Apparent photosphere, thermalization surface and spectrum of black hole winds: Frequency-dependent case

We examine the apparent photosphere, thermalization surface and expected spectrum of a black hole wind, which is an optically thick, spherically symmetric outflow blown off from the very center of a black hole, taking into account the frequency dependence of opacities. In the case of the optically thick spherical wind, the apparent photosphere is generally aspherical, since the wind density gradually decreases with radius. In addition, if electron scattering is important, the thermalization surface decouples with the apparent photosphere, and is located deep inside it. Furthermore, since the free–free opacity depends on frequency, the location of the thermalization surface also depends on frequency. We find that the shape of the apparent photosphere is aspherical, but does not depend on frequency so much. On the other hand, in the low-frequency regime the thermalization surface is located somewhat closely to the apparent photosphere, and its shape is aspherical, since the free–free opacity dominates the electron scattering one at low frequencies. In the high-frequency regime, however, the thermalization surface is located deep inside the flow, and its shape is nearly spherical, since the electron-scattering opacity dominates the free–free one at high frequencies. As a result, the expected spectrum becomes a multi-temperature blackbody one; the spectrum has a Wien peak, but the spectral slope below the peak is shallower than the Rayleigh–Jeans slope. This is partly due to the non-spherical shapes of the apparent photosphere and thermalization surface in some cases, but mainly because we observe a different part for different frequencies; i.e., low-frequency photons come from larger thermalization radii with lower temperatures, while high-frequency ones come from smaller thermalization radii with higher temperatures.