11institutetext: Lund Observatory, Division of Astrophysics, Department of
Physics, Lund University, Box 43, 221 00 Lund, Sweden
11email<EMAIL_ADDRESS>22institutetext: Center for Space and
Habitability, University of Bern, Gesellschaftsstrasse 6, CH-3012 Bern,
Switzerland 33institutetext: INAF – Osservatorio Astrofisicodi Arcetri, Largo
Enrico Fermi 5, 50125 Firenze, Italy 44institutetext: European Southern
Observatory, Alonso de Córdova 3107, Vitacura, Región Metropolitana, Chile
55institutetext: Astrophysics, Department of Physics, University of Oxford,
Keble Road, Oxford, OX1 3RH, UK 66institutetext: Département de Physique,
Institut Trottier de Recherche sur les Exoplanètes, Université de Montréal,
Montréal, Québec, H3T 1J4, Canada ††thanks: Trottier Postdoctoral Fellow
77institutetext: University Observatory, Faculty of Physics, Ludwig Maximilian
University, Scheinerstrasse 1, D-81679 Munich, Germany 88institutetext: ARTORG
Center for Biomedical Engineering Research, Murtenstrasse 50, CH-3008, Bern,
Switzerland 99institutetext: Astronomy & Astrophysics Group, Department of
Physics, University of Warwick, Coventry CV4 7AL, United Kingdom

# The Mantis Network IV:

A titanium cold-trap on the ultra-hot Jupiter WASP-121 b.

H.J. Hoeijmakers, D. Kitzmann Corresponding author1122 B.M. Morris 22 B.
Prinoth 11 N. Borsato 11 B. Thorsbro 11 L. Pino 33 E. K. H. Lee 22 C. Akın 22
J.V. Seidel 44 J.L. Birkby 55 R. Allart 66 K. Heng 778899

(Received September 13, 2022; not yet accepted)

###### Abstract

Context. Using emission lines by metals we investigate the three-dimensional
distribution of temperature and chemistry in ultra-hot Jupiters.

Aims. Existing observations of WASP-121 b have suggested an under-abundance of
titanium and titanium-oxide from its terminator region. In this study, we aim
to determine whether this depletion is global by investigating the day-side
emission spectrum.

Methods. We analyze eight epochs of high-resolution spectra obtained with the
ESPRESSO spectrograph, targeting orbital phases when the day-side is in view.
We use a cross-correlation method to search for various atoms, TiO and VO and
compare to models. We constrain the velocities and phase-function of the
emission signal using a Bayesian framework.

Results. We report significant detections of Ca I, V I, Cr I, Mn I, Fe I, Co I
and Ni I, but not Ti or TiO. Models containing titanium are unable to
reproduce the data. The detected signals are consistent with the known orbital
and systemic velocities and with peak emission originating from the sub-
stellar point.

Conclusions. We find that titanium is depleted from regions of the atmosphere
where transmission and emission spectroscopy are sensitive. Supported by
recent HST observations of the night-side, we interpret this as evidence for
the night-side condensation of titanium, preventing it from being mixed back
into the upper layers of the atmosphere elsewhere on the planet. Species with
lower condensation temperatures are unaffected, implying sharp chemical
transitions exist between ultra-hot Jupiters that have slight differences in
temperature or dynamical properties. As TiO can act as a strong source of
stratospheric heating, cold-trapping creates a coupling between the thermal
structures on the day-side and night-side, and thus condensation chemistry
needs to be included in global circulation models. Observed elemental
abundances in hot Jupiters will not reliably be representative of bulk
abundances unless night-side condensation is robustly accounted for or the
planet is hot enough to avoid night-side cold-traps entirely. Secondary
eclipse observations by JWST/NIRISS have the potential to confirm an absence
of TiO bands at red-optical wavelengths. We also find that the abundance
ratios of metal oxides to their atomic metals (e.g. TiO/Ti) depend strongly on
the atmospheric C/O ratio, and that planetary rotation may significantly lower
the apparent orbital velocity of the emission signal.

###### Key Words.:

planets and satellites: atmospheres – planets and satellites: composition –
planets and satellites: gaseous planets – methods: observational – techniques:
spectroscopic

##  1 Introduction

WASP-121 b is a highly inflated ($R=1.753\pm 0.036R_{J}$, $M=1.157\pm
0.070M_{J}$), highly irradiated ($T_{\textrm{eq}}=2358\pm 52K$) exoplanet
orbiting a relatively bright ($V=10.4$) F6V star with a short orbital period
of 1.27 days (Delrez et al., 2016; Bourrier et al., 2020). Because of its high
temperature, it is classified (Evans et al., 2017) as a member of the class of
ultra-hot Jupiters (UHJ). The atmospheres of UHJs are theorized to be largely
atomic, as all but the most strongly bound molecules dissociate (Arcangeli et
al., 2018; Kitzmann et al., 2018; Lothringer et al., 2018; Parmentier et al.,
2018). As the system is observationally favorable, WASP-121 b has been
targeted intensively over the past years with several ground-based and space-
based facilities, including optical and infrared spectrographs to study the
planet’s atmosphere. Initially, it has been observed extensively with the WFC3
and STIS instruments on the Hubble Space Telescope (HST). These observations
revealed emission by H2O (Evans et al., 2017) that is indicative of a thermal
inversion, now commonly observed in ultra-hot Jupiters (e.g. Nugroho et al.,
2020; Pino et al., 2020; May et al., 2021). The optical transmission spectrum
appears to be complex, with the absorption of metals and possibly TiO or VO
leading to significant variability in the transit radius between near-UV,
optical and near infra-red wavelengths (Evans et al., 2016, 2018). Recent
phase-curve observations by Mikal-Evans et al. (2022) have placed tight
constraints on the temperature profiles of the day and night-sides, as well as
the metallicity, which appears to be elevated.

Numerous transit observations have also been obtained using ground-based high-
resolution spectrographs (Hoeijmakers et al., 2020; Merritt et al., 2021;
Borsa et al., 2021). With spectral resolving powers of $R\sim 10^{5}$, such
instruments resolve individual absorption lines of atoms and molecules in the
spectra of exoplanets, and measure Doppler shifts down to less than 1 km/s,
enabling observations of the effects of atmospheric dynamics (Snellen et al.,
2010). As the transmission spectra of UHJs are typically rich in metal
absorption lines, optical high-resolution spectrographs have proven to be
highly capable of identifying metals in the atmospheres of this type of
planet, including WASP-121 b, by use of the cross-correlation technique
(Snellen et al., 2010) that combines the contributions of many individual
lines. Observations taken with ESO’s HARPS, UVES and ESPRESSO spectrographs
have revealed the following species: H I, Li I, Na I, Mg I, K I, Ca I, Ca II,
Sc II, V I, Cr I, Mn I, Fe I, Co I and Ni I (Bourrier et al., 2020; Cabot et
al., 2020; Hoeijmakers et al., 2020; Merritt et al., 2021; Borsa et al.,
2021). Ti and TiO were predicted to cause observable absorption and have been
searched for repeatedly, without either of them being detected (Hoeijmakers et
al., 2020; Merritt et al., 2021; Gibson et al., 2020). Recent advances in the
application of the high-resolution cross-correlation technique have allowed
for the retrieval of elemental abundances and abundance ratios from this type
of data (Gibson et al., 2020), also confirming the depletion of titanium
compared to other metals at the terminator region. The apparent absence of Ti
and TiO are consistent with the HST STIS & WFC3 transmission spectra, which
favor VO bands combined with a depletion of TiO (Evans et al., 2018). It has
been hypothesized that the depletion of Ti from the observable part of the
atmosphere is caused by condensation of Ti out of the gas phase (Hoeijmakers
et al., 2020; Mikal-Evans et al., 2022). A question that arises is where in
the atmosphere this condensation of Ti occurs and to what extent it is
distributed around the planet. Are Ti and TiO missing from the transmission
spectrum because Ti is condensing locally at the terminator region, or because
condensation happens at a cold point elsewhere on the planet (e.g. the night-
side), where it remains locked up in what is known as a cold-trap (Spiegel et
al., 2009). The observation of V and the simultaneous absence of Ti/TiO
suggests that this condensation mechanism is ineffective for vanadium, placing
the temperature profile in the coldest regions of the atmosphere between the
stability curves of CaTiO3 and VO, which are the highest-temperature
condensates of Ti and V respectively at solar element abundances (Lodders,
2002). The peak day-side temperature of WASP-121 b has most recently been
measured to be over 3,000 K (Mikal-Evans et al., 2022), well above the
condensation temperature of CaTiO3. The same observations constrained the
night-side temperature to be near or below the condensation curve of CaTiO3,
supporting the hypothesis that titanium can indeed condense on the night-side.

