Evidence for a 2:3 resonance in Sco X-1 kHz QPOs

Abstract

Abstract. We find evidence that the two high frequency QPOs in Sco X-1 are, more often than not, approximately in the 2:3 frequency ratio familiar from studies of black hole candidates (e.g., XTE J1550-564, Remillard et al. 2002). This implies that the double kHz QPO phenomenon in neutron stars has its origin in properties of strong-field gravity and has little to do with the rotation of a stellar surface or any magnetic field structure anchored in the star.Key words. dense matter -general relativity -stars: neutron -stars: Sco X-1 -X-rays: stars The larger pictureRecent X-ray observations showed that in some black holes, as in neutron stars, high frequency quasi-periodic oscillations (QPOs) come in pairs. This in itself suggests that the QPO phenomenon in black holes and in neutron stars may have the same origin. We think that the frequency ratios may be even more revealing.The frequencies of these QPO pairs in the first three black hole sources where they have been observed (Strohmayer 2001a,b;Remillard et al. 2002) are 300 Hz and 450 Hz (in GRO J1655-40), 42 Hz and 70 Hz (in GRS 1915+105) and 184 Hz and 276 Hz (in XTE J1550-564). Clearly, they are in a 2:3 ratio in two of the sources, and in a 3:5 ratio in the third Remillard et al. 2002).In this paper we examine the published frequency data of the well-studied source Sco X-1, a prototype of bright neutronstar candidates, to see whether the two "kHz" QPO frequencies may be in the ratio of two low integers, such as 2:3 or 3:5, as they are in black hole systems. If such a similarity were well established between neutron stars and black holes, it would imply that the "twin" high frequency QPOs originate in a mechanism operating independently of the presence of any stellar surface with its co-rotating magnetic fields. If the high frequency QPOs are fundamentally similar in neutron stars and in black holes, they are all likely to be a manifestation of strong-field gravity.Send offprint requests to: W. Kluźniak, e-mail: wlodek@camk.edu.pl The inner disc radius in neutron-star LMXBsThe kHz QPOs have fairly similar properties in a wide range of systems. In particular, the highest frequencies have similar values in X-ray bursters and the much brighter sources, such as Sco X-1 (see van der Klis 2000, for a review). This argues against any special mechanism related to accidental properties of the system, such as the value of the magnetic field or of the accretion rate (although many models based on such finely tuned properties have been proposed).If the oscillation arises in the accretion-disk flow, the orbital frequency sets the scale of expected oscillation frequencies (Bath 1973). In fact, the relevant frequency is the meridional epicyclic frequency. It is identical to the Keplerian frequency for Newtonian 1/r gravity, but in general relativity for accretion disks around neutron stars the meridional epicyclic frequency is typically somewhat smaller than the orbital frequency. Observations of a kHz frequency then strongly disfavor a geometry of accretion in which t...

High frequency QPOs, nonlinear oscillations in strong gravity

“…There are three points to be made. One is that the histogram of frequency ratios for individual neutron star sources, as well as for all of them jointly, peaks near the value 1.5 (Abramowicz, et al 2003a). This is apparent in the inset of the figure (where actually the ratio of the lower frequency to the higher is plotted, so that the peak is close to 0.67).…”

“…The common intersection point of (some of) the neutron star lines greatly strengthens the evidence for the 3:2 resonance in neutron star QPOs, as well as for the strong gravitational field origin of the high frequency QPO phenomenon. Abramowicz et al 2003a for references). Note that the neutron star points are scattered about a line intersecting the line of a 3:2 ratio in a single point ∼ (600 Hz, 900 Hz), and that all black hole frequencies are lower, consistent with a 1/M dependence.…”

Internal resonance in nonlinear disk oscillations and the amplitude evolution of neutron-star kilohertz QPOs

“…1. In this work, we explored only the 3:2 resonance, which is one of the most prominent in the data (Abramowicz et al 2003a;Török et al 2008). The examination of other resonances may be completed in an analogous way.…”

“…We chose this resonance because it is the most prominent one evident in the QPO data (Abramowicz et al 2003a;Török et al 2008). The degree of closeness to the rational ratio is expressed by the detuning parameter σ ≡ 2ω u − 3ω l .…”

Disc-oscillation resonance and neutron star QPOs: 3:2 epicyclic orbital model

“…It is however interesting that most of the twin QPOs with high statistical significance have been detected at lower QPO frequencies 600−700 Hz and upper QPO frequencies 900−1200 Hz. Because of this the twin QPO frequency ratio clusters mostly around ≈3:2 value posing thus some analogy to BH case (see Abramowicz et al 2003a;Belloni et al 2007;Török et al 2008a,b,c;Boutelier et al 2009, for details and a related discussion). In several NS sources, the difference in the amplitudes of the two peaks changes sign as their frequency ratio passes through the (same) 3:2 value (Török 2009).…”