Neutral Cr and V in the Atmosphere of Ultra-hot Jupiter WASP-121 b

We examine the atomic abundances in the photospheres of UHJs under the assumption of thermochemical equilibrium. The chemical calculations were conducted using the HSC Chemistry software (version 8).⁵ We assumed solar elemental abundances (Asplund et al. 2009). The input species were expanded upon those used by Harrison et al. (2018) to include important molecular, atomic, and ionic forms of the top 36 elements in solar abundance. Other similar calculations show the prominence of atomic species in UHJs (e.g., Kitzmann et al. 2018; Lothringer et al. 2018; Nugroho et al. 2020).

Although the equilibrium temperature of WASP-121b is ∼2400 K, we expect its observed composition to be characteristic of the  2800 K temperatures at ∼0.1–1 bar (Gandhi & Madhusudhan 2019) due to strong vertical mixing (Parmentier et al. 2013). Figure 1 shows abundances of some prominent transition metals as a function of temperature at 0.1 bar. It can be seen that above ∼2500 K these elements are primarily found in their neutral atomic form rather than in molecules. We thus take the total elemental abundance, which we have assumed to be solar, as a good approximation for the abundance of neutral atomic species above 2500 K.

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We calculate atomic absorption cross sections for a large number of elements in order to investigate their spectral features. We rank the elements by their solar abundances (Asplund et al. 2009), excluding H, noble gases, and halogens. We calculate the cross sections for all the neutral and singly ionized forms of the top 30 elements, following the methods of Gandhi & Madhusudhan (2017). We use atomic line lists provided by Kurucz (2018) similar to the approach in other recent studies (e.g., Hoeijmakers et al. 2018; Casasayas-Barris et al. 2019; Nugroho et al. 2020). We determine the partition functions from the energy levels and statistical weights from the NIST database (Kramida et al. 2018). We include the effect of thermal broadening of the atomic lines, but do not consider pressure broadening as high-resolution spectra probe lower pressure regions in the upper atmosphere (Snellen et al. 2010; Wyttenbach et al. 2015). Our calculations do not include the effect of rotation and atmospheric expansion on the shape of the lines. All our models also include Rayleigh scattering from H₂ and collision-induces-absorption (CIA) from H₂–H₂ and H₂–He (Richard et al. 2012). An example of these cross sections scaled by solar abundance for some prominent transition metals can be found in Figure 1.

We investigate the spectral signatures of the atomic species discussed above using both simple semi-analytic models as well as fully numerical models. First, we compute transmission spectra of WASP-121 b using the analytic formulation originally derived by Lecavelier Des Etangs et al. (2008; see also, e.g., de Wit & Seager 2013; Bétrémieux & Swain 2017). This prescription assumes an isothermal atmosphere with a uniform composition and a constant scale height. The wavelength dependent effective height of the atmosphere is given by

$$\begin{eqnarray}&&h(\lambda )=H\mathrm{ln}\left(\displaystyle \frac{\sqrt{2\pi {R}_{\mathrm{pl}}H}{n}_{0}}{{\tau }_{\mathrm{eq}}}{\sigma }_{\mathrm{total}}\right),\end{eqnarray} \tag{ 1 }$$

with total opacity

$$\begin{eqnarray}&&{\sigma }_{\mathrm{total}}=\sum _{i}{\chi }_{i}{\sigma }_{i}(\lambda )+{\sigma }_{{\rm{R}}}(\lambda )+{n}_{0}{\sigma }_{\mathrm{CIA}}(\lambda ),\end{eqnarray} \tag{ 2 }$$

where σ_R is the opacity due to Rayleigh scattering, σ_i and χ_i are the absorption cross section and mixing ratio of species i, and n₀σ_CIA is the appropriately scaled CIA cross section. The CIA approximation in Equation (2) is adequate here considering that the CIA contribution in the optical is negligible. The scale height is given by $H=({k}_{{\rm{B}}}T)/(\mu g)$ where k_B is the Boltzmann constant, T is the temperature, μ is the mean molecular mass, and g is the gravitational acceleration. R_pl is the planet continuum radius, n₀ is the number density at a given reference pressure P₀, and τ_eq = 0.56 (Lecavelier Des Etangs et al. 2008). For a star of radius R_star the absorption spectrum is then

$$\begin{eqnarray}&&\delta (\lambda )=\displaystyle \frac{{\left({R}_{{\rm{pl}}}+h(\lambda \right))}^{2}}{{R}_{{\rm{star}}}^{2}}\end{eqnarray} \tag{ 3 }$$

We generate such analytic spectra for atomic species in the atmosphere of the UHJ WASP-121 b. We consider the contribution to the opacity of only one species j at a time, in addition to continuum opacity due to Rayleigh scattering and CIA, to calculate the spectrum δ_c+j. Here χ_j is taken to be the solar elemental mixing ratio of the species j. The corresponding atomic cross sections are calculated at 2000 K as described in Section 2.2. Examples for Fe i, Cr i, V i, and Ti i can be seen in Figure 2. We adopt the planet parameters from Delrez et al. (2016) as ${R}_{p}=1.828{R}_{J}$, ${M}_{p}=1.183{M}_{J},{R}_{\mathrm{star}}=1.458{R}_{\mathrm{sun}}$. We assume μ = 2.22 (similar to Jupiter), P₀ = 0.1 bar and T = 2000 K, and calculate the spectra from 0.4 to 0.7 μm with a resolution of R = 10⁵. We use these analytic model spectra to compute our detectability metric for the different species, as discussed in Section 4.1.

