PEPSI Investigation, Retrieval, and Atlas of Numerous Giant Atmospheres (PIRANGA). IV. High-resolution Phased-resolved Spectroscopy of the Ultra-hot-Jupiter KELT-20 b
Victoria Bonidie, Marshall C. Johnson, Ji Wang, Sydney Petz, Jake Kamen, Calder Lenhart, Alison Duck, Carles Badenes, Klaus Strassmeier, Ilya Ilyin
TL;DR
This study uses high-resolution spectroscopy to analyze the atmosphere of the ultra-hot-Jupiter KELT-20 b, revealing temperature differences and chemical abundances on its day and night sides.
Contribution
The paper provides the first measurements of Ni and Ca abundances in emission for KELT-20 b and compares chemical abundance ratios across different atmospheric regions.
Findings
Abundance ratios [Ni/Fe] and [Ca/Fe] are consistent with solar values within 2σ.
The evening side of KELT-20 b is hotter than the morning side by ∼100 K.
Chemical abundance ratios remain relatively constant despite significant phase-dependent abundance variations.
Abstract
We present five datasets of high-resolution optical emission spectra of the ultra-hot-Jupiter KELT-20 b with the PEPSI spectrograph. Using a Bayesian retrieval framework, we constrain its dayside pressure–temperature profile and abundances of Fe, Ni, and Ca, providing the first measurements for Ni and Ca for KELT-20 b in emission. We retrieve the preeclipse and posteclipse datasets separately (corresponding to the evening and morning sides, respectively), and compare the constraints on their thermal structures and chemical abundances. We constrain lower abundances in the pre-eclipse datasets compared to the posteclipse datasets. We interpret these results with an equilibrium chemistry model which suggests ∼10–30× supersolar refractory abundances. Due to the well-known degeneracy between absolute abundances and continuum opacities, the abundance ratios are more precise probes of the…
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Figure 9| Date (UT) |
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| Exp. Time | Airmass Range | Phases Covered | SNRblue | SNRred |
|---|---|---|---|---|---|---|---|
| (s) | |||||||
| 2021 May 1 | 46 | 47 | 300 | 1.01–2.03 | 0.53–0.58 | 301 | 340 |
| 2021 May 18 | 44 | 45 | 300 | 1.00–1.48 | 0.42–0.47 | 347 | 397 |
| 2023 Apr 30 | 45 | 45 | 300 | 1.00–2.10 | 0.37–0.42 | 272 | 498 |
| 2023 Jun 15 | 46 | 46 | 300 | 1.00–1.17 | 0.60–0.66 | 244 | 431 |
| 2024 May 16 | 42 | 44 | 200 | 1.00–1.17 | 0.34–0.37 | 351 | 374 |
| Parameter | Symbol (Unit) | Value | Source |
|---|---|---|---|
| Planet radius | 1.741 | a | |
| Planet mass | 3.382 | a | |
| Stellar radius | 1.565 | a | |
| Stellar mass | 1.76 | a | |
| Effective temperature | 8720 | a | |
| Systemic velocity | 22.78 | b | |
| Orbital period | 3.47410151 | c | |
| Epoch of midtransit | 2459757.811176 | c | |
| Transit duration | 0.147565 | c |
| Parameter Name | Symbol | Prior | Value | ||
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| Preeclipse | Posteclipse | Combined | |||
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| log Fe volume-mixing ratio | Fe |
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| log Ni volume-mixing ratio | Ni |
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| log Ca volume-mixing ratio | Ca |
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| log infrared opacity (cm2 g−1) |
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| log visible-to-infrared opacity |
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| Irradiation temperature (K) |
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| RV offset (km s−1) | Δ |
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| RV semiamplitude (km s−1) |
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| Nickel-to-Iron abundance ratio | [Ni/Fe] | ⋯ |
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| Calcium-to-Iron abundance ratio | [Ca/Fe] | ⋯ |
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- —National Aeronautics and Space Administration (NASA) 10.13039/100000104
- —HHS ∣ National Institutes of Health (NIH) 10.13039/100000002
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Taxonomy
TopicsAstro and Planetary Science · Astronomy and Astrophysical Research · Stellar, planetary, and galactic studies
Introduction
Since the discovery of the first hot Jupiter exoplanet by M. Mayor & D. Queloz (1995), the field of Jupiter-like exoplanets has evolved rapidly, now entering a phase where we can answer questions about their atmospheric composition and temperature structure. Advancements in both ground-based spectrographs with resolving powers exceeding *R *= 25,000, as well as improved techniques in data processing methodology, have allowed us to access the hundreds to thousands of individual absorption and emission lines from the planetary atmosphere that would be unresolved at lower spectral resolution.