The objective of this study is to present observational evidence that titanium
is missing from the day-side emission spectrum of the planet, implying that it
is depleted globally and thus indeed cold-trapped. Section 2 describes the
ESPRESSO observations and the data reduction and pre-processing. Section 3
describes the analysis methodology, based on the high-resolution cross-
correlation technique (Snellen et al., 2010). Section 4 summarizes and
discusses the results and important implications.

##  2 Observations and data reduction

We observed the WASP-121 system (spectral type F6, V=10.4) during 8 epochs
with the ESPRESSO instrument at ESO’s 8.2 m VLT (PID 0105.C-0591 &
0106.C-0737, P.I. Hoeijmakers), yielding 8 continuous time-series of the high-
resolution spectrum of the system. The observations were carried out from
January to April 2021, at various phases of the planet, with four epochs
before and four epochs after the secondary eclipse to cover phase ranges in
which the planet accelerates in opposing directions. The observations are
summarized in Table 1, and the resulting raw data can be accessed publicly
from ESO’s Science Archive Facility. The observations used the standard
calibration plan of the instrument, including flat-field and wavelength
calibrations. In all cases, the instrument was used in 1-UT, high-resolution
mode with 300 s exposures, yielding spectra with a resolving power of $R\sim
140,000$) and a typical SNR of 50. The instrument was set to a readout mode of
2x1 binning with fiber B on sky.

Table 1: Overview of the observing epochs, where $N_{\mathrm{exp}}$ is the number of exposures taken during each run, $\phi$ is the range of orbital phases of WASP-121 b covered and weight is the relative weight of each night, when used to combine the cross-correlation functions in Section 4. In particular the fifth night is weighed down because those observations covered orbital phases near quadrature where the change in radial velocity is small, leading to partial self-subtraction of the planetary signal. # | Date | $N_{\mathrm{exp}}$ | $\phi$ | weight
---|---|---|---|---
1 | 2021-01-11 | 41 | 0.272 – 0.403 | 0.211
2 | 2021-01-23 | 37 | 0.563 – 0.684 | 0.156
3 | 2021-02-06 | 37 | 0.569 – 0.694 | 0.165
4 | 2021-03-21 | 43 | 0.225 – 0.370 | 0.099
5 | 2021-04-04 | 33 | 0.190 – 0.307 | 0.026
6 | 2021-04-07 | 28 | 0.575 – 0.667 | 0.059
7 | 2021-04-08 | 37 | 0.326 – 0.447 | 0.190
8 | 2021-04-16 | 34 | 0.603 – 0.715 | 0.096

We reduced the data using the ESPRESSO Data Reduction Software (DRS) version
2.3.3. The DRS produces extracted echelle orders (S2D), as well as stitched,
resampled and blaze-corrected spectra (S1D) spanning the full wavelength range
of the instrument. The signal-to-noise ratios achieved during each of these
observations as estimated by the pipeline are shown in Fig. 1. Throughout the
analysis, we use the extracted spectra from the science fiber (A) without sky
subtraction to preserve the blaze function and with it, the true flux recorded
by the instrument.

Figure 1: The signal-to-noise ratio and orbital phase of each of the eight
time-series. The top-panel shows pre-eclipse data and the bottom panel shows
post-eclipse data with the phase axis reversed, such that the secondary
eclipse is on the right (highlighted in gray). The signal-to-noise ratio is as
measured by the DRS in order 102, covering wavelengths around 550 nm. The
time-series are numbered chronologically, corresponding to Table 1

##  3 Data processing and cross-correlation analysis

We proceed to investigate the high-resolution spectrum of WASP-121 b using a
cross-correlation-based approach that closely follows the methodology used in
earlier work where we analyzed high-resolution time-series spectra of
transiting UHJs (e.g. Hoeijmakers et al., 2020; Prinoth et al., 2022), and is
summarized here with emphasis on aspects that are particular to ESPRESSO.

###  3.1 Telluric correction

We model the telluric transmission spectrum by using molecfit version 1.5.9,
applied to each of the S1D spectra (Smette et al., 2015) 111molecfit version
1.5.9 is the last version of molecfit that can be installed stand-alone. We
modified its GUI-environment to be python3-compatible and removed one
duplicate entry in the line-list of water near 580 nm. We are willing to
redistribute our version of this package upon reasonable request.. The fitting
of the telluric models to the S1D spectra is carried out in the Earth’s rest-
frame by reversing the barycentric velocity correction that is applied by the
ESPRESSO pipeline by default. These are then Doppler-shifted, re-interpolated
and divided out of the S2D spectra, yielding telluric-corrected time-series
spectra for each of the echelle orders.

###  3.2 Post-processing

The telluric-corrected spectra are aligned with the inertial frame of the star
by shifting the wavelength solution back to the barycentric rest-frame and
removing the Keplerian component caused by the gravitational pull of the
planet, as predicted using the known semi-major radial velocity amplitude $K$
and the orbital ephemeris (Bourrier et al., 2020). After these velocity
corrections, the spectra are re-interpolated onto a common wavelength grid.
This is the only re-interpolation of the extracted orders carried out during
this analysis, and is done to allow for the spectral orders to be treated as
2D variables (wavelength versus time) from here on.

For each order222Because the fiber is sliced into two halves, each spectral
order is recorded twice by the detector. In this analysis we treat each copy
as though it was an independent spectral order with its own wavelength and
time axes. we determine the time-average flux and divide it to normalize the
order to its average flux; while saving the relative flux differences for
later use as weights. We then determine the time-average spectrum and divide
it out to obtain nearly flat residuals, to which we apply color correction and
outlier rejection. Color correction is done by fitting a $3^{\rm{rd}}$ order
polynomial to each exposure in the time series and dividing it out. This
removes broad-band time-variability in the spectrograph’s effective
throughput, such as variability due to atmospheric dispersion. On these
residuals we apply a running median average deviation (MAD) filter with a
width of 20 pixels wavelength columns, to approximate the standard deviation
in the order as a function of wavelength. All flux values more than $5\sigma$
away from the local median are flagged as bad data. All columns with more than
20% of pixels flagged as such are instead flagged entirely. All other outliers
are replaced by linear interpolates. We then visually inspect all orders and
flag remaining bad columns, e.g. due to the presence of telluric emission
lines (e.g. sodium) or regions with very low flux at some order edges. We also
reject columns where telluric lines absorb more than 20 % of the flux. In
total, $6.32\times 10^{5}$ (0.166%) values are replaced by interpolates and
$9.72\times 10^{6}$ (2.56%) are in columns that are masked entirely. These
columns are ignored in the remainder of the analysis.

