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Understanding Black Holes in Einstein's General Relativity

Recap of lectures on black holes by Prof. Chris Done regarding their size, variability, accretion flows, and spectral states in the context of General Relativity. Explore key concepts including thermal Comptonization and spectral indices.

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Understanding Black Holes in Einstein's General Relativity

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  1. Black holes in EinsteinGeneral Relativity Prof Chris Done, University of Durham

  2. Lecture 1-2 recap: Size in units of Rg= GM/c2 = 1.5 105M/M cm a=0, RH=2Rg, Risco=6Rg: a=0.998 RH~Rg, Risco=1.23Rg Gravity energy L ~ GM dM/dt = h(a)dM/dt c2 2Rin EddingtonLedd=4cpGM/sT=1.3 1038 M/M ergs/s

  3. Variability of disc:long timescale • L/LEddAT4maxConstant size scale – last stable orbit!! • TAIL!! What is this??

  4. Spectral states • 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! very high disk dominated high/soft Gierlinski & Done 2003

  5. Variability of disc: short timescale • Timescale to change mass accretion rate through disc • tvisc= a-1 (H/R)-2torb =5 a-1 (H/R)-2 (r/6) -3/2ms • ~ 500s at last stable orbit for 10M • No rapid variability of disc 0.5 1.0 2.0

  6. Low/hard state variability • Low/Hard state variability down to few 10s of ms • tvisc= a-1 (H/R)-2tdyn = 5 a-1 (H/R)-2 (r/6) -3/2ms • IF viscous timescale then H/R~1 0.5 1.0 2.0

  7. Accretion flows without discs • 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 nfv(n) Log n

  8. 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

  9. Compton scattering theory eout ein • 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 qie qoe g qio

  10. Compton scattering theory eout ein • Easiest to talk about if scale energies to mc2 so electron energy gmc2 just denoted g while photon energy becomes e=hn/mc2=E/511 for E (keV) qie qoe g qio eout = ein(1 - bcos qei) 1- bcos qeo+ (ein/g) (1- cosqio)

  11. How much energy ? • Compton scattering seed photons from accretion disk. Photon energy boosted by factor De/e ~ 4Q+16Q2if thermal in each scattering.

  12. Process cross-section s. Sweep out volume s R Number of particles in that volume is n s R = t How many scatterings? s cm2

  13. How much scattering ? • Determined by optical depth, t=snR • Scattering probability exp(-t) • Optically thin t << 1 prob ~ t average number ~ t • Optically thick t>>1 prob~1 • average number ~ t2 R

  14. How much total energy exchange? • Total fractional energy gain = frac.gain in 1 scatt x no.scatt • y = (4Q+16Q2) (t+t2 ) ~ 4Qt2 for Q<1 t>1 • y>1 flat spectrum • y<1 steep spectrum R

  15. Optically thin thermal compton • power law by multiple scattering of thermal electrons • Compton scattering conserves photon number • Number of photons dN/dEdE = E dN/dEdLog E = f (e) dlogE • For t<1 scatter t photons each time to energy eout=(1+4Q+16Q2)ein Log fn Log N(g) Log g Log n

  16. Optically thin thermal compton • For t<1 scatter t photons each time to energy eout=(1+4Q+16Q2)ein Log fn Log N(g) Log g Log n

  17. Optically thin thermal compton • For t<1 scatter t photons each time to energy eout=(1+4Q+16Q2)ein Log fn Log N(g) Log g Log n

  18. Optically thin thermal compton • For t<1 scatter t photons each time to energy eout=(1+4Q+16Q2)ein • Makes power law F(E) = A E-aas same fractional energy gain and same fraction of photons scattered Log fn Log N(g) Log g Log n

  19. Question • Find the spectral index from F(E) = A E-a • Hint: first scattering is at E1, F1, second peaks at E1 (1+4Q+16Q2) and F1 t Log fn Log N(g) Log g Log n

  20. Answer • F1= A E1-a • F2 = A E2-a but F2=F1 t and E2=E1 (1+4Q+16Q2) so F1 t= A E1-a (1+4Q+16Q2) -a divide and get a=-log t/log (1+4Q+16Q2) Log fn Log N(g) Log g Log n

