Structure and Instabilities of an Irradiated Viscous Protoplanetary Disk

Abstract

We investigate the structure and instabilities of a protoplanetary disk that is heated by a viscous process in itself and by its central star. The disk is set to rotate with Keplerian velocity and has the surface density distribution of a minimum-mass solar nebula. We assume vertical hydrostatic equilibrium and radiative equilibrium at each point and solve the two-dimensional radiative transfer equation by means of the short characteristics method in spherical coordinates in order to determine the disk structure. Our calculation shows that at the outer region of the disk, with a distance from the central star of x > 1 AU, the radiative heating from the inner disk dominates the viscous heating, even near the midplane. This is because of the high temperature distribution in the optically thin surface layer and the relatively high disk height (z∞ ~ 0.7x at x ~ 1 AU) as a consequence of the irradiation from the inner hot region of the disk. In addition, we examine the convective and the magnetorotational instabilities of the disk. We find that the whole disk is convectively stable, since the dusty region is not heated by the viscous dissipation from the midplane, but by the radial radiative heating. On the other hand, almost all the disk is magnetorotationally unstable, except for the region near the equatorial plane of 2 AU < x < 10 AU. Finally, we discuss the growth and the size distribution of dust particles in the disk, which suggest that there exist centimeter-sized particles in the surface layer, namely, in the exposed region of the disk.