Differentiating formation models with new dynamical masses for the PDS 70 protoplanets

¹ Max-Planck-Institut für Astronomie, Königstuhl 17, 69117 Heidelberg, Germany
² Universität Heidelberg, Grabengasse 1, 69117 Heidelberg, Germany
³ Center for Interdisciplinary Exploration and Research in Astrophysics (CIERA) and Department of Physics and Astronomy, Northwestern University, Evanston, IL 60208, USA
⁴ Institute of Astronomy, KU Leuven, Celestijnenlaan 200D, Leuven, Belgium
⁵ Space sciences, Technologies & Astrophysics Research (STAR) Institute, Université de Liège, Allée du Six Août 19c, 4000 Sart Tilman, Belgium
⁶ School of Physics and Astronomy, Monash University, Clayton, VIC 3800, Australia
⁷ LESIA, Observatoire de Paris, Université PSL, CNRS, Sorbonne Université, Université Paris Cité, 5 place Jules Janssen, 92195 Meudon, France
⁸ European Southern Observatory (ESO), Karl-Schwarzschild-Straße 2, 85748 Garching, Germany
⁹ Université Aix-Marseille, CNRS, CNES, LAM, Marseille, France
¹⁰ Department of Physics & Astronomy, Johns Hopkins University, 3400 N. Charles Street, Baltimore, MD 21218, USA
¹¹ Space Telescope Science Institute (STScI), 3700 San Martin Drive, Baltimore, MD 21218, USA
¹² Université Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
¹³ Laboratoire Lagrange, Université Côte d’Azur, CNRS, Observatoire de la Côte d’Azur, 06304 Nice, France
¹⁴ INAF – Osservatorio Astronomico di Padova, Vicolo dell’Osservatorio 5, 35122 Padova, Italy
¹⁵ University of Exeter, Physics Building, Stocker Road, Exeter EX4 4QL, UK
¹⁶ Fakultät für Physik, Universität Duisburg–Essen, Lotharstraße 1, 47057 Duisburg, Germany
¹⁷ Physikalisches Institut, Universität Bern, Gesellschaftsstr. 6, 3012 Bern, Switzerland
¹⁸ Academia Sinica, Institute of Astronomy and Astrophysics, 11F Astronomy-Mathematics Building, NTU/AS campus, No. 1, Section 4, Roosevelt Rd., Taipei 10617, Taiwan
¹⁹ European Space Agency (ESA), ESA Office, STScI, 3700 San Martin Drive, Baltimore, MD 21218, USA
²⁰ Instituto de Astronomía, Universidad Nacional Autónoma de México, Apdo. Postal 70264, Ciudad de México 04510, Mexico

^★ Corresponding author.

Received: 28 January 2025
Accepted: 15 April 2025

Abstract

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.