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For the cross-correlation analyses we use fully numerical models to compute the transmission spectra for the species discussed above. We use an adapted version of the forward model in the AURA retrieval code (Pinhas et al. 2018). AURA computes line-by-line radiative transfer for a plane-parallel atmosphere in transmission geometry, assuming hydrostatic equilibrium. We assume uniform chemical abundances and an isothermal temperature profile at 2000 K. The sources of opacity and spectral range are the same as described above for the analytic models. We compare the numerical models with the analytic models discussed above and find them to be in good agreement.

The majority of our analysis involves common steps in high-resolution atmospheric spectroscopy (Snellen et al. 2010; Brogi et al. 2012; Birkby 2018; Casasayas-Barris et al. 2019; Hoeijmakers et al. 2019). We use the X-COR cross-correlation software suite, previously used for molecular detections (Hawker et al. 2018; Cabot et al. 2019) in the near-infrared, and atomic detections on the present data set (Cabot et al. 2020). We briefly describe our procedures here as follows; further details can be found in Cabot et al. (2020).

We divide the data by a telluric model, which is fitted and computed by molecfit v1.5.7 (Smette et al. 2015). We mask the HARPS chip gap, plus 1% of data from either end of the observed spectrum that are otherwise affected by low throughput or severe telluric contamination. We shift all spectra into the rest frame of the star by correcting for the planetary-induced radial velocity signal. Next, we construct a master stellar spectrum by co-adding all out-of-transit spectra. Each in-transit spectrum is then divided by the master stellar spectrum. We fit and divide each spectrum by a fifth-degree polynomial, and remove remaining broadband variation with a 75 pixel high-pass filter. We are left with individual transmission spectra (Equation (3)), which contain spectral features originating in the planet's atmosphere. Continuum information was removed in the above normalization.

We form cross-correlation templates by subtracting the continua from the numerical model transmission spectra computed in Section 2.3. We convolve the templates with a narrow Gaussian (FWHM ∼ 0.8 km s⁻¹) to approximate the HARPS spectral resolution. The cross-correlation function (CCF) between the model template m(λ) and observed transmission spectra f(λ, t) is defined as

$$\begin{eqnarray}&&\mathrm{CCF}(v,t)=\displaystyle \frac{{\sum }_{\lambda }m(\lambda ;v)f(\lambda ,t)/{\sigma }^{2}(\lambda )}{{\sum }_{\lambda }m(\lambda ;v)/{\sigma }^{2}(\lambda )},\end{eqnarray} \tag{ 4 }$$

where we weight summation over wavelength bins λ by the inverse of their time-axis variance σ²(λ). This step prevents noisy data (e.g., in the former cores of telluric or stellar lines) from dominating the dot-product. The model is Doppler shifted by velocities −600 ≤ v ≤ 600 km s⁻¹ in steps of 2 km s⁻¹. The planetary atmospheric signal manifests as a light trail in the CCF, tracing velocities that correspond to the radial component of its orbital motion (which varies by ∼100 km s⁻¹ throughout the course of the transit). For species in common with the host star, we also observe a dark trail due to the Rossiter–McLaughlin effect (Cegla et al. 2016); a result of stellar rotation and the planet selectively occulting portions of the star. We correct for the Doppler Shadow as in Cabot et al. (2020). Following Brogi et al. (2012), we stack the CCFs in time for various values of semi-amplitude K_p. Excess signal from stacking under the true K_p, offset by the true systemic velocity V_sys, constitutes an atmospheric detection. The final CCFs combine data from Nights 1 and 3.

Here we use a simple metric to predict the detectability of a given atomic species using high-resolution optical transmission spectra of a UHJ. Our metric is guided by the fact that detecting N_lines lines using the cross-correlation method boosts the S/N by $\sqrt{{N}_{\mathrm{lines}}}$ (Birkby 2018). These lines are those that are strong enough to be detectable. The contribution of species $j$ to the spectrum is given by

$$\begin{eqnarray*}&&{\rm{\Delta }}{\delta }_{j}={\delta }_{{\rm{c}}+j}-{\delta }_{{\rm{c}}},\end{eqnarray*}$$

where δ_c and ${\delta }_{{\rm{c}}+j}$ are model transmission spectra with just the continuum opacity and that with contribution from the species $j$, respectively (see Section 2).

