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

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

The truncated disc model Moving truncation radius varies the number of seed photons seen by the flow XTE

The truncated disc model Moving truncation radius varies the number of seed photons seen by the flow XTE

The truncated disc model Moving truncation radius varies the number of seed photons seen by the flow XTE

The truncated disc model Moving truncation radius varies the number of seed photons seen by the flow XTE

The truncated disc model Moving truncation radius varies the number of seed photons seen by the flow XTE

The truncated disc model Moving truncation radius varies the number of seed photons seen by the flow XTE

The truncated disc model Moving truncation radius varies the number of seed photons seen by the flow XTE

Summary of variability features ν QPO XTE Red = above 10keV Black = total

Summary of variability features ν QPO νhνh νbνb XTE Red = above 10keV Black = total

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

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

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)

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

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

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

Analysis of 4U and 4U 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

Analysis of 4U and 4U 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

Analysis of 4U and 4U 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

Analysis of 4U and 4U 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

v h = v visc (r i ) = Ar i -β => r i = [A/v h ] 1/β ~ r * Analysis of 4U and 4U

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

Testing Lense-Thirring precession ζ=0 works quite well

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

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

Thank you!

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

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

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

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

Solid body precession of the flow

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

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

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

Black holes vs Neutron stars ν QPO νhνh νbνb XTE Red = above 10keV Black = total

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

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