ASTROPHYSICAL BLACK HOLES

SOME HISTORY

Escape velocity vu2 = 2 GM/R

Earth vesc = 11 km/s

Jupiter vesc = 60 km/s

Sun vesc = 600 km/s

Moon vesc = 2 km/s

J. Michel

P. Laplace r(vesc=c) = ?

r = 2 G M/vesc2

rg = 2 G M/c2

rg gravitational radius

Schwarzshild’s radius (rS)

radius of event horizon

rg = 3 M/MSUN km

Term „black hole” introduced by J. Wheeler in 1964

For neutron star: rg ≈ 4.2 km rNS ≈ 10 km

From 7 orbits:

MBH = (3.7 ± 0.2) x 106 MSUN

(Ghez & al., 2005)

Star S0-16 approaches the focus of the orbit to a distance of ~ 45 A.U. (~ 6 light hours or ~ 600 RS )

From new analysis of orbit of S0-2 (astrometry & RVs from Keck 10 m):

MBH = (4.5 ± 0.4) x 106 MSUN

independently D = 8.4 ± 0.4 kpc

(Ghez & al., 2008)

HOW ARE BLACK HOLES CREATED ?

They are evolutionary remnants of massive stars

FINAL PRODUCTS OF STELLAR EVOLUTION

● low mass stars (M ≤ 10 MSUN)

● massive stars (10 MSUN ≤ M ≤ 20 MSUN)

WHITE DWARFS M ~ 0.2 ÷ 1.3 MSUN, R ~ 10 000 km

NEUTRON STARS M ~ 1 ÷ 2 MSUN, R ~ 10 km

BLACK HOLES M ≥ 3 MSUN

observed M ~ 4 ÷ 33 MSUN

● very massive stars (M ≥ 20 MSUN)

X-RAY SKY (UHURU, 1977)

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.

● STELLAR MASS BHs

● SUPERMASSIVE BHs

● INTERMEDIATE MASS BHs

3 CLASSES OF BHs

HOW DO WE KNOW THAT BLACK HOLES ARE THERE ?

ALL THESE ARGUMENTS PROVIDE ONLY CIRCUMSTANTIAL EVIDENCE

HARD EVIDENCE COMES ONLY FROM DYNAMICAL ESTIMATE OF THE MASS OF THE COMPACT OBJECT

UPPER MASS LIMIT for NSs

● THEORY

● OPPENHEIMER-VOLKOFF MASS:

MOV ≈ 1.4 ÷ 2.7 MSUN depending on the equation of state

FOR EXTREME EQUATION OF STATE : P=ρc2 (assuming only GR

and causality):

MOV ≈ 3.2 MSUN for non-rotating NS

MOV ≈ 3.9 MSUN for maximally rotating NS

● OBSERVATIONS

● BINARY RADIO PULSARS

MNS ≈ 1.33 ÷ 1.44 MSUN (until recently)

● BINARY X-RAY PULSARS MNS ≈ 1.1 ÷ 1.9 MSUN (large errors)

NEW DETERMINATIONS OF NS MASSES

● PSR J0737-3039B M = 1.250 ± 0.005 MSUN (Lyne & al., 2004)

● PSR J1903+0327 M = 1.67 ± 0.01 MSUN

(Champion & al., 2008)

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

PSR J1903+0327

Freire, 2009

CONFIRMED BHs IN XRBs

Name Porb Opt. Sp. X-R C MBH/Msun

Cyg X-1 5d6 O9.7 Iab pers μQ 20 ± 5

LMC X-3 1d70 B3 V pers 6 ÷ 9

LMC X-1 4d22 O7-9 III pers 10.9 ± 1.4

SS 433 13d1 ~ A7 Ib pers μQ 16 ± 3

LS 5039 3d906 O7f V pers μQ 2.7 ÷ 5.0

XTE J1819-254 2d817 B9 III T μQ 6.8 ÷ 7.4

GX 339-4 1d76 F8-G2 III RT μQ ≥ 6

GRO J0422+32 5h09 M2 V T 4 ± 1

A 0620-00 7h75 K4 V RT 11 ± 2

GRS 1009-45 6h96 K8 V T 4.4 ÷ 4.7

XTE J1118+480 4h1 K7-M0 V T 8.5 ± 0.6

GS 1124-684 10h4 K0-5 V T 7.0 ± 0.6

CONFIRMED BHs IN XRBs (cont.)

