Keck/OSIRIS Pa$\beta$ high-contrast imaging and updated constraints on PDS~70b

We present a high-contrast imaging search for Pa$\beta$ line emission from protoplanets in the PDS~70 system with Keck/OSIRIS integral field spectroscopy. We applied the high-resolution spectral differential imaging technique to the OSIRIS $J$-band data but did not detect the Pa$\beta$ line at the level predicted using the parameters of \cite{Hashimoto2020}. This lack of Pa$\beta$ emission suggests the MUSE-based study may have overestimated the line width of H$\alpha$. We compared our Pa$\beta$ detection limits with the previous H$\alpha$ flux and H$\beta$ limits and estimated $A_{\rm V}$ to be $\sim0.9$ and 2.0 for PDS~70~b and c respectively. In particular, PDS~70~b's $A_{\rm V}$ is much smaller than implied by high-contrast near-infrared studies, which suggests the infrared-continuum photosphere and the hydrogen-emitting regions exist at different heights above the forming planet.