Black holes in Einstein General Relativity Prof Chris
Black holes in Einstein General Relativity Prof Chris Done, University of Durham
Lecture 1 -2 recap: • Black holes and neutron stars binaries both show major spectral transition from sum of blackbody disc dominated to compton tail dominated. • Comparison shows evidence for existance of event horizon in BH • So what is it? ? • Done, Gierlinski & Kubota 2007
Spectral transitions in BHB Disk dominated Comptonised spectrum Gierlinski et al 1999
Variability of disc: short timescale 0. 5 1. 0 2. 0 • Timescale to change mass accretion rate through disc • tvisc= a-1 (H/R)-2 torb =5 a-1 (H/R)-2 (r/6) -3/2 ms • ~ 500 s at last stable orbit for 10 M • No rapid variability of disc
Low/hard state variability 0. 5 1. 0 2. 0 • Low/Hard state variability down to few 10 s of ms • tvisc= a-1 (H/R)-2 tdyn = 5 a-1 (H/R)-2 (r/6) -3/2 ms • IF viscous timescale then H/R~1
• Low L/Ledd: another stable solution of accretion flow • Hot, optically thin, geometrically thick inner flow replacing the inner disc (Shapiro et al. 1976; Narayan & Yi 1995 - ADAF) • No disc so seed photons for compton from thermal electrons spiraling round B field (cyclo-sync) Log n fv(n) Accretion flows without discs Log n
Moving disc – moving QPO • Energy spectra need disc to move from 50 -6 ish Rg as make transition DGK 07
Seed photons in low/hard state • Low/hard state outburst • Swift optical/UV/X-ray plus RXTE 3 -200 ke. V • Low Nh (2 x 1021 cm-2) • Factor 10 ↓ in 3 months • Seed photons disc at peak • Probably cyclo-sync later 3 months x 10 Chiang & Done 2009
Variability of disc: short timescale 0. 5 1. 0 2. 0 • Timescale to change mass accretion rate through disc • tvisc= a-1 (H/R)-2 torb =5 a-1 (H/R)-2 (r/6) -3/2 ms • ~ 500 s at last stable orbit for 10 M • No rapid variability of disc
0. 5 1. 0 2. 0 Low/hard state variability- QPO
Quantifying variability: the power spectral density (PSD) of Cyg X-1 P(f) f 0 Phil Uttley P(f) f-2
0. 5 1. 0 2. 0 Low/hard state variability- QPO
XTE J 1550564
fb XTE J 1550564 fh
f. QPO XTE J 1550564
Moving disc – moving QPO • Energy spectra need disc to move from 50 -6 ish Rg as make transition • Power spectra: low frequency break moves, high frequency power more or less constant! Large radius moves, Small radii constant • Low frequency QPO moves with low frequency break • QPO big, must be fundamental DGK 07
Low frequency QPO • Spectra need disc to move from Rtr = 50 -6 ish Rg as make transition • Observed QPO frequencies go from ~0. 110 Hz • See similar range in ALL BHB – so either all BHB have same spin or not much spin dependence on QPO • Not n(j) as too fast! Ingram, Done & Fragile 2009
Low frequency QPO • Stella & Vietri 1998 – GR potential not spherically symmetric so vertically offset circular orbit has n(q) ≠ n(j) • Lense-Thirring precession n. LT = n(q) - n(j) Lamb & Markovic
Does it work ? • Not really • Edge of disc would have blackbody spectrum. QPO has spectrum of hot inner flow! Zycki & Sobolewska 2005; 2006 Ingram, Done & Fragile 2009
a < H/R precession a > H/R Ingram, Done & Fragile 2009 Warped disc
LT precession of hot flow? • Truncates at ~ bending wave radius • QPO frequency given by weighted average of LT precession frequency over all radii in hot flow • Gets the frequencies correct!! • Modulates Compton region so gets spectrum! Ingram, Done & Fragile 2009
QPO and broadband noise • Low frequency QPO moves with low frequency break • Same relation for BH and NS Wijnands & van der Klis 1989
Krolik, de Villiers, Hawley Origin of variability: MRI
Propagating fluctuations Pf • But emission depends on Mdot • Mdot can’t vary on shorter timescales than the local viscous timescale, tvisc(r) MRI f
Propagating fluctuations Pf • But emission depends on Mdot • Mdot can’t vary on shorter timescales than the local viscous timescale, tvisc(r) Mdot f
Propagating fluctuations f Pf • But emission depends on Mdot • Mdot can’t vary on shorter timescales than the local viscous timescale, tvisc(r) Kotov et al 2001; Arevelo & Uttley 2006 f
