Properties of an accretion disc with a power-law stress-pressure relationship

Abstract

Recent numerical simulations of magnetized accretion discs show that the radial-azimuthal component of the stress tensor due to the magnetorotational instability (MRI) is well represented by a power-law function of the gas pressure rather than a linear relation which has been used in most of the accretion disc studies. The exponent of this power-law function which depends on the net flux of the imposed magnetic field is reported in the range between zero and unity. However, the physical consequences of this power-law stress-pressure relation within the framework of the standard disc model have not been explored so far. In this study, the structure of an accretion disc with a power-law stress-pressure relation is studied using analytical solutions in the steady-state and time-dependent cases. The derived solutions are applicable to different accreting systems, and as an illustrative example, we explore structure of protoplanetary discs using these solutions. We show that the slopes of the radial surface density and temperature distributions become steeper with decreasing the stress exponent. However, if the disc opacity is dominated by icy grains and value of the stress exponent is less than about $0.5$, the surface density and temperature profiles become so steep that make them unreliable. We also obtain analytical solutions for the protoplanetary discs which are irradiated by the host star. Using these solutions, we find that the effect of the irradiation becomes more significant with decreasing the stress exponent.