Multi-resonance orbital model of high-frequency quasi-periodic oscillations: possible high-precision determination of black hole and neutron star spin

Abstract

Context. Using known frequencies of the twin-peak high-frequency quasiperiodic oscillations (HF QPOs) and known mass of the central black hole, the black-hole dimensionless spin a can be determined by assuming a concrete version of the resonance model. However, a wide range of observationally limited values of the black hole mass implies low precision of the spin estimates. Aims. We discuss the possibility of higher precision for the black hole spin a measurements in the framework of a multi-resonance model inspired by observations of more than two HF QPOs in the black hole systems, which are expected to occur at two (or more) different radii of the accretion disc. This framework is also applied in a modified form to the neutron star systems. Methods. We determine the spin and mass dependence of the twin-peak frequencies with a general rational ratio n:m, assuming a non-linear resonance of oscillations with the epicyclic and Keplerian frequencies or their combinations. In the multi-resonant model, the twin-peak resonances are combined properly to give the observed frequency set. For the black hole systems we focus on the special case of duplex frequencies, when the top, bottom, or mixed frequency is common at two different radii where the resonances occur giving triple frequency sets. Results. The sets of triple frequency ratios and the related spin a are given. The resonances are considered up to n = 5 since excitation of higher order resonances is improbable. The strong resonance model for "magic" values of the black hole spin means that two (or more) versions of resonance could occur at the same radius, allowing cooperative effects between the resonances. For neutron star systems we introduce a resonant switch model that assumes switching of oscillatory modes at resonant points. Conclusions. In the case of doubled twin-peak HF QPOs excited at two different radii with common top, bottom, or mixed frequency, the black hole spin a is given by the triple frequency ratio set. The spin is determined precisely, but not uniquely, because the same frequency set could correspond to more than one concrete spin a. The black hole mass is given by the magnitude of the observed frequencies. The resonant switch model puts relevant limits on the mass and spin of neutron stars, and we expect a strong increase in the fitting procedure precision when different twin oscillatory modes are applied to data in the vicinity of different resonant points. We expect the multi-resonance model to be applicable to data from the planned LOFT or similar X-ray satellite observatory.

Models of quasi-periodic oscillations related to mass and spin of the GRO J1655-40 black hole

“…1. From the variants of the RP model (Stuchlík et al 2013), we select the RP1 model introduced in Bursa (2005), where ν U = ν θ and ν L = ν φ − ν r , and the "total precession model" RP2 introduced in Stuchlík et al (2013), where ν U = ν φ and ν L = ν θ − ν r (see Table 1). Both the RP1 and RP2 models predict frequencies ν U and ν L close to those of the RP model.…”

“…We extend this selection for the tidal disruption model where the twin HF QPOs are created by inhomogeneities deformed to a ring by tidal forces of the black hole (Čadež et al 2008;Kostić et al 2009), and by the model of warped thin disc oscillations (Kato 2004(Kato , 2008. Frequencies of the twin oscillatory modes used in the twin HF QPO models are given in Table 1. Contrary to the Monte Carlo technique applied in Motta et al (2014a), here we use the frequency ratio technique inspired by the resonance conditions relating the dimensionless black hole spin a to the common dimensionless radius x in the resonance models of the twin HF QPOs (Stuchlík et al , 2013.…”

Quasi-harmonic oscillatory motion of charged particles around a Schwarzschild black hole immersed in a uniform magnetic field

“…1. Many individual charged particles will probably not create complete accretion disc, since the fluid element of the accretion disk will be largely charge neutral, but the charged particle epicyclic motion can still be used for dynamics of ionized blob structures created by instabilities or by irradiation in otherwise neutral accretion disk [9].…”

Constraining Models of Twin-Peak Quasi-Periodic Oscillations With Realistic Neutron Star Equations of State

“…Many models have been proposed to explain the rich phenomenology of twin peak QPOs Lamb et al 1985;Miller et al 1998;Psaltis et al 1999;Wagoner 1999;Wagoner et al 2001;Kato 2001;Titarchuk & Wood 2002;Abramowicz et al 2003b,c;Rezzolla et al 2003;Kluźniak et al 2004;Pétri 2005;Zhang 2005;Bursa 2005;Török et al 2007;Kato 2007Kato , 2008Stuchlík et al 2008;Čadež et al 2008;Kostić et al 2009;Germanà et al 2009;Mukhopadhyay 2009;Stuchlík et al 2013Stuchlík et al , 2014Török et al 2016;Wang et al 2015;Stuchlík et al 2015, and several others). While any acceptable model should address both the excitation mechanism and subsequent modulation of the resulting X-ray signal as well as their overall observational properties, most of the theoretical effort has been so far devoted to the observed frequencies.…”