High-resolution cross-correlation spectroscopy (HRCCS) has emerged as a powerful tool to enable precise detections of the chemical composition of close-in planets (e.g., I. A. G. Snellen et al. 2010; M. Brogi et al. 2012). This technique takes advantage of the fact that planetary spectral lines are Doppler shifted during an observation, carrying the planetary spectrum across multiple resolution elements of the spectrograph, whereas the spectral contaminants (telluric and stellar) remain quasi-stationary, allowing the planetary signal to be disentangled.
Furthermore, applying these methods on multiphase datasets have enabled us to begin studying the 3D structure of these planets. HRS observations in transmission and phase-curves have detected species through cross correlation across different planetary phases (e.g., D. Ehrenreich et al. 2020; G. Mraz et al. 2024; J. P. Wardenier et al. 2024; C. Lenhart et al. 2025). These studies have targeted ultrahot Jupiters (UHJs), a class of gas giant exoplanets with equilibrium temperatures exceeding 2200 K. These extreme temperatures increase their scale heights, improving their transmission detectability, and increases their flux ratio with respect to the star, improving their detectability for emission spectroscopy, making them ideal targets in HRCCS studies. UHJs are expected to be tidally locked, therefore performing HRCCS studies as a function of orbital phase probes different planetary longitudes.
While cross-correlation is an efficient method to detect chemical species in the atmospheres of exoplanets, it does not provide quantitative constraints on their atmospheric properties. To overcome this limitation, novel techniques have been developed to “map” the cross-correlation to a likelihood (M. Brogi & M. R. Line 2019; N. P. Gibson et al. 2020), which can then be integrated into a Bayesian framework to explore the range of atmospheric properties that fit a given spectrum. This technique, known as an atmospheric retrieval, has been widely adopted in the field and has demonstrated the ability to obtain quantitative constraints on atmospheric properties, such as pressure–temperature (P–T) profiles and chemical abundances. Atmospheric retrievals of UHJs are often applied to datasets with limited phase coverage or lower resolution spectra, where multi-epoch spectral information cannot be resolved, effectively reducing their atmospheric properties to one dimension. However, there has been new focus on performing atmospheric retrievals as a function of planetary phases in both transmission (e.g., S. Gandhi et al. 2022; C. Maguire et al. 2024), and in emission (e.g., L. Pino et al. 2022; L. van Sluijs et al. 2023; S. Ramkumar et al. 2025). This new frontier of high-resolution multiphase observations of UHJ targets opens new opportunities to place quantitative atmospheric constraints at different planetary longitudes.
In this paper, we present a phase-resolved Bayesian atmospheric retrieval analysis of KELT-20 b, (M. B. Lund et al. 2017), also known as MASCARA-2 b (G. J. J. Talens et al. 2018), an UHJ orbiting a bright A2-type star with an orbital period of ∼3.5 days. It has been the target of many high-resolution spectroscopic studies in both emission and transmission, yielding detections of several refractory metals such as Fe, Na, Mg, Mn, Ni, Cr, Ca, Si, Ti, and V (e.g., N. Casasayas-Barris et al. 2019; H. J. Hoeijmakers et al. 2020; S. K. Nugroho et al. 2020; M. Stangret et al. 2020; A. Bello-Arufe et al. 2022; F. Borsa et al. 2022; D. Cont et al. 2022; F. Yan et al. 2022; S. Gandhi et al. 2023; M. C. Johnson et al. 2023; S. Petz et al. 2025), as well as molecular species such as H_2_O and CO (e.g., D. Kasper et al. 2023; L. Finnerty et al. 2025) in its atmosphere. We perform separate retrievals on the combined, preeclipse, and posteclipse datasets to place quantitative constraints on its vertical temperature structure and chemical abundances and explore the difference between the morning and evening sides.
This paper is organized as follows: in Section 2, we present our observations and data preparation; in Section 3, we outline our retrieval framework; in Section 4 we present and contextualize our retrieval results for each dataset by comparing them to literature values and equilibrium chemistry models before concluding in Section 5.
Observations and Data Preparation
We obtained our data on KELT-20 b using the Potsdam Échelle Polarimetric and Spectrographic Instrument (PEPSI; K. G. Strassmeier et al. 2015) on the Large Binocular Telescope (LBT) located on Mt. Graham, Arizona, USA. We use the time-series spectra of the preeclipse (2021 May 18 UT) and posteclipse (2021 May 1 UT) observations of KELT-20 b, presented in M. C. Johnson et al. (2023), along with three additional observations (two preeclipse and one posteclipse) further from secondary eclipse. See Table 1 and Figure 1 for further information of these observations, and Table 2 for the stellar and planetary parameters of the KELT-20 system.