We calculate the number of strong lines N_lines in this signal by choosing a noise level ξ and discarding all lines weaker than ξ. The S/N for a line is given by Δδ_j/ξ for that line. We take into account the strength of these N_lines lines by calculating their average S/N, denoted as S/N_av. Finally, our metric for assessing the detectability is given by ${\rm{\Psi }}=\sqrt{{N}_{{\rm{lines}}}}\cdot {{\rm{S}}/{\rm{N}}}_{{\rm{av}}}$.

For WASP-121 b, we use this method and the analytic model spectra of 30 neutral atomic species, as described in Section 2, to evaluate their detectability. Here, we adopt a conservative noise level of ξ = 2000 ppm at R = 10⁵. We present the metric for all species with strong lines above the continuum in Table 1. Following these results, in our analysis of observed spectra of WASP-121 b we search for all the species with N_lines > 25: Fe i, Ti i, V i, Cr i, Sc i, Y i, and Zr i. These are the species that we predict to be likely detectable in the transmission spectra of WASP-121 b, with Fe i, Ti i, V i, and Cr i being the four most likely. We note that this metric is only applicable to the species that we expect to find under equilibrium conditions, typically seen in the lower atmosphere.

Based on the predictions above we search for neutral and singly ionized Fe, V, Cr, Ti, Sc, Y, and Zr in WASP-121 b using high-resolution optical transmission spectra as discussed in Section 3. The detections from our cross-correlation analyses are shown in Figure 3. We report new detections of V i with 4.5σ and Cr i with 3.6σ significance, and confirm the previous detection of neutral Fe at 6.0σ significance (Bourrier et al. 2020; Cabot et al. 2020; Gibson et al. 2020). We find no significant excess signal in the CCFs of Ti i, Sc i, Y i, or Zr i. We also report a detection of Fe ii in the optical, confirming its previous detection by Sing et al. (2019) in the ultraviolet (UV). The weights in the CCF in Equation (4) are not optimized for model injection and recovery (Hoeijmakers et al. 2019). As such, our quoted detection significances represent conservative estimates.

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The K_p and V_sys values derived from the detected planetary absorption signals are consistent, within 1–2σ, with the true values of K_p = 217 ± 19 km s⁻¹ and V_sys = 38.350 ± 0.021 km s⁻¹ (Delrez et al. 2016). Our measurements of K_p and V_sys are listed in Table 2. Our detections of neutral species exhibit blueshifts between 1 and 3 km s⁻¹ at a ≲2σ level. This may be explained by wind speeds in the photosphere, as inferred in other hot Jupiter atmospheres (e.g., Louden & Wheatley 2015) and predicted by models of atmospheric dynamics (Showman et al. 2009; Miller-Ricci Kempton & Rauscher 2012). The large spread in K_p results from sampling a small portion of the planet's full orbit (Brogi et al. 2018).

Table 2.  Summary of Species Detected in the Atmosphere of WASP-121 b

Species	S/N	Weighted Absorption	Kp	${V}_{\mathrm{sys}}$
Fe i	6.0	0.11%	${196}_{-11}^{+35}$	${35}_{-1}^{+2}$
Cr i	3.6	0.10%	${245}_{-18}^{+15}$	${37}_{-2}^{+2}$
V i	4.5	0.08%	${229}_{-23}^{+20}$	${35}_{-3}^{+2}$
Fe ii	3.6	0.23%	${255}_{-13}^{+6}$	${37}_{-1}^{+1}$

Note. The S/N corresponds to the peak of CCF in the K_p–V_sys plane. The weighted absorption provides a measure of the average line strength.

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We estimate the neutral Fe, Cr, and V to pertain to lower regions in the atmosphere relative to Fe ii. The weighted absorption (Hoeijmakers et al. 2019) by neutral species corresponds to ∼1.02 to 1.04R_p, whereas Fe ii extends to ∼1.07R_p. For a scale height of ∼1000 km (Evans et al. 2018), and nominal pressure of 0.1 bar at the base of the atmosphere (Welbanks & Madhusudhan 2019), the neutral species lie at altitudes corresponding to 3 × 10⁻³ to 9 × 10⁻⁴ bar. For comparison, the stratosphere (Evans et al. 2017) corresponds to approximately 10⁻² to 10⁻⁴ bar. On the other hand, we infer Fe ii to be present in the upper atmosphere ($\sim 6\times {10}^{-6}$ bar) suggesting it originates in photoionization of Fe i in agreement with Sing et al. (2019).

The detections that we report and the order of their significances are consistent with our predictions. However, we do not detect Ti i even though its predicted detectability (Ψ) is similar to V i. This suggests that Ti i is depleted in the observable atmosphere relative to the solar abundance assumed when calculating Ψ. We estimate the Ti i abundance to be at least 10× below the solar abundance value for its detectability to fall below our threshold.