Astrophysical Black Holes Ramesh Narayan

What Is a Black Hole? “Normal” Object Black Hole Surface Black Hole Singularity Event Horizon Black Hole: A remarkable prediction of Einstein’s General Theory of Relativity – represents the victory of gravity Matter is crushed to a SINGULARITY Surrounding this is an EVENT HORIZON

Space Near a BH is Strange Light rays are strongly bent Close enough to a BH, you will be able to see the back of your head! Other strange effects near a spinning BH: Space-time dragging BH

What is the Mass of a BH? A BH can have any mass above 10-5 g (Planck mass --- quantum gravity limit) Unclear if very low-mass BHs form naturally BHs more massive than ~3M are very likely: Form quite naturally by gravitational collapse of massive stars at the end of their lives No other stable equilibrium available at these masses Enormous numbers of such BHs in the universe

Astrophysical Black Holes Two distinct varieties of Black Holes are known in astrophysics: Stellar-mass BHs: M ~ 5–20 M Supermassive BHs: M ~ 106–1010 M There are intriguing claims of a class of Intermediate Mass BHs (103–105 M), but the evidence is not yet compelling

Image credit: Robert Hynes X-ray Binaries MBH ~ 5—20 M Image credit: Robert Hynes

Galactic Nuclei MBH ~ 106—1010 M Image credit: Lincoln Greenhill, Jim Moran

A Black Hole is Extremely Simple Mass: M Spin: a* (J=a*GM2/c) Charge: Q A Black Hole has no Hair! (No Hair Theorem)

The black holes of nature are the most perfect macroscopic objects there are in the universe: the only elements in their construction are our concepts of space and time. And since the general theory of relativity provides only a single unique family of solutions for their description, they are the simplest objects as well. Chandrasekhar: Prologue to his book “The Mathematical Theory of Black Holes”

Chandrasekhar: Nora & Edward Ryerson Lecture “Patterns of Creativity” In my entire scientific life, extending over forty-five years, the most shattering experience has been the realization that an exact solution of Einstein's equations of general relativity, discovered by the New Zealand mathematician, Roy Kerr, provides the absolutely exact representation of untold numbers of massive black holes that populate the universe. Chandrasekhar: Nora & Edward Ryerson Lecture “Patterns of Creativity”

Measuring Mass is “Easy” Astronomers have been measuring masses of heavenly bodies for centuries Mass of the Sun measured using the motion of the Earth Masses of planets like Jupiter, Saturn, etc., from motions of their moons Masses of stars, galaxies,…

Measuring Mass in Astronomy The best mass estimates in astronomy are dynamical: a test particle in a circular orbit satisfies (by Newton’s laws): If v and P are measured, we can obtain M Earth-Sun: v=30 km/s, P=1yr  M v M

Masses of Stars in Binaries Observations give vr : radial velocity of secondary P : orbital period of binary These two quantities give the mass function: Often, Ms  MX, so finite Ms is not an issue for measuring MX The inclination i is more serious : Various methods to estimate it Eclipsing systems are best GRS 1009-45 Filippenko et al. (1999)

M33 X-7: eclipsing BH XRB (Pietsch et al. 2006; Orosz et al. 2007) This BH is more than 100 times farther than most known BHs in our Galaxy and yet it has quite a reliable mass!

Binary Likely MX(M) f(M)=MX,min(M) LMC X-1 9.4—12.4 0.130.05 Cyg X-1 13.8—15.8 0.244 0.005 4U1543-47 8.4—10.4 0.25  0.01 M33 X-7 14.2—17.1 0.46  0.08 GRO J0422+32 3.2—13.2 1.19  0.02 LMC X-3 5.9—9.2 2.3  0.3 A0620-00 6.3—6.9 2.72  0.06 GRO J1655-40 6.0—6.6 2.73  0.09 XTE J1650-500 >2.2 2.730.56 GRS 1124-683 6.5—8.2 3.01  0.15 SAX J1819.3-2525 6.8—7.4 3.13  0.13 GRS 1009-45 6.3—8.0 3.17  0.12 H1705-250 5.6—8.3 4.86  0.13 GS 2000+250 7.1—7.8 5.01 0.12 GS 1354-64 >5.4 5.750.30 GX 339-4 >5.3 5.80.5 GS 2023+338 10.1—13.4 6.08  0.06 XTE J1118+480 6.5—7.2 6.1  0.3 XTE J1550-564 8.5—9.7 6.86  0.71 XTE J1859+226 7.6—12.0 7.4  1.1 GRS 1915+105 10—18 9.5  3.0