Signal-to-noise ratio of our observations as a function of orbital phase. Each observation was taken with a 300 s exposure time. The PEPSI red and blue arms are shown as the solid and dotted lines, respectively. The signal-to-noise ratios (SNRs) reported correspond to the 95th percentile per-pixel SNRs for each spectrum. The change from CD II to CD III in the 2023 observations resulted in a significant decrease in SNR in the blue arm.
As illustrated in Figure 2, the preeclipse datasets observe more of the evening side of KELT-20 b, while the posteclipse datasets probe the morning side. All observations were taken using the 200 μm fiber, which provides a constant resolving power of *R *= 130,000. For the observations in in 2021 and 2024, we used the PEPSI cross dispersers (CD) III and V, providing a wavelength coverage of 4800–5441 Å and 6278–7419 Å in the blue and red channels, respectively. Further details of the 2021 observations can be found in M. C. Johnson et al. (2023) and S. Petz et al. (2025).
Top-down view of KELT-20 b’s orbit as it passes behind its host star, moving counterclockwise from preeclipse to posteclipse. The orange side depicts the hot dayside, while the blue side corresponds to the cooler night side of the tidally locked planet. The translucent gray side depicts the side of the planet that is outside of the view of the observer, who is positioned off the bottom of the page.
For the observations in 2023, we switched to CD II instead of CD III due to a mechanical issue with the spectrograph, so we instead had the wavelength coverage of 4265–4800 Å in the blue arm. The data were reduced using the SDS4PEPSI pipeline (K. G. Strassmeier et al. 2018; I. V. Ilyin 2000), which performs a standard data reduction and outputs a one-dimensional, wavelength-calibrated, continuum-normalized spectrum. The pipeline also estimates the variance in each pixel, which we use to propagate uncertainties throughout our analysis.
Extraction of the Planetary Spectra
2.1.
To extract the faint exoplanetary signal from contaminants, we take advantage of the fact that stellar and telluric lines remain (quasi-)static during the observation, while the spectrum of the planet undergoes a Doppler shift of the order of several tens of km s.^−1^ Our procedure mirrors that of M. C. Johnson et al. (2023), and we provide only a brief summary here. First, we run the MOLECFIT package (W. Kausch et al. 2015; A. Smette et al. 2015) on the red arm of each PEPSI spectrum to model out the telluric lines. This treatment was not necessary for the blue arm as it was largely telluric free. Next, we stack the spectra to create a median-combined spectrum and subtract it from each of the time-series spectra in order to remove stellar lines and time invariant components.
We then use the SYSREM (O. Tamuz et al. 2005) algorithm to correct for any residuals left over after the MOLECFIT treatment. We adapt the python implementation of SYSREM, PySysRem8 ^8^ https://github.com/stephtdouglas/PySysRem , in order to apply it to the PEPSI data. The algorithm iteratively subtracts linear trends in time from each spectral pixel, thus removing the quasi-static telluric and stellar lines that were not fully removed by MOLECFIT, or any instrumental systematics, leaving residuals consisting only of noise and the planetary signal.
In order to maximize the signal strength, we adopt the methodology presented in E. F. Spring & J. L. Birkby (2025, in preparation) to stop SYSREM once the removal of a successive systematic fails to improve to residuals by more than 1 part in 10.^4^ The number of systematics removed is low, ranging from 0 to 2 per night and per arm.
Retrieval Framework
Forward Model
3.1.
We used the radiative transfer code petitRADTRANS P. Mollière et al. (2019) at the default resolution (R = 10^6^) to forward model the emission spectrum of KELT-20 b. We include continuum opacity collision-induced absorption of H_2_–H_2_ and H_2_–He, and Rayleigh scattering due to H_2_ and He, and H^−^ bound-free and free–free absorption. We compute the volume-mixing ratios (VMRs) for H^−^, H, and e^−^ using FastChem (J. W. Stock et al. 2018) for each temperature structure produced at every iteration of the Monte–Carlo–Markov–Chain MCMC. This allows the continuum opacity species to vary without increasing the number of free parameters in our retrieval. We include the VMRs for Fe, Ni, and Ca as free parameters, assumed to be constant as a function of vertical depth. We chose these species as they each yield ≥4σ detections in their combined cross-correlation functions (CCFs; S. Petz et al. 2025; J. Kamen et al. 2025, in preparation), as well as greater than ≥3σ detections in their preeclipse and posteclipse CCFs, as shown in Figure 3.
