1. Accretion flows onto black holes
Chris Done
University of Durham

2. Observed disc spectra Bewildering variety
Pick ONLY ones that look like a disc!
L/LEdd T4max (Ebisawa et al 1993; Kubota et al 1999; 2001)
Constant size scale – last stable orbit!!
Proportionality constant gives a measure Rlso i.e. spin
Consistent with low to moderate spin not extreme spin nor extreme versions of higher dimensional gravity - braneworlds (Gregory, Whisker, Beckwith & Done 2004)

3. Disc spectra: last stable orbit
Bewildering variety
Pick ONLY ones that look like a disc!
L/LEdd T4max (Ebisawa et al 1993; Kubota et al 1999; 2001)
Constant size scale – last stable orbit!!
Proportionality constant gives a measure Rlso i.e. spin
Consistent with low to moderate spin not extreme spin nor extreme versions of higher dimensional gravity - braneworlds (Gregory, Whisker, Beckwith & Done 2004)
Gierlinski & Done 2003

4. But rest are not simple…
Bewildering variety of spectra from single object
Underlying pattern
High L/LEdd: soft spectrum, peaks at kTmax often disc-like, plus tail
Lower L/LEdd: hard spectrum, peaks at high energies, not like a disc
Gierlinski & Done 2003

5. Compton scattering theory
eout
ein
Collision – redistribute energy
If photon has more energy than electron then it loses energy – downscattering
If photon has less energy than electron then it gains energy – upscattering
Easiest to talk about if scale energies to mc2
Electron energy gmc2 just denoted g or Q=kT/mc2
Photon energy becomes e=hn/mc2=E/511 for E (keV) g
De/e ~ 4Q – e
De/e ~ max(g2,g)

6. How much scattering ?
Compton scattering seed photons from accretion disk. Photon energy boosted by factor De/e ~ 4Q if thermal in each scattering.
Number of times scattered given by optical depth, t=snR
Scattering probability exp(-t)
Optically thin t << 1 prob ~ t average number ~ t
Optically thick t>>1 prob~1
and average number ~ t2
Total fractional energy gain = frac.gain in 1 scatt x no.scatt R
Compton y ~ 4Q (t+t2)

7. Optically thin thermal compton
power law by multiple scattering of thermal electrons f (e)  e-a
index a=log(prob)/log(energy boost) ~ -log t/log (1+4Q)
More generally depends on t, Q (or y) steeper if small t, and/or Q
BUT BUMPY spectrum if t <<1
Log N(g)
Log fn
Log g
Log n

8. Optically thin thermal compton
power law by multiple scattering of thermal electrons f (e)  e-a
index a=log(prob)/log(energy boost) ~ -log t/log (1+4Q)
More generally depends on t, Q (or y) steeper if small t, and/or Q
BUT BUMPY spectrum if t <<1
Log N(g)
Log fn
Log g
Log n

9. Spectral index a~0.6 so t~1 smooth spectrum as seen!
Cyg X-1: Gierlinski et al 1999
kTe~ 100keV so Q>0.2
Spectral index a~0.6 so t~1 smooth spectrum as seen!

10. Spectral index a~1.2 so t=0.02 so should be bumpy! But its smooth!!!
Cyg X-1: Gierlinski et al 1999
kTe> 500keV so Q>1
Spectral index a~1.2 so t=0.02 so should be bumpy! But its smooth!!!

11. Optically thin nonthermal compton
power law by single scattering of nonthermal electrons N (g)  g-p
index a = (p-1)/2
Starts a factor t down from seed photons, extends to gmax2 ein
Ends at gmax
f(e)  e-(p-1)/2
Log N(g)
Log nfn
N (g)  g-p
Log g
gmax
ein
Log n
gmax2 ein

12. Nonthermal - single scattering
Cyg X-1: Gierlinski et al 1999
Nonthermal - single scattering
kTbb=0.2 keV boosted by g2 to emax = gmax2 kTbb> 1000 keV so gmax > 70!!!
Spectral index a=1.2=(p-1)/2 so N(g)=g-3.4 not dependent on t for nonthermal! So harder to constrain t

13. Hardness – intensity diagram
Outburst starts hard, source stays hard as source brightens
Then softens to intermediate/very high state/steep power law state major hard-soft state transition
Then disc dominated, then hardens to make transition back to low/hard state – hysteresis as generally at lower L
Fender Belloni & Gallo 2004

