Thermal Radiation from Thin Accretion Disks in a Deformed Kerr Spacetime

We study the thermal radiation from geometrically thin, optically thick accretion disks in the framework of the δ-Kerr spacetime, which parametrizes deviations from the Kerr geometry through a deformation parameter δ. Focusing on equatorial circular orbits, we compute the specific energy, angular momentum, and the innermost stable circular orbit (ISCO) as functions of black hole spin and the 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, accounting for 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 arising in the innermost disk regions. Although these modifications are clearly visible in temperature maps, their impact on the integrated thermal spectra is modest within the parameter range considered. In particular, spectra corresponding to different values of the deformation parameter are nearly indistinguishable across most of the energy range, with only subtle differences near the spectral peak and high-energy tail. By contrast, variations in spin and inclination produce significantly stronger spectral changes. These results indicate that, within the thin-disk continuum framework, thermal emission alone provides limited sensitivity to small deviations from the Kerr geometry due to parameter degeneracies. Combining thermal spectra with complementary observables, such as X-ray reflection features, polarization, or timing information, may offer a more effective approach for testing deviations from the Kerr spacetime.