###  3.3 Cross-correlation templates and models

We created grids of 1D models of the planet emission spectrum for use as
cross-correlation templates, as well as to allow for model comparison. The
principal free parameter in models of the thermal emission spectrum is the
temperature-pressure (T-P) profile. Our choice of T-P profile is based on the
recent analysis by Mikal-Evans et al. (2022), who find that the emission
spectrum is well reproduced with a 1D model with a temperature of 2,500 K in
the deep atmosphere that increases to 3,500 K at pressures between 10 and 1
mbar Mikal-Evans et al. (see Fig. 2 as well as Fig. 3 in 2022). At pressures
below 1 mbar, their best-fit model increases towards 4,000 K but these
pressures are not constrained by the HST data. We therefore construct a class
of models that follow the inversion as constrained by Mikal-Evans et al.
(2022), but that becomes isothermal for $\log P<-2.8$ at a temperature that we
vary from 3,100 K to 3,500 K towards the top of the atmosphere (see Fig. 2).
Later in the analysis, we find that models with peak temperatures between
3,200 K and 3,300 K are best capable of explaining our high-resolution data.
Our models further assume a metallicity value of either $5\times$ (0.7 dex) or
$10\times$ solar (1.0 dex) based on the findings by Mikal-Evans et al. (2022)
that the metallicity of WASP-121 b is likely elevated. As in previous work
(Hoeijmakers et al., 2020), we assume chemical equilibrium and model the
composition of the atmosphere given a value for the metallicity using FastChem
2.0 (Stock et al., 2022). Radiative transfer is done following the procedure
in (Gaidos et al., 2017), with line opacity by 151 atoms ions, 8 molecules and
continuum opacity caused by Rayleigh scattering, collision-induced absorption
and continuum absorption (see Kitzmann et al., 2021, for details). Opacity
functions are computed with HELIOS-K 2.0 (Grimm et al., 2021) based on line
lists adopted from VALD and Kurucz for atoms (Kurucz, 2017; Pakhomov et al.,
2019; Ryabchikova et al., 2015), and Exomol for molecules (Barber et al.,
2014; Li et al., 2015; McKemmish et al., 2016; Polyansky et al., 2018;
Bernath, 2020; Bowesman et al., 2021; Syme & McKemmish, 2021), including the
recently updated TiO line-list (McKemmish et al., 2019). Model spectra are
computed in units of spectral flux density (erg s-1 cm-2 $\mu$m-1), and are
converted to contrast by dividing by the flux density of the star, modeled as
a 6335 K blackbody (Polanski et al., 2022), and then multiplying with the
square of the radius ratio of the planet and the star.

Figure 2: The temperature-pressure profiles used in this work (purple),
compared to the best-fit profile by Mikal-Evans et al. (2022) (green). The
thick green line indicates the area where the HST data is sensitive. We chose
to explore a variety of isothermal profiles at lower pressures. The T-P
profile as plotted in Mikal-Evans et al. (2022) was digitized using
WebPlotDigitizer, https://github.com/ankitrohatgi/WebPlotDigitizer

Models containing all opacity sources are injected into the data by
multiplication with a weight that is a function of orbital phase following
Herman et al. (2022), as:

$f(\lambda)_{\mathrm{injected}}=f_{\mathrm{obs}}(\lambda)f(\lambda)_{\mathrm{model}}\cdot
0.5\cdot(1+\cos(2\pi(\phi-\theta)-\pi)^{\gamma}),$ (1)

where $f_{\mathrm{obs}}(\lambda)$ is the data after the masking of bad columns
(see above), $f(\lambda)_{\mathrm{injected}}$ is the data with the injected
model $f(\lambda)_{\mathrm{model}}$, $\phi$ is the orbital phase, $\theta$ is
an offset between the sub-stellar point and the peak of the emission, and
$\gamma$ acts to steepen the phase function near secondary eclipse 333For
$\gamma=1$, this expression is equivalent to the expression of Herman et al.
(2022), with a contrast parameter $C=1$ and a scaling factor $\alpha=1$..
Values of $\gamma=1$ and $\theta=0$ are adopted for model injection and
comparison, as later we will find that the data do not support significant
deviations from these values. We also compare this phase-function to the
broad-band light-curve of WASP-121 b modeled using Spiderman (Louden &
Kreidberg, 2018), assuming day-side and night-side temperatures of 3200 K and
1800 K, instantaneous re-radiation, the known system parameters (Bourrier et
al., 2020) and a uniform passband from 400 to 800 nm. We find that this phase-
curve is well approximated for values of $\gamma\approx 2$ (see Fig. 3, but we
note that at present, our high-resolution data does not constrain $\gamma$
very accurately, nor should it be expected that line-emission is described by
the same phase-function as broad-band continuum emission.

Figure 3: Model of the broad-band phase-curve of WASP-121 b with day-side and
night-side temperatures of 3200 K and 1800 K, instantaneous re-radiation
integrated over a uniform passband from 400 to 800 nm, compared to our
parameterized phase-function of equation 1.

Cross-correlation templates are constructed by including the opacity of
continuum absorbers and only a single species at each time, with a peak
temperature of 3,200 K. A model without any line absorbers is subtracted to
obtain a continuum-subtracted template for each species. We perform cross-
correlation (equation 1 in Hoeijmakers et al., 2020) using templates for Na I,
Mg I, K I, Ca I, Ca II, Sc I, Ti I, Ti II, V I, Cr I, Mn I, Fe I, Fe II, Co I,
Ni I, Sr I, Y I, Zr I, Nb I, Ba I, La I, Ce I, AlO, TiO and VO, over a
velocity range of $\pm$ 1000 km s-1 with steps of 1 km s-1 on each of the
eight time-series (epochs). The resulting cross-correlation time-series are
each co-added to the rest-frame of the planet, by assuming a range of possible
values for the orbital velocity $K_{p}$ while fixing the time of transit
center (Bourrier et al., 2020) and weighing by the flux in the exposures (as
determined before in section 3.2).

##  4 Results and discussion

We co-added the cross-correlation functions in the planetary rest-frame for
each of the time-series, and then combined these with weights equal to the
relative detection strength of Fe I of the injected model with $T=3,200$ K and
$5\times$ solar metallility (see Table 1). This produces the velocity-velocity
diagrams that are shown in Fig. 4, Fig. 5 and Fig. 6 for Ca I, Cr I, Fe I, Ni
I, Mn I, Co I, Ti I, TiO, V I and VO, as well as tentative signals of Na I and
Mg I. The cross-correlation functions of all tested species are shown in the
appendix in Fig. 11, including species for which no detection was made. Based
on these results, we report detections of line emission by Ca I, V I, Cr I, Mn
I, Fe I, Co I and Ni I.