Top row: shifted and combined CCF Fe, for the combined (left), preeclipse (middle), and posteclipse (right) datasets. Middle row: same as the top row, but for Ni. Bottom row: same as the top row, but for Ca. Each ≥3σ detection falls within our tentative detection range. The vertical and horizontal dashed lines in all CCF maps represent the Kp and vsys parameters for which we should expect to find a signal.
We model the atmosphere of KELT-20 b using 100 log-uniform spaced pressure layers between 10^2^ and 10^−6^ bar and assume an inverted pressure–temperature (P–T) profile of the form given by Equation (29) T. Guillot (2010) with four variables: Tirr (irradiation temperature), κ (infrared opacity), γ (visible-to-infrared opacity ratio), and Tint (intrinsic temperature). Of these variables, we fix Tint to a constant 100 K, as is often done in other high-resolution studies (e.g., C. Maguire et al. 2024; S. Ramkumar et al. 2025), and leave the rest as free parameters in our retrieval. We assume a tidally locked rotation rate (e.g., M. C. Johnson et al. 2023; L. Finnerty et al. 2025) and convolve the models with a rotational broadening kernel using Equation (18.14) of D. F. Gray (2005), and an instrumental broadening kernel using a Gaussian line spread function with a width corresponding to the PEPSI resolving power of *R *= 130,000 (K. G. Strassmeier et al. 2018). We then calculate the planet-to-star flux ratio by dividing the model by a Phoenix stellar model spectrum (T.-O. Husser et al. 2013) corresponding to the stellar effective temperature from M. B. Lund et al. (2017).
The forward model spectra are then Doppler shifted by linear interpolation to the radial velocity of each of our time-series spectra given by:
\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{eqnarray*}{V}_{p}={K}_{p}\sin (2\pi \phi )+{V}_{\mathrm{sys}},\end{eqnarray*}\end{document}where Kp is the planetary radial velocity semiamplitude, Vsys is the systemic velocity, and ϕ is the orbital phase of the planet.
Table 2: A Summary of the Stellar, Planetary, and Ephemeris Values Used in Our Retrieval
Sysrem Distortion
3.2.
Applying SYSREM not only removes the static-stellar and telluric signals in the data, but also distorts the underlying planetary spectrum. This effect must be accounted for in order to retrieve accurate parameters from the planetary spectra. We follow the methodology of N. P. Gibson et al. (2022) to apply a corresponding distortion to the model spectra. The corrected model is, from Equation (7) of N. P. Gibson et al. (2022)
\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{eqnarray*}{\boldsymbol{M}}^{\prime} ={\boldsymbol{U}}{({\mathrm{\Lambda }}{\boldsymbol{U}})}^{\dagger }({\mathrm{\Lambda }}{\boldsymbol{M}})\end{eqnarray*}\end{document}where M is a matrix holding the Doppler-shifted forward-model spectra for one night and one PEPSI arm, repeated for each night-arm combination; U is a matrix containing the SYSREM correction coefficients, with one additional row filled with ones in order to account for the effects of median-correcting the spectra; and Λ is a diagonal matrix where the diagonal terms are the inverse of the mean variance of each spectrum. ^†^ denotes the Moore–Penrose inverse, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} {{\boldsymbol{X}}}^{\dagger }={({{\boldsymbol{X}}}^{{\mathrm{T}}}{\boldsymbol{X}})}^{-1}{{\boldsymbol{X}}}^{{\mathrm{T}}}\end{document} . We applied the filter to each model during the retrieval.
Log-likelihood Analysis
3.3.
