Thermal Radiation from Thin Accretion Disks in a Deformed Kerr Spacetime
Temurbek Mirzaev
1,2,*
1 Institute for Advanced Studies, New Uzbekistan University , Movarounnahr str. 1, Tashkent 100007, Uzbekistan
2 Ulugh Beg Astronomical Institute of the Uzbekistan Academy of Sciences , Astronomy St. 33, Tashkent 100052, Uzbekistan
Abstract
We study the thermal radiation from geometrically thin, optically thick accretion disks in the framework of the $\delta$-Kerr spacetime, which parametrizes deviations from the Kerr geometry through a deformation parameter $\delta$. Focusing on equatorial circular orbits, we compute the specific energy, angular momentum, and innermost stable circular orbit (ISCO) as functions of the black hole spin and deformation parameter. These quantities are used within the Novikov–Thorne formalism to determine the disk radiative flux and effective temperature profile.
Relativistic ray tracing is employed to construct observed temperature maps and thermal spectra, taking into account gravitational redshift, Doppler boosting, light bending, and a fixed color correction factor. We analyze the dependence of the ISCO radius, radial temperature profiles, observed temperature distributions, and thermal spectra on the deformation parameter, black hole spin, and observer inclination.
We find that deviations from the Kerr geometry modify the ISCO location and the inner disk temperature, with the strongest effects occurring in the innermost disk regions. While these modifications are clearly visible in the temperature maps, their impact on the integrated thermal spectra is modest for the parameter range considered. In particular, the thermal spectra corresponding to different values of the deformation parameter are nearly indistinguishable over most of the energy range, with only subtle differences appearing near the spectral peak and high-energy tail. By contrast, variations in the black hole spin and inclination produce significantly stronger spectral changes.
Our results indicate that, within the thin-disk continuum framework, thermal emission alone provides limited sensitivity to small deviations from the Kerr geometry, due to degeneracies between the deformation parameter, spin, inclination, and radiative efficiency. Combining thermal spectra with complementary observables, such as X-ray reflection features, polarization, or timing information, may offer a more promising avenue for testing deviations from the Kerr spacetime.
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Cite this article
Mirzaev, T., Thermal Radiation from Thin Accretion Disks in a Deformed Kerr Spacetime, Turanian J. Vol. 1, No. 4 (010401), 2025