1. ASTROPHYSICAL BLACK HOLES

2. SOME HISTORY Escape velocity v u 2 = 2 GM/R Earth v esc = 11 km/s Jupiter v esc = 60 km/s Sun v esc = 600 km/s Moon v esc = 2 km/s J. Michel P. Laplace r(v esc =c) = ? r = 2 G M/v esc 2

3. r g = 2 G M/c 2 r g gravitational radius Schwarzshild’s radius (r S ) radius of event horizon r g = 3 M/M SUN km Term „black hole” introduced by J. Wheeler in 1964 For neutron star: r g ≈ 4.2 km r NS ≈ 10 km

6. From 7 orbits: M BH = (3.7 ± 0.2) x 10 6 M SUN (Ghez & al., 2005) Star S0-16 approaches the focus of the orbit to a distance of ~ 45 A.U. (~ 6 light hours or ~ 600 R S )

7. From new analysis of orbit of S0-2 (astrometry & RVs from Keck 10 m) : M BH = (4.5 ± 0.4) x 10 6 M SUN independently D = 8.4 ± 0.4 kpc (Ghez & al., 2008)

8. HOW ARE BLACK HOLES CREATED ? They are evolutionary remnants of massive stars

9. FINAL PRODUCTS OF STELLAR EVOLUTION ● low mass stars (M ≤ 10 M SUN ) ● massive stars (10 M SUN ≤ M ≤ 20 M SUN ) WHITE DWARFS M ~ 0.2 ÷ 1.3 M SUN, R ~ 10 000 km NEUTRON STARS M ~ 1 ÷ 2 M SUN, R ~ 10 km BLACK HOLES M ≥ 3 M SUN observed M ~ 4 ÷ 33 M SUN ● very massive stars (M ≥ 20 M SUN )

13. X-RAY SKY (UHURU, 1977)

14. Black holes can grow up i.e. increase their masses. This is done by attracting the matter from the neighbourhood (BH acts as a „vacuum cleaner”) or by mergers. In this way intermediate mass BHs (thousands solar masses) and then supermassive black holes (millions to billions solar masses) are created.

15. ● STELLAR MASS BHs ● SUPERMASSIVE BHs ● INTERMEDIATE MASS BHs 3 CLASSES OF BHs

16. HOW DO WE KNOW THAT BLACK HOLES ARE THERE ?

26. ALL THESE ARGUMENTS PROVIDE ONLY CIRCUMSTANTIAL EVIDENCE HARD EVIDENCE COMES ONLY FROM DYNAMICAL ESTIMATE OF THE MASS OF THE COMPACT OBJECT

27. UPPER MASS LIMIT for NSs ● THEORY ● OPPENHEIMER-VOLKOFF MASS: M OV ≈ 1.4 ÷ 2.7 M SUN depending on the equation of state FOR EXTREME EQUATION OF STATE : P=ρc 2 (assuming only GR and causality): M OV ≈ 3.2 M SUN for non-rotating NS M OV ≈ 3.9 M SUN for maximally rotating NS

28. ● OBSERVATIONS ● BINARY RADIO PULSARS M NS ≈ 1.33 ÷ 1.44 M SUN (until recently) ● BINARY X-RAY PULSARS M NS ≈ 1.1 ÷ 1.9 M SUN (large errors)

29. NEW DETERMINATIONS OF NS MASSES ● PSR J0737-3039B M = 1.250 ± 0.005 M SUN (Lyne & al., 2004) ● PSR J1903+0327 M = 1.67 ± 0.01 M SUN (Champion & al., 2008)

30. NGC 6440B After ~1 year timing this pulsar, we have obtained a good measurement of the rate of advance of periastron. If fully relativistic, this implies a total system mass of ~2.92 ± 0.25 solar masses! The companion has likely only ~0.1 solar masses. Median of probability for pulsar mass is 2.74 solar masses. There is a 99% probability of mass being larger than 2 solar masses, 0.1% probability of having a “normal” mass. Is this a super-massive neutron star? From: Freire et al. (2008a), ApJ 675, 670