Figure 4: Detections of Ca, Cr, Fe and Ni in the emission spectrum of WASP-121
b in velocity-velocity space (upper panels) and the extracted one-dimensional
CCFs (bottom panels). The one-dimensional CCFs are extracted at an orbital
velocity of 216.0 km/s (gray line) slightly below the expected velocity of
$221.1$ km/s as derived from the known orbital parameters, or at the orbital
velocity at which the peak occurs (black line), to illustrate the effect of
the choice of orbital velocity at which to extract. The vertical axis
indicates weighted emission line-strength (not relative signal-to-noise). This
quantity derives its physical meaning from comparison with injected models.
Colored dashed lines indicate the signals caused by injected models with and
without Ti/TiO at a metallicity of 5$\times$ solar (equal to 0.7 dex, the
metallicity found and used by Mikal-Evans et al., 2022), with an inverted
temperature-pressure profile that is isothermal at 3200 K at pressures of
$\log(P)=-2.8$ and below. At altitudes above this pressure, the HST data
published by (Mikal-Evans et al., 2022) do not constrain the TP-profile.
Horizontal bars indicate the signal strength of models with variations of this
peak temperature, and thus the strength of the thermal inversion. The solid
bars indicate models with a metallicity of 5$\times$ solar, and the dashed
bars indicate 10$\times$ solar. Figure 5: Similar to Fig. 4, for Ti, TiO, V
and VO. Ti and TiO are not detected but are predicted by models that contain
Ti/TiO opacity. VO is not detected nor does the model indicate that the data
are sensitive regardless of temperature, unless the metallicity is
significantly increased. The horizontal bars of VO for different temperatures
overlap so only 3200 K is shown. In-set scaling factors denote the factor by
which the y-axis was zoomed, to allow the signals to be plot on the same
scale. 50% means that the vertical axis labels should be read as being a
factor of 2 bigger, and vice versa. Figure 6: Similar to Fig. 4, for Mn, Co,
Na and Mg. Mn and Co are detected significantly, while Na and Mg are tentative
because of the presence of a strong shift in systemic and orbital velocity in
the apparent signal of Na (though see Seidel et al., 2023), and an strong
unexplained alias in the CCF of Mg. Figure 7: The cross-correlation functions
of Fe I of all 8 time-series binned onto a common phase-grid with steps of
0.01, in both the stellar rest-frame (top panel) and the planetary rest-frame
(bottom panel). The trace caused by the emission of Fe I is clearly visible
and increases towards the secondary eclipse. The exposures are averaged with
equal weights and uncertainties are propagated accordingly when fitting the
model of Eq. 2.

Besides co-adding the cross-correlation functions into velocity-velocity
diagrams, we rebin and average the cross-correlation functions of the eight
epochs onto a common phase grid with a step size of 0.01 in phase, without
applying weights. This allows the Doppler-shifted emission of the planet to be
visualized as a function of the orbital phase (see Fig. 7), while a lack of
weights precludes biasing towards a particular epoch or phase-range (at some
cost in signal-to-noise ratio). Fe I emission clearly traces the radial
velocity of the planet both prior to the secondary eclipse and afterwards. The
line strength increases towards the secondary eclipse which is expected
because most of the hotter sub-stellar point is in view. Using the same phase
function as before, we model the two-dimensional emission profile as:

$\text{CCF}=Ae^{\frac{-(v-v_{t})^{2}}{2\sigma_{w}^{2}}}\cdot\left(0.5+0.5\cos\left(2\pi(\phi_{t}-\theta)-\pi\right)\right)^{\gamma}+C,$
(2)

with $v_{t}=v(t)=v_{\textrm{sys}}+v_{\textrm{orb}}\sin(2\pi\phi_{t})\sin(i)$
the radial velocity of the planet as a function of orbital phase
$\phi_{t}=\phi(t)$. The model has the following free parameters and we define
priors for the purpose of carrying out Bayesian inference:

  * •

The peak amplitude of the emission line $A\sim\mathcal{U}(-300,3000)$ in ppm.

  * •

The systemic velocity $v_{\textrm{sys}}\sim\mathcal{U}(32,44)$ in km s-1,
centered on the known systemic velocity of 38.3 km s-1 (Bourrier et al.,
2020).

  * •

The orbital velocity $v_{\textrm{orb}}\sim\mathcal{U}(210,230)$ in km s-1.

  * •

The Gaussian line-width $\sigma_{w}\sim\mathcal{U}(2,10)$ in km s-1.

  * •

The offset angle of the peak emission $\theta\sim\mathcal{U}(-70,70)$ in
degrees, analogous to the hot-spot offset typically fit in broad-band phase-
curve observations.

  * •

The index of the phase function $\gamma\sim\mathcal{U}(0,6)$

  * •

A constant offset $C\sim\mathcal{U}(-3,3)$ in ppm.

We sample from these prior distributions and evaluate the likelihood in a
Bayesian framework using a No U-Turn Sampler (see Betancourt, 2017, for a
review) implemented using NumPyro and Jax (Bradbury et al., 2018; Bingham et
al., 2019; Phan et al., 2019). Fitting results are summarized in Table 2, and
the posterior distributions and the best-fit models for all detected species
are shown in Fig. 14.

###  4.1 Velocity traces

The parameters that describe the shape and location of the trace
($v_{\textrm{orb}}$, $v_{\textrm{sys}}$, $\gamma$, $\theta$ and $\sigma_{w}$)
are consistent between all species to within $3\sigma$, though variations may
exist in particular in the apparent value of $v_{\textrm{orb}}$. This has been
observed previously in transit transmission spectra of UHJ’s, where planetary
rotation and dynamical effects cause variations in the peak location of cross-
correlation signals in $K_{p}$-$v_{\textrm{sys}}$ space (e.g. Prinoth et al.,
2022) as modeled using global circulation models (Wardenier et al., 2021; Lee
et al., 2022). Without recourse to a GCM, we follow Pino et al. (2022)
producing a simple model of narrow line-emission originating from particular
points on the tidally locked surface of WASP-121 b. The velocity of a point on
the equator is assumed to be equal to the (circular) orbital velocity plus
synchronous rotation of the planet, leading to the following expression:

$v_{r}(t)|_{\theta}=\frac{2\pi}{P}\left(a\sin(\phi_{t})-R_{p}\sin(\phi_{t}-\theta)\right)$
(3)

with $R_{p}$ the radius of the planet, $a$ the semi-major axis of the orbit
(which may also be expressed in terms of $P$ and $M_{*}$), and $\theta$ now
equal to the angle between the emitting point and the sub-stellar point. A
reduction in orbital velocity may thus be large for inflated, close-in planets
(with large values of $\frac{R_{p}}{a}$). We construct a model of the emission
lines of three points on the surface, for $\theta=\pm 0.3\pi$ and $\theta=0$,
i.e. near the limbs on the day-side and the sub-stellar point – as a function
of radial velocity and orbital phase (i.e. a CCF, see Fig. 8), with equal
strength but scaled with a projection factor $\cos{\phi_{t}-\theta-\pi}$. We
then construct a velocity-velocity diagram like before, and note that
synchronous rotation of the surface lowers the orbital velocity at which the
emission signal maximizes significantly by approximately 10 km/s. Emission
from points offset from the sub-stellar point may additionally be
significantly blue or red-shifted. We note that the peak of emission for our
detected species tend to cluster lie near 216 km/s, approximately 5 km/s below
the true orbital velocity of 221.1 km/s. This could indicate that the majority
of emission originates from near the sub-stellar point. The tentative signal
of Na I stands out, with a significantly higher orbital velocity and blue-
shift, which may be related to the observation by Seidel et al. (2023) of a
high-velocity sodium component. On the other hand, we note that our fit of its
trace is poorly converged (see Fig. 14), so more observations are needed to
confirm the presence of Na I emission. The effect of planetary rotation may be
capable of explaining similar shifts in H2O and CO emission observed in
WASP-18 b by Brogi et al. (2023), or the seeming orbital eccentricity of
KELT-9 b by Pino et al. (2022).

Figure 8: Model of the velocity traces of three points on the day-side near
the morning limb (A), sub-stellar point (B) and the evening limb (C). Left
panel: Schematic of the WASP-121 b system to scale, with orbital phases
between quadrature and secondary eclipse. The line-of-sight is along the
vertical axis. Middle panels: Model of the cross-correlation traces, assuming
that line emission originates from each of the three spots in equal strength,
with a line-width corresponding to the instrumental resolving power. Planetary
rotation causes small differences in the location of each trace. Right panel:
Co-added velocity-velocity diagram showing the signal due to each of the three
points. White dotted lines indicate the true orbital velocity and the velocity
at which the sub-stellar point peaks.

