On the thermal stability of irradiation-dominated pre-main-sequence disks

The dusty disks of many young stars are probably heated mostly by absorption of light from the central star. This stellar irradiation can control the vertical structure of the disk, particularly in the outer regions. Because the irradiation heating is sensitive to the disk structure-the disk vertical thickness and the tilt of the disk photosphere relative to the star-the possibility of an unstable feedback is present. To study this problem, we present calculations of the evolution of perturbations in vertically isothermal disks. We find that such disks are generally stable. In outer disk regions of T Tauri stars, linear analysis indicates that the radiative cooling time is so short that temperature perturbations will be damped faster than the disk structure can respond. Using our results for steady "alpha" viscosity disks, we estimate that this is true for distances larger than 2 AU ((M) over dot/10(-8) M. yr(-1))(7/9)(alpha/0.01)(-7/9) for typical T Tauri stars. Inside this radius, if the disk surface tilt ("flaring") is still significant, numerical finite-amplitude calculations show that temperature perturbations will travel inward as they damp. We find that disk self-shadowing has a small effect on the results because the perturbation is damped on a timescale shorter than the time in which the shadowed disk region can respond. Our results help justify steady, smooth treatments of the effects of irradiation on the disks of young stellar objects.