1. A physical interpretation of variability in X-ray binaries Adam Ingram Chris Done P Chris Fragile Durham University

2. The truncated disc model Cool, optically thick disc thermalises to emit a multi coloured black body spectrum Hot electrons in high scale height, optically thin flow Compton upscatter disc seed photons to give power law emmission Moving truncation radius varies the number of seed photons seen by the flow XTE 1550-564

3. The truncated disc model Moving truncation radius varies the number of seed photons seen by the flow XTE 1550-564

4. The truncated disc model Moving truncation radius varies the number of seed photons seen by the flow XTE 1550-564

5. The truncated disc model Moving truncation radius varies the number of seed photons seen by the flow XTE 1550-564

6. The truncated disc model Moving truncation radius varies the number of seed photons seen by the flow XTE 1550-564

7. The truncated disc model Moving truncation radius varies the number of seed photons seen by the flow XTE 1550-564

8. The truncated disc model Moving truncation radius varies the number of seed photons seen by the flow XTE 1550-564

9. The truncated disc model Moving truncation radius varies the number of seed photons seen by the flow XTE 1550-564

10. Summary of variability features ν QPO XTE 1550-564 Red = above 10keV Black = total

11. Summary of variability features ν QPO νhνh νbνb XTE 1550-564 Red = above 10keV Black = total

12. Summary of variability features ν QPO νhνh νbνb XTE 1550-564 Red = above 10keV Black = total Want to explain QPO AND the broadband noise continuum

13. QPO Model: Lense-Thirring precession of the flow a * =0.5 a * =0.9

14. Modeling the broadband noise log[ v P( v )] log[v] v visc at:roro riri vbvb vhvh Lense-Thirring QPO (Ingram, Done & Fragile 2009 – IDF09)

15. log[ v P( v )] log[v] Lense-Thirring QPO (Ingram, Done & Fragile 2009 – IDF09) Upper and lower kHz QPOs: is the upper the Keplerian frequency at the truncation radius (e.g. Stella & Veitri 1998)? vbvb vhvh Modeling the broadband noise v visc at:roro riri

16. log[ v P( v )] log[v] Lense-Thirring QPO (Ingram, Done & Fragile 2009 – IDF09) Upper and lower kHz QPOs: is the upper the Keplerian frequency at the truncation radius (e.g. Stella & Veitri 1998)? vbvb vhvh Modeling the broadband noise v visc at:roro riri

17. log[ v P( v )] log[v] Lense-Thirring QPO (Ingram, Done & Fragile 2009 – IDF09) Upper and lower kHz QPOs: is the upper the Keplerian frequency at the truncation radius (e.g. Stella & Veitri 1998)? vbvb vhvh Modeling the broadband noise v visc at:roro riri

18. Analysis of 4U 1728+34 and 4U 0614+09 Data from van Straaten et al (2002)Ingram & Done (2010) vhvh riri Atolls show kHz QPOs – assume v ukHz = v kep (r o ) (e.g. Stella & Vietri 1999) Therefore, we can “SEE” the truncation radius! Assume: v visc (r) ~ α(h/r) 2  = Ar -β …but the parameters can change throughout the evolution of the spectrum

19. Analysis of 4U 1728+34 and 4U 0614+09 Atolls show kHz QPOs – assume v ukHz = v kep (r o ) (e.g. Stella & Vietri 1999) Therefore, we can “SEE” the truncation radius! Assume: v visc (r) ~ α(h/r) 2  = Ar -β …but the parameters can change throughout the evolution of the spectrum Data from van Straaten et al (2002)Ingram & Done (2010) vhvh riri

20. Analysis of 4U 1728+34 and 4U 0614+09 Atolls show kHz QPOs – assume v ukHz = v kep (r o ) (e.g. Stella & Vietri 1999) Therefore, we can “SEE” the truncation radius! Assume: v visc (r) ~ α(h/r) 2  = Ar -β …but the parameters can change throughout the evolution of the spectrum Data from van Straaten et al (2002)Ingram & Done (2010) vhvh riri