31. PSR J1903+0327 Freire, 2009

36. CONFIRMED BHs IN XRBs Name P orb Opt. Sp. X-R C M BH /M sun Cyg X-15 d 6 O9.7 Iab pers μQ 20 ± 5 LMC X-31 d 70 B3 V pers 6 ÷ 9 LMC X-14 d 22 O7-9 III pers 10.9 ± 1.4 SS 433 13 d 1 ~ A7 Ib pers μQ 16 ± 3 LS 5039 3 d 906 O7f V pers μQ 2.7 ÷ 5.0 XTE J1819-254 2 d 817 B9 III T μQ 6.8 ÷ 7.4 GX 339-4 1 d 76 F8-G2 III RT μQ ≥ 6 GRO J0422+32 5 h 09 M2 V T 4 ± 1 A 0620-00 7 h 75 K4 V RT 11 ± 2 GRS 1009-45 6 h 96 K8 V T 4.4 ÷ 4.7 XTE J1118+480 4 h 1 K7-M0 V T 8.5 ± 0.6 GS 1124-684 10 h 4 K0-5 V T 7.0 ± 0.6

37. CONFIRMED BHs IN XRBs (cont.) Name P orb Opt. Sp. X-R C M BH /M sun GS 1354-645 2 d 54 G0-5 III T > 7.8 ± 0.5 4U 1543-47 1 d 12 A2 V RT 8.5 ÷ 10.4 XTE J1550-564 1 d 55 K3 III RT μQ 10.5 ± 1.0 XTE J1650-500 7 h 63 K4 V T μQ 4.0 ÷ 7.3 GRO J1655-40 2 d 62 F3-6 IV RT μQ 6.3 ± 0.5 4U 1705-250 12 h 54 K5 V T 5.7 ÷ 7.9 GRO J1719-24 14 h 7 M0-5 V T > 4.9 XTE J1859+226 9 h1 6 ~ G5 T 8 ÷ 10 GRS 1915+105 33 d 5 K-M III RT μQ 14 ± 4.4 GS 2000+25 8 h 26 K5 V T 7.1 ÷ 7.8 GS 2023+3386 d 46 K0 IV RT 10.0 ÷ 13.4

38. INTERMEDIATE MASS BHs ● range of masses: ~ 10 2 ÷ 10 4 M SUN TWO CLASSES OF CANDIDATES: ● ULXs ● globular clusters

39. GLOBULAR CLUSTERS Do some of them contain IMBHs ? Some of them, probably, yes. How many – it remains an open question.

40. Brightness profiles r c /r h clusters with IMBHs have expanded cores (r c /r h > 0.1)

42. Trenti (2006) considered a sample of 57 old globular clusters For at least half of them, he found r c /r h ≥ 0.2 IMBHs necessary !

43. Velocity dispersion correlates well with M BH (IMBH or SMBH)

44. Gebhardt et al., 2002

45. STRONGEST CANDIDATES ● [ G1 M BH ~ 20 000 M SUN Gebhardt et al., 2005 ] ● M15 M BH ~ 2 000 M SUN Gerssen et al., 2003 ● ω Cen M BH ~ 50 000 M SUN Noyola et al., 2006

47. Are ULXs BH binaries (IMBH binaries) ? Some of them – yes! The term „ULXs” is probably a sort of an umbrella covering several different classes of objects One of them is, most likely, a class of XRBs containing IMBHs

48. L x ≈ (2.4 ÷ 16) x 10 40 erg/s (if L x = L Ed, M x = 150 ÷ 1000 M sun ) QPOs: 0.054 & 0.114 Hz M x ~ 200 ÷ 5000 M sun probably accreting from a ~ 25 M sun giant filling its Roche lobe P orb ≈ 62 d M 82 X-1 In dense stellar cluster MGG-11, 7 ÷ 12 Myr old (Patruno et al., 2006)

49. SUPERMASSIVE BHs ● range of masses: 3x10 5 ÷ 6x10 10 M SUN

50. DIFFERENT WAYS OF DETERMINING M BH ● Kepler’s law ● individual stars ● water masers ● M BH –M bulge relation ● „reverberation” (also based on Kepler’s law) ● „variance” (X-ray variability)

51. Kepler’s law – water masers

52. NGC 4258 M BH = (3.9 ± 0.1) x 10 7 M SUN (Herrnstein et al., 1999)

53. M BH -M bulge relation Hoering & Rix, 2004

54. ● highest masses TON 618 M BH ≈ 6.6 x 10 10 M SUN 5 AGNs with M BH > 10 10 M SUN ● lowest masses NGC 4395 M BH ≈ 3.6 x 10 5 M SUN Sgr A * M BH ≈ 4 x 10 6 M SUN

55. A binary composed of two supermassive BHs Quasar OJ287 P orb ≈ 12 yr e = 0.66 M 1 ≈ 18 bilions of solar masses M 2 ≈ 100 milions of solar masses optical flashes twice per orbital period strong GR effects