Stellar Dynamics at the Galactic Center Schodel et al. (2002) Ghez et al. (2005) M=4.5106 M

Supermassive Black Holes in Other Galactic Nuclei BHs identified in nuclei of many other galaxies BH masses obtained in several cases, though not as cleanly as in the case of our own Galaxy MBH ~ 106—1010M Virtually every galaxy has a supermassive black hole at its center!

The MBH- Relation There is a remarkable correlation between the mass of the central supermassive black hole and the velocity dispersion of the stars in the galaxy bulge: MBH- relation There is also a relation between MBH and galaxy luminosity L Important clue on the formation/evolution of SMBHs and galaxies Gultekin et al. (2009)

Black Hole Spin Mass: M  Spin: a*  Charge: Q

Black Hole Spin The material from which a BH forms always has some angular momentum Also, accretion adds angular momentum So we expect astrophysical BHs to be spinning: J = a*GM2/c, 0  a*  1 a*=0 (no spin), a*=1 (maximum spin) How do we measure a* ?

Mass is Easy, Spin is Hard Mass can be measured in the Newtonian limit using test particles (e.g., stellar companion) at large radii Spin has no Newtonian effect To measure spin we must be in the regime of strong gravity, where General Relativity operates Need test particles at small radii Fortunately, we have the gas in the accretion disk…

Estimating Black Hole Spin X-Ray Continuum Spectrum  Relativistically Broadened Iron Line  Quasi-Periodic Oscillations ?

Circular Orbits In Newtonian gravity, stable circular orbits are available at all R Not true in General Relativity For a non-spinning BH (Schwarzschild metric), stable orbits only for R  6M R=6M is the innermost stable circular orbit, or ISCO, of a non-spinning BH The radius of the ISCO (RISCO) depends on the BH spin

Innermost Stable Circular Orbit (ISCO) RISCO/M depends on the value of a* If we can measure RISCO, we will obtain a* Note factor of 6 variation in RISCO Especially sensitive as a*1

Innermost Stable Circular Orbit (ISCO) RISCO/M depends on the value of a* If we can measure RISCO, we will obtain a* Note factor of 6 variation in RISCO Especially sensitive as a*1

Measure radius of hole by estimating area of the bright inner disk The Basic Idea Measure radius of hole by estimating area of the bright inner disk

How to Measure the Radius? How can we measure the radius of something that is so small even our best telescopes cannot resolve it? Use Blackbody Theory!

BlackBody Radiation The theory of radiation was worked out by many famous physicists: Rayleigh, Jeans, Wien, Stefan, Boltzmann, Planck, Einstein,… Blackbody spectrum from a hot opaque object for different temperatures (ref: Wikipedia)

Measuring the Radius of a Star Measure the flux F received from the star Measure the temperature T* (from spectrum) R*

Measuring the Radius of the Disk Inner Edge We want the radius of the “hole” in the disk emission Same principle as for a star From X-ray data we obtain FX and TX  bright Knowing distance D and inclination i we get RISCO (some geometrical factors) From RISCO/M we get a* Zhang et al. (1997); Li et al. (2005); Shafee et al. (2006); McClintock et al. (2006); Davis et al. (2006); Liu et al. (2007); Gou et al. (2009,2010); … RISCO RISCO

Relativistic Effects Movie credit: Chris Reynolds Consistent disk flux profile (Novikov & Thorne 1973) Doppler shifts (blue and red) of the orbiting gas Gravitational redshift Deflection of light rays Self-irradiation of the disk All these have to be included consistently (Li et al. 2005)