We additionally detect no significant offset in the phase angle of peak
emission for any species, and the model that was injected with an index of
$\gamma=1$ is not significantly discrepant for any of the species. We note
that observations of in particular Fe I emission in ultra-hot Jupiters can be
very sensitive to shape-parameters and peak-offsets, and comparisons with
predictions from global circulation models as well as observations of similar
systems around brighter host stars are warranted. We also acknowledge that in
the presence of significant post-processing of the observed spectra (e.g. in
the form of filtering algorithms, imperfect removal of telluric lines or
stellar lines, or dividing out the time-average especially near quadrature),
the planetary line shape can change significantly (Gibson et al., 2020)
potentially biasing the location of the best-fit parameters and needs to be
modeled consistently. However in the present analysis, the most significant
filtering was a relatively wide high-pass filter. Most nights cover a large
shift in radial velocity (the smallest being 15 km s-1 in night # 5) and all
telluric lines deeper than 20% were masked entirely. Besides the decreased
orbital velocity due to the planets’ rotation, we do not observe anomalous
shifts in radial velocity and therefore conclude that atmospheric dynamic
effects do not seem to significantly impact our analysis.

Table 2: Summary of the best-fit parameters obtained by fitting the Doppler-shifted emission trace of each of the detected species according to equation 2. These values reflect the median and standard deviations of the marginalized posterior distributions for purposes of clarity. In reality, some posteriors are asymmetric. Refer to Fig. 14 for the uncertainty intervals in the positive and negative direction separately. Element | $A$ | $C$ | $\gamma$ | $\sigma_{w}$ | $\theta$ | $v_{orb}$ | $v_{sys}$
---|---|---|---|---|---|---|---
Ca I | $149\pm 40$ | $-0.53\pm 0.68$ | $3.1\pm 1.5$ | $6.36\pm 0.96$ | $4\pm 12$ | $220.2\pm 1.7$ | $37.8\pm 1.1$
Ti I | $-19\pm 19$ | $0.05\pm 0.41$ | $3.7\pm 1.6$ | $4.8\pm 2.1$ | $17\pm 46$ | $221.5\pm 7.0$ | $35.3\pm 3.0$
V I | $92\pm 17$ | $-0.33\pm 0.54$ | $0.68\pm 0.64$ | $3.98\pm 0.74$ | $23\pm 23$ | $216.8\pm 1.1$ | $39.09\pm 0.78$
Cr I | $81\pm 18$ | $-0.37\pm 0.53$ | $1.15\pm 0.84$ | $5.12\pm 0.89$ | $11\pm 21$ | $214.9\pm 1.3$ | $39.8\pm 1.0$
Mn I | $137\pm 39$ | $-0.7\pm 1.3$ | $1.3\pm 1.2$ | $5.7\pm 1.5$ | $-7\pm 27$ | $216.9\pm 2.5$ | $39.2\pm 2.1$
Fe I | $130\pm 15$ | $-0.47\pm 0.35$ | $1.37\pm 0.45$ | $4.21\pm 0.36$ | $-1.5\pm 7.6$ | $216.24\pm 0.51$ | $38.72\pm 0.37$
Ni I | $177\pm 39$ | $-0.6\pm 1.1$ | $0.42\pm 0.62$ | $3.12\pm 0.71$ | $3\pm 31$ | $214.89\pm 0.83$ | $38.33\pm 0.71$
Co I | $194\pm 55$ | $-0.49\pm 0.94$ | $4.5\pm 1.1$ | $5.3\pm 1.4$ | $3.1\pm 7.0$ | $217.8\pm 2.2$ | $39.5\pm 1.3$

###  4.2 Model comparison

The cross-correlation signals in Figs. 4 and 5 are compared with the strengths
of models with and without titanium, for temperatures ranging from 3,100 K to
3,500 K and for two values of the metallicity of 5 and 10 times solar (0.7 and
1.0 dex). As expected, the line strength increases strongly with the assumed
temperature difference across the inversion. Removing Ti from the atmosphere
causes the removal of TiO. Because TiO absorbs strongly and thereby masks
lines of other species, models with Ti require higher temperatures to match
the observed signals of other atoms. For example, the signal of Ca I is well
reproduced by a model with a metallicity of $5\times$ solar and a peak
temperature of 3,400 K if Ti/TiO are present, but only 3,200 K is needed
without Ti/TiO. This underscores the importance of model completeness in
explanet spectroscopy: Even molecules that are not individually detected or
detectable may produce significant (pseudo-continuum) absorption that affects
the relative line strengths of other species that are observed. The success of
spectroscopic model inference depends on the completeness of the set of
opacities that are included in the model. In the case of WASP-121 b
previously, missing opacity also led to an apparently anomalous spectral slope
in the transmission spectrum that is reproduced well when metal line
absorption is included (Hoeijmakers et al., 2020).

Fig. 5 shows non-detections of both Ti I and TiO, a robust detection of V I
and a non-detection of VO, which is predicted to be too faint to detect with
models at these temperatures unless the metallicity is significantly higher.
From these comparisons, we conclude that models that contain Ti/TiO are not
capable of reproducing the data for two reasons:

  1. 1.

TiO is strongly ruled out, even for the model with the lowest expected TiO
line strength (3,100 K and 10$\times$ solar metallicity).

  2. 2.

To explain the line strengths of the other species, a peak temperature of
approximately 3,400 K is needed for models with Ti/TiO. However, at such a
temperature, Ti I would be detected very strongly.

Furthermore, based on the model comparison, we predict that with additional
observations, other species may be detectable if they are not depleted
similarly to Ti I, including Sc I and Y I (see Fig. 11). We also note that
generally, ions that are very strongly observed in transmission are
essentially undetectable in emission in this planet and this is expected given
that the emitted flux decreases sharply towards shorter wavelengths, and the
fact that ions mainly exist at much lower altitudes to which emission
spectroscopy is inherently less sensitive.

###  4.3 Depletion of the Ti inventory

Ti is not detected in emission in this study, nor in previous observations of
the transmission spectrum (Hoeijmakers et al., 2020; Merritt et al., 2021;
Gibson et al., 2020) even though other absorbers are, in particular V. The
injected models, which reproduce detections of other species within a factor
of order unity, predict that Ti should have been significantly detected.
Similarly, TiO is expected to be detected strongly assuming that the line-list
(McKemmish et al., 2019) is sufficiently accurate. The recent detection of TiO
in the transmission spectrum of WASP-189 b indicates that it is (Prinoth et
al., 2022). A recent study of global circulation models of this planet using
non-elevated metallicity predicts that the thermal inversion occurs at
slightly higher pressures (100 to 10 mbar), and that under such circumstances
TiO should still be recoverable from this data, even if Ti may not be (Lee et
al., 2022). Note that our models assume solar elemental ratios, while the
abundance of Ti in the host star WASP-121 is significantly greater than that
of V (Polanski et al., 2022), making a non-detection of Ti relative to V even
more robust.

The apparent absence of emission by Ti and TiO suggests that the abundances of
Ti and Ti-bearing molecules are reduced compared to what is expected from
stellar elemental abundance ratios and chemical equilibrium. Assuming that
there is no bulk depletion of Ti in WASP-121 b, there is a physical mechanism
that causes depletion of Ti from the hot day-side as well as the terminator
regions. We hypothesize that this depletion is caused by condensation of Ti,
predicted to condense as CaTiO3 (perovskite) at one of the highest
temperatures of all atoms (Lodders, 2002). Recent observations of the phase-
curve of WASP-121 b with HST Mikal-Evans et al. (2022) imply that the night-
side temperature profile indeed lies below the condensation curve of
perovskite, meaning that significant condensation of perovskite should occur
on the night-side. However, on the hot day-side with a temperature over 3,000
K, condensation is not expected to play a role. Instead, we infer that night-
side condensation of Ti causes it to be cold-trapped (Spiegel et al., 2009),
unable to recirculate back to regions of the atmosphere probed by emission and
transmission spectroscopy. The night-side cold-trap thus causes titanium to be
depleted globally, including in regions where the temperature is far above its
condensation curve. Although titanium initially condenses with Ca to form
CaTiO3, this is not expected to significantly alter the atmospheric Ca
abundance because it has a significantly greater elemental abundance (Asplund
et al., 2009).