56. Emission of gravitational waves is very efficient. In a few thousand years one black hole will crash into another.

57. SPINS of BHs Spins of accreting BHs could be deduced from: 1. X-ray spectra (continua) require the knowledge of M BH, i & d 2. X-ray spectra (lines) require the proper substraction of continuum 3. kHz QPOs require the knowledge of M BH and the proper theory of QPOs

58. Specific angular momentum for circular orbits

61. X-RAY SPECTRA Zhang et al. (1997): GRO J1655-40 a* = 0.93 GRS 1915+105 a* ≈ 1.0 Gierliński et al. (2001): GRO J1655-40 a* = 0.68 ÷ 0.88 McClintock et al. LMC X-3 a* < 0.26 (2006, 2009): GRO J1655-40 a* = 0.65 ÷ 0.80 4U 1543-47 a* = 0.70 ÷ 0.85 LMC X-1 a* = 0.81 ÷ 0.94 GRS 1915+105 a* > 0.98

62. SPECTRAL LINES MODELING THE SHAPE OF Fe Kα LINE Miller et al. (2004): GX339-4 a* ≥ 0.8 ÷ 0.9 Miller et al. (2005): GRO J1655-40 a* > 0.9 XTE J1550-564 a* > 0.9 Miller et al. (2002): XTE J1650-500 a* ≈ 1.0

64. Miller (2004)

65. Reis et al. (2008) determined the spin of BH in GX 339-4 (from RXTE & XMM): a* = 0.935 ± 0.02 at 90 % confidence (!) r in = 2.02 +0.02 -0.06 r g at very high state r in = 2.04 +0.07 -0.02 r g at low/hard state Miller et al. (2008) did this from Suzaku & XMM: a* = 0.93 ± 0.05 NEW ERA OF PRECISION

66. SUMMARY OF SPIN DETERMINATIONS FROM Fe Kα LINE Cyg X-1 a* = 0.05 (1) 4U 1543-475 a* = 0.3 (1) SAX J1711.6-3808 a* = 0.2 ÷ 0.8 SWIFT J1753.5-0127 a* = 0.61 ÷ 0.87 XTE J1908+094 a* = 0.75 (9) XTE J1550-564 a* = 0.76 (1) XTE J1650-500 a* = 0.79 (1) GX 339-4 a* = 0.94 (2) GRO J1655-40 a* = 0.98 (1) Miller et al., 2009

67. GRO J1655-40 300 ± 23 6.3 ± 0.5 450 ± 20 XTE J1550-564 184 ± 26 10.5 ± 1.0 272 ± 20 H 1743-322 166 ± 8 240 ± 3 GRS 1915+105 41 ± 1 14 ± 4.4 67 ± 5 113 164 ± 2 4U 1630-472 184 ± 5 XTE J1859+226 193 ± 4 9 ± 1 XTE J1650-500 250 5.5 ± 1.5 kHz QPOs Name ν QPO [Hz] M BH [M SUN ]

69. MASS ESTIMATES BASED ON SPINS PARAMETRIC EPICYCLIC RESONANCE THEORY (Abramowicz & Kluzniak, since 2001) ● simple resonance (2:1, 3:2 etc.) ● „humpy” resonance

70. a ≈ 0.7 ÷ 0.99 a* ≈ 0.7 ÷ 0.99

72. BHs SPINS (summary) (1) GRS 1915+105 has a rotation close to nearly maximal spin ( a* >0.98) (2) several other systems (GX 339-4, LMC X-1, GRO J1655-40, XTE J1650-500, XTE J1550-564, XTE J1908+094 and SWIFT J1753.5-0127 have large spins (a* ≥ 0.65) (3) not all accreting black holes have large spins (robust results a* < 0.26 for LMC X-3 and a* ≈ 0.05 for Cyg X-1)

73. New VLBI observations at 1.3 mm (Doeleman et al., 2008) permitted us to see (for the first time) the structures on the scale of the event horizon!

74. Doeleman et al., 2008

75. The diameter of the event horizon of Sgr A* is ~ 20 μas (for d = 8 kpc) The apparent size for a distant observer should be (due to light bending) ~ 52 μas for non-rotating BH or ~ 45 μas for maximally rotating BH The measured size (major-axis) of Sgr A* is 37 +16 -10 μas the emission from Sgr A* is not exactly centered on a BH (jet?, disc?)

76. Images calculated for RIAF disc emission close to the event horizon (Yuan et al., 2009) indicate that disc is highly inclined or Sgr A* is rotating fast.

77. Yuan et al., 2009