Detectability of resolved hydrogen lines from the accretion shock at gas giants and their CPDs

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 tools up to now, which should increase search yields. We examine what METIS, the first-generation ELT spectrograph with R=1e5, can reveal about accreting gas giants. We focus on the accessible hydrogen recombination lines, mainly Brackett alpha and Pfund-series lines. Our approach is general but we take PDS70b as a fiducial case. It is similar to WISPIT2b. To calculate high-resolution line profiles, we combine a semianalytical multi-D description of the flow onto an accreting planet and its circumplanetary disc (CPD) with local non-LTE shock-emission models. We assume the limiting scenario of no extinction, appropriate for gas giants in gaps, and negligible contribution from magnetospheric accretion. We use simulated detector sensitivities to compute needed observing times. Both the planet- and the CPD-surface shocks contribute to the line, which has a Gaussian core but wider, asymmetrical wings. The line is much narrower than the free-fall velocity, and in fact has a nearly constant FWHM=30--40 km/s at low densities. For our fiducial accretion rate onto PDS70b, the Br-a line peak excess is as strong as the photospheric continuum, modulated mostly by H2O features. However, the planet's spin broadens them, helping the shock excess stand out. At Br-a, already the continuum of PDS 70 b yields a per-bin S/N=12 in 4h. The peak excess should require only 10 min to reach S/N=3. For pure shock emission, the line shape is barely sensitive to the planetary or system parameters. A complex profile would indicate that magnetospheric accretion contributes significantly. The high resolution of METIS will help remove the pseudocontinuum, evincing line shapes even of faint accretors with great fidelity.