The present observations do not constrain where, or how the titanium is
trapped. It may be that titanium-bearing condensates are prevented from
recirculating back to the day-side due to inefficient advection (horizontal
mixing), although (Seidel et al., 2023) find evidence for strong day-to-night
flows. Alternatively, titanium-bearing condensates may indeed recirculate back
to the day-side but are confined to high pressures, at altitudes below the
thermal inversion on the day-side, (i.e. below the mbar to $\mu$bar pressures
probed in emission and transmission). We believe that this scenario is
currently not supported by global circulation models, which predict strong
vertical mixing (Parmentier et al., 2013; Menou, 2019) that increases strongly
with planet equilibrium temperature (Komacek et al., 2019). However,
regardless of the location at which the titanium is trapped, we derive several
important implications from these observations:

  1. 1.

High-resolution emission spectroscopy of ultra-hot Jupiter atmospheres can be
used to impose limits on the efficiency with which condensates are remixed to
the high-temperature day-side by global circulation, or if it is remixed
horizontally, the efficiency by which it is mixed vertically across the
temperature inversion (i.e. $K_{zz}$). In the latter case, these observations
demonstrate that the atmospheres of ultra-hot Jupiters cannot be assumed to be
well mixed on the day-side.

  2. 2.

The process of condensation and limited remixing observed in this study is
specific to the Ti inventory, and not e.g. Fe, V, Ni or Cr. Therefore, we
hypothesize that the temperature profile on much of the night-side lies
between the condensation curves of CaTiO3 and VO. This is fully consistent
with the night-side temperature profile derived from spectroscopic phase-curve
observations recently published by Mikal-Evans et al. (2022).

  3. 3.

In this formulation of the cold-trap hypothesis, an element is depleted from
the gas-phase on a global scale if the night-side temperature profile is below
a threshold and if re-circulation or vertical mixing is inefficient. This
implies that planets with slight differences in equilibrium temperature and/or
global circulation properties can have drastically different atmospheric
compositions, with one or multiple species depleted compared to less volatile
species. For example, on planets with slightly lower night-side temperatures
than WASP-121 b both Ti and V may be removed from the gas-phase globally.
Conversely, a slightly hotter planet may have both titanium and vanadium-
bearing species in the gas-phase. We therefore predict that there exists no
smooth continuum in the atmospheric composition (terminator nor day-side) of
hot Jupiters as a function of equilibrium temperature. Instead, we expect that
there are sharp chemical transitions with a complex dependency on both
equilibrium temperature and global circulation.

  4. 4.

At solar metallicity, aluminum condenses at higher temperatures than titanium
in the form of spinel (MgAl2O4)444Although aluminum may condense along with
magnesium in the form of spinel, this should not significantly deplete the
magnesium reservoir because magnesium is much more abundant than aluminium
(Asplund et al., 2009). or corundrum (Al2O3) (Lodders, 2002). If our
formulation of the cold-trap effect is correct, this means that aluminium
should be expected to be cold-trapped together with titanium. This would
explain the absence of Al I absorption from the HST/STIS spectrum (Evans et
al., 2018), rather than photo-ionization as hypothesised by us earlier
(Hoeijmakers et al., 2020). This also means that bands of AlO should be
generally unobservable in planets cooler than WASP-121 b, e.g. in WASP-43 b
(Chubb & Min, 2022).

  5. 5.

As metals and metal-oxides are expected to provide important sources of
heating of the upper atmospheres of hot Jupiters (Lothringer et al., 2018), we
predict that the temperature structures of the day- and night-sides should be
strongly coupled. A consequence is that the atmospheric opacity computed as
part of 3D global circulation models need to be computed self-consistently,
where the opacity on the day-side is dependent on the minimum night-side
temperature and the effects of condensation there. Condensation physics and
transport of condensate particles need to be built into GCMs to explain the
observed properties of ultra-hot Jupiters.

  6. 6.

Simpler 1D models of day-side or terminator temperature profiles also need to
take into account non-local condensation in order to be self-consistent. The
effect of cold-trapping can be parameterized via reduction of the abundances
of certain metals and molecules, but this would need to take into account the
condensation sequence: Depletion of e.g. vanadium without depletion of
titanium would not be self-consistent.

  7. 7.

The fact that metals may be depleted globally due to condensation effects
challenges notions of metallicity and elemental abundance ratios to describe
the bulk compositions of hot Jupiters. In all likelihood, the bulk titanium
abundance of WASP-121 b is not anomalously low even though observations of the
day-side and transmission spectra indicate depletion. Any theories that would
rely on the bulk titanium abundance (e.g. theories about formation history,
see e.g. Lothringer et al., 2021) would be poorly constrained. For species
that are sensitive to cold-trapping, apparent measurements of elemental
abundances or abundance ratios cannot be translated into bulk abundances
without taking into account depletion via non-local condensation (this was
also explored by Pelletier et al., 2021). Direct measurements of bulk metal
abundances from emission or transmission spectra will only be possible if the
planet is sufficiently hot on the night-side to prevent cold-trapping, or if
models accurately include condensation chemistry and global transport.

  8. 8.

We have simulated the emission spectrum as it is expected to be observed with
NIRISS SOSS (see Fig. 9) as part of GTO program #1201 (P.I. Lafreniere). These
observations will confirm the presence or absence of TiO bands at short
wavelengths with very high confidence, but will not be very sensitive to VO as
its (integrated) absorption bands are weaker.

Figure 9: Simulated emission spectra of the day-side as observed with
JWST/NIRISS SOSS, using Pandexo (Batalha et al., 2017). Solid lines: high-
resolution models assuming a temperature inversion up to 3200 K (see Fig. 2)
at a metallicity of (solid lines). Transparent dots: Pandexo simulation at the
native instrument resolution. Solid dots: binned to a resolving power of 100.
Purple: Model with Ti/TiO. Orange: Model without Ti/TiO. If TiO is indeed
absent from the day-side emission spectrum of WASP-121 b, TiO bands will be
strongly ruled out at the shortest wavelengths of NIRISS, while the VO band
strength near 1 $\mu$m will be hard to discern. Note that the water band at
$1.4\mu$m is barely visible by eye due to the scale of the axes, but the
increased contrast from 1000 to 1500 ppm between $1.3$ and $1.6\mu$m is
consistent with the WFC3 data (see Fig. 2 Evans et al., 2017).

###  4.4 Ti/TiO as tracers of atmospheric structure and chemistry

The equilibrium-chemistry abundance profiles of Ti and TiO are shown in Fig.
13. We observe that because of the large temperature difference across the
inversion, the predicted abundance of TiO drops by orders of magnitude due to
dissociation, sharply increasing the abundance of Ti. As both Ti and TiO have
rich optical emission spectra, spectra at optical wavelengths are highly
sensitive to the presence of titanium in the case of an inverted atmosphere.
We predict that this strong temperature dependence makes the Ti/TiO pair an
especially sensitive probe of the T-P profile of ultra-hot Jupiter atmospheres
that can be used in high-resolution retrieval analyses (Brogi & Line, 2019;
Gibson et al., 2020), as long as the planet is hot enough to avoid cold-
trapping (e.g. WASP-189 b for which Ti has been detected. Prinoth et al.,
2022). The profile of V shows a similar behavior but is less pronounced
because the overall abundance of VO is smaller. We also note from Fig. 13 that
the abundances of Ti and V depend relatively weakly on the elemental Ti and V
ratios at temperatures around 2,500 K. An increase in the metallicity from
$5\times$ to $10\times$ solar increases the abundance of V from approximately
3.5 ppb to 4.5 ppb. Increasing these elemental ratios instead manifests itself
mostly as an increase in the abundances of TiO and VO (see also the discussion
in Hoeijmakers et al., 2020). As can be seen in Fig. 5, this translates to a
strong dependence of the VO emission strength with metallicity.