Propagating fluctuations f Pf • But emission depends on Mdot • Mdot can’t vary on shorter timescales than the local viscous timescale, tvisc(r) Kotov et al 2001; Arevelo & Uttley 2006 f
Propagating fluctuations f Pf • But emission depends on Mdot • Mdot can’t vary on shorter timescales than the local viscous timescale, tvisc(r) Kotov et al 2001; Arevelo & Uttley 2006 f
Propagating fluctuations f Pf • But emission depends on Mdot • Mdot can’t vary on shorter timescales than the local viscous timescale, tvisc(r) Kotov et al 2001; Arevelo & Uttley 2006 f
The rms-flux relation of Cygnus X-1 [Uttley & Mc. Hardy 2001 (UM 01)] 1 s segments 0 1 2 3 4 5 6 7 8 rms = sqrt [ (1/N) ∑i=1, N (fluxi - 9 10 mean)2 ] Linear rms-flux relations are also seen in AGN, e. g. NGC 4051 (UM 01, Mc. Hardy et al. 2004) Unbinned 2 -20 Binned 2 -20 Hz. Hz rms vs. vs flux NGC 4051 rms-flux
Flux distribution of variability Has very characteristic shape – not symmetric. Skewed to higher flux levels. Lightcurve is ‘flare-y’ Uttley, Mc. Hardy & Vaughan 2005
Implies log normal flux distribution Normalised flux -0. 2 0 0. 2 log (flux) Cannot get this from SHOTS, or any SUM of independent events Or from self organised criticality (wait till critical value to trigger) Uttley, Mc. Hardy & Vaughan 2005
Origin of variability The model is multiplicative, not additive: fractional mdot variations on different time-scales multiply together: Uttley 2006
fh log[f. P(v)] fb log[f]
fh log[f. P(v)] fb log[f]
fh log[f. P(v)] fb log[f]
Fitting to XTE J 1550 -564 ro=68. 0
Fitting to XTE J 1550 -564 ro=45. 7
Fitting to XTE J 1550 -564 ro=25. 0
Fitting to XTE J 1550 -564 ro=16. 3
Fitting to XTE J 1550 -564 ro=12. 8 Ingram & Done 2011
Moving disc – moving QPO • Energy spectra need disc to move from 50 -6 ish Rg as make transition • Power spectra: low frequency break moves, high frequency power more or less constant! Large radius moves, Small radii constant • Low frequency QPO moves with low frequency break • QPO big, must be fundamental DGK 07
High L/Ledd? • Complex spectra as L~Ledd ? • Or when it changes rapidly • But not many sources get to Ledd… • Accretion discs are often unstable in binary systems - transients
• • Differential Keplerian rotation Viscosity B: gravity heat Thermal emission: L = As. T 4 Temperature increases inwards until minimum radius Rlso(a*) For a*=0 and L~LEdd Tmax is • 1 ke. V (107 K) for 10 M • 10 e. V (105 K) for 108 M Log n f(n) Spectra of accretion flow: disc Log n
Disc instabilities –H ionisation • Steady state has d. M/dt = constant at all radii • Then balance heating=cooling at each radius • Heating from gravity via viscosity. Cooling from radiation diffusing out from disc (depends on optical depth) • Hydrogen ionisation instability as cooling no longer efficient
As seen in most BH in our galaxy J. Orosz • Transient outer disc k. T < 4000 K (H ionisation) • Small Mdot and/or large outer radius • Persistent – need large mdot and/or small
Disc instabilities –H ionisation
NS smaller - likely to be stable
Disc instabilities • Radiation pressure instability • Heating Q = a P= a(Pgas+Prad) = a(nk. T +s. T 4) • Stabilized by advection cooling (radial transport of radiation)
HMXRB • wind accretion from high mass companion • Overflows roche lobe only if close enough • If not quite close enough then wind gets focussed onto blakc hole (like Cyg X-1)
Ultraluminous X-ray sources ULX • L~1039 -40 ergs s-1 in spiral arms of nearby starforming galaxies • M~10 -100 M L <Ledd • Single star evolution BH <~ 50 M • Either IMBH (hard to make) or (majority) are L/LEdd > 1 HMXRB • Mildly supereddington onto 30 M BH? • Highly supereddington onto magnetic NS!!!? ? ? Gao et al 2003
Conclusions • Transitions can be explained as advection dominated/radiatively inefficient flow at low L/Ledd collapsing to radiatively efficient thin disc • Fits spectral evolution and PREDICTS evolution of fast variability – origin of QPO • …. . to be continued….
- Slides: 54