Statistical properties of twin kilohertz quasi‐periodic oscillations in neutron star low‐mass X‐ray binaries

Abstract

We collect the data of twin kilohertz quasi-periodic oscillations (kHz QPOs) published before 2012 from 26 neutron star (NS) low-mass X-ray binary (LMXB) sources, then we analyze the centroid frequency (ν) distribution of twin kHz QPOs (lower frequency ν1 and upper frequency ν2) both for Atoll and Z sources. For the data without shift-and-add, we find that Atoll and Z sources show the different distributions of ν1, ν2 and ν2/ν1, but the same distribution of ∆ν (difference of twin kHz QPOs), which indicates that twin kHz QPOs may share the common properties of LXMBs and have the same physical origins. The distribution of ∆ν is quite different from constant value, so is ν2/ν1 from constant ratio. The weighted mean values and maxima of ν1 and ν2 in Atoll sources are slightly higher than those in Z sources. We also find that shift-and-add technique can reconstruct the distribution of ν1 and ∆ν. The K-S test results of ν1 and ∆ν between Atoll and Z sources from data with shift-and-add are quite different from those without it, and we think that this may be caused by the selection biases of the sample. We also study the properties of the quality factor (Q) and the root-mean-squared (rms) amplitude of 4U 0614+09 with the data from the two observational methods, but the errors are too big to make a robust conclusion. The NS spin frequency (νs) distribution of 28 NS-LMXBs show a bigger mean value (∼ 408 Hz) than that (∼ 281 Hz) of the radio binary millisecond pulsars (MSPs), which may be due to the lack of the spin detections from Z sources (systematically lower than 281 Hz). Furthermore, on the relations between the kHz QPOs and NS spin frequency νs, we find the approximate correlations of the mean values of ∆ν with NS spin and its half, respectively.

The impact of neutron star spin on X-ray spectra

“…Spin frequencies correspond to burst oscillation frequencies presented by Galloway et al (2008) and Strohmayer et al (2008) (in the case of 4U 0614+09). * * For 4U 1705 − 44 we quote the difference in kHz QPO frequencies as an approximation of the true spin frequency (Ford et al 1998), baring in mind the possible uncertainties inherent to this method of spin determination (Wang et al 2014).…”

“…Early studies noted that the measured difference in frequencies of the two kHz QPO was compatible with either the NS spin frequency or its half, depending on the source (van der Klis 2000;Psaltis 2001). This scenario is attractive in the context of beat frequency models, where the lower frequency QPO arises from the beat between the upper kHz QPO and spin frequency (Miller et al 1998;Lamb & Miller 2001 Wang et al (2014) plot 12 sources with measured kHz QPO pairs against spin, and conclude there is a 'clustering with a high scatter' around ∆ν kHz ≈ 0.5νspin and ∆ν kHz ≈ νspin, but it is not clear whether there is a relationship. It was also found that the kHz-QPO frequency correlates with the X-ray flux and spectral shape as characterised by the position on the colour-colour diagram (Méndez et al 1999;Barret 2001).…”

Test of the string loop oscillation model using kHz quasiperiodic oscillations in a neutron star binary

“…In the LMXB systems containing a black hole, so called microquasars, the twin HF QPOs occur at fixed frequencies that are usually at the exact 3 : 2 ratio [46]. On the other hand, in the LMXB systems containing a neutron star, large scatter of the twin HF QPOs is observed, and their frequency ratio varies across the frequency ratio 3 : 2 down to 5 : 4 ratio in the atoll sources [6,8,74,85,86], while it varies in the range 4 : 1 to 2 : 1 in the Z-source Circinus X1 [13,75].…”

Kilohertz quasi-periodic oscillations as probes of the X-ray color-color diagram and neutron star accretion-disk structure for Z sources

“…Twin kilohertz quasi-periodic oscillations (kHz QPOs) have been detected both in atoll and Z sources by the Rossi X-ray Timing Explorer (RXTE; van der Klis et al 2006). These high frequency QPOs usually appear in pairs (lower ν 1 and upper ν 2 ) in the frequency range of 100−1300 Hz (Wang et al 2014), and show a nonlinear relation between ν 1 and ν 2 (Belloni et al 2005(Belloni et al , 2007Zhang et al 2006). The frequencies of kHz QPOs often increase monotonically along both the atoll tracks (e.g., Di Salvo et al 2001;van Straaten et al 2000van Straaten et al , 2003Altamirano et al 2008) andZ tracks (e.g., van der Klis et al 1996;Wijnands et al 1997aWijnands et al , 1998aHoman et al 2002;Jonker et al 2002;Lin et al 2012), which also show an indirect correlation with the NS spin frequency, and with other temporal and spectral features (e.g., Ford & van der Klis 1998;Jonker et al 1998;Kaaret et al 1998;Psaltis et al 1999;Belloni et al 2002;Di Salvo et al 2003;Méndez 2006;Ribeiro et al 2017;Zhang et al 2017;Troyer et al 2018;van Doesburgh & van der Klis 2019).…”