Adam Ingram Chris Done P Chris Fragile A

The truncated disc model Cool, optically thick disc thermalises to emit a multi coloured

The truncated disc model XTE 1550 -564 Moving truncation radius varies the number of

Summary of variability features XTE 1550 -564 Red = above 10 ke. V Black

Summary of variability features XTE 1550 -564 νb νQPO νh Red = above 10

QPO Model: Lense -Thirring precession of the flow a *=0. 9 a *=0. 5

Modeling the broadband noise ro ri vb vh log [v P (v )] v

Modeling the broadband noise ro ri vb vh log[v. P(v)] v visc at: Upper

Analysis of 4 U 1728+34 and 4 U 0614+09 • Atolls show k. Hz

Analysis of 4 U 1728+34 and 4 U 0614+09 v h = v visc

Testing Lense -Thirring precession • ζ=0 works quite well

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

Conclusions • Use model designed to describe the energy spectra in order to explain

Lense-Thirring precession • • An orbiting particle can be described by the coordinates φ(t),

Where is the inner edge? • • The surface density is influenced by the

Solid body precession of the flow • But we’re NOT looking at point particles!

Modelling the broadband noise × • Large scale height flow => MRI fluctuations •

Propagating fluctuations This gives the noise spectrum EMMITED at each annulus e. g. Lyubarskii

Total power spectrum νb νh Therefore, this model gives: ν b =ν visc (r

Black holes vs Neutron stars XTE 1550 -564 νb νQPO νh Red = above

Black holes vs Neutron stars 4 U 1728 -34 νb νQPO All frequencies slightly

Slides: 45

Download presentation

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

The truncated disc model Cool, optically thick disc thermalises to emit a multi coloured black body spectrum XTE 1550 -564 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

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

Summary of variability features XTE 1550 -564 Red = above 10 ke. V Black = total νQPO

Summary of variability features XTE 1550 -564 νb νQPO νh Red = above 10 ke. V Black = total

Summary of variability features XTE 1550 -564 νb νQPO νh Red = above 10 ke. V Black = total Want to explain QPO AND the broadband noise continuum

QPO Model: Lense -Thirring precession of the flow a *=0. 9 a *=0. 5

Modeling the broadband noise ro ri vb vh log [v P (v )] v visc at: Lense-Thirring QPO (Ingram, Done & Fragile 2009 – IDF 09) log[ v ]

Modeling the broadband noise ro ri vb vh log[v. P(v)] v visc at: Upper and lower k. Hz QPOs: is the upper the Keplerian frequency at the truncation radius (e. g. Stella & Veitri 1998)? Lense-Thirring QPO (Ingram, Done & Fragile 2009 – IDF 09) log[v]

Analysis of 4 U 1728+34 and 4 U 0614+09 • Atolls show k. Hz QPOs – assume v uk. Hz = 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 vh Data from van Straaten et al (2002) ri Ingram & Done (2010)

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

Analysis of 4 U 1728+34 and 4 U 0614+09 v h = v visc (r i) = Ar i-β => r i = [A/ v h ]1/β ~ r * => r * ~ 4. 5 Rg ~ 9. 2 km

Testing Lense -Thirring precession • ζ=0 works quite well

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

Conclusions • Use model designed to describe the energy spectra in order to explain – the LF QPO, – the broadband noise continuum and – the uk. Hz 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 νφ = νθ = νr which gives elliptical orbits with fixed axes and fixed orbital plane. νφ ≠ νr => z r y θ φ x y x Precession of an ellipse

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! λ α r 9/4 a*-1/2 • Waves can turn over at r~ λ/4 so this is where the shape goes weird! ri α ri 9/4 a*-1/2 ri α a*2/5

Solid body precession of the flow • But we’re NOT looking at point particles! Optically thin flow Optically 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 body Bardeen-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) e. g. Balbus & Hawley 1998 = e. g. Psaltis & Norman 2000 This gives the noise spectrum GENERATED at each

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

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

Black holes vs Neutron stars XTE 1550 -564 νb νQPO νh Red = above 10 ke. V Black = total

Black holes vs Neutron stars 4 U 1728 -34 νb νQPO All frequencies slightly higher, consistent with mass scaling νuk. Hz (ν lk. Hz ) νh

QPO Model: Lense -Thirring precession of the flow a *=0. 9 a *=0. 5