Relativistic Thermal Emission from Accretion Disks in Kerr-MOG Spacetimes

Abstract

In Scalar-Tensor-Vector Gravity (STVG, also known as MOG), a massive vector field $ϕ_μ$ generates a repulsive fifth force that endows rotating black holes with a gravitational charge $Q \propto \sqrtα\,M$, modifying the near-horizon geometry through a single deformation parameter $α$. We investigate how this vector-field coupling imprints itself on the thermal continuum emission of geometrically thin, optically thick accretion disks in the Kerr-MOG black hole. By re-deriving the innermost stable circular orbit (ISCO), the Novikov-Thorne radiative flux, the relativistic energy shift, and the null geodesic structure for the Kerr-MOG spacetime, we compute fully relativistic disk spectra across a broad range of spins, inclinations, and fifth-force strengths using a dedicated \textsc{xspec} spectral model (\texttt{kmspec}). We find that the fifth-force charge pushes the ISCO outward, lowers the peak disk temperature, and systematically softens the thermal continuum relative to its Kerr black hole counterpart at the same spin, with the deviation amplified at high observer inclinations. The resulting spectral modification closely mimics a reduction of spin in the pure Kerr black hole framework, indicating that independent spin measurements from, e.g., iron-line reflection spectroscopy are indispensable for disentangling the vector-field contribution. All results recover the standard Kerr black hole predictions when $α= 0$, and the model is validated against independent analytic and numerical benchmarks to machine precision. Application to a 69.6~ks \textit{XMM-Newton} observation of LMC~X-1 yields $α< 0.044$ at 90\% confidence, consistent with the Kerr metric and general relativity.