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 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 quasiperiodic 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 whole the 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 M82X−1 > 130 M ⊙ 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 M82X−1 < 1500 M ⊙ . The range 37 mHz-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 ⊙ < M M82X−1 < 660 M ⊙ for the mass parameter, and 0.05 < a M82X−1 < 0.6 for the spin parameter.

A BROADBAND X-RAY SPECTRAL STUDY OF THE INTERMEDIATE-MASS BLACK HOLE CANDIDATE M82 X-1 WITH NuSTAR, CHANDRA, AND SWIFT

“…Our mass estimates are considerably lower than those from thin-disk modeling (Feng & Kaaret 2010) or QPO analysis (Pasham et al 2014). A subsequent analysis of the QPOs by Stuchlík & Kološ (2015) found that the black hole mass estimate from these are strongly model dependent, and given this put a range on the mass as 140 <M BH < 660 M , where the lower masses correspond to a non-spinning black hole, and as such are at odds with our result. In our estimation, we have assumed a face-on inclination of the disk.…”

Possible signature of the magnetic fields related to quasi-periodic oscillations observed in microquasars

“…These models were applied to match the twin HF QPOs and the LF QPO for the microquasar GRO J1655-40 in [47]. Of course, the models can be applied also for intermediate massive black holes [44].…”

Quasi-periodic oscillations around Kerr-MOG black holes

“…These models were applied to match the twin HF QPOs and the LF QPO for the microquasar GRO J1655-40 in [45]. Of course, the models can be applied also for intermediate massive BHs [43].…”