower BIC indicates a better fit. A $\Delta\rm{BIC}{<}2$ can be deemed insignificant. | Best-fit | Posterior Median |  $3\sigma$ Limits
---|---|---|---|---|---
| Dayside | Transmission |  | Parametersbb Parameters used for the best-fit spectra in Figure 4. The haze formation rate $\eta$ is given in g cm-2s-1.  | Valuescc Median values of the MCMC posterior distributions. They can deviate significantly from the best-fit values because the model grid parameter space is limited and the posteriors are therefore truncated and asymmetrical. The model parameter space is limited to ($0\leq[M/H]\leq 1$), ($0.5\leq f_{\rm{sed}}\leq 2$), and ($-14\leq\rm{log}_{10}(\eta)\leq-9$). |
| Spectrum | Spectrum |  |  |  |
| Models Fit to the Dayside Spectrum
Clear | $1.4$ |  $6.5$dd We generated a transmission spectrum from the atmospheric model that best fits the dayside spectrum, and compared it to the HST/Spitzer transmission data. | $0$ | $[M/H]=0.20$ | $[M/H]=0.24^{+0.20}_{-0.15}$ | $[M/H]<0.91$
Clouds | $0.6$ | $2.0$ | $-1.3$ | $[M/H]=0.03$ | $[M/H]=0.30^{+0.24}_{-0.20}$ | $[M/H]<0.94$
|  |  |  | $f_{\rm{sed}}=0.50$ | $f_{\rm{sed}}=1.19^{+0.6}_{-0.5}$ |  $f_{\rm{sed}}$ is unconstrained
Soot haze | $1.2$ | $2.3$ | $+1.0$ | $[M/H]=0.21$ | $[M/H]=0.33^{+0.4}_{-0.22}$ | $[M/H]<0.99$
|  |  |  | log${}_{10}(\eta)=-13.5$ | log${}_{10}(\eta)=-13.3\pm 0.5$ | log${}_{10}(\eta)<-10.7$
Tholin haze | $1.3$ | $6.5$ | $+1.6$ | $[M/H]=0.20$ | $[M/H]=0.22^{+0.20}_{-0.15}$ | $[M/H]<0.89$
|  |  |  | log${}_{10}(\eta)$$=-14.0$ | log${}_{10}(\eta)=-13.2^{+0.7}_{-0.6}$ | log${}_{10}(\eta)<-12.0$
| Models Fit to the Transmission Spectrum
Clear |  $1.6$ee We generated a dayside spectrum from the atmospheric model that best fits the transmission spectrum, and compared it to the HST/Spitzer dayside data. | $6.2$ | $0$ | $[M/H]=0.0$ | $[M/H]=0.12^{+0.8}_{-0.10}$ |  $[M/H]$ is unconstrained ff The metallicity posterior of the clear atmosphere model is double-peaked at $[M/H]=0$ and $[M/H]>1$ (see Figure 5). A solar metallicity composition fits the water spectrum in the G141 wavelength range well, while higher metallicities suit the CO2/CH4ratio probed by the longer wavelength Spitzer points better.
Clouds | $4.2$ | $1.8$ | $-136$ | $[M/H]=1.0$ | $[M/H]=0.84^{+0.12}_{-0.25}$ | $[M/H]>0.06$
|  |  |  | $f_{\rm{sed}}=0.50$ | $f_{\rm{sed}}=0.57^{+0.10}_{-0.06}$ | $f_{\rm{sed}}<1.0$
Soot haze | $2.9$ | $1.1$ | $-156$ | $[M/H]=1.0$ | $[M/H]=0.84^{+0.12}_{-0.22}$ | $[M/H]>0.12$
|  |  |  | log${}_{10}(\eta)=-12.97$ | log${}_{10}(\eta)=-12.96^{+0.12}_{-0.09}$ |  $-13.22<$log${}_{10}(\eta)<-12.59$
Tholin haze | $7.4$ | $1.1$ | $-156$ | $[M/H]=1.0$ | $[M/H]=0.91^{+0.07}_{-0.14}$ | $[M/H]>0.40$
|  |  |  | log${}_{10}(\eta)=-12.13$ | log${}_{10}(\eta)=-12.13^{+0.14}_{-0.11}$ |  $-12.41<$log${}_{10}(\eta)<-11.65$

Notes.