Title: Analytic Expressions for the Inner-Rim Structure of Passively Heated Protoplanetary Disks,
Abstract: We analytically derive the expressions for the structure of the inner region
of protoplanetary disks based on the results from the recent hydrodynamical
simulations. The inner part of a disk can be divided into four regions:
dust-free region with gas temperature in the optically thin limit, optically
thin dust halo, optically thick condensation front and the classical optically
thick region in order from the inside. We derive the dust-to-gas mass ratio
profile in the dust halo using the fact that partial dust condensation
regulates the temperature to the dust evaporation temperature. Beyond the dust
halo, there is an optically thick condensation front where all the available
silicate gas condenses out. The curvature of the condensation surface is
determined by the condition that the surface temperature must be nearly equal
to the characteristic temperature $\sim 1200{\,\rm K}$. We derive the mid-plane
temperature in the outer two regions using the two-layer approximation with the
additional heating by the condensation front for the outermost region. As a
result, the overall temperature profile is step-like with steep gradients at
the borders between the outer three regions. The borders might act as planet
traps where the inward migration of planets due to gravitational interaction
with the gas disk stops. The temperature at the border between the two
outermost regions coincides with the temperature needed to activate
magnetorotational instability, suggesting that the inner edge of the dead zone
must lie at this border. The radius of the dead-zone inner edge predicted from
our solution is $\sim$ 2-3 times larger than that expected from the classical
optically thick temperature.