Differentiating Formation Models with New Dynamical Masses for the PDS 70 Protoplanets

Hot- and cold-start planet formation models predict differing luminosities for the young, bright planets that direct imaging surveys are most sensitive to. However, precise mass estimates are required to distinguish between these models observationally. The presence of two directly imaged planets, PDS 70 b and c, in the PDS 70 protoplanetary disk provides us a unique opportunity for dynamical mass measurements, since the masses for these planets are currently poorly constrained. Fitting orbital parameters to new astrometry of these planets, taken with VLTI/GRAVITY in the $K$~band, we find $2\sigma$ dynamical upper mass limits of 4.9 $M_{\rm Jup}$ for b and 13.6 $M_{\rm Jup}$ for c. Adding astrometry from the newly proposed planet candidate PDS 70 d into our model, we determine $2\sigma$ dynamical upper mass limits of 5.3 $M_{\rm Jup}$, 7.5 $M_{\rm Jup}$ and 2.2 $M_{\rm Jup}$ for b, c, and the candidate d respectively. However, $N$-body analysis of the orbits fit in this case suggest that the inclusion of $d$ makes the system unstable. Using the upper mass limits for b and c we rule out the coldest-start formation models for both planets, calculating minimum post-formation entropies ($S_i$) of 9.5 $k_{\rm B}/{\rm baryon}$ and 8.4 $k_{\rm B}/{\rm baryon}$ respectively. This places PDS 70 b and c on the growing list of directly-imaged planets inconsistent with cold-start formation.