Name Porb Opt. Sp. X-R C MBH/Msun

GS 1354-645 2d54 G0-5 III T > 7.8 ± 0.5

4U 1543-47 1d12 A2 V RT 8.5 ÷ 10.4

XTE J1550-564 1d55 K3 III RT μQ 10.5 ± 1.0

XTE J1650-500 7h63 K4 V T μQ 4.0 ÷ 7.3

GRO J1655-40 2d62 F3-6 IV RT μQ 6.3 ± 0.5

4U 1705-250 12h54 K5 V T 5.7 ÷ 7.9

GRO J1719-24 14h7 M0-5 V T > 4.9

XTE J1859+226 9h16 ~ G5 T 8 ÷ 10

GRS 1915+105 33d5 K-M III RT μQ 14 ± 4.4

GS 2000+25 8h26 K5 V T 7.1 ÷ 7.8

GS 2023+338 6d46 K0 IV RT 10.0 ÷ 13.4

INTERMEDIATE MASS BHs

● range of masses: ~ 102 ÷ 104 MSUN

TWO CLASSES OF CANDIDATES:

● ULXs

● globular clusters

GLOBULAR CLUSTERS

Do some of them contain IMBHs ?

Some of them, probably, yes.

How many – it remains an open question.

Brightness profiles

rc/rh

clusters with IMBHs have expanded cores (rc/rh > 0.1)

Trenti (2006) considered a sample of 57 old globular clusters

For at least half of them, he found rc/rh ≥ 0.2

IMBHs necessary !

Velocity dispersion

correlates well with MBH

(IMBH or SMBH)

Gebhardt et al., 2002

STRONGEST CANDIDATES

● [G1 MBH ~ 20 000 MSUN Gebhardt et al., 2005]

● M15 MBH ~ 2 000 MSUN Gerssen et al., 2003

● ω Cen MBH ~ 50 000 MSUN Noyola et al., 2006

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

Lx ≈ (2.4 ÷ 16) x 1040 erg/s (if Lx = LEd, Mx = 150 ÷ 1000 Msun)

QPOs: 0.054 & 0.114 Hz

Mx ~ 200 ÷ 5000 Msun

probably accreting from a ~ 25 Msun giant filling its Roche lobe

Porb ≈ 62 d

M 82 X-1

In dense stellar cluster MGG-11, 7 ÷ 12 Myr old

(Patruno et al., 2006)

SUPERMASSIVE BHs

●range of masses: 3x105 ÷ 6x1010 MSUN

DIFFERENT WAYS OF DETERMINING MBH

● Kepler’s law

● individual stars

● water masers

● MBH–Mbulge relation

● „reverberation” (also based on Kepler’s law)

● „variance” (X-ray variability)

Kepler’s law – water masers

NGC 4258 MBH = (3.9 ± 0.1) x 107 MSUN (Herrnstein et al., 1999)

MBH-Mbulge relation

Hoering & Rix, 2004

● highest masses

TON 618 MBH ≈ 6.6 x 1010 MSUN

5 AGNs with MBH > 1010 MSUN

● lowest masses

NGC 4395 MBH ≈ 3.6 x 105 MSUN

Sgr A* MBH ≈ 4 x 106 MSUN

A binary composed of two supermassive BHs

Quasar OJ287

Porb ≈ 12 yr

e = 0.66

M1 ≈ 18 bilions of solar masses

M2 ≈ 100 milions of solar masses• optical flashes twice per orbital period

• strong GR effects

Emission of gravitational waves is very efficient.

In a few thousand years one black hole will crash into another.

SPINS of BHs Spins of accreting BHs could be deduced

from:

1. X-ray spectra (continua)

require the knowledge of MBH, i & d

2. X-ray spectra (lines)

require the proper substraction of continuum

3. kHz QPOs

require the knowledge of MBH and the proper theory of QPOs

Specific angular momentum for circular orbits

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

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

Miller (2004)

Reis et al. (2008) determined the spin of BH in GX 339-4 (from RXTE & XMM):

a* = 0.935 ± 0.02 at 90 % confidence (!)

rin = 2.02+0.02-0.06 rg at very high state

rin = 2.04+0.07-0.02 rg at low/hard state

Miller et al. (2008) did this from Suzaku & XMM:

a* = 0.93 ± 0.05

NEW ERA OF PRECISION

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

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 νQPO [Hz] MBH [MSUN]

MASS ESTIMATES BASED ON SPINS

PARAMETRIC EPICYCLIC RESONANCE THEORY

(Abramowicz & Kluzniak, since 2001)

● simple resonance (2:1, 3:2 etc.)

● „humpy” resonance

a ≈ 0.7 ÷ 0.99a* ≈ 0.7 ÷ 0.99

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)

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!

Doeleman et al., 2008

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?)

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.

Yuan et al., 2009

Yuan et al., 2009