14. And the radio jet… link to spin?
No special mQSO class – they ALL produce jets, consistent with same radio/X ray evolution
Jet links to spectral state
Steady jet in low/hard state, power depends on accretion rate! i.e. L/LEdd (Merloni et al 2003; Falke et al 2004)
so jet powered by mass accretion rate ie gravity
Bright radio flares in rapid low/hard to high/soft associated with outbursts. (Fender et al 2004)
Scaling these models up to the supermassive black holes in quasars, the only change should be that the disc emission is in the UV rather than X-ray region. The problem is knowing how far to scale them for an individual qso, knowing the BH mass. This has only recently become possible with the discovery of the relationships between the BH mass and the properties of the galaxy as a whole. Big BH live in big galaxies, little BH live in small ones. Also, only recently that enough high s/n data has become available to test these models – xmm-newton database
Gallo et al 2003

15. Accretion flows without discs
Disc models assumed thermal plasma – not true at low L/LEdd
Instead: hot, optically thin, geometrically thick inner flow replacing the inner disc (Shapiro et al. 1976; Narayan & Yi 1995)
Hot electrons Compton upscatter photons from outer cool disc
Few seed photons, so spectrum is hard
Jet from large scale height flow velocity linked to launch radius
Log n f(n)
The disc models assumed that the emission thermalised. That’s not necessarily true at low L/Ledd where the flow is not very dense. If its not thermalising then its not cooling as efficiently so the flow heats up. This can lead to a hot, optically thin, geometrically thick inner flow replacing the inner disc. The hot electrons in this flow can compton upscatter any low energy photons from a residual outer disc, but there are not many of these, so the spectrum is hard
Log n

16. Moving disc – moving QPO
Low frequency QPO – very strong feature at softest low/hard and intermediate and very high states (disc+tail)
Moves in frequency: correlated with spectrum
Moving inner disc makes sense of this. Disc closer in, higher f QPO. More soft photons from disc so softer spectra (di Matteo et al 1999)
DGK07

17. Accretion flows without discs
Disc models assumed thermal plasma – not true at low L/LEdd
Instead: hot, optically thin, geometrically thick inner flow replacing the inner disc (Shapiro et al. 1976; Narayan & Yi 1995)
Hot electrons Compton upscatter photons from outer cool disc
Few seed photons, so spectrum is hard
Jet from large scale height flow velocity linked to launch radius
Log n f(n)
The disc models assumed that the emission thermalised. That’s not necessarily true at low L/Ledd where the flow is not very dense. If its not thermalising then its not cooling as efficiently so the flow heats up. This can lead to a hot, optically thin, geometrically thick inner flow replacing the inner disc. The hot electrons in this flow can compton upscatter any low energy photons from a residual outer disc, but there are not many of these, so the spectrum is hard
Log n

18. No inner disc
Disc models assumed thermal plasma – not true at low L/LEdd
Instead: hot, optically thin, geometrically thick inner flow replacing the inner disc (Shapiro et al. 1976; Narayan & Yi 1995)
Hot electrons Compton upscatter photons from outer cool disc
Few seed photons, so spectrum is hard
Jet from large scale height flow velocity linked to launch radius
Log n f(n)
The disc models assumed that the emission thermalised. That’s not necessarily true at low L/Ledd where the flow is not very dense. If its not thermalising then its not cooling as efficiently so the flow heats up. This can lead to a hot, optically thin, geometrically thick inner flow replacing the inner disc. The hot electrons in this flow can compton upscatter any low energy photons from a residual outer disc, but there are not many of these, so the spectrum is hard
Log n

19. No inner disc
Disc models assumed thermal plasma – not true at low L/LEdd
Instead: hot, optically thin, geometrically thick inner flow replacing the inner disc (Shapiro et al. 1976; Narayan & Yi 1995)
Hot electrons Compton upscatter photons from outer cool disc
Few seed photons, so spectrum is hard
Jet from large scale height flow velocity linked to launch radius
Log n f(n)
The disc models assumed that the emission thermalised. That’s not necessarily true at low L/Ledd where the flow is not very dense. If its not thermalising then its not cooling as efficiently so the flow heats up. This can lead to a hot, optically thin, geometrically thick inner flow replacing the inner disc. The hot electrons in this flow can compton upscatter any low energy photons from a residual outer disc, but there are not many of these, so the spectrum is hard
Log n

