Hydrogen-line profiles from accreting gas giants and their CPDs

TL;DR

This paper develops a framework to predict spectrally resolved hydrogen accretion-line profiles from forming gas giants observed with the ELT/METIS, focusing on Br$\alpha$ and Pfund lines and using PDS~70~b as a fiducial case. It combines a semi-analytical ballistic inflow model for the planet and its circumplanetary disc with non‑equilibrium shock emission calculations, under the assumption of negligible extinction and no magnetospheric accretion. Applying the model to the fiducial PDS~70~b system, Br$\alpha$ is predicted to be detectable in short integrations, with a line profile that can constrain the planet’s mass and radius and shed light on the accretion mechanism. The work argues that METIS will enable direct, high-SNR insights into planet formation through resolved line profiles, providing complementary information to continuum and flux-based diagnostics and extending to other low-mass accretors beyond PDS~70.

Abstract

Far fewer gas giants have been caught in their accretion phase than mature ones are known. Extremely Large Telescope (ELT) instruments will have a higher sensitivity and a smaller inner working angle than instruments up to now, which should allow more productive searches and detailed characterisation. We study the observability of accreting gas giants with METIS, the first-generation ELT spectrograph. We focus on the accretion-tracing hydrogen recombination lines accessible at a resolution R=1e5, mainly Brackett alpha and Pfund-series lines. Our approach is general but we take PDS 70 b as a fiducial case. To calculate high-resolution line profiles, we combine a semianalytical multidimensional description of the flow onto an accreting planet and its circumplanetary disc (CPD) with local non-equilibrium shock-emission models. We assume the limiting scenario of no extinction appropriate for gas giants in gaps and negligible contribution from magnetospheric accretion columns. We use simulated detector sensitivities to compute required observing times. Both the planet surface and the CPD surface shocks contribute to the total line profile, which is non-Gaussian and much narrower than the free-fall velocity. For the adopted baseline accretion rate onto PDS 70 b, the Br alpha line peak is equal to the photospheric continuum modulated mostly by water features. However, the rotation of the planet broadens the features, helping the shock excess stand out. At Br alpha, already the continuum of PDS 70 b should yield SNR=12 in 4 h. The peak excess should require only about 15 min to reach SNR=3. Br alpha is a potent planet formation tracer accessible to METIS in little integration time. Resolved line profiles will place independent constraints especially on the mass and radius of an accreting planet, and help identify the accretion mechanism(s) at work.

Figures (18)

• Figure 1: H i lines in the $L$ and $M$ bands of METIS, where it offers $R=10^5$. We show the Brackett (Br; lower level $n_\ell\xspace=4$), Pfund (Pf; $n_\ell\xspace=5$), and Humphries (Hu; $n_\ell\xspace=6$) series. Relative heights are schematic.
• Figure 2: Results for the shock excess line emission (i.e., without the thermal emission) in the fiducial case (for PDS 70 b-like parameters, including $d=113.4$ pc and $i=50{\hbox{\textdegree}}$; see Table \ref{['Tab:Par']}). The planet is in the centre and the inner part of the CPD is visible. The diffraction-limited beam of the ELT is $26$ mas, about 1000 times larger than the panels. (Left) Preshock velocity $v_0$ at the surface of the planet ($v_r$ velocity component; the bright central parts) or of the CPD (polar component $v_\theta$). (Right) Intensity of the emission at the central wavelength of Br $\alpha$. The planet and CPD rotation are neglected for the line emission because it originates from postshock layers that are assumed not yet to have joined the Keplerian rotation. The shock is much brighter per area at the planet surface than at the CPD, and only the closest regions of the CPD, out to $r\approx(3$--$4)R_{\mathrm{p}}\xspace$, contribute somewhat to the total flux. The sharp red transition at $r\approx1.2R_{\mathrm{p}}\xspace$ is a minor effect coming from the linear interpolation of the $F_\lambda(v_0)$ tables.
• Figure 3: Total emission line (thick black line), which sums the planetary- and CPD-surface contributions (dashed red and blue, respectively) corresponding to Figure \ref{['Abb:Bild']} (parameters in Table \ref{['Tab:Par']}). At this mass, the planet surface dominates the sum. A best-fitting Gaussian (thick mint curve) is also shown, with circles delimiting the region within which the fit is better than 10 %. The line is clearly narrower ($\mathrm{FWHM}\xspace=31~\mathrm{km}\,\mathrm{s^{-1}}\xspace$) than ${\varv_{\textrm{ff},\,\infty}}\xspace=94~\mathrm{km}\,\mathrm{s^{-1}}\xspace$ (thick grey bar).
• Figure 4: Line-integrated luminosity in our models (blue circles) compared to the observational constraints at PDS 70 b (gold symbols), not correcting for extinction. We use the fiducial parameters (Table \ref{['Tab:Par']}) and vary only the gas surface density at the Hill sphere (hues of blue), a proxy for the mass accretion rate. The golden diamonds and arrows show detections and 3-$\sigma$ upper limits and the thick crosses at Br $\alpha$ are the corresponding prediction using the AMIM21L scalings (see text).
• Figure 5: Line shapes (solid: total, i.e., planet and CPD; dashed: CPD contribution), normalised to each maximum, varying respectively the gas surface density $\Sigma$, inclination $i$, opening angle of the CPD $\theta_{\textrm{CPD}}$, planet mass $M_{\mathrm{p}}$, and planet radius $R_{\mathrm{p}}$, all at Br $\alpha$, or for the fiducial values, the hydrogen line (last panel). See respective legends. The fiducial values (black line, same in each panel) are as in Table \ref{['Tab:Par']}. We note in the legend the change in total flux relative to the fiducial case for all but the panels in which $M_{\mathrm{p}}$ or the transition is varied.