LMC X-3: 1983 - 2009 L / LEdd LMC X-3

LMC X-3: 1983 - 2009 Thick Disk L / LEdd Hard State LMC X-3

403 spectra (assuming M=10M, i=67o) LMC X-3: 1983 - 2009 L / LEdd LMC X-3 Rin Steiner et al. (2010) 403 spectra (assuming M=10M, i=67o)

XTE J1550-564 Estimates of disk inner edge Rin and BH spin parameter a* from 35 TD (superb) and 25 SPL/Intermediate (so-so) data (Steiner et al. 2010)

BH Masses and Spins Source Name BH Mass (M) BH Spin (a*) A0620-00 6.3—6.9 0.12 ± 0.19 LMC X-3 5.9—9.2 ~0.25 XTE J1550-564 8.5—9.7 0.34±0.24 GRO J1655-40 6.0—6.6 0.70 ± 0.05 4U1543-47 8.4—10.4 0.80 ± 0.05 M33 X-7 14.2—17.1 0.84 ± 0.05 LMC X-1 9.4—12.4 0.92 ± 0.06 Cyg X-1 13.8—15.8 > 0.97 GRS 1915+105 10—18 > 0.98 Shafee et al. (2006); McClintock et al. (2006); Davis et al. (2006); Liu et al. (2007,2009); Gou et al. (2009,2010, 2011); Steiner et al. (2010)

Importance of BH Spin Of the two parameters, mass and spin, spin is more fundamental Mass is merely a scale – just tells us how big the BH is Spin fundamentally affects the basic properties of space-time around the BH More than a simple re-scaling

Spinning BHs Horizon shrinks: e.g., RHGM/c2 as a*1 Particle orbits are modified Singularity becomes ring-like Frame-dragging --- Ergosphere Energy can be extracted from the BH (Penrose 1969) Does this explain jets?

Relativistic Jets Cygnus A

Superluminal Relativistic Jets Chandra XRC Chandra XRC Radio Quasar 3C279 with MBH ~ few x 107 M⊙(?) X-ray Binary GRS 1915+105 with MBH ~ 15 M⊙ 16 March 1994 NRAO/AUI 27 March 1994 3 April 1994 9 April 1994 16 April 1994 3.5c 1.9c

Energy from a Spinning Black Hole A spinning BH has free energy that can in principle be extracted (Penrose 1969), The BH is like a flywheel But how do we “grip” the BH and access this energy?! Most likely with magnetic fields (“Magnetic Penrose Effect”)

Semenov et al. (2004)

BH Spin Values vs Relativistic Jets Source Name BH Mass (M) BH Spin (a*) A0620-00 (J) 6.3—6.9 0.12 ± 0.19 LMC X-3 5.9—9.2 ~0.25 XTE J1550-564 (J) 8.5—9.7 0.34±0.24 GRO J1655-40 (J) 6.0—6.6 0.70 ± 0.05 4U1543-47 (J) 8.4—10.4 0.80 ± 0.05 M33 X-7 14.2—17.1 0.84 ± 0.05 LMC X-1 9.4—12.4 0.92 ± 0.06 Cyg X-1 (J) 13.8—15.8 > 0.97 GRS 1915+105 (J) 10—18 > 0.98 Shafee et al. (2006); McClintock et al. (2006); Davis et al. (2006); Liu et al. (2007,2009); Gou et al. (2009,2010, 2011); Steiner et al. (2010)

Can We Test the No-Hair Theorem? After we measure M, a* with good accuracy for a number of BHs, what next? Plenty of astrophysical phenomenology could potentially be explained… Perhaps we can come up with a way of testing the No-Hair Theorem No good idea at the moment…

Relevance of Black Hole Spin Spin is likely important in a variety of contexts in ASTROPHYSICS: May be responsible for relativistic jets May be connected to gamma-ray bursts Angular momenta of progenitor stars Clues to galaxy merger history Affects gravitational wave signals …

Summary Many astrophysical BHs have been discovered during the last ~20 years There are two distinct populations: X-ray binaries: 5—20 M (107 per galaxy) Galactic nuclei: 106-10 M (1 per galaxy) BH spin estimates are now possible Profound effects may be connected to spin Next frontier: The No-Hair Theorem