20. Collapse of hot inner flow
Disc models assumed thermal plasma – not true at low L/LEdd
Instead: hot, optically thin, geometrically thick inner flow replacing the inner disc (Shapiro et al. 1976; Narayan & Yi 1995)
Hot electrons Compton upscatter photons from outer cool disc
Few seed photons, so spectrum is hard
Jet from large scale height flow velocity linked to launch radius collapse of flow=collapse of jet
Log n f(n)
The disc models assumed that the emission thermalised. That’s not necessarily true at low L/Ledd where the flow is not very dense. If its not thermalising then its not cooling as efficiently so the flow heats up. This can lead to a hot, optically thin, geometrically thick inner flow replacing the inner disc. The hot electrons in this flow can compton upscatter any low energy photons from a residual outer disc, but there are not many of these, so the spectrum is hard
Log n

21. Done Gierlinski & Kubota 2007
No jet HS
Decrease fraction of power in nonthermal reconnection above disc HS
VHS
Disc to minimum stable orbit
VHS
Decrease inner disc radius, and maybe radial extent of corona giving increasing LF QPO frequency
LS (bright)
Jet gets faster, catches up with slower outflow, get flares of radio emission from internal shocks Fender (2004)
LS (dim)
Done Gierlinski & Kubota 2007

22. Black holes
Appearance of BH should depend only on mass and spin (black holes have no hair!)
Plus mass accretion rate, giving observed luminosity L
Maximum luminosity ~LEdd where radiation pressure blows further infalling material away
Get rid of most mass dependance as accretion flow should scale with L/LEdd
M: Quasars
(?) M: ULX
3-20 M: Galactic black holes

23. AGN spectral states
Stretched out by lower disc temperature so not so obvious as in BHB but still….
…AGN NOT all the same underneath absorption!! Their SED should depend intrinsically on L/LEdd in same way as BHB
So need to know AGN mass in order to calculate LEdd

24. Mass of AGN??
Magorrian-Gebhardt relation gives BH mass!! Big black holes live in host galaxies with big bulges! Either measured by bulge luminosity or bulge mass (stellar velocity dispersion) or BLR
109
Black hole mass
Scaling these models up to the supermassive black holes in quasars, the only change should be that the disc emission is in the UV rather than X-ray region. The problem is knowing how far to scale them for an individual qso, knowing the BH mass. This has only recently become possible with the discovery of the relationships between the BH mass and the properties of the galaxy as a whole. Big BH live in big galaxies, little BH live in small ones. Also, only recently that enough high s/n data has become available to test these models – xmm-newton database
103
Stellar system mass
106
1012

25. AGN/QSO Zoo!!! Optical
Bright, blue continuum from accretion disc. Gas close to nucleus irradiated and photo-ionised – lines!
Broad permitted lines ~ 5000 km/s (BLR)
Narrow forbidden lines ~ 200 km/s (NLR)
Forbidden lines suppressed if collisions so NLR is less dense than BLR
Lines give diagnositic of unobservable EUV disc continuum
Scaling these models up to the supermassive black holes in quasars, the only change should be that the disc emission is in the UV rather than X-ray region. The problem is knowing how far to scale them for an individual qso, knowing the BH mass. This has only recently become possible with the discovery of the relationships between the BH mass and the properties of the galaxy as a whole. Big BH live in big galaxies, little BH live in small ones. Also, only recently that enough high s/n data has become available to test these models – xmm-newton database
Francis et al 1991

26. AGN/QSO Zoo!!! Optical

27. AGN/QSO unification Bigger range in mass 105-109
L varies without much else changing if same L/LEdd with different BH mass: Sey/QSO
Cold absorption from torus along equatorial plane
BLR and disc within torus so obscured if line of sight intersects torus. See only NLR
But can see BLR in polarised (scattered!) light
Unification of narrow and broad line Sey1/Sey 2 via inclination
Urry & Padovani 1995

