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We calculate the quasi-stationary structure of a radiating shock wave propagating through a spherically symmetric shell of cold gas by solving the time-dependent equations of radiation hydrodynamics on an adaptive grid. We show that this code successfully resolves the shock wave in both the subcritical and supercritical cases and, for the first time, we have reproduced all the expected features -including the optically thin temperature spike at a supercritical shock front -without invoking analytic jump conditions at the discontinuity. We solve the full moment equations for the radiation flux and energy density, but the shock wave structure can also be reproduced if the radiation flux is assumed to be proportional to the gradient of the energy density (the diffusion approximation), as long as the radiation energy density is determined by the appropriate radiative transfer moment equation.We find that Zel'dovich and Raizer's analytic solution for the shock wave structure accurately describes a subcritical shock but it underestimates the gas temperature, pressure, and the radiation flux in the gas ahead of a supercritical shock. We argue that this discrepancy is a consequence of neglecting terms which are second order in the minimum shock compression ratio [η 1 = (γ − 1)/(γ + 1), where γ is the adiabatic index] and the inaccurate treatment of radiative transfer near the discontinuity. In addition, we verify that the maximum temperature of the gas immediately behind the shock is given by T + = 4T 1 /(γ + 1), where T 1 is the gas temperature far behind the shock.

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We present an improved calculation of the vertical structure and ultraviolet spectrum of a dissipative accretion disk in an AGN. We calculate model spectra in which the viscous stress is proportional to the total pressure, the gas pressure only and the geometric mean of the radiation and gas pressures (cf. Laor & Netzer 1989: LN89). As a result of a more complete treatment of absorptive opacity, we find greater overall spectral curvature than did LN89, as well as larger amplitudes in both the Lyman and HeII photoionization edges. The local black body approximation is not a good description of the near UV spectrum. With relativistic corrections (appropriate to non-rotating black holes) included, we find that the near UV spectrum hardens with increasingṁ/m 8 (ṁ is the accretion rate in Eddington units, m 8 the black hole mass in units of 10 8 M ⊙ ). The near UV spectrum is consistent with observations ifṁm −1 8 ∼ 10 −3 , but disks this cold would have large, and unobserved, absorption features at the Lyman edge. The edge amplitude is reduced whenṁ/m 8 is larger, but then the near-UV slope is too hard to match observations. We conclude that models in which conventional disks orbit non-rotating black holes do not adequately explain UV continuum production in AGN.