Rotation curves in protoplanetary disks with thermal stratification

Physical model and observational evidence in MAPS disks

¹ Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria 16, Milano, 20133, Italy
² Leiden Observatory, Leiden University, PO Box 9513, 2300 RA Leiden, The Netherlands
e-mail: martire@strw.leidenuniv.nl
³ Laboratoire Lagrange, Université Côte d’Azur, CNRS, Observatoire de la Côte d’Azur, 06304 Nice, France
⁴ School of Physics and Astronomy, Monash University, Clayton, VIC 3800, Australia
⁵ Univ. Grenoble Alpes, CNRS, IPAG, 38000 Grenoble, France
⁶ Alma Mater Studiorum Università di Bologna, Dipartimento di Fisica e Astronomia (DIFA), Via Gobetti 93/2, 40129 Bologna, Italy
⁷ INAF – Osservatorio Astrofisico di Arcetri, L.go E. Fermi 5, 50125 Firenze, Italy
⁸ Institute of Astronomy, University of Cambridge, Madingley Road, Cambridge CB3 0HA, UK
e-mail: e-mail: cl2000@cam.ac.uk

Received: 10 November 2023
Accepted: 16 February 2024

Abstract

Context. In recent years, the gas kinematics probed by molecular lines detected with ALMA has opened a new window into the of study protoplanetary disks. High spatial and spectral resolution observations have revealed the complexity of protoplanetary disk structure. Drawing accurate interpretations of these data allows us to better comprehend planet formation.

Aims. We investigate the impact of thermal stratification on the azimuthal velocity of protoplanetary disks. High-resolution gas observations reveal velocity differences between CO isotopologues, which cannot be adequately explained with vertically isothermal models. The aim of this work is to determine whether a stratified model can explain this discrepancy.

Methods. We analytically solved the hydrostatic equilibrium for a stratified disk and we derived the azimuthal velocity. We tested the model with SPH numerical simulations and then we used it to fit for the star mass, disk mass, and scale radius of the sources in the MAPS sample. In particular, we used ¹²CO and ¹³CO datacubes.

Results. When thermal stratification is taken into account, it is possible to reconcile most of the inconsistencies between rotation curves of different isotopologues. A more accurate description of the CO rotation curves offers a deeper understanding of the disk structure. The best-fit values of star mass, disk mass, and scale radius become more realistic and more in line with previous studies. In particular, the quality of the scale radius estimate significantly increases when adopting a stratified model. In light of our results, we computed the gas-to-dust ratio and the Toomre Q parameter. Within our hypothesis, for all the sources, the gas-to-dust ratio appears higher but still close to the standard value of 100 (within a factor of 2). The Toomre Q parameter suggests that the disks are gravitationally stable (Q > 1). However, the systems that show spirals presence are closer to the conditions of gravitational instability (Q ~ 5).