28. AGN/QSO Zoo!!! Radio loud
Some have enormous, powerful jets on Mpc scales
How QSO first found. But now most known to be radio quiet
FRI (fuzzy lobes, 2 sided jet) FRII (bright hot spot, 1sided jet)
Scaling these models up to the supermassive black holes in quasars, the only change should be that the disc emission is in the UV rather than X-ray region. The problem is knowing how far to scale them for an individual qso, knowing the BH mass. This has only recently become possible with the discovery of the relationships between the BH mass and the properties of the galaxy as a whole. Big BH live in big galaxies, little BH live in small ones. Also, only recently that enough high s/n data has become available to test these models – xmm-newton database

29. LS LINERS? Hard (low L/LEdd) Soft (high L/LEdd) VHS NLS1 HS QSO US QSO
The models I developed are quantatative as well as qualitative, so I can scale them up. The blue spectra show a the models which work so well for the galactic systems. The red spectra show what the models predict for the SAME accretion flow geometries onto a supermassive black hole – UV disc, doesn’t extend into x-ray range, and these lower energy seed photons mean that compton cooling is slightly more efficient, high energy spectra are steeper US
QSO
Done & Gierliński 2005

30. AGN - spin Origin of jet – L/LEdd ?
But standard QSO’s can be radio loud OR radio quiet at high L/LEdd
Environment difference? Radio loud in ellipticals so can have high spin from accretion spinup in major mergers
Low spin in spirals from random orientation small accretion events (Sikora Stawarz & Lasota 2007)

31. AGN/QSO Zoo!!! Host galaxy
Link to galaxy formation – ellipticals/bulge from major mergers so accretion spins up BH to maximal – more powerful jet
Spirals from random small satellite galaxy accretion – low spin (Volonteri et al 2007)
Scaling these models up to the supermassive black holes in quasars, the only change should be that the disc emission is in the UV rather than X-ray region. The problem is knowing how far to scale them for an individual qso, knowing the BH mass. This has only recently become possible with the discovery of the relationships between the BH mass and the properties of the galaxy as a whole. Big BH live in big galaxies, little BH live in small ones. Also, only recently that enough high s/n data has become available to test these models – xmm-newton database

32. Conclusions
Test GR - X-rays from accreting black holes produced in regions of strong gravity
Last stable orbit (ONLY simple disc spectra) L T4max
Low to moderate spin in LMXB as expected
Corrections to GR from proper gravity must be smallish
Accretion flow NOT always simple disc – X-ray tail!
Mass ~10 Msun. Accretion flow + jet change with L/LEdd
Apply to AGN – mass has bigger spread (105-9 Msun)
More complex environment – torus/dust obscuration – inclination!
Spectrum and jet change with L/LEdd but jet probably depends on spin as well. Feedback from this controls galaxy formation
PHYSICS  ASTROPHYSICS  ASTRONOMY
Fabulous time, both in terms of data available and for me personally. For the first time there is enough data

33. Relativistic smearing: spin
Relativistic effects (special and general) affect all emission
Emission from side of disc coming towards us:
Doppler blueshifted
Beamed from length contraction
Time dilation as fast moving (SR)
Gravitational redshift (GR)
Fe Ka line from irradiated disc should be broad and skewed, and shape depends on Rin (and spin)
Fabian et al. 1989
Energy (keV)
flux
Another area where Astro e2 will give major progress in an independent test of the accretion flow models. The accretion disc moves fast in a strong gravitational field, so both special and general relativistic effects modify its spectrum. Doppler shifts and length contraction mean that the emission from the disc moving towards us is blueshifted and boosted, while that moving away is redshifted and suppressed. Then time dilation and gravitational redshift drag everything redwards. The strength of these all effects decrease with radius. All emission from the disc is affected, but its much easier to see on intrinsically narrow features – lines. X-ray illumination of the disc gives iron Kalpha line. Moving inner disc models predict broader line in softer spectra. But the measured line profile can be distorted by narrow absorption features superimposed on the emission. The high spectral resolution of Astro e2 will unambiguously show these, enabling the intrinsic line profile to be measured.

