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

## TL;DR

This paper introduces a 2+1-dimensional numerical model for circumstellar disk evolution that incorporates vertical structure calculations, leading to more accurate predictions of disk properties and gravitational fragmentation.

## Contribution

The paper develops an improved 2+1D hydrodynamics model that includes vertical structure calculations, enhancing the realism of circumstellar disk simulations.

## Key findings

- Disks are systematically colder with the 2+1D model.
- Warmer parental clouds increase disk gravitational instability.
- More gravitational fragments form in 2+1D simulations.

## Abstract

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. We present a new 2+1-dimensional numerical hydrodynamics model of circumstellar disk evolution, in which 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. 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. 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.