In order to compute the likelihood of the model fit to our data, we rely on the commonly used technique in high-resolution Bayesian statistics (M. Brogi & M. R. Line 2019; N. P. Gibson et al. 2020) to “map” cross-correlation values of an atmospheric model onto a log-likelihood value. For this work, we compute the log-likelihood as defined in N. P. Gibson et al. (2020), namely,
\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{eqnarray*}{\mathrm{ln}}{ \mathcal L }=-\frac{N}{2}{\mathrm{ln}}2\pi -N{\mathrm{ln}}\beta -\displaystyle \sum _{i}^{N}{\mathrm{ln}}{\sigma }_{i}-\frac{1}{2}{\chi }^{2}\end{eqnarray*}\end{document}where
\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{eqnarray*}{\chi }^{2}=\frac{1}{{\beta }^{2}}\left(\displaystyle \sum _{i}^{N}\frac{{f}_{i}^{2}}{{\sigma }_{i}^{2}}+{\alpha }^{2}\displaystyle \sum _{i}^{N}\frac{{m}_{i}^{2}}{{\sigma }_{i}^{2}}-2\alpha \displaystyle \sum _{i}^{N}\frac{{f}_{i}{m}_{i}}{{\sigma }_{i}^{2}}\right)\end{eqnarray*}\end{document}and where, for sums over pixels i = 1, …, N, fi and σi are the flux and uncertainty in each pixel, mi is the model at each pixel (where each mi corresponds to a single element in a matrix \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} {{\boldsymbol{M}}}^{{\prime} }\end{document} ), and α and β are multiplicative scaling parameters for the model and uncertainties, respectively. For simplicity, here we assume α = β = 1. Unlike N. P. Gibson et al. (2020), we keep the constant terms because we compute \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} {\mathrm{ln}}{ \mathcal L }\end{document} separately for the blue and red arms of PEPSI as they contain a different number of spectra and must ensure that they are properly scaled when we combine them. The log-likelihood function is computed individually for each dataset, and these values are subsequently summed to derive the combined log-likelihood function.
Temperature Prior
3.4.
To validate our retrieval framework, we tested it using mock data generated with the methods described in Section 3.1, but with the addition of Gaussian noise at a SNR of 400, representative of realistic observational conditions. We initially apply uniform or log-uniform priors for all parameters of interest, and use the emcee tool (D. Foreman-Mackey et al. 2013) to compute their posteriors. The retrieval tightly constrained the VMRs, but weakly constrained irradiation temperature Tirr, resulting in a large dynamic range in the location of the inversion layer. Runs of our retrieval with no prior on Tirr resulted in temperatures ranging from 1400 to 3400 K, a far larger range than physically plausible. All of these solutions have a similar upper atmospheric temperature, as the emission-line data is primarily sensitive to the properties of the atmosphere at and above the inversion, and only poorly constrains the lower atmosphere. To address this limitation, we repeated the analysis with a Gaussian prior applied to Tirr. The resulting posteriors were consistent with those without the addition of the temperature prior, but the resulting P–T profile had a more realistic spread of temperatures at the bottom of the inversion, demonstrating that a tighter prior on Tirr is essential for our retrieval framework to effectively constrain the P–T profile when working with comparable datasets.
In the T. Guillot (2010) parameterization of the P–T profile, the quantity Tirr is the irradiation temperature at the substellar point and is larger than the more commonly computed equilibrium temperature Teq by a factor of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \sqrt{2}\end{document} . Empirically, for our case of a strong temperature inversion, Tirr is the temperature of the atmosphere near the bottom of the inversion (which is approximately isothermal at deeper pressures). Our emission-line data has little to no constraining power on this parameter, as the emission lines are by definition formed at the inversion. We therefore choose to put a prior on Tirr as an estimate of the planet’s dayside temperature based on the atmospheric temperature measured from the TESS secondary eclipse. The TESS measurement is complementary to the high-resolution emission spectra as it provides information about the continuum that the emission spectra cannot probe, as shown in the contribution function in Figure 4. The additional information from TESS helps to anchor our retrieval where our data does not probe.
Combined contribution function for Fe, Ni, and Ca given the best fit P–T profile from the combined, preeclipse, and posteclipse retrievals. We note that the VMRs of Fe, Ni, and Ca are assumed to be constant as a function of pressure, while the continuum opacity species computed with FastChem (H, H−, e−) vary with altitude.
The TESS (G. R. Ricker et al. 2015) 120 s presearch data conditioning simple aperture photometry from sectors 40, 41, 54, 74, and 75 were detrended using a 3 times transit-duration median filter implemented by wotan (M. Hippke et al. 2019). Then Exofastv2 (J. D. Eastman 2017) was used to fit the primary and secondary eclipses of KELT-20. We measured a secondary eclipse depth of 140 ± 7 ppm. The secondary eclipse is then related to the planetary dayside temperature through Equation (5) where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} {\delta }{\sec }\end{document} is the eclipse depth, Ag is the geometric albedo, a is the orbital semimajor axis, and Bλ_ represents the Planck function integrated over the wavelengths of the TESS bandpass accounting for the bandpass response function.
