Black holes in Einstein General Relativity Prof Chris
Black holes in Einstein General Relativity Prof Chris Done, University of Durham
Lecture 1 -2 recap: Size in units of Rg = GM/c 2 = 1. 5 105 M/M cm a=0, RH=2 Rg, Risco=6 Rg: a=0. 998 RH~Rg, Risco=1. 23 Rg Gravity energy L ~ GM d. M/dt = h(a) d. M/dt c 2 2 Rin Eddington Ledd=4 cp. GM/s. T =1. 3 1038 M/M ergs/s
Variability of disc: long timescale • L/LEdd AT 4 max Constant size scale – last stable orbit!! • TAIL!! What is this? ?
Spectral states very high • Disc dominated - look like a disc but small tail to high energies • Very high/intermediate states at least know something about a disc • Low/hard state look really different, not at all like a disc! disk dominated high/soft Gierlinski & Done 2003
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
Radiation processes to get high energy radiation • ACCRETION FLOW • Thermal Comptonisation (BHB+AGN) • Cyclo-synchrotron from thermal electrons • JETS!! • Synchrotron from Nonthermal electrons • Comptonisation from Non-thermal electrons
Compton scattering theory • Collision – redistribute energy • If photon energy bigger than electron then it loses energy – downscattering • If photon has less energy than electron then it gains energy – upscattering eout ein qie g qoe qio
Compton scattering theory • Easiest to talk about if scale energies to mc 2 so electron energy gmc 2 just denoted g while photon energy becomes e=hn/mc 2=E/511 for E (ke. V) eout ein qie g eout = qoe qio ein(1 - bcos qei) 1 - bcos qeo+ (ein/g) (1 - cosqio)
How much energy ? • Compton scattering seed photons from accretion disk. Photon energy boosted by factor De/e ~ 4 Q+16 Q 2 if thermal in each scattering.
How many scatterings? • Process cross-section s. Sweep out volume s R • Number of particles in that volume is n s R = t s cm 2
How much scattering ? • Determined by optical depth, t=sn. R • Scattering probability exp(-t) • Optically thin t << 1 prob ~ t average number ~ t • Optically thick t>>1 prob~1 • average number ~ t 2 R
How much total energy exchange? • Total fractional energy gain = frac. gain in 1 scatt x no. scatt • y = (4 Q+16 Q 2) (t+t 2 ) ~ 4 Qt 2 for Q<1 t>1 • y>1 flat spectrum • y<1 steep spectrum R
Optically thin thermal compton • power law by multiple scattering of thermal electrons Log N(g) Log fn • Compton scattering conserves photon number • Number of photons d. N/d. E = E d. N/d. E d. Log E = f (e) dlog E • For t<1 scatter t photons each time to energy eout=(1+4 Q+16 Q 2)ein Log g Log n
Optically thin thermal compton Log N(g) Log fn • For t<1 scatter t photons each time to energy eout=(1+4 Q+16 Q 2)ein Log g Log n
Optically thin thermal compton Log N(g) Log fn • For t<1 scatter t photons each time to energy eout=(1+4 Q+16 Q 2)ein Log g Log n
Optically thin thermal compton Log N(g) Log fn • For t<1 scatter t photons each time to energy eout=(1+4 Q+16 Q 2)ein • Makes power law F(E) = A E-a as same fractional energy gain and same fraction of photons scattered Log g Log n
Question Log N(g) Log fn • Find the spectral index from F(E) = A E-a • Hint: first scattering is at E 1, F 1, second peaks at E 1 (1+4 Q+16 Q 2) and F 1 t Log g Log n
Answer Log N(g) Log fn • F 1= A E 1 -a • F 2 = A E 2 -a but F 2=F 1 t and E 2=E 1 (1+4 Q+16 Q 2) so F 1 t= A E 1 -a (1+4 Q+16 Q 2) -a divide and get a=-log t/log (1+4 Q+16 Q 2) Log g Log n
Log EF(E) Practice!! Mystery object 1 • Estimate alpha, Q and t 10 Log E (ke. V) 100
• Plot nf(n) as this peaks at energy where power output of source peaks. • N(E)=AE -G • F(E)=EN(E)= AE-G+1=AE-a a=G-1 Log Ef(E)E) Spectra hard spectrum Most power at high E a<1 G<2 Log E d. L= F(E) d. E = EF(E) d. E/E = EF(E) dlog E d. N= N(E) d. E = EN(E)d. E/E = F(E) dlog. E
• Plot nf(n) as this peaks at energy where power output of source peaks. • N(E)=AE -G • F(E)=EN(E)= AE-G+1=AE-a a=G-1 Log Ef(E) Spectra Soft spectrum Most power at low E a>1 G>2 Log E d. L= F(E) d. E = EF(E) d. E/E = EF(E) dlog E
Optically thin thermal compton Log N(g) Log fn • Spectral index the same for different Q, t Log g Log n
Optically thin thermal compton Log N(g) Log fn • Spectral index the same for different Q, t • But spectrum goes bumpy for high Q Log g Log n
Spectral transitions in BHB Comptonised spectrum Tail is NONTHERMAL comptonisation !! Gierlinski et al 1999
And B fields • Generally there will be some B field • thermal electrons can spiral around the B field lines - cyclotron radiation Q <<1 • cyclo-synchrotron if Q close to 1 or above • v. B= e. B/(2πmec) = 2. 6 x 106 B Hz
And B fields Log vfn • Steep spectrum with exponential cutoff ν~ νBθ 2 • So much lower than electron temperature itself! Log n
And B fields Log vfn • But strongly self absorbed – electrons in the vicinity of a B field will absorb radiation • These can be the seed photons for comptonisation Log n
