Constraining Planetary Gas Accretion Rate from H α Line Width and Intensity: Case of PDS 70 b and c

Recent observations of protoplanets embedded in circumstellar disks have shed light on the planet formation process. In particular, detection of hydrogen Balmer-line (Hα) emission gives direct constraints on late-stage accretion onto gas giants. Very recently Haffert et al. measured the spectral line widths, in addition to intensities, of ${\rm{H}}\alpha $ emission from the two protoplanets orbiting PDS 70. Here, we study these protoplanets by applying radiation-hydrodynamic models of the shock-heated accretion flow onto protoplanets that Aoyama et al. have recently developed. As a result, we demonstrate that Hα line widths combined with intensities lead to narrowing down the possible ranges of the protoplanetary accretion rate and/or mass significantly. While the current spectral resolution is not high enough to derive a definite conclusion regarding their accretion process, high-resolution spectral imaging of growing protoplanets is highly promising.