Figure 10: Equilibrium-chemistry solution of the atmosphere of WASP-121 b
assuming a metallicity of $5\times$ solar, a temperature inversion with a
maximum temperature of 3200 K and a low or a high C/O ratio. The C/O ratio is
varied by modifying the abundance of carbon while leaving oxygen fixed.

By varying the abundance of carbon, we observe that the abundance of TiO is a
strong function of C/O ratio, consistent with the argument originally
formulated by Madhusudhan et al. (2011) in the context of TiO/VO-driven
thermal inversions. In the case of a C/O ratio of 1.0, the TiO abundance drops
by three orders of magnitude compared to solar C/O, increasing the abundance
of Ti, as well as TiH (see Fig. 10). However an elevated C/O ratio cannot
explain our reported absence of TiO in the transmission and emission spectra
of WASPS-121 b, as this would be inconsistent with the strong detection of
water emission, which suggests an elevated oxygen abundance (used as a proxy
for metallicity) was inferred (Mikal-Evans et al., 2022). Nevertheless, Fig.
10 implies that the abundance ratio of a metal to its oxide (e.g. Ti/TiO or
V/VO) can generally be used to constrain the C/O ratio using spectra at
optical wavelengths alone.

##  5 Conclusions

In this paper, we present observations of line emission by metals in the day-
side of WASP-121 b using the high-resolution ESPRESSO spectrograph. We report
strong detections of Ca I, V I, Cr I, Mn I, Fe I, Co I and Ni I, and note an
absence of signals by Ti and TiO, indicating that these species are depleted
from the day-side atmosphere. This is consistent with earlier observations of
the transmission spectrum that also failed to detect these species
(Hoeijmakers et al., 2020; Merritt et al., 2021; Gibson et al., 2020). We
infer that titanium condenses on the cold night-side due to the relatively
high condensation temperature of perovskite and is unable to circulate back to
high altitudes on the day-side and terminator regions, and is hence cold-
trapped (Spiegel et al., 2009). We conclude that the chemistry of ultra-hot
Jupiters does not lie on a smooth continuum with equilibrium temperature, but
instead features strong transitions. Species may deplete globally from the gas
phase with small changes in equilibrium temperature, depending on the lowest
night-side temperature and the efficiency of advection and vertical mixing.
Consequently, we expect that Ti, TiO and also aluminum-bearers should be
undetectable for any planet cooler than WASP-121 b, and that the transition
above which Ti/TiO become detectable lies between the equilibrium temperatures
of WASP-121 b ($2358\pm 52K$) and WASP-189 b ($2,641\pm 34K$) (Prinoth et al.,
2022). This causes complex coupling between the day-side and night-side
temperature profiles, as metals and metal oxides are strong sources of
stratospheric heating on the day-side. Although elemental abundance ratios can
be measured from high-resolution spectra (Gibson et al., 2020), the
interpretation of such measurements is dependent on our understanding of
condensation chemistry on the night-side, which is hard to observe directly.
Similarly, although the emission line strength is strongly dependent on the
temperature-pressure profile, the temperature inference depends significantly
on the presence or absence of masking TiO bands – a symptom of the more
general question of model completeness in exoplanet spectroscopy. We have also
found that the apparent orbital velocity of most detected species is
significantly smaller than the true orbital velocity, by approximately 5 km/s,
and we attribute this to the effect of planetary rotation. This effect implies
that unless the distribution of line emission on the day-side is known (e.g.
from spectroscopic eclipse mapping observations) or the equatorial rotation
velocity is small, high-resolution day-side observations do not provide
reliable measurements of the planet orbital velocity and by extension, the
dynamical mass of the star. Instead, accurate knowledge of the stellar mass is
required in order to obtain reliable insight into atmospheric dynamics as
probed via high-resolution cross-correlation spectroscopy.

###### Acknowledgements.

This study is based on observations collected at the European Southern
Observatory under ESO programme(s) 0105.C-0591 & 0106.C-0737. This research
has made use of the services of the ESO Science Archive Facility. E.K.H. Lee
is supported by the SNSF Ambizione Fellowship grant (#193448). B.P. & H.J.
acknowledge partial financial support from The Fund of the Walter Gyllenberg
Foundation. R. A. is a Trottier Postdoctoral Fellow and acknowledges support
from the Trottier Family Foundation. This work was supported in part through a
grant from the Fonds de Recherche du Québec - Nature et Technologies (FRQNT).
This work was funded by the Institut Trottier de Recherche sur les Exoplanètes
(iREx). JLB acknowledges funding from the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation program under
grant agreement No 805445. We thank S. Pelletier for useful discussions and
input.

