Solutions to the relativistic precession model

TL;DR

This paper introduces an analytical solution to the relativistic precession model equations, significantly reducing computational effort and enabling more efficient black hole parameter estimation from oscillation data.

Contribution

The authors develop an analytical approach to solve the RPM equations, replacing previous numerical methods and providing new techniques for limited oscillation data scenarios.

Findings

Analytical solution reduces computational effort for RPM equations.

Method enables parameter estimation with fewer oscillations detected.

Provides a way to constrain black hole properties with minimal data.

Abstract

The relativistic precession model (RPM) can be used to obtain a precise measurement of the mass and spin of a black hole when the appropriate set of quasi periodic oscillations is detected in the power-density spectrum of an accreting black hole. However, in previous studies the solution of the RPM equations could be obtained only through numerical methods at a price of an intensive computational effort. Here we demonstrate that the RPM system of equations can be solved analytically, drastically reducing the computational load, now limited to the Monte-Carlo simulation necessary to estimate the uncertainties. The analytical method not only provides an easy solution to the RPM system when three oscillations are detected, but in all the cases where the detection of two simultaneous oscillations is coupled with an independent mass measurement. We also present a computationally inexpensive method to place limits on the black hole mass and spin when only two oscillations are observed.