Improving the thin-disk models of circumstellar disk evolution. The 2+1-dimensional model

¹ Institute of Fluid Mechanics and Heat Transfer, TU Wien, 1060 Vienna, Austria
e-mail: eduard.vorobiev@univie.ac.at
² Research Institute of Physics, Southern Federal University, Stachki Ave. 194, 344090 Rostov-on-Don, Russia
³ University of Vienna, Department of Astrophysics, Vienna 1180, Austria
⁴ Institute of Astronomy of the Russian Academy of Sciences, Pyatnitskaya str. 48, 119017 Moscow, Russia

Received: 28 January 2017
Accepted: 27 May 2017

Abstract

Context. Circumstellar disks of gas and dust are naturally formed from contracting pre-stellar molecular cores during the star formation process. To study various dynamical and chemical processes that take place in circumstellar disks prior to their dissipation and transition to debris disks, the appropriate numerical models capable of studying the long-term disk chemodynamical evolution are required.

Aims. We improve the frequently used 2D hydrodynamical model for disk evolution in the thin-disk limit by employing a better calculation of the disk thermal balance and adding a reconstruction of the disk vertical structure. Together with the hydrodynamical processes, the thermal evolution is of great importance since it influences the strength of gravitational instability and the chemical evolution of the disk.

Methods. We present a new 2+1-dimensional numerical hydrodynamics model of circumstellar disk evolution, where the thin-disk model is complemented with the procedure for calculating the vertical distributions of gas volume density and temperature in the disk. The reconstruction of the disk vertical structure is performed at every time step via the solution of the time-dependent radiative transfer equations coupled to the equation of the vertical hydrostatic equilibrium.

Results. We perform a detailed comparison between circumstellar disks produced with our previous 2D model and with the improved 2+1D approach. The structure and evolution of resulting disks, including the differences in temperatures, densities, disk masses, and protostellar accretion rates, are discussed in detail.

Conclusions. The new 2+1D model yields systematically colder disks, while the in-falling parental clouds are warmer. Both effects act to increase the strength of disk gravitational instability and, as a result, the number of gravitationally bound fragments that form in the disk via gravitational fragmentation as compared to the purely 2D thin-disk simulations with a simplified thermal balance calculation. The presented method has a lower time overhead than the purely 2D models and is particularly suited for the long-term simulations of circumstellar disks including compact chemical reaction networks.