The Mantis Network IV. A titanium cold trap on the ultra-hot Jupiter WASP-121 b

Context. Using emission lines from metals, we investigate the three-dimensional distribution of temperature and chemistry in ultra-hot Jupiters. Aims. Existing observations of WASP-121b have suggested an underabundance of titanium and titanium oxide in its terminator region. In this study, we aim to determine whether this depletion is global by investigating the dayside emission spectrum. Methods. We analyzed eight epochs of high-resolution spectra obtained with the ESPRESSO spectrograph, targeting orbital phases when the dayside is in view. We used a cross-correlation method to search for various atoms, TiO, and VO, and compare the results to models. We constrained 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 substellar 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 nightside, we interpret this as evidence for the nightside condensation of titanium, which prevents it from being mixed back into the upper layers of the atmosphere elsewhere on the planet. Species with lower condensation temperatures are unaffected, implying that 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 dayside and nightside, 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 nightside condensation is robustly accounted for or the planet is hot enough to avoid nightside 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.


Introduction
WASP-121 b is a highly inflated (R = 1.753 ± 0.036R J , M = 1.157 ± 0.070M J ), highly irradiated (T eq = 2358 ± 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 (UHJs).The atmospheres of UHJs are theorized to be largely ⋆ Trottier Postdoctoral Fellow.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 few years with several ground-based and space-based facilities, including optical and infrared spectrographs, to study the planet's atmosphere.Initially, it was extensively observed with the WFC3 and STIS instruments on the Hubble Space Telescope (HST).These observations revealed emission by H 2 O (Evans et al. 2017) that is indicative of a thermal inversion, now commonly observed in UHJs (e.g., Nugroho et al. 2020; A139, page 1 of 22 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-infrared wavelengths (Evans et al. 2016(Evans et al. , 2018)).Recent phase-curve observations by Mikal-Evans et al. (2022) have placed tight constraints on the temperature profiles of the day and nightsides as well as on 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 ∼ 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 −1 , 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 highresolution spectrographs have proven to be highly capable of identifying metals in the atmospheres of this type of planet, including WASP-121 b, via use of the cross-correlation technique (Snellen et al. 2010), which 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 in the terminator region.The apparent absence of Ti and TiO is consistent with the HST STIS and 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).Questions that arise are: where in the atmosphere this condensation of Ti occurs, and to what extent it is distributed around the planet; and whether Ti and TiO are 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 nightside), 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 and 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 CaTiO 3 and VO, which are the highest-temperature condensates of Ti and V, respectively, at solar element abundances (Lodders 2002).The peak dayside temperature of WASP-121 b has most recently been measured to be over 3000 K (Mikal-Evans et al. 2022), well above the condensation temperature of CaTiO 3 .The same observations constrained the nightside temperature to be near or below the condensation curve of CaTiO 3 , supporting the hypothesis that titanium can indeed condense on the nightside.
The objective of this study is to present observational evidence that titanium is missing from the dayside emission spectrum of the planet.This implies that it is depleted globally and thus indeed cold-trapped.Section 2 describes our ESPRESSO observations and the data reduction and preprocessing.Notes.N exp is the number of exposures taken during each run, ϕ 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 CCFs in Sect. 4. In particular, the fifth night is weighed down because the observations covered orbital phases near quadrature, where the change in radial velocity is small, leading to partial self-subtraction of the planetary signal.
Section 3 describes the analysis methodology, which is based on the high-resolution cross-correlation technique (Snellen et al. 2010).Section 4 summarizes and discusses the results and important implications.

Observations and data reduction
We observed the WASP-121 system (spectral type F6, V = 10.4) during eight epochs with the ESPRESSO instrument at ESO's 8.2 m VLT (PID 0105.C-0591 & 0106.C-0737, P.I.Hoeijmakers), which yielded eight 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, highresolution mode with 300 s exposures, yielding spectra with a resolving power of R ∼ 140 000) and a typical S/N of 50.The instrument was set to a readout mode of 2 × 1 binning with fiber B on sky.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 blazecorrected 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 used 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.

Data processing and cross-correlation analysis
We proceeded 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 Fig. 1.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 posteclipse 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.
summarized here with emphasis on aspects that are particular to ESPRESSO.

Telluric correction
We modeled the telluric transmission spectrum by using molecfit version 1.5.9, applied to each of the S1D spectra (Smette et al. 2015) 1 .The fitting of the telluric models to the S1D spectra was carried out in the Earth's rest frame by reversing the barycentric velocity correction that is applied by the ESPRESSO pipeline by default.They were then Dopplershifted, re-interpolated, and divided out of the S2D spectra, which yielded telluric-corrected time-series spectra for each of the echelle orders.