• Black hole binary – optical and xrays join up, so probably cyclosynchrotron in the optical as the seed photons for thermal comptonisation Chiang et al 2010 Log vfn And B fields
• 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) Log n fv(n) Accretion flows without discs Log n
Accretion flows without discs Log n fv(n) • Large scale height flow = large scale height B field close to horizon – jet !! • NOT the G=15 jets seen in blazars – these have G~1. 5! Log n
Accretion flows – Jet Very high High/soft Low/hard Corbel et al 2012
Spectral transitions in BHB Disk dominated Comptonised spectrum Gierlinski et al 1999
Accretion flows – Jet Chaty et al 2003
AGN/QSO Zoo!!! Radio loud • Enormous, powerful, relativistic jets on Mpc scales • FRI (fuzzy) - BL lacs FRII (hot spots) – FSRQ • Urry & Padovani 1992; 1995
FRI is top of ADAF branch (low/hard state BHB) but G=15! L/LEdd BHB Ghisellini et al 2010
Optically thin nonthermal compton • power law by single scattering of nonthermal electrons N (g) g-p • index a = (p-1)/2 (p >2 so a > 0. 5 – monoenergetic injection) • Starts a factor t down from seed photons, extends to gmax 2 ein eout~g 2 ein f(e) e-a e-(p-1)/2 Log fn Log N(g) g N (g) g-p Log g gmax ein Log n gmax 2 ein
Nonthermal synchrotron • power law by single scattering of nonthermal electrons N (g) g-p • index a = (p-1)/2 (p >2 so a > 0. 5 – monoenergetic injection) • Starts a factor t down from seed photons, extends to gmax 2 ein eout~g 2 ein f(e) e-a e-(p-1)/2 Log fn Log N(g) g N (g) g-p Log g gmax ein Log n gmax 2 ein
Synchrotron self compton Log vfn • Put in vfv • Expect index a = (p-1)/2~0. 6 for p=2. 2 from shocks gmax ein Log n gmax 2 ein
Synchrotron self compton Log vfn • Klein nisina cutoff – can’t have more energy than electron had to start with g 2 hn < g mc 2 so g e < 1 where e=hn/mc 2 • Synchrotron self absorption gmax ein Log n gmax 2 ein
Synchrotron self compton Log vfn • Klein nisina cutoff – can’t have more energy than electron had to start with g 2 hn < g mc 2 so g e < 1 where e=hn/mc 2 • Synchrotron self absorption gmax ein Log n gmax 2 ein
Synchrotron self compton Log vfn • Doppler boosting due to bulk motion G (don’t confuse with lorentz factor of electrons g) – d = 1/[G(1 -bcosq)] • Eobs=Eint d • Fobs=Fint d 3+a gmax ein Log n gmax 2 ein
Synchrotron self compton Log vfn • What we see in BL Lacs (Tavecchio et al 2010)
BL Lacs as SSC • need G ~ 10 -20, q<5 o, gmax~105 double power law electron distribution • Can’t make FSRQ Ghisellini et al 2010
Broad line region • AGN: complex environment • Scatters disc radiation
FSRQ –disc and BLR • Disc is behind jet so strongly deboosted • BLR may be much more isotropic so these external seed photons can be more important self produced synchrotron Ghisellini et al 2009
FSRQ –disc and BLR Log vfn • Disc is behing jet so strongly deboosted • BLR may be much more isotropic so these external seed photons can be more important self produced synchrotron gmax ein Log n gmax 2 ein Ghisellini et al 2009
FSRQ –disc and BLR Log vfn • need G ~ 10 -20, q<5 o, gmax~105 double power law electron distribution similar to BL Lacs gmax ein Log n gmax 2 ein Ghisellini et al 2009
Kinetic luminosity of the jet • Estimate Pjet from models (only small fraction of power is radiated) • See disc as well as jet so compare Pjet with Pdisc • About equal in FSRQ Ghisellini et al 2014
Kinetic luminosity of the jet • Can’t do this in BL Lacs so easily • but many FRI are in clusters of galaxies • Jets expand as bubbles in hot cluster gas – so measure total energy input from Pd. V work
Extended jet • That was all from single piece of jet • Jet has extended structure • Kinetic Energy density d. L/d. V • d. L mdot dz • Conical jet r=Az • d. V=pr 2 dz= p A 2 z 2 dz • UKE mdot (z/z 0)-2 • UB=UB(r 0) (z/z 0)-2 • Urel=Urel(r 0)(z/z 0)-2 • N(g)=K f(g) so K goes as z -2
Lognf(n) • Self absorption gives flat spectrum • And all emission above SSA is dominated by base (Konigl 1981) Radio IR optical UV X-ray
Log nf(n) • Self absorption gives flat spectrum • And all emission above SSA is dominated by base (Konigl 1981) Radio IR optical UV X-ray
Jet in Blazars is G~15 -20 ! L/LEdd FSRQ/FRII Bl Lacs/FRI
Jets – theory challenge! Jet in BHB is G~1. 5 -2 WHY? ? • No jet in disc dominated state • Radio collapses at transition – jet needs large scale height flow ? • Compton dominated state - steady, compact jet, bulk outflow G~1. 5 -2: LR Lx 0. 7 L/LEdd
Jet in Cyg X-1
Conclusions • Thermal compton + cyclosynchroton from a hot flow to describe the low/hard spectral state in BHB • Need jet also, non-thermal electrons synchrotron-self compton but NOT strong bulk outflow • Blazar jets in AGN – need non-thermal electrons synchrotron-self compton (Bl Lacs/FRI like the low/hard state) or synchrotron-self compton with external compton (FSRQ/FRII with strong disc) but very fast bulk outflow • Why are they different? ?
- Slides: 60