34. Observations: tail as well as disc tail probably Compton scattering
Cyg X-1: Gierlinski et al 1999
High state spectra need predominantly non-thermal electron distribution
Low state spectra peak at 100 keV. Well modelled by thermal electron distribution

35. Optically thick thermal
Optical depth t>1, multiple scattering – average N ~ t2
Not much left of original seed photon spectrum exp(-t)
if (1+4Q) N ein > 3Q (y>>1) then majority of photons reach 3Q
Can’t go any higher so they pile up – try to thermalise but little true absorption so still comptonised. Wien peak.
Log N(g)
Log nfn
Log g
Log n

36. Practice!! Thermal compton
Suppose kTe=100 keV and t=0.5
Calculate Q=kT/511
Spectrum extends to ~3Q ~ 300 keV
Calculate y=(t + t2)(1+4Q+16 Q2)
Is y>> 1 ie does spectrum thermalise? if not, calculate the spectral index a = -log t/log (1+4Q+16Q2)
Original blackbody seed at kTbb=0.2 keV
Only e-t of original blackbody seen
Sketch spectrum in vfv – we have f (e)  e-a so plot as
ef (e)  e-a+1

37. Practice!! Mystery object
But do see more disc than expected! Says some disc photons don’t intercept the hot flow ie diagnostic of geometry!!

38. Synchrotron (self compton)
Same as compton scattering except seed photons are virtual from magnetic field ncyc = eB/2p mc = 2.8x106 B Hz so radio
Normally deal with nonthermal so energy boost is g2
f(e)  e-(p-1)/2
Log N(g)
Log nfn
N (g)  g-p
Log g
gmax
ecyc
Log n
gmax2 ein

39. Bremstrahlung: hot gas
Classical way is electron accelerates in field of atom so radiates
f(e)  n2 T1/2 e-e
Log nfn
ecyc
Log n
gmax2 ein

40. Bremstrahlung
But easier way to think is that it’s the same as compton scattering except seed photons are virtual from electric field
Self compton if ni ne < ne ng (density of photon field) so compton dominates in radiation dominated environments (black hole accretion flows) and brems dominates in rarified hot gas (galaxies + clusters)
f(e)  n2 T1/2 e-e
Log N(g)
Log nfn
Log g
ecyc
Log n
gmax2 ein

41. Bremstrahlung
But easier way to think is that it’s the same as compton scattering except seed photons are virtual from electric field
Temperatures of K dominated by LINES
Log nfn
f(e)  n2 T1/2 e-e
ecyc
Log n
gmax2 ein

42. Bremstrahlung
Same as compton scattering except seed photons are virtual from electric field
Temperatures of K dominated by LINES
Below 103 K then electrons bound in H atoms so no brems anyway!
Log N(g)
Log nfn
f(e)  n2 T1/2 e-e
Log g
ecyc
Log n

43. Conclusions Compton scattering – just photon and electrons!
Incredible variety and subtle interplay
Only approximately a power law
low energy break (seed photons)
high energy break (mean electron energy)
Thermal – black hole tail in low/hard state
Nonthermal – black hole tail in high states
Synchrotron - compton scattering of virtual B photons
Then can self-comptonise (Sync-self-compton) –jets!
Hot gas – clusters and galaxy halo where electrons scatter virtual photons from electroic field of ion.
Log n

44. Transients
Huge amounts of data, long term variability (days –years) in mass accretion rate (due to H ionisation instability in disc)
Observational template of accretion flow as a function of L/LEdd onto ~10 M BH
DGK07
2 years

45. Spectra of accretion flow: disc
Differential Keplerian rotation
Viscosity B: gravity  heat
Thermal emission: L = AsT4
Temperature increases inwards until minimum radius Rlso(a*) For a*=0 and L~LEdd Tmax is
1 keV (107 K) for 10 M
10 eV (105 K) for 108 M
big black holes luminosity scales with mass but area scales with mass2 so T goes down with mass!
Maximum spin Tmax is 3x higher
Log n f(n)
Accretion discs are the most well known form of the accretion flow. Inner radii rotate faster so there is viscous friction (a magnetic dynamo) which converts gravitational energy to heat. If this thermalises then at large radii there is not much gravitational energy and a lot of area, so producing low temperature, while at small radii there is lots of energy and not much area, so high temperature. There is a minimum radius – the last stable orbit which is a GR prediction – so there is a maximum temperature. At LEdd this is of order 1keV, or 10 million degrees for GBH, or 10eV, a hundred thousand degrees for a supermassive BH.
Log n