\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{eqnarray*}{\delta }_{\sec }={\left(\displaystyle \frac{{R}_{p}}{{R}_{* }}\right)}^{2}\displaystyle \frac{{B}_{\lambda }({T}_{p})}{{B}_{\lambda }({T}_{* })}+{A}_{{\mathrm{g}}}{\left(\displaystyle \frac{{R}_{p}}{a}\right)}^{2}.\end{eqnarray*}\end{document}L. Dang et al. (2025) shows compelling evidence for very low levels of albedo for highly irradiated planets so we fix the geometric albedo term to zero. Then, we employ an MCMC to sample ranges of planetary dayside temperatures that best reproduce our measured eclipse depth. Thus, we estimate the dayside temperature of KELT-20 b to be 2862 ± 24 K based on the TESS secondary eclipse depth. Similarly, L. Dang et al. (2025) estimates a dayside temperature for KELT-20b of 2820 ± 80 K based on Spitzer (M. W. Werner et al. 2004) 4.5* μ*m phase curve observations.
MCMC Setup
3.5.
We apply the retrieval framework to the preeclipse, posteclipse, and combined datasets, following the same steps as detailed in our mock retrieval analysis. For each retrieval, we run our MCMC with 40 walkers for 3000 steps, with a burn-in length of 1000, resulting in 80,000 samples of the posterior. All of the prior ranges are listed in Table 3. We apply uniform or log-uniform priors on each of our free parameters, except for Tirr, for which we apply a Gaussian prior with the mean and standard deviation obtained from the methods described in Section 3.4.
Table 3: Description of Retrieved Parameters (Including Prior Ranges), Derived Parameters, and Fixed Parameters
Results and Discussion
Retrieved Abundances
4.1.
With all five nights of observation combined, we constrain the log of the VMRs of Fe ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} -3.9{6}{-0.17}^{+0.32}\end{document} ), Ni ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} -5.1{3}{-0.24}^{+0.33}\end{document} ), and Ca ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} -7.4{6}{-0.24}^{+0.32}\end{document} ). We note that this work provides the first constraints on Ni and Ca in emission for KELT-20 b. In our preeclipse only retrieval, we find slightly lower abundances of Fe ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} -4.2{9}{-0.15}^{+0.19}\end{document} ), Ni ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} -5.2{0}{-0.22}^{+0.24}\end{document} ), and Ca ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} -7.8{3}{-0.30}^{+0.32}\end{document} ) than the results from the combined datasets. In contrast, our posteclipse retrieval constrains slightly higher abundances of Fe ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} -3.4{9}{-0.38}^{+0.38}\end{document} ), Ni ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} -5.0{6}{-0.43}^{+0.45}\end{document} ), and Ca ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} -6.9{4}_{-0.43}^{+0.45}\end{document} ), but all species’ abundances remain consistent with the combined datasets within 1σ due to larger uncertainties. For ease of comparison, all abundance constraints are listed side-by-side as log(VMRs) in Table 3 and their posteriors are shown in Figure 8 for the combined datasets, and Figure 9 for the preeclipse and posteclipse datasets.
Our Fe abundances from each dataset are in agreement with those reported in D. Kasper et al. (2023), but are ∼1–2 dex higher than those reported in L. Finnerty et al. (2025) in emission and S. Gandhi et al. (2023) in transmission. For Ni and Ca, we compare our values to those reported in S. Gandhi et al. (2023) with transmission spectra (listed as MASCARA-2 b). We find our Ni abundances exceed their upper limit of −6.04, and our Ca abundances exceed their constraint of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} 8.4{9}_{-0.31}^{+0.33}\end{document} by ∼1–2 dex.
The discrepancies in our retrieved abundances may suggest a longitudinally asymmetric distribution of metals across the surface of KELT-20 b. The preeclipse datasets are dominated by light from the evening side, where the atmospheric material is rotating from the hot dayside into the cooler night side, whereas the posteclipse datasets probe the morning side, receiving material from the cooler night side. Therefore, a depletion in the Fe and Ca abundances in the preeclipse data could be due to a higher ionization fraction on the evening side. However, we note that do not find significant (>3σ) evidence for these ionized species in the CCFs. While this can be explained for Ni+ and Ca+ which have few lines within the PEPSI bandpass, it is more puzzling for Fe+ which has many lines. When we inject Fe+ into our spectra at a VMR of 10^−5^ we detect it in the combined CCF with a >10σ significance, suggesting that Fe+ should be detectable if present within the pressure levels probed with PEPSI. Therefore, this simple assumption of ionization may not be capturing the mechanisms causing these discrepancies. Furthermore, if there were a significant difference in the ionization of refractory metals between the evening and morning sides, we would not expect the abundance of neutral Ni to stay relatively constant between both datasets.
Comparison to FastChem
4.2.
