The influence of realistic cooling on the structure and spectrum of self-gravitating protoplanetary discs

Protoplanetary gas discs are affected by gravitational instability (GI) during their evolution. In the nonlinear regime, self-gravitating turbulence, the efficient redistribution of mass and angular momentum and disc fragmentation and the formation of bound objects can be produced by GI. Thermodynamics have a crucial role in the fragmentation of protoplanetary discs. We consider the realistic cooling (radiative cooling) in our numerical, thin, unmagnetized, steady-state and optically thin disc model via heating mechanism by viscosity. We wish to study the vertical structure and the radiative properties of three types of protoplanetary disc (Elias 20, TW Hya and GY 91) in an approach that takes the presence of the radiation cooling into account. Spectral energy distributions (SEDs) of three protoplanetary discs are compared to observation documents. We have supposed all three components of velocity in spherical coordinates. Both inflow and outflow parts are shown in our similarity solutions. In our model, the disc becomes thicker in the presence of radiation. Radiation leads to an increase in both inflow and outflow parts. So the fragmentation regions increase by radiation. Radiation provides latitudinal energy transport, and so, the flow rotates more slowly. We have showed that in the weak turbulence (alpha similar to 0.001\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha \sim 0.001$$\end{document}), the peak of the power spectrum is in full agreement with observation. The spectral energy distribution (SED) of three ALMA discs appears to peak at far-infrared wavelengths. Our results have indicated the protoplanetary discs like GY 91 (with lower mass central star) is more consistent with observations.