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 semimajor 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 the spectral orders to be treated as two-dimensional variables (wavelength versus time) from here on.
For each order 2 we determined the time-average flux and divided it to normalize the order to its average flux, while saving the relative flux differences for later use as weights.We then determined the time-average spectrum and divided it out to obtain nearly flat residuals, to which we applied color correction and outlier rejection.Color correction was done by fitting a third-order polynomial to each exposure in the time series and dividing it out.This removes broadband 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 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 5σ 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 inspected all orders and flagged the remaining bad columns due to, for example, the presence of telluric emission lines (e.g.sodium) or regions with very low flux at some T (K) Fig. 2. T -P 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 are 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/WebPlotDigitizerorder edges.We also reject columns where telluric lines absorb more than 20% of the flux.In total, 6.32 × 10 5 (0.166%) values are replaced by interpolates and 9.72 × 10 6 (2.56%) are in columns that are masked entirely.These columns are ignored in the remainder of the analysis.

Cross-correlation templates and models
We created grids of one-dimensional 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 temperaturepressure (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 one-dimensional model with a temperature of 2500 K in the deep atmosphere that increases to 3500 K at pressures between 10 and 1 mbar Mikal-Evans et al. (2022, see Fig. 2 as well as Fig. 3).At pressures below 1 mbar, their best-fit model increases toward 4000 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 3100 K to 3500 K toward the top of the atmosphere (see Fig. 2).Later in the analysis, we find that models with peak temperatures between 3200 K and 3300 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. 2023, 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 µm −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.Models containing all opacity sources were injected into the data via multiplication by a weight that is a function of orbital phase following Herman et al. (2022): where f obs (λ) is the data after the masking of bad columns (see above), f (λ) injected is the data with the injected model f (λ) model , ϕ is the orbital phase, θ is an offset between the substellar point and the peak of the emission, and γ acts to steepen the phase function near secondary eclipse3 .Values of γ = 1 and θ = 0 are adopted for model injection and comparison, as later we find that the data do not support significant deviations from these values.We also compared this phase function to the broadband light curve of WASP-121 b modeled using Spiderman (Louden & Kreidberg 2018), assuming dayside and nightside 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 γ ≈ 2 (see Fig. 3), but we note that at present, our high-resolution data do not constrain γ very accurately, nor should it be expected that line emission is described by the same phase function as broadband continuum emission.
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 3200 K.A model without any line absorbers is subtracted to obtain a continuum-subtracted template for each species.We performed cross-correlation (Eq.(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 ± 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 Sect.3.2).

Results and discussion
We co-added the cross-correlation functions (CCFs) 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 = 3200 K and 5 times solar metallicity (see Table 1).This produces the velocity-velocity diagrams that are shown in Figs. 4,  Besides co-adding the CCFs into velocity-velocity diagrams, we re-binned and averaged the CCFs 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 toward a particular epoch or phase-range (at some cost in signal-tonoise ratio).Fe I emission clearly traces the radial velocity of the planet both prior to the secondary eclipse and afterward.The line strength increases toward the secondary eclipse, which is expected because most of the hotter substellar point is in view.Using the same phase function as before, we modeled the two-dimensional emission profile as We sampled from these prior distributions and evaluated the likelihood in a Bayesian framework using a no U-turn sampler (see Betancourt 2017, for a review) implemented using NumPyro

Velocity traces
The parameters that describe the shape and location of the trace (v orb , v sys , γ, θ, and σ w ) are consistent between all species to within 3σ, though variations may exist in particular in the apparent value of v orb .This has been observed previously in transit transmission spectra of UHJs, where planetary rotation and dynamical effects cause variations in the peak location of crosscorrelation signals in K p -v 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 global circulation model, we followed Pino et al. (2022) in 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 was assumed to be equal to the (circular) orbital A139, page 6 of 22 velocity plus synchronous rotation of the planet, leading to the following expression: with R p the radius of the planet, a the semimajor axis of the orbit (which may also be expressed in terms of P and M * ), and θ now equal to the angle between the emitting point and the substellar point.A reduction in orbital velocity may thus be large for inflated, close-in planets (with large values of R p a ).We constructed a model of the emission lines of three points on the surface, for θ = ±0.3πand θ = 0 (i.e., near the limbs on the dayside and the substellar 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 ϕ t − θ − π.We then constructed 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 −1 .Emission from points offset from the substellar 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 −1 , approximately 5 km s −1 below the true orbital velocity of 221.1 km s −1 .This could indicate that the majority of emission originates from near the substellar point.The tentative signal of Na I stands out, with a significantly higher orbital velocity and blueshift, 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. A.4), 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 H 2 O 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).
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 γ = 1 is not significantly discrepant for any of the species.We note that observations of in particular Fe I emission in UHJs can be very sensitive to shapeparameters 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 on 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.