In order to contextualize our results, we compare our retrieved abundances to FastChem equilibrium chemistry models, assuming solar, 10× solar, and 30× solar compositions. Figure 5 shows the histograms of our retrieved posteriors compared to the computed FastChem models for Fe, Ni, and Ca, plotted as a function of pressure (i.e., altitude). As our contribution function in Figure 4 shows, we are able to probe layers between 10^−3^ and 10^−6^ bar, we find our retrieved abundances for Fe to be most consistent with a 10–30× solar model, whereas Ca is broadly consistent with both solar and supersolar models, depending on the exact pressure level probed. However, Ni seems to only be consistent with the 30× solar model at the deepest pressure layers probed. Our assumed constant-with-altitude VMRs are more heavily weighted toward the deeper pressure layers before strong ionization occurs (e.g., D. Kasper et al. 2023), so comparing our retrieved abundances to the deepest pressure levels probed is a justifiable comparison. However, we caution against relying on absolute abundance constraints alone to infer a metallicity, as we will discuss in Section 4.3 that high-resolution studies are better at constraining abundance ratios than absolute abundances.
Comparison of retrieved abundances to those predicted from FastChem equilibrium chemistry models. Each panel shows the histograms from the retrieved posteriors for the log VMRs of Fe, Ni, and Ca, respectively, from our preeclipse (red), posteclipse (blue), and combined (purple) datasets. The dashed lines show the vertical abundances profiles from FastChem computed from our best fit P–T profile from our combined sample, and the shaded regions show that from our preeclipse and posteclipse P–T profiles. The FastChem models assuming solar abundances are provided in black, the 10× in orange, and the 30× solar in green. Our retrieved abundances suggest a supersolar composition.
Abundance Ratios
4.3.
As previous works have demonstrated that high resolutions spectroscopy is more sensitive to the relative strengths of spectral lines than the absolute level (e.g., N. P. Gibson et al. 2022; S. Gandhi et al. 2023; C. Maguire et al. 2024), we also measure the nickel-to-iron [Ni/Fe] and calcium-to-iron [Ca/Fe] ratios normalized to solar values calculated in M. Asplund et al. (2009). This helps to mitigate the degeneracies between our retrieved abundances and the opacity level, i.e., high abundances with low opacity can produce the same emission features as low abundances with high opacity. This is especially true with high opacity species like Fe, so normalizing to Fe abundance helps constrain the relative concentrations independently of the opacity. We note that we do not correct for ionization effects when computing the abundance ratios, so they should be interpreted as lower limits.
We measure a [Ni/Fe] ratio that is consistent with solar in the combined and posteclipse datasets, but a slightly supersolar [Ni/Fe] in the preeclipse dataset. For [Ca/Fe], we measure a significantly subsolar (2–3 dex) abundance for each dataset, as listed in Table 3. These constraints are broadly consistent with previous measurements for KELT-20 b in transmission in S. Gandhi et al. (2023). We plot these values along with those from S. Gandhi et al. (2023) in Figure 6.
Computed nickel-to-iron and calcium-to-iron abundance rations normalized to solar for the preeclipse (red), posteclipse (blue), and combined (purple) datasets. Also plotted are the [Ni/Fe] and [Ca/Fe] abundance ratios from S. Gandhi et al. (2023), computed for KELT-20 b from their constraints on Fe, Ni, and Ca from transmission spectroscopy.
Despite the differences in our retrieved posteriors for our VMRs, our calculated [Ni/Fe] and [Ca/Fe] ratios from the preeclipse, posteclipse, and combined datasets are within 1σ agreement with each other. Combined with the abundance ratios calculated by S. Gandhi et al. (2023), this suggests that the [Ni/Fe] and [Ca/Fe] ratios stay relatively constant (within 2σ) throughout the secondary eclipse, as well as during transit. The consistency in these results across multiple observations, coupled with previous results using different instruments and retrieval frameworks, provides another testament of the reliability of high-resolution atmospheric retrieval (C. Maguire et al. 2024; S. Ramkumar et al. 2025).
Pressure–Temperature Profile
4.4.
While there is a broad spread in the previously reported P–T profiles for KELT-20 b (e.g., F. Borsa et al. 2022; G. Fu et al. 2022; F. Yan et al. 2022; D. Kasper et al. 2023; L. Finnerty et al. 2025), our retrieved P–T profiles for the combined, preeclipse, and posteclipse datasets lie within the scatter of published results, as shown in Figure 7. The reason for this wide spread in retrieved P–T profiles is unclear, but like the abundance disagreements discussed in Section 4.1, this could be due to either real heterogeneity of the atmosphere, or differing assumptions in the retrieval frameworks.