21. Analysis of 4U 1728+34 and 4U 0614+09 Atolls show kHz QPOs – assume v ukHz = v kep (r o ) (e.g. Stella & Vietri 1999) Therefore, we can “SEE” the truncation radius! Assume: v visc (r) ~ α(h/r) 2  = Ar -β …but the parameters can change throughout the evolution of the spectrum Data from van Straaten et al (2002)Ingram & Done (2010) vhvh riri

22. v h = v visc (r i ) = Ar i -β => r i = [A/v h ] 1/β ~ r * Analysis of 4U 1728+34 and 4U 0614+09

23. v h = v visc (r i ) = Ar i -β => r i = [A/v h ] 1/β ~ r * Analysis of 4U 1728+34 and 4U 0614+09 => r * ~ 4.5Rg ~ 9.2km

24. Testing Lense-Thirring precession ζ=0 works quite well

25. Testing Lense-Thirring precession ζ=0 works quite well Increasing ζ works very well!

26. Conclusions Use model designed to describe the energy spectra in order to explain – the LF QPO, – the broadband noise continuum and – the ukHz QPO This also predicts the sigma-flux relation and time lags between hard and soft X-ray bands

27. Thank you!

28. Lense-Thirring precession An orbiting particle can be described by the coordinates φ(t), θ(t) and r(t) which vary periodically with frequency, ν In Newtonian orbits ν φ = ν θ = ν r which gives elliptical orbits with fixed axes and fixed orbital plane. φ θ r y x z y x ν φ ≠ ν r => Precession of an ellipse

29. Lense-Thirring precession An orbiting particle can be described by the coordinates φ(t), θ(t) and r(t) which vary periodically with frequency, ν In Newtonian orbits ν φ = ν θ = ν r which gives elliptical orbits with fixed axes and fixed orbital plane. φ θ r y x z z ν φ ≠ ν θ => Lense-Thirring precession

30. Where is the inner edge? The surface density is influenced by the shape of the flow Warps propagated by bending waves which: allow solid body precession, give it a weird shape at small r! Waves can turn over at r~ λ/4 so this is where the shape goes weird! λ α r 9/4 a * -1/2 r i α r i 9/4 a * -1/2 r i α a * 2/5

31. Solid body precession of the flow But we’re NOT looking at point particles! Optically thin flowOptically thick disc Geometrically thick, advection prominent, hard spectrum Geometrically thin, blackbody spectrum Warps from differential twisting communicated by wavelike diffusion Warps from differential twisting communicated by viscous diffusion Warps propagated outwards at the local sound speed Warps propagated outwards at the local viscous speed Sound crossing timescale < precession timescale Viscous timescale < precession timescale only at small r Flow precesses as a solid bodyBardeen-Petterson effect

32. Solid body precession of the flow

40. Modelling the broadband noise Large scale height flow => MRI fluctuations In a given annulus of the flow, the MRI produces a white noise of fluctuations Mass accretion rate (luminosity) cannot vary on shorter timescales than the local viscous timescale (flow response) × = This gives the noise spectrum GENERATED at each annulus e.g. Psaltis & Norman 2000e.g. Balbus & Hawley 1998

41. Propagating fluctuations This gives the noise spectrum EMMITED at each annulus e.g. Lyubarskii 1997; Arevalo & Uttley 2007

42. Total power spectrum νhνh νbνb Therefore, this model gives: ν b =ν visc (r o ) ν h =ν visc (r i )

43. Black holes vs Neutron stars ν QPO νhνh νbνb XTE 1550-564 Red = above 10keV Black = total

44. Black holes vs Neutron stars 4U 1728-34 ν QPO νhνh νbνb ν ukHz (ν lkHz ) All frequencies slightly higher, consistent with mass scaling

45. QPO Model: Lense-Thirring precession of the flow a * =0.5 a * =0.9