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 3100 K to 3500 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× solar and a peak temperature of 3400 K if Ti and TiO are present, but only 3200 K is needed without Ti and TiO.This underscores the importance of model completeness in exoplanet 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).
Figure 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 and TiO are not capable of reproducing the data for two reasons: 1. TiO is strongly ruled out, even for the model with the lowest expected TiO line strength (3100 K and 10× solar metallicity).2. To explain the line strengths of the other species, a peak temperature of approximately 3400 K is needed for models with Ti and 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. A.1).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 toward shorter wavelengths, and the fact that ions mainly exist at much lower altitudes to which emission spectroscopy is inherently less sensitive.

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 linelist (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 these 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 dayside as well as the terminator regions.We hypothesize that this depletion is caused by condensation of Ti, predicted to condense as CaTiO 3 (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 nightside temperature profile indeed lies below the condensation curve of perovskite, meaning that significant condensation of perovskite should occur on the nightside.However, on the hot dayside with a temperature over 3000 K, condensation is not expected to play a role.Instead, we infer that nightside condensation of Ti causes A139, page 8 of 22 Hoeijmakers, H. J., et al.: A&A, 685, A139 (2024) 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 nightside 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 CaTiO 3 , 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 dayside 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 dayside but are confined to high pressures, at altitudes below the thermal inversion on the dayside (i.e., below the mbar to µbar 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. High-resolution emission spectroscopy of UHJ atmospheres can be used to impose limits on the efficiency with which condensates are remixed to the high-temperature dayside 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 UHJs cannot be assumed to be well mixed on the dayside; 2. The process of condensation and limited remixing observed in this study is specific to the Ti inventory, and not, for example, Fe, V, Ni, or Cr.Therefore, we hypothesize that the temperature profile on much of the nightside lies between the condensation curves of CaTiO 3 and VO.This is fully consistent with the nightside temperature profile derived from spectroscopic phase-curve observations recently published by Mikal-Evans et al. (2022); 3.In this formulation of the cold trap hypothesis, an element is depleted from the gas-phase on a global scale if the nightside 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 nightside 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 dayside) of hot Jupiters as a function of equilibrium temperature.Instead, we expect that there are sharp chemical transitions with a complex dependence on both equilibrium temperature and global circulation; 4. At solar metallicity, aluminum condenses at higher temperatures than titanium in the form of spinel (MgAl 2 O 4 )4 or corundrum (Al 2 O 3 ; Lodders 2002).If our formulation of the cold trap effect is correct, this means that aluminum 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 photoionization as hypothesized 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, for example WASP-43 b (Chubb & Min 2022); 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 nightsides should be strongly coupled.A consequence is that the atmospheric opacity computed as part of three-dimensional global circulation models need to be computed self-consistently, where the opacity on the dayside is dependent on the minimum nightside temperature and the effects of condensation there.Condensation physics and the transport of condensate particles need to be built into global circulation models to explain the observed properties of UHJs; 6. Simpler one-dimensional models of dayside or terminator temperature profiles also need to take into account nonlocal 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, for example, vanadium without depletion of titanium would not be self-consistent; 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 dayside 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 nonlocal 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 nightside to prevent cold-trapping, or if models accurately include condensation chemistry and global transport; 8.We 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.

Ti and TiO as tracers of atmospheric structure and chemistry
The equilibrium-chemistry abundance profiles of Ti and TiO are shown in Fig. A.3.We observe that because of the large because magnesium is much more abundant than aluminum (Asplund et al. 2009).
A139, page 9 of 22 Hoeijmakers, H. J., et al.: A&A, 685, A139 (2024) Fig. 9. Simulated emission spectra of the dayside as observed with JWST/NIRISS SOSS, using Pandexo (Batalha et al. 2017).Solid lines: highresolution models assuming a temperature inversion up to 3200 K (see Fig. 2) at a metallicity of 5 times solar (solid lines).Transparent dots: Pandexo simulation at the native instrument resolution.Solid dots: Binned to a resolving power of 100.Purple: model with Ti and TiO.Orange: model without Ti and TiO.If TiO is indeed absent from the dayside 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 µm will be hard to discern.We note that the water band at 1.4 µm 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 µm is consistent with the WFC3 data (see Fig. 2 of Evans et al. 2017).
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 UHJ atmospheres that can be used in highresolution 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. A.3 that the abundances of Ti and V depend relatively weakly on the elemental Ti and V ratios at temperatures around 2500 K.An increase in the metallicity from 5× to 10× 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 correlation between the VO emission strength and metallicity.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, and recent work by Tsai et al. (2021).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 WASP-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; 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.10 13 10 12 10 11 10 10 10 9 10 8 10 7 10 6 10 5 10 4 VMR

