Simple analytic formula relating the mass and spin of accreting compact objects to their rapid X-ray variability

Abstract

Following the previous research on epicyclic oscillations of accretion disks around black holes (BHs) and neutron stars (NSs), a new model of high-frequency quasi-periodic oscillations (QPOs) has been proposed (CT model), which deals with oscillations of fluid in marginally overflowing accretion tori (i.e., tori terminated by cusps). According to preliminary investigations, the model provides better fits of the NS QPO data compared to the relativistic precession (RP) model. It also implies a significantly higher upper limit on the Galactic microquasars BH spin. A short analytic formula has been noticed to well reproduce the model's predictions on the QPO frequencies in Schwarzschild spacetimes. Here we derive an extended version of this formula that applies to rotating compact objects. We start with the consideration of Kerr spacetimes and derive a formula that is not restricted to a particular specific angular momentum distribution of the inner accretion flow, such as Keplerian or constant. Finally, we consider Hartle-Thorne spacetimes and include corrections implied by the NS oblateness. For a particular choice of a single parameter, our relation provides frequencies predicted by the CT model. For another value, it provides frequencies predicted by the RP model. We conclude that the formula is well applicable for rotating oblateness NSs and both models. We briefly illustrate application of our simple formula on several NS sources and confirm the expectation that the CT model is compatible with realistic values of the NS mass and provides better fits of data than the RP model.

9 pages, 5 figures, accepted for publication in The Astrophysical Journal

References in corpus (18)

• The coherence of kHz quasi-periodic oscillations in the X-rays from accreting neutron stars
• Tidal effects on small bodies by massive black holes
• On the kHz QPO frequency correlations in bright neutron star X-ray binaries
• Puffy accretion disks: sub-Eddington, optically thick, and stable
• On mass-constraints implied by the relativistic precession model of twin-peak quasi-periodic oscillations in Circinus X-1
• Diskoseismology and QPOs Confront Black Hole Spin
• Discovery of the upper kilo-Hz QPO from the X-ray transient Aql X-1
• Timescale of twin-peak quasi-periodic oscillations and mass of accreting neutron stars
• Mass-angular-momentum relations implied by models of twin peak quasi-periodic oscillations
• String loops oscillating in the field of Kerr black holes as a possible explanation of twin high-frequency quasiperiodic oscillations observed in microquasars
• Upper-twin-peak quasiperiodic oscillation in x-ray binaries and the energy from tidal circularization of relativistic orbits
• Epicyclic oscillations in the Hartle-Thorne external geometry
• Constraining models of twin peak quasi-periodic oscillations with realistic neutron star equations of state
• Neutron Star QPOs from Oscillating, Precessing Hot, Thick Flow
• Mass and spin measurements for the neutron star 4U1608-52 through the relativistic precession model
• Correlations between the frequencies of twin kHz QPOs and spins of neutron stars in LMXBs
• On one-parametric formula relating the frequencies of twin-peak quasi-periodic oscillations
• Association of the 3:2 HFQPO Pairs with the Broad Fe K Line in XTE J1550-564 and GRO J1655-40

Cited by in corpus (1)

• Timing of accreting neutron stars with future X-ray instruments: towards new constraints on dense matter equation of state