Multi-modal atmospheric characterization of $β$ Pictoris b: Adding high-resolution continuum spectra from GRAVITY

TL;DR

This study integrates four self-consistent atmospheric grids (Exo-REM, ATMO, BT-Settl, Sonora) with a multimodal MOSAIC framework to jointly analyze GRAVITY high-resolution (R~4000) K-band spectra and extensive broad-band data for β Pictoris b. The GRAVITY data reveal a continuum shaped by H$_2$O and strong molecular features, enabling robust estimates of $T_{\mathrm{eff}}$, $\log(g)$, and $[\mathrm{M/H}]$, with a near-solar $C/O$ and a tentative CO isotopologue constraint hindered by telluric residuals. Including archival and multi-resolution data shifts the inferred $T_{\mathrm{eff}}$ downward (to ~$1500$–$1600$ K) and reinforces a high metallicity; $^{12}$CO/$^{13}$CO remains not decisively detected due to systematics. The results emphasize how continuum+line information in the K band strongly informs metallicity and cloud properties, and they illustrate the potential and limitations of multimodal atmospheric retrievals for directly imaged planets. The work also provides a roadmap for future multi-modal analyses with GRAVITY$^+$, JWST, and ELT-era observations to refine formation-history inferences for β Pictoris b.

Abstract

We present the first VLTI/GRAVITY observations at R$_λ\sim 4000$ of $β$ Pic b. These four high S/N ($\sim$20) K-band spectra conserve both the pseudo-continuum and molecular absorption patterns. We analyze them with four self-consistent forward model grids (Exo-REM, ATMO, BT-Settl, Sonora) exploring $T_{\mathrm{eff}}$, log(g), metallicity, C/O, and $^{12}$CO/$^{13}$CO ratio. We also upgrade our forward modeling code ForMoSA to account for the data multi-modality and combine the GRAVITY epochs with published 1-5 $μ$m photometry, low- to medium-resolution spectra (0.9-7 $μ$m), and high-resolution echelle spectra (2.1-5.2 $μ$m). Sonora and Exo-REM are statistically preferred. Exo-REM yields $T_{\mathrm{eff}}$ $=1607.45^{+4.85}_{-6.20}$ K and log(g) $=4.46^{+0.02}_{-0.04}$ dex from GRAVITY alone, and $T_{\mathrm{eff}}$ $=1502.74^{+2.32}_{-2.14}$ K and log(g) $=4.00\pm0.01$ dex when including all datasets. Archival data significantly affect the retrieved parameters. C/O remains solar ($0.552^{+0.003}_{-0.002}$) while [M/H] reaches super-solar values (0.50$\pm$0.01). We report the first tentative constraint on log($^{12}$CO/$^{13}$CO) $\sim$1.12, though this remains inconclusive due to telluric residuals. Additionally, we estimate the luminosity to be log(L/L$_\odot$) $=-4.01^{+0.04}_{-0.05}$, implying a heavy-element content of up to $\sim$5% (20-80 M$_\oplus$) given the system age and dynamical mass measurements. Access to both continuum and molecular lines at K-band significantly impacts the metallicity, possibly owing to collision-induced absorption shaping the continuum. Echelle spectra do not dominate the final fit with respect to lower resolution data. Future multi-modal frameworks should include weighting schemes reflecting bandwidth and central wavelength coverage.

Figures (18)

• Figure 1: Spectral resolution, R$_{\lambda}$, as a function of the wavelength coverage for each forward modeling used in this study. The observed data are represented by the black lines while the forward models are in shades of color. Dotted lines represent the extensions (both in wavelength and resolution) used in Sects. \ref{['sec4']} and \ref{['sec5']}.
• Figure 2: Schematic of MOSAIC. Here, "data" refer to spectroscopic and/or photometric observations and the "model" is a pre-computed grid of forward model spectra. $\theta$ represents the grid parameters (i.e $\mathrm{T_{eff}}$, log(g), [M/H]), and $\theta'$ the extra-grids parameters that can be defined separately (or not) for each sub-inversions (i.e., rv, $v\sin i$, ...). $\ln\mathcal{L}_{final}$ is the final log-likelihood function that goes in the nested-sampling algorithm and is computed with the assumption of independent observations, i.e $\ln\mathcal{L}_{final}=\sum_i \ln\mathcal{L}_i$.
• Figure 3: Results of the forward modeling of the $\beta$ Pic b GRAVITY spectrum. The combined GRAVITY spectrum (in black) compared data from the other panels in this figure. First panel: Best-fit Exo-REM (in blue). Second panel: Best-fit ATMO (in green). Third panel: Best-fit BT-Settl (in red). Fourth panel: Best-fit Sonora (in yellow). The two $^{13}$CO absorption lines are annotated at 2.345 µm and 2.374 µm; the four $^{12}$CO lines at 2.294 µm, 2.323 µm, 2.352 µm and 2.383 µm as well as the two H$_2$O band heads between 1.75--2.05 µm and 2.3--3.2 µm. Bottom panel: Residuals for each fit. Dotted lines represents the $\pm\sigma$ (68$\%$) confidence interval
• Figure 4: Retrieved best-fit pressure-temperature profiles when using GRAVITY (light blue) and all datasets except CRIRES$_+$ (dark blue) for Exo-REM forward modeling. Shaded regions represent the 1 and 2 $\sigma$ confidence interval, respectively. They are compared with the cloud optical depths of Mg$_2$SiO$_4$ (dashed brown) and Fe (dashed gray) defined as d$\tau=\sigma_c$ n dz with $\sigma_c$ the effective extinction cross-section of the cloud (in m$^2$), n its concentration (in particles/m$^3$) and dz the thickness of the atmospheric layer (in m). The red curve represents the photosphere (region from which most thermal emission originates). In practice, we used a similar approach as charnay_self-consistent_2018 and constrained the pressure-temperature between the minimum and maximum of the brightness temperature computed between 0.625 to 10 µm.
• Figure 5: Cross-correlation function (CCF) between the observational residuals (i.e., data minus model without $^{13}$CO) and the $^{13}$CO model template (i.e., model with $^{13}$CO minus model without $^{13}$CO) for the two highest resolution data sets (GRAVITY and SINFONI). The sum of all CCFs is shown in blue, while the CCFs for GRAVITY and SINFONI are shown in red and orange, respectively. The auto-correlation function (dashed-black) has been re-normalized to the peak of the CCF. The CCF has been computed between 2.33--2.40 µm with a skipedge of 50 bins to properly cover the two $^{13}$CO band heads. The S/N corresponds to that of the central peak and was computed using equation (1) of Houlle_2020 for each individual CCF, then propagated.