Heat and dust in active layers of protostellar disks

Requirements for magnetic coupling and accretion in the active layer of a protostellar disk are re-examined, and some implications for thermal emission from the layer are discussed. The ionization and electrical conductivity are calculated following the general scheme of Ilgner and Nelson but with an updated UMIST database of chemical reactions and some improvements in the grain physics, and for the minimum-mass solar nebula rather than an alpha disk. The new limits on grain abundance are slightly more severe than theirs. Even for optimally sized grains, the layer should be at least marginally optically thin to its own thermal radiation, so that narrow, highly saturated emission lines of water and other molecular species would be expected if accretion is driven by turbulence and standard rates of ionization prevail. If the grain size distribution extends broadly from well below a micron to a millimeter or more, as suggested by observations, then the layer may be so optically thin that its cooling is dominated by molecular emission. Even under such conditions, it is difficult to have active layers of more than 10 g cm^-2 near 1 AU unless dust is entirely eliminated or greatly enhanced ionization rates are assumed. Equipartition-strength magnetic fields are then required in these regions of the disk if observed accretion rates are driven by magnetorotational turbulence. Wind-driven accretion might allow weaker fields and less massive active layers but would not heat the layer as much as turbulence and therefore might not produce emission lines.