Mass and distance of AGN black holes from warped accretion disks

TL;DR

The paper tackles the challenge of independently determining the mass $M$ and distance $D$ of supermassive black holes in AGN megamaser systems, where previous GR analyses naturally tied these quantities through the ratio $M/D$. By introducing a slight warping in the masing disk, the authors derive analytical, decoupled expressions for $M$ and $D$ that depend on observables (maser frequency shifts and sky positions), the disk warp parameters, and the host galaxy's peculiar redshift $z_p$. The core contributions are closed-form formulas for $D$ and $M$ in terms of $R=1+z_{tot_1}$, $B=1+z_{tot_2}$, angular separation $\Theta$, and disk parameters, including an explicit $\sin^{-1}$ dependence that arises from the warp, effectively removing the $\tilde{M}$–disk degeneracy. This approach enables extracting BH properties and cosmological distances from a single galaxy without relying on the cosmic distance ladder, with potential for improved calibration of extragalactic distances and insights into BH growth in AGN.

Abstract

Along the last ten years, a general relativistic method has been developed to generate analytical expressions for the black hole (BH) parameters in terms of observations, namely the frequency shift of photons emitted by orbiting test particles and their positions on the sky. Applications of the method to astrophysical systems such as Active Galactic Nuclei (AGNs), in particular to megamaser systems orbiting the central BH on their flat accretion disks, showed a coupling behavior in the mass-to-distance ratio $M/D$. Estimates for the ratio $M/D$ of a sample of BHs hosted at the core of several AGNs have been performed in recent years with the help of this method. However, both analytical expressions and statistical estimations depend only on the $M/D$ ratio rather than on independent parameters. It is of current general interest to work with decoupled parameters in order to safeguard the intrinsic physical information encoded in each of them, given their high scientific relevance in understanding the structure of our Universe. The purpose of this work is to find analytical expressions for the mass and distance of a Schwarzschild BH in terms of astrophysical observations by introducing a slight warping in the accretion disk of the orbiting megamasers. As a result, independent analytical formulas for the mass and distance of AGN supermassive BHs are presented in terms of astrophysical observations: maser frequency shifts, disk parameters, and the galaxy's peculiar redshift.