Conclusions
In this paper, we present observations of line emission by metals on the dayside of WASP-121 b detected 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, which indicates that these two species are depleted from the dayside 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 nightside due to the relatively high condensation temperature of perovskite and is unable to circulate back to high altitudes on the dayside and terminator regions, and is hence cold-trapped (Spiegel et al. 2009).We conclude that the A139, page 10 of 22 Hoeijmakers, H. J., et al.: A&A, 685, A139 (2024) chemistry of UHJs 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 nightside temperature and the efficiency of advection and vertical mixing.Consequently, we expect that Ti and TiO as well as aluminum-bearers should be undetectable for any planet cooler than WASP-121 b, and that the transition above which Ti and TiO become detectable lies between the equilibrium temperatures of WASP-121 b (2358 ± 52 K) and WASP-189 b (2641 ± 34 K; Prinoth et al. 2022).This causes complex coupling between the dayside and nightside temperature profiles, as metals and metal oxides are major sources of stratospheric heating on the dayside.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 the condensation chemistry on the nightside, which is hard to observe directly.Similarly, although the emission line strength is strongly dependent on the T-P profile, a temperature determination depends heavily 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 lower than the true orbital velocity, by approximately 5 km s −1 , and we attribute this to the effect of planetary rotation.This effect implies that unless the distribution of line emission on the dayside is known (e.g., from spectroscopic eclipse mapping observations) or the equatorial rotation velocity is low, high-resolution dayside observations do not provide reliable measurements of the planet orbital velocity or, by extension, the dynamical mass of the star.Instead, accurate knowledge of the stellar mass is required to obtain reliable insight into atmospheric dynamics as probed via high-resolution cross-correlation spectroscopy.Fe Ti

Fig. 3 .
Fig.3.Model of the broadband phase curve of WASP-121 b with dayside and nightside temperatures of 3200 K and 1800 K and instantaneous re-radiation integrated over a uniform passband from 400 to 800 nm, compared to our parameterized phase function of Eq. (3.3).

Fig. 4 .
Fig. 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 were extracted at an orbital velocity of 216.0 km s −1 (gray line), i.e., slightly below the expected velocity of 221.1 km s −1 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 the weighted emission line strength (not the 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 and 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 T-P 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 T -P profile.Horizontal bars indicate the signal strength of models with variations in 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.
5 and 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 CCFs of all tested species are shown in Fig. A.1, 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.
the radial velocity of the planet as a function of orbital phase ϕ t = ϕ(t).The model has the following free parameters, and we defined priors for the purpose of carrying out Bayesian inference:-The peak amplitude of the emission line A ∼ U(−300, 3000) in ppm.-The systemic velocity v sys ∼ 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 orb ∼ U(210, 230) in km s −1 .-The Gaussian line-width σ w ∼ U(2, 10) in km s −1 .-The offset angle of the peak emission θ ∼ U(−70, 70) in degrees, analogous to the hot-spot offset typically fit in broadband phase-curve observations.-The index of the phase function γ ∼ U(0, 6).-A constant offset C ∼ U(−3, 3) in ppm.
Fig.5.Same as Fig.4, but for Ti, TiO, V, and VO.Ti and TiO are not detected but are predicted by models that contain Ti and 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 into to allow the signals to be plotted on the same scale.50% means that the vertical axis labels should be read as being a factor of 2 bigger, and vice versa.

Fig. 6 .
Fig. 6.Same as Fig. 4, but for Mn, Co, Na, and Mg.Mn and Co are definitely detected, while detections of Na and Mg are deemed tentative because of the presence of a strong shift in the systemic and orbital velocity in the apparent signal of Na (though see Seidel et al. 2023) and a strong unexplained alias in the CCF of Mg.

Fig. 7 .
Fig. 7. CCFs of Fe I of all eight 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 toward the secondary eclipse.The exposures are averaged with equal weights, and uncertainties were propagated accordingly when fitting the model of Eq. (4).

Fig. 8 .
Fig. 8. Model of the velocity traces of three points on the dayside near the morning limb (A), substellar 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 substellar point peaks.

Fig. 10 .
Fig.10.Equilibrium-chemistry solution for 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 high C/O ratio.The C/O ratio is varied by modifying the abundance of carbon while leaving oxygen fixed.

Fig
Fig. A.3.Abundance 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 metallicity values (increasing from left to right as 1 time, 5 times, and 10 times solar) and for five isothermal peak temperature values (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) are sensitive, and where the temperature inversion takes place.

Fig. A. 4 .
Fig. A.4. Posterior distributions of the model parameters of equation 4 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.

Table 1 .
Overview of the observing epochs.

Table 2 .
Best-fit parameters obtained by fitting the Doppler-shifted emission trace of each of the detected species according to Eq. (4).