Vertical dissipation profiles and the photosphere location in thin and slim accretion disks

As several authors in the past, we calculate optically thick but geometrically thin (and slim) accretion disk models and perform a ray-tracing of photons in the Kerr geometry to calculate the observed disk continuum spectra. Previously, it was common practice to ray-trace photons assuming that they are emitted from the Kerr geometry equatorial plane, z = 0. We show that the continuum spectra calculated with this assumption differ from these calculated under the assumption that photons are emitted from the actual surface of the disc, z = H(r). This implies that a knowledge of the location of the thin disk effective photosphere is relevant for calculating the continuum emission. In this paper we investigate, in terms of a simple model, a possible influence of the (unknown, and therefore assumed ad hoc) vertical dissipation profiles on the vertical structure of the disk and thus on the location of the effective photosphere, and on the observed continuum spectra. For disks with moderate and high mass accretion rates ((m) over dot > 0.01(m) over dot(C)), we find that the photosphere location in the inner, radiation pressure dominated, disk region (where most of the radiation comes from) does not depend on the dissipation profile and therefore emerging disk spectra are insensitive to the choice of the dissipation function. For lower accretion rates, the photosphere location depends on the assumed vertical dissipation profile down to the disk inner edge, but the dependence is very weak and thus of minor importance. We conclude that the continuum spectra of optically thick accretion disks around black holes should be calculated with ray-tracing from the effective photosphere and that, fortunately, the choice of a particular vertical dissipation profile does not substantially influence the calculated emission.