A General Relativistic Magnetohydrodynamic Model of High Frequency Quasi-periodic Oscillations in Black Hole Low-Mass X-ray Binaries

arXiv:1003.5034v1 [astro-ph.HE] 26 Mar 2010 A General Relativistic Magnetohydrodynamic Model of High Frequency Quasi-periodic Oscillations in Black Hole Low-Mass X-ray Binaries Chang-Sheng Shi1,2,3 and Xiang-Dong Li1,2 ABSTRACT We suggest a possible explanation for the high frequency quasi-periodic os- cillations (QPOs) in black hole low mass X-ray binaries. By solving the pertur- bation general relativistic magnetohydrodynamic equations, we find two stable modes of the Alf´ven wave in the the accretion disks with toroidal magnetic fields. We suggest that these two modes may lead to the double high frequency QPOs if they are produced in the transition region between the inner advection dom- inated accretion flow and the outer thin disk. This model naturally accounts for the 3 : 2 relation for the upper and lower frequencies of the QPOs, and the relation between the black hole mass and QPO frequency. Subject headings: magnetohydrodynamics – QPOs – accretion disc – stars: black hole 1. Introduction Low-mass X-ray binaries (LMXBs) are binary systems consisting of a neutron star (NS) or black hole (BH) accreting from a low-mass (≲1M⊙) companion star. X-ray emission of LMXBs often shows fast X-ray variability in the form of high frequency quasi-periodic oscil- lations (HFQPOs), which frequently appear in pairs in certain state simultaneously (van der Klis 2006). Abramowicz & Klu´zniak (2001) pointed out that the frequency ratio of the twin- peak HFQPOs in the BH source GRO J1655-40 equals 3/2, and that this commensurability of frequencies may be a signature of a non-linear resonance. Later, Abramowicz et al. (2003) 1Department of Astronomy, Nanjing University, Nanjing 210093, China; E-mail: scs1217@gmail.com, lixd@nju.edu.cn 2Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education, Nanjing 210093, China 3College of Material Science and Chemical Engineering, Hainan University, Hainan 570228, China – 2 – found a signature of the same commensurable ratio in the twin-peak HFQPOs observed in an NS-LMXB, Sco X-1. Based on this observational evidence, Klu´zniak and Abramowicz argued in several papers (Klu´zniak & Abramowicz 2001; Klu´zniak, Abramowicz, & Lee 2004; Klu´zniak et al. 2004) that the twin-peak HFQPOs in both BH and NS sources are due to the same physical mechanism — a non-linear parametric resonance in accretion disk global oscillations. However, while for the BH sources the commensurable ratio 3/2 was quickly confirmed and generally accepted (e.g. Remillard & McClintock 2006), the presence of the same com- mensurability in the NS sources is denied by several experts (e.g. Boutelier et al., 2009). There is no consensus whether the nature of the twin-peak HFQPOs in the two types of LMXBs is the same. We have proposed a mechanism for the twin kilohertz QPOs in NS- LMXBs using the magnetohydrodynamic (MHD) Alf´ven wave oscillations, and the results seem to fit the observation well (Li & Zhang 2005; Shi & Li 2009). In this paper we focus on an MHD explanation of the HFQPOs in BH-LMXBs. Barret et al. (2005) measured the quality factor Q for the HFQPOs measured in the NS-LMXB 4U 1608-52, and found that Q ∼200. They argued that such high coherency is impossible to achieve from kinematic effects in orbital motion of hot spots, clumps or other similar features located at the accretion disk surface, because these features are too quickly sheared out by the differential rotation. Although orbital motion cannot explain the the HFQPOs in LMXBs, the frequencies of several fluid oscillatory modes are expressed by the three characteristic orbital frequencies: the “Keplerian” frequency, the “radial” epicyclic frequency, and the “vertical” epicyclic frequency. In the Kerr metric, these three orbital frequencies and the Lense-Thirring “frame-dragging” frequency have been listed (e.g. Perez et al. 1997). Several HFQPOs models use their ratios (in various combinations) to explain the observed 3/2 commensurability. Cui, Zhang, & Chen (1998) suggested the Lense-Thirring nodal precession frequency near the inner stable circular orbit (ISCO) radius as the lower HFQPO frequency, such as the 300 Hz QPOs in GRO J1655-40. The relativistic precession model of Stella et al. (1999) applies to both BH and NS sources; the pariastron precession frequency and the Keplerian frequency were taken as the lower and upper frequencies of the twin HFQPOs, respectively, whereas the QPOs at much lower frequencies were interpreted in terms of the Lense-Thirring nodal precession ferquency. Wang et al. (2003, 2005) suggested that a non-axisymmetric magnetic coupling of a rotating BH with its surrounding accretion disk coexists with the Blandford-Znajek process. The two frequencies were supposed as the Keplerian frequencies of two hotspots, one near the inner edge of the disk and the other somewhere outside, respectively. Wagoner et al. (2001) considered the modes of the diskoseismic wave, such as g-modes, – 3 – p-modes an

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