2025A&A...698A..19T

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 of 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 2σ dynamical upper mass limits of 4.9 M_Jup for b and 13.6 M_Jup for c. Adding astrometry from the newly proposed planet candidate PDS 70 d into our model, we determine 2σ dynamical upper mass limits of 5.3 M_Jup, 7.5 M_Jup, and 2.2 M_Jup for b, c, and the candidate d, respectively. However, N-body analysis of the orbits' fit in this case suggests 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_B/baryon and 8.4 k_B/baryon, respectively. This places PDS 70 b and c on the growing list of directly imaged planets inconsistent with cold-start formation.