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We analytically derive the expressions for the structure of the inner regionof protoplanetary disks based on the results from the recent hydrodynamicalsimulations. The inner part of a disk can be divided into four regions:dust-free region with gas temperature in the optically thin limit, opticallythin dust halo, optically thick condensation front and the classical opticallythick region in order from the inside. We derive the dust-to-gas mass ratioprofile in the dust halo using the fact that partial dust condensationregulates the temperature to the dust evaporation temperature. Beyond the dusthalo, there is an optically thick condensation front where all the availablesilicate gas condenses out. The curvature of the condensation surface isdetermined by the condition that the surface temperature must be nearly equalto the characteristic temperature $\sim 1200{\,\rm K}$. We derive the mid-planetemperature in the outer two regions using the two-layer approximation with theadditional heating by the condensation front for the outermost region. As aresult, the overall temperature profile is step-like with steep gradients atthe borders between the outer three regions. The borders might act as planettraps where the inward migration of planets due to gravitational interactionwith the gas disk stops. The temperature at the border between the twooutermost regions coincides with the temperature needed to activatemagnetorotational instability, suggesting that the inner edge of the dead zonemust lie at this border. The radius of the dead-zone inner edge predicted fromour solution is $\sim$ 2-3 times larger than that expected from the classicaloptically thick temperature.

Analytic Expressions for the Inner-Rim Structure of Passively Heated Protoplanetary Disks