  21. Practice!! Mystery object • Estimate alpha, Q and t Log EF(E) 1 10 100 Log E (keV)

  22. Spectra • 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 LogEf(E)E) hard spectrum Most power at high E a<1 G<2 Log E dL= F(E) dE = EF(E) dE/E = EF(E) dlog E dN= N(E) dE = EN(E)dE/E = F(E) dlogE

  23. Spectra • 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) Soft spectrum Most power at low E a>1 G>2 Log E dL= F(E) dE = EF(E) dE/E = EF(E) dlog E

  24. Optically thin thermal compton • Spectral index the same for different Q, t Log fn Log N(g) Log g Log n

  25. Optically thin thermal compton • Spectral index the same for different Q, t • But spectrum goes bumpy for high Q Log fn Log N(g) Log g Log n

  26. Spectral transitions in BHB Comptonised spectrum Tail is NONTHERMAL comptonisation !! Gierlinski et al 1999

  27. And B fields • Generally there will be some B field • the thermal electrons can spiral around the B field lines - cyclotron radiation Q <<1 • cyclo-synchrotron if Q close to 1 or above • vB= eB/(2πmec) = 2.6x106 B Hz Chiang & Done 2009

  28. And B fields • Steep spectrum with exponential cutoffν~ νBθ2 • So much lower than electron temperature itself! Log vfn Log n Chiang & Done 2009

  29. And B fields • But strongly self absorbed – electrons in the vicinity of a B field will absorb radiation • These can be the seed photons for comptonisation Log vfn Log n Chiang & Done 2009

  30. And B fields • Black hole binary – optical and x-rays join up, so probably cyclo-synchrotron in the optical as the seed photons for thermal comptonisation Chiang et al 2010 Log vfn

  31. Accretion flows without discs • 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 nfv(n) Log n

  32. Accretion flows without discs • 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 nfv(n) Log n

  33. Accretion flows – Jet Low/hard High/soft Very high Corbel et al 2012

  34. Spectral transitions in BHB Disk dominated Comptonised spectrum Gierlinski et al 1999

  35. Accretion flows – Jet Chaty et al 2003

  36. AGN/QSO Zoo!!! Radio loud • Enormous, powerful, relativistic jets on Mpc scales • FRI (fuzzy) - BL lacs FRII (hot spots) – FSRQ • Urry & Padovani 1992; 1995

  37. FRI is top of ADAF branch (low/hard state BHB) but G=15! L/LEdd BHB Ghisellini et al 2010

  38. 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 gmax2ein ein eout~g2ein f(e)  e-a e-(p-1)/2 g Log fn Log N(g) N (g)  g-p Log g gmax gmax2ein ein Log n

  39. 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 gmax2ein ein eout~g2ein f(e)  e-a e-(p-1)/2 g Log fn Log N(g) N (g)  g-p Log g gmax gmax2ein ein Log n

  40. Synchrotron self compton • Put in vfv • Expect index a = (p-1)/2~0.6 for p=2.2 from shocks Log vfn gmax gmax2ein ein Log n

  41. Synchrotron self compton • Klein nisinacutoff – can’t have more energy than electron had to start with g2 hn < g mc2 so ge< 1 where e=hn/mc2 • Synchrotron self absorption Log vfn gmax gmax2ein ein Log n

  42. Synchrotron self compton • Klein nisinacutoff – can’t have more energy than electron had to start with g2 hn < g mc2 so ge< 1 where e=hn/mc2 • Synchrotron self absorption Log vfn gmax gmax2ein ein Log n

  43. Synchrotron self compton • Doppler boosting due to bulk motion G (don’t confuse with lorentz factor of electrons g) – d = 1/[G(1-bcosq)] • Eobs=Eintd • Fobs=Fintd3+a Log vfn gmax gmax2ein ein Log n

  44. Synchrotron self compton • What we see in BL Lacs (Tavecchio et al 2010) Log vfn

  45. BL Lacs as SSC • need G ~ 10-20, q<5o, gmax~105double power law electron distribution • Can’t make FSRQ Ghisellini et al 2010

  46. Broad line region • AGN: complex environment • Scatters disc radiation

  47. 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

  48. FSRQ –disc and BLR • 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 Log vfn gmax gmax2ein ein Log n Ghisellini et al 2009

  49. FSRQ –disc and BLR • need G ~ 10-20, q<5o, gmax~105 double power law electron distribution similar to BL Lacs Log vfn gmax gmax2ein ein Log n Ghisellini et al 2009

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