## References

  * Arcangeli et al. (2018) Arcangeli, J., Désert, J.-M., Line, M. R., et al. 2018, ApJ, 855, L30
  * Asplund et al. (2009) Asplund, M., Grevesse, N., Sauval, A. J., & Scott, P. 2009, ARA&A, 47, 481
  * Barber et al. (2014) Barber, R. J., Strange, J. K., Hill, C., et al. 2014, MNRAS, 437, 1828
  * Batalha et al. (2017) Batalha, N. E., Mandell, A., Pontoppidan, K., et al. 2017, PASP, 129, 064501
  * Bernath (2020) Bernath, P. F. 2020, J. Quant. Spec. Radiat. Transf., 240, 106687
  * Betancourt (2017) Betancourt, M. 2017, arXiv e-prints, arXiv:1701.02434
  * Bingham et al. (2019) Bingham, E., Chen, J. P., Jankowiak, M., et al. 2019, J. Mach. Learn. Res., 20, 28:1
  * Borsa et al. (2021) Borsa, F., Allart, R., Casasayas-Barris, N., et al. 2021, A&A, 645, A24
  * Bourrier et al. (2020) Bourrier, V., Ehrenreich, D., Lendl, M., et al. 2020, A&A, 635, A205
  * Bowesman et al. (2021) Bowesman, C. A., Shuai, M., Yurchenko, S. N., & Tennyson, J. 2021, MNRAS, 508, 3181
  * Bradbury et al. (2018) Bradbury, J., Frostig, R., Hawkins, P., et al. 2018, JAX: composable transformations of Python+NumPy programs
  * Brogi et al. (2023) Brogi, M., Emeka-Okafor, V., Line, M. R., et al. 2023, AJ, 165, 91
  * Brogi & Line (2019) Brogi, M. & Line, M. R. 2019, AJ, 157, 114
  * Cabot et al. (2020) Cabot, S. H. C., Madhusudhan, N., Welbanks, L., Piette, A., & Gandhi, S. 2020, MNRAS, 494, 363
  * Chubb & Min (2022) Chubb, K. L. & Min, M. 2022, A&A, 665, A2
  * Delrez et al. (2016) Delrez, L., Santerne, A., Almenara, J. M., et al. 2016, MNRAS, 458, 4025
  * Evans et al. (2018) Evans, T. M., Sing, D. K., Goyal, J. M., et al. 2018, AJ, 156, 283
  * Evans et al. (2017) Evans, T. M., Sing, D. K., Kataria, T., et al. 2017, Nature, 548, 58
  * Evans et al. (2016) Evans, T. M., Sing, D. K., Wakeford, H. R., et al. 2016, ApJ, 822, L4
  * Gaidos et al. (2017) Gaidos, E., Kitzmann, D., & Heng, K. 2017, MNRAS, 468, 3418
  * Gibson et al. (2020) Gibson, N. P., Merritt, S., Nugroho, S. K., et al. 2020, MNRAS, 493, 2215
  * Grimm et al. (2021) Grimm, S. L., Malik, M., Kitzmann, D., et al. 2021, ApJS, 253, 30
  * Herman et al. (2022) Herman, M. K., de Mooij, E. J. W., Nugroho, S. K., Gibson, N. P., & Jayawardhana, R. 2022, AJ, 163, 248
  * Hoeijmakers et al. (2020) Hoeijmakers, H. J., Seidel, J. V., Pino, L., et al. 2020, A&A, 641, A123
  * Kitzmann et al. (2018) Kitzmann, D., Heng, K., Rimmer, P. B., et al. 2018, ApJ, 863, 183
  * Kitzmann et al. (2021) Kitzmann, D., Hoeijmakers, J. H., Grimm, S. L., et al. 2021, arXiv e-prints, arXiv:2112.11380
  * Komacek et al. (2019) Komacek, T. D., Showman, A. P., & Parmentier, V. 2019, ApJ, 881, 152
  * Kurucz (2017) Kurucz, R. L. 2017, Canadian Journal of Physics, 95, 825
  * Lee et al. (2022) Lee, E. K. H., Prinoth, B., Kitzmann, D., et al. 2022, MNRAS
  * Li et al. (2015) Li, G., Gordon, I. E., Rothman, L. S., et al. 2015, ApJS, 216, 15
  * Lodders (2002) Lodders, K. 2002, ApJ, 577, 974
  * Lothringer et al. (2018) Lothringer, J. D., Barman, T., & Koskinen, T. 2018, ApJ, 866, 27
  * Lothringer et al. (2021) Lothringer, J. D., Rustamkulov, Z., Sing, D. K., et al. 2021, ApJ, 914, 12
  * Louden & Kreidberg (2018) Louden, T. & Kreidberg, L. 2018, MNRAS, 477, 2613
  * Madhusudhan et al. (2011) Madhusudhan, N., Mousis, O., Johnson, T. V., & Lunine, J. I. 2011, ApJ, 743, 191
  * May et al. (2021) May, E. M., Komacek, T. D., Stevenson, K. B., et al. 2021, AJ, 162, 158
  * McKemmish et al. (2019) McKemmish, L. K., Masseron, T., Hoeijmakers, H. J., et al. 2019, MNRAS, 488, 2836
  * McKemmish et al. (2016) McKemmish, L. K., Yurchenko, S. N., & Tennyson, J. 2016, MNRAS, 463, 771
  * Menou (2019) Menou, K. 2019, MNRAS, 485, L98
  * Merritt et al. (2021) Merritt, S. R., Gibson, N. P., Nugroho, S. K., et al. 2021, MNRAS, 506, 3853
  * Mikal-Evans et al. (2022) Mikal-Evans, T., Sing, D. K., Barstow, J. K., et al. 2022, Nature Astronomy [arXiv:2202.09884]
  * Nugroho et al. (2020) Nugroho, S. K., Gibson, N. P., de Mooij, E. J. W., et al. 2020, ApJ, 898, L31
  * Pakhomov et al. (2019) Pakhomov, Y. V., Ryabchikova, T. A., & Piskunov, N. E. 2019, Astronomy Reports, 63, 1010
  * Parmentier et al. (2018) Parmentier, V., Line, M. R., Bean, J. L., et al. 2018, A&A, 617, A110
  * Parmentier et al. (2013) Parmentier, V., Showman, A. P., & Lian, Y. 2013, A&A, 558, A91
  * Pelletier et al. (2021) Pelletier, S., Benneke, B., Darveau-Bernier, A., et al. 2021, AJ, 162, 73
  * Phan et al. (2019) Phan, D., Pradhan, N., & Jankowiak, M. 2019, arXiv preprint arXiv:1912.11554
  * Pino et al. (2022) Pino, L., Brogi, M., Désert, J. M., et al. 2022, A&A, 668, A176
  * Pino et al. (2020) Pino, L., Désert, J.-M., Brogi, M., et al. 2020, ApJ, 894, L27
  * Polanski et al. (2022) Polanski, A. S., Crossfield, I. J. M., Howard, A. W., Isaacson, H., & Rice, M. 2022, Research Notes of the American Astronomical Society, 6, 155
  * Polyansky et al. (2018) Polyansky, O. L., Kyuberis, A. A., Zobov, N. F., et al. 2018, MNRAS, 480, 2597
  * Prinoth et al. (2022) Prinoth, B., Hoeijmakers, H. J., Kitzmann, D., et al. 2022, Nature Astronomy, 6, 449
  * Ryabchikova et al. (2015) Ryabchikova, T., Piskunov, N., Kurucz, R. L., et al. 2015, Phys. Scr, 90, 054005
  * Seidel et al. (2023) Seidel, J. V., Borsa, F., Pino, L., et al. 2023, A&A, 673, A125
  * Smette et al. (2015) Smette, A., Sana, H., Noll, S., et al. 2015, A&A, 576, A77
  * Snellen et al. (2010) Snellen, I. A. G., de Kok, R. J., de Mooij, E. J. W., & Albrecht, S. 2010, Nature, 465, 1049
  * Spiegel et al. (2009) Spiegel, D. S., Silverio, K., & Burrows, A. 2009, ApJ, 699, 1487
  * Stock et al. (2022) Stock, J. W., Kitzmann, D., & Patzer, A. B. C. 2022, arXiv e-prints, arXiv:2206.08247
  * Syme & McKemmish (2021) Syme, A.-M. & McKemmish, L. K. 2021, MNRAS, 505, 4383
  * Wardenier et al. (2021) Wardenier, J. P., Parmentier, V., Lee, E. K. H., Line, M. R., & Gharib-Nezhad, E. 2021, MNRAS, 506, 1258

##  Appendix A Overview of all cross-correlation functions, chemistry and
posterior distributions

Figure 11: Collection of the cross-correlation functions of all species
searched for in this study, similar to Fig. 4. The cross-correlation functions
are organized in two pairs of columns, with the KpVsys diagram on the left,
and the one-dimensioanl CCF extracted at an orbital velocity of 216.0 km/s
(gray lines) or at the orbital velocity at which the CCF peaks (black lines),
as in Fig. 4. The values in the top-left corner are the peak position. The
orange lines indicate the expected signal of a model spectrum without Ti/TiO
and a temperature inversion from 2500 K to 3200 K. Figure 12: Same as Fig. 11
Figure 13: The abundances profiles of Fe, Ti, V and TiO, for the different T-P
profiles described in Section 3.3. Each species is plotted for three different
values of the metallicity (increasing from left to right as $1\times$,
$5\times$ and $10\times$ solar) and for five values of the isothermal peak
temperature (3100 K to 3500 K), indicated by the double digit labels at the
top. The shaded horizontal region indicates the range of pressures over which
the HST data analyzed by Mikal-Evans et al. (2022) is sensitive, and where the
temperature inversion takes place. Figure 14: Posterior distributions of the
model parameters of equation 2 for Ca I. The top-right panels show the CCF of
all eight epochs combined binned to a common phase grid (top), and the model
with parameters equal to the median of their posterior (bottom panel). For Ca
I the signal is poorly visible by eye in the CCF, but for Cr I and Fe I it can
be discerned (see below). The fit of Na I is poorly converged and consequently
we classify the Na I signal as tentative. Figure 15: Same as Fig. 14, for V I.
Figure 16: Same as Fig. 14, for Cr I. Figure 17: Same as Fig. 14, for Mn I.
Figure 18: Same as Fig. 14, for Fe I. Figure 19: Same as Fig. 14, for Co I.
Figure 20: Same as Fig. 14, for Ni I. Figure 21: Same as Fig. 14, for Na I.