Comparison of our median retrieved P–T profiles for our preeclipse, posteclipse, and combined datasets along with the published P–T profiles retrieved by F. Borsa et al. (2022), F. Yan et al. (2022), G. Fu et al. (2022), D. Kasper et al. (2023), and L. Finnerty et al. (2025). Each of these published P–T profiles is retrieved from datasets including both preeclpise and posteclipse observations, except for L. Finnerty et al. (2025), who only observed KELT-20 b posteclipse. We note that we used only an approximation to the P–T profile retrieved by G. Fu et al. (2022) as described in M. C. Johnson et al. (2023).
Full retrieval results for KELT-20 b. The medians and 1σ confidence intervals are denoted in the histograms with dashed lines and are listed above each histogram panel, as well as in Table 3. Upper right: the median retrieved P–T profile shown as a thick black line, with thinner purple lines representing 50 P–T profiles randomly extracted from the MCMC posteriors.
Same as Figure 8, but with the preeclipse (red) and posteclipse (blue) datasets shown separately.
We constrain difference in upper temperature between the posteclipse and preeclipse datasets on the order of a few hundred kelvin. GCMs across a wide range of giant planets predict a prominent east–west flow from equatorial jets in the deep atmosphere that weaken at higher altitudes, where the day–night flow begins to dominant (e.g., A. P. Showman & T. Guillot 2002; T. Kataria et al. 2016; E. Flowers et al. 2019). For example, J. P. Wardenier et al. (2025), Figure 2 shows drag free models for WASP-76 b for two different pressure levels (P = 10^−1^ bar and P = 10^−4^ bar). In the P = 10^−1^ bar model, the preeclipse (phase = 0.375) dayside temperature is significantly hotter than the posteclipse (phase = 0.625) dayside. However, in the P = 10^−4^ bar models the temperatures on the preeclipse and posteclipse phases are about the same. Therefore these data probe a pressure regime where day–night winds should begin to dominate over the equatorial jet. These results suggest that a minimal temperature gradient between KELT-20 b’s morning and evening sides persists in this pressure regime, and could be due to a weakened east–west wind flow dumping hot atmospheric material on the dayside.
Conclusions
We have presented five high-resolution emission spectroscopy observations of the UHJ KELT-20 b using the PEPSI spectrograph, covering the phases before and after secondary eclipse. We applied a Bayesian retrieval framework to constrain the VMRs of Fe, Ni, and Ca, providing the first constraints reported on Ni and Ca in emission for KELT-20 b. We applied the same retrieval framework to the preeclipse datasets, probing the evening side, and to the posteclipse datasets, probing the morning side, and find a slightly higher abundance of the detected refractory species on the morning side.
We compare our results to a FastChem equilibrium chemistry model and find that our retrieved abundances suggest a supersolar composition, ranging between 10 and 30× solar. However, we caution against drawing strong conclusions from our absolute abundance constraints due to the degeneracies between the absolute abundances and the opacity level. Instead, we rely on the robustness of abundance ratios to further interpret our results. We calculate the nickel-to-iron and calcium-to-iron abundances for the preeclipse, posteclipse, and combined posteriors. We find these ratios to all be consistent with each other within 1σ. This constraint, when combined with the [Ni/Fe] and [Ca/Fe] values calculated in S. Gandhi et al. (2023) during transit, suggests that even though the abundances of the neutral species vary significantly during multiple phases of KELT-20 b’s orbit, their abundance ratios remain relatively constant. This result underscores the robustness of constraining abundance ratios with high-resolution spectroscopy, as previously demonstrated in other HRS studies (e.g., N. P. Gibson et al. 2022; C. Maguire et al. 2024; S. Ramkumar et al. 2025).
Our measured pressure–temperature profiles fall within the spread of previously published results. We constrain a slightly higher temperature at the top of the thermal inversion on the evening side as compared to the morning side, suggesting possibly longitudinal temperature differences across the dayside of KELT-20 b. This analysis demonstrates that additional information can be gained when performing retrievals on multiple phases of high-resolution spectra.
Performing retrievals on separate orbital phases can help us probe the longitudinal patterns and the altitudinal temperature structure, allowing us to study these planets as 3D structures. While our study employs a particularly high SNR, large phase range dataset, these methods can be applied to other datasets in both emission and transmission with smaller phase ranges. Further phase-resolved atmospheric studies will continue to build our understanding of the evolving dynamics and chemical processes of these planetary systems.
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