Super-spinning compact objects and models of high-frequency quasi-periodic oscillations observed in Galactic microquasars

II. Forced resonances

¹ Institute of Physics and Research Centre for Computational Physics and Data Processing, Faculty of Philosophy & Science, Silesian University in Opava, Bezručovo nám. 13, 746 01 Opava, Czech Republic
e-mail: Andrea.Kotrlova@fpf.slu.cz
² Institute of Physics and Research Centre for Theoretical Physics and Astrophysics, Faculty of Philosophy & Science, Silesian University in Opava, Bezručovo nám. 13, 746 01 Opava, Czech Republic
³ Nicolaus Copernicus Astronomical Centre, Bartycka 18, 00716 Warsaw, Poland

Received: 9 February 2017
Accepted: 11 July 2017

Abstract

In our previous work (Paper I) we applied several models of high-frequency quasi-periodic oscillations (HF QPOs) to estimate the spin of the central compact object in three Galactic microquasars assuming the possibility that the central compact body is a super-spinning object (or a naked singularity) with external spacetime described by Kerr geometry with a dimensionless spin parameter a ≡ cJ/GM² > 1. Here we extend our consideration, and in a consistent way investigate implications of a set of ten resonance models so far discussed only in the context of a < 1. The same physical arguments as in Paper I are applied to these models, i.e. only a small deviation of the spin estimate from a = 1, a ≳ 1, is assumed for a favoured model. For five of these models that involve Keplerian and radial epicyclic oscillations we find the existence of a unique specific QPO excitation radius. Consequently, there is a simple behaviour of dimensionless frequency M × ν_U(a) represented by a single continuous function having solely one maximum close to a ≳ 1. Only one of these models is compatible with the expectation of a ≳ 1. The other five models that involve the radial and vertical epicyclic oscillations imply the existence of multiple resonant radii. This signifies a more complicated behaviour of M × ν_U(a) that cannot be represented by single functions. Each of these five models is compatible with the expectation of a ≳ 1.