1. Correlations Between the Twin kHz QPO Frequencies in Neutron Star Low-Mass X-ray Binaries 尹红星 张承民 NAOC, CAS April 22th, 2006

2. Outline kHz QPOs in neutron star LMXBs Basic models A typical Z source: Sco X-1 Power law correlations in Atoll and Z sources Power law and linear correlations in 4 Atoll and 4 Z sources and their chi-square tests

3. kHz QPOs in NS LMXBs QPO in NS LMXBs NBO, ~5 Hz HBO, ~20-70 Hz Hundred, ~100 Hz kHz, ~300-1300 Hz Burst oscillation, ~300 Hz Spin frequency, ~300 Hz Low, high QPO, ~0.1 Hz Etc. Sco X-1, van der Klis et al. 1997

4. kHz QPOs in NS LMXBs See: Zhang, C.M., et al., 2006 19 twin kHz QPO sources 6 Z + 11 Atoll + 2 AMXP XTE J1807-294(Linares 2005 and Zhang, F., et al., 2006)

5. Basic models Basic models for kHz QPOs i.Beat-Frequency Model (Stroh. et al. 1996; Miller 1998) ii.Resonance Model (Abramowicz et al. 2003) iii.Relativistic Precession Model(Stella and Vietri 99 etc.) iv.Alfven Wave Oscillation Model(Zhang 04; Li & Zhang 05)

6. A typical Z source: Sco X-1 Yin et al. 2005 Psaltis et al 1998

7. Power law correlations in Atoll and Z sources See: Zhang, C.M., et al., 2006 i.The power law index b is somewhat larger in Z sources than that in Atoll sources. ii.The data of Z sources show a inflexion around 840Hz of the upper kHz QPO frequencies.

8. Power law correlations in Atoll and Z sources

9. Chi-square tests: i.For the typical Z source Sco X-1and the typical Atoll source 4U 1728-34, their reduced chi-squares are smaller than 1. But for all Z and Atoll data, those are much larger than 1. ii.The distribution and reduced chi- squares of the averaged peak separation and peak ratio are all much larger than 1, which incompatible with the constant peak separation and constant peak ratio predicted by beat-frequency model and resonance model, respectively. iii.But the power law correlations between the twin kHz QPOs consist with the relativistic precession model and the Alven wave oscillation model.

10. Power law and linear correlations in 4 Atoll and 4 Z sources Power law correlations following Psaltis et al. (1999)

11. Power law and linear correlations in 4 Atoll and 4 Z sources Linear correlations following Belloni et al. (2005)

12. Power law and linear correlations in 4 Atoll and 4 Z sources Chi-square tests

13. Power law and linear correlations in 4 Atoll and 4 Z sources The chi-square tests indicate that, for a individual source, both the power law model and the linear model can fit the data well. By now, we cannot discuss which model is better. Need more data?……

14. Thanks!