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We present 2-D axisymmetric hydrodynamical simulations of thermally driven winds from accretion disks which result from the absorption of X-rays from a central compact object ($\approx 10^8M_\odot$). We have assumed the accretion disk flares with radius so that the outer parts can be directly exposed to the ionizing radiation from the central source. The effects of rotation, central gravity from the compact object, and optically thin heating and cooling have been added to a second-order Godunov scheme employing local adaptive mesh refinement. Each model exhibits solutions where there is a gravitationally bound, nearly isothermal corona for streamlines emanating from small radii, and a free flowing wind for streamlines from large radii. We have calculated models for a range of luminosities which show the different types of wind solutions possible. These range from a rapidly-heated, nearly isothermal wind for high luminosities to a slowly-heated, gravitationally inhibited wind for low luminosities. A direct comparison is made to the analytic prediction of mass loss rate as a function of radius of Begelman, McKee, and Shields (1983). We find good agreement at high luminosities; however, discrepancies are found at low luminosities indicating an improved description of the transition to a gravitationally retarded wind. Finally, for the purposes of X-ray spectroscopy of the wind, we present the column density of various iron ions as a function of inclination angle of the disk for a few of our models.
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