Temperature structure of protoplanetary disks undergoing layered accretion

We calculate the temperature structures of protoplanetary disks (PPDs) around T Tauri stars heated by both incident starlight and viscous dissipation. We present a new algorithm for calculating the temperatures in disks in hydrostatic and radiative equilibrium, based on Rybicki's method for iteratively calculating the vertical temperature structure within an annulus. At each iteration, the method solves for the temperature at all locations simultaneously, and converges rapidly even at high (≫10⁴) optical depth. The method retains the full frequency dependence of the radiation field. We use this algorithm to study for the first time disks evolving via the magnetorotational instability. Because PPD midplanes are weakly ionized, this instability operates preferentially in their surface layers, and disks will undergo layered accretion. We find that the midplane temperatures T _mid are strongly affected by the column density Σ_a of the active layers, even for fixed mass accretion rate . Models assuming uniform accretion predict midplane temperatures in the terrestrial planet forming region several × 10² K higher than our layered accretion models do. For and the column densities Σ_a < 10 g cm^-2 associated with layered accretion, disk temperatures are indistinguishable from those of a passively heated disk. We find emergent spectra are insensitive to Σ_a, making it difficult to observationally identify disks undergoing layered versus uniform accretion.