Mass of intermediate black hole in the source M82 X-1 restricted by models of twin high-frequency quasi-periodic oscillations

Abstract

We apply the relativistic precession (RP) model with its variants and the resonance epicyclic model with its variants, based on the frequencies of the geodesic epicyclic motion in the field of a Kerr black hole, to put limits on the mass of the black hole in the ultraluminous X-ray source M82 X-1 demonstrating twin high-frequency quasi-periodic oscillations (HF QPOs) with the frequency ratio near 3:2. The mass limits implied by the geodesic HF QPO models are compared to those obtained due to the model of string loop oscillations around a stable equilibrium position. Assuming the whole range of the black hole dimensionless spin, 0 < a < 1, the restrictions on the black hole mass related to the twin HF QPOs are widely extended and strongly model dependent; nevertheless, they give the lower limit M_{M82 X-1} > 130 M_{sun} confirming existence of an intermediate black hole in the M82 X-1 source. The upper limit given by one of the variants of the geodesic twin HF QPO models goes up to M_{M82 X-1}<1500 M_{sun}. The range 37-210 mHz of the low-frequency QPOs observed in the M82 X-1 source introduces additional restrictive limits on the black hole mass, if we model the low-frequency QPOs by nodal precession of the epicyclic motion. The nodal precession model restrictions combined with those implied by the geodesic models of the twin HF QPOs give allowed ranges of the M82 X-1 black hole parameters, namely 140 M_{sun}<M_{M82 X-1}<660 M_{sun} for the mass parameter and 0.05<a_{M82 X-1}<0.6 for the spin parameter.