X-ray variability, viscous time scale & Lindblad resonances in LMXBs

1. X-ray variability, viscous time scale &Lindblad resonances in LMXBs Marat Gilfanov & Vadim Arefiev

2. X-ray variability in LMXBs n-1.3 power law RXTE/ASM RXTE/PCA EXOSAT Z-90, 23/12/2004

3. Timescales • observed: from ≤10-2 sec to ≥108 sec • X-ray emitting regionsize: ~3-50 Rgtimescales: ~ sec – msecthe longest timescale ~ sec Z-90, 23/12/2004

4. Timescales tvisc longest X-ray variability timescale output X-rays steady Mdot tvisc sink Z-90, 23/12/2004

5. Timescales low frequency perturbations are generated in the outer disk and propagated to the X-ray emitting region power spectrum of the outer disk inner region Z-90, 23/12/2004

6. Viscous time scale & PDS • disk – finite size tvisc - the longest time scale • power density spectrumflat at f ≤ fvisc~1/tvisc lg(P) lg(f) fvisc~1/tvisc Z-90, 23/12/2004

7. Viscous time scale a-parameterization of viscosity (Shakura & Sunayev, 1973): Z-90, 23/12/2004

8. Viscous time scale +3rd Kepler law  expected numbers:  Z-90, 23/12/2004

9. Sample of LMXBs • ~persistent • Porb is known and within accessible range • sufficiently bright • ASM (RXTE) • EXOSAT  12 sources Z-90, 23/12/2004

10. Power density spectra • low frequency break~flat @ lower freqs. • power law @higher frequencies Z-90, 23/12/2004

11. Broad band power spectra Z-90, 23/12/2004

12. Power density spectra one exception 4U1636-536 Z-90, 23/12/2004

13. Assumption break frequency viscous time scale fbreak ~fvisc = 1/tvisc Z-90, 23/12/2004

14. Cir X-1 • eccentric orbite~0.7-0.9 • Roche lobe overflow at periastron • substitution: from Johnston et al., 1999 Z-90, 23/12/2004

15. Break frequency Z-90, 23/12/2004

16. Break frequency Z-90, 23/12/2004

17. fvisc/forb • predicted: ~ 10-3-10-2observed: ~ 0.1-2 • tvisc is shorter • 2 possibilities: • Rd is smaller • VR is larger fvisc/forb Z-90, 23/12/2004

18. CV data:Hessman, 1988, Hessman & Hopp, 1990; Rutten et al., 1992; Harrop-Allin & Warner, 1996 LMXB data:Orosz & Kuulkers, 1999; Shahbaz et al., 2004; Torres et al., 2004; Zurita et al., 2000 Rd~Rtidal Disk radius Z-90, 23/12/2004

19. in standard disk theory VR H/R H/R~ few  10-2 tvisc data H/R~0.1 Disk thickness Z-90, 23/12/2004

20. Further comments • robust conclusion - H/R~10-2 would require a ~ 5-800 or Rd/a ~ 0.005-0.05 • thickness of the outer disk • appears to be supported by the eclipsers statistics Z-90, 23/12/2004

21. Semi-thick disk ? vertical optical depth of disk • disk with given H/Rt(H/R)-(123) • H/R~0.1   • contradicts to optical data standard disk + coronal flow Z-90, 23/12/2004

22. Disk + coronal flow Mdot(disk) ~ Mdot(corona) corona/disk~(Hc/Hd)-20.1 (Jimenez-Garate et al., 2002) Tcorona~10-2 Tvir~105-106 K nH~1023 cm-2 nR~1024 cm-2 Z-90, 23/12/2004

23. Chandra and XMM-Newton observations • X-ray spectroscopy of high inclination LMXBs • complex absorption and emission features • photoionized corona EXO 0748-676 from Jimenez-Garate et al., 2003 Z-90, 23/12/2004

24. Other evidence • ADC (accretion disk corona) sources • partial eclipses (~10-50 %) in LMXBs • modeling of eclipse light curves  corona parameters Z-90, 23/12/2004

25. Origin of the coronal flow • disk evaporation (Meyer & Meyer-Hofmeister, 1994, 2000) • role of irradiation • Compton cooling/heating of the corona • heating of the outer disk disk evaporation rate - simple theory Meyer & Meyer-Hofmeister, 1994, 2000 Z-90, 23/12/2004

26. Viscous time in wide and compact systems Z-90, 23/12/2004

27. Tidal resonances in binaries • resonance:Wpcommensurate withWorb • radial location of resonances: k Wp= mWorbR/a=(k/m)2/3(1+q)-1/3 • strongest - low order resonances Wp Worb Z-90, 23/12/2004

28. Tidal resonances • disk extends to the resonance radius • 2:1 resonance: q<0.02 • 3:1 resonance: q<0.35 • superhumps in CVs Z-90, 23/12/2004

29. SPH simulations q=0.07 t=6 Porb t=90 Porb t=190 Porb From Truss et al., 2002 Z-90, 23/12/2004

30. Tidal resonances 3:1 resonance: q<0.35 detection of superhumps in LMXBs, incl. 4U1916-053 (e.g. Callanan et al., 1995; Haswell et al., 2001) Z-90, 23/12/2004

31. How does it work ? • disk truncation – unlikely • mass transfer in tidal waves • extra heating in the outer disk by tidal fources • non-trivial definition of the tvisc for an eccentric precessing disk Z-90, 23/12/2004

32. GRS1915+105 transient source: • Rdisk ~ Rcirc < Rrescf. CVs - no superhumps in normal outbursts • tidal instab. growth time(Whitehurst & King, 1991; Lubow, 1991)t  102Porb~10 yrs fvisc/forb=Porb/tvisc ? Z-90, 23/12/2004

33. Conclusions • features in PDS due to viscous time of the disk • coronal flow with H/R~0.1Mdot(corona) ~ Mdot(disk) • 3:1 Lindblad resonances in small-q systems Z-90, 23/12/2004

34. The End Z-90, 23/12/2004

35. Power density spectra Z-90, 23/12/2004

36. Power density spectra Z-90, 23/12/2004

37. Tidal resonances. • disk extends to the resonance radius • 2:1 resonance: q<0.02 • 3:1 resonance: q<0.35 Z-90, 23/12/2004

38. Power density spectra • two possible exceptions4U1820-303 & 4U1636-536 Z-90, 23/12/2004

39. 4U1820-303 Z-90, 23/12/2004

40. 4U1636-536 Z-90, 23/12/2004

41. Break frequency Z-90, 23/12/2004

42. Viscous time in wide and compact systems Z-90, 23/12/2004

43. Break frequency Z-90, 23/12/2004