the Black Hole Event Horizon

1. Ramesh Narayan the Black Hole Event Horizon

2. “Normal” Object Black Hole Event Horizon Surface Singularity The Black Hole • A remarkable prediction of theGeneral Theory of Relativity • Matter is crushed to a SINGULARITY • Surrounding this is an EVENT HORIZON • BH is defined by the presence of an Event Horizon

3. Conceptually, a BH is Very Strange & Mysterious • Just because our theory/equations (GR) give BH solutions, should we believe that BHs actually do exist? • Surely, Nature must have some trick up her sleeve to avoid forming BHs • Many great scientists (even Chandrasekhar himself for a while?) have wondered • However…

4. The Universe Appears to be Full of Black Holes • Theory: Neutron stars, strange stars, or other kinds of compact objects cannot be more massive than ~ 3M • Observations: The most massive neutron star discovered so far is ~ 2M • Any compact relativistic object with mass > 3MMUST BE A BLACK HOLE • Huge numbers of these in the Universe

5. X-ray Binaries MBH ~ 5—20 M Millions of these BHs in each galaxy Image credit: Robert Hynes

6. Galactic Nuclei MBH ~ 106—1010 M One supermassive BH in each galaxy Image credit: Lincoln Greenhill, Jim Moran

7. But: Are Astrophysical Black Holes Really Black Holes? • We know that astrophysical “BHs” are: • Compact: R  few RS (RS2GM/c2) • Massive: M  3M(not neutron stars) • But can we be sure that they are really BHs? • Would be good to find independent evidence that BH candidates actually possess Event Horizons • Recall: BH is DEFINED by Event Horizon (not mass)

8. In Search of the Event Horizon • Accretion flows are very useful, since inflowing gas reaches the center and “senses” the nature of the central object: • Can distinguish Event Horizon from Stellar Surface

9. Signatures of the Event Horizon (Lack of a Surface) • Differences in quiescent luminosities of XRBs(Narayan, Garcia & McClintock 1997; Garcia et al. 2001; McClintock et al. 2003;…) • Differences in Type I X-ray bursts between NSXRBs and BHXRBs(Narayan & Heyl 2002; Tournear et al. 2003; Yuan, Narayan & Rees 2004; Remillard et al. 2006) • Differences in X-ray colors of XRBs (Done & Gierlinsky 2003) • Differences inthermal surface emission ofNSXRBs andBHXRBs (McClintock, Narayan & Rybicki 2004) • Infrared flux ofSgr A*(Broderick & Narayan 2006, 2007; Broderick, Loeb & Narayan 2009) 

10. Physics of Accretion • Gas with angular momentum goes into orbit at a large radius around the BH • Slowly spirals in by “viscosity” (magnetic stresses) and falls into the BH at the center • Potential energy is converted into orbital kinetic energy and thermal energy: • Thermal energy is radiated, partly from the disk and partly from the stellar surface

11. Basic Idea • The surface luminosity from the central star is predicted to be always important: Lsurf  Lacc • Unless there is no surface of course (i.e., a BH) • We look for systems that have negligible surface luminosity  these must be BHs • This is potentially a very robust argument since it uses only energy conservation

12. How Much Luminosity from the Surface? • In a Newtonian analysis, if the accretion disk extends down to the radius of the central star R*, the binding energy of • a circular orbit at R* is GM/2R* • material at rest on stellar surface is ~GM/R*

13. Relativistic Case

14. On To Our “Evidence” for the Event Horizon • An exercise in logic using simple physics • Discussion is in two parts: • The “Evidence” • Search for Loopholes

15. The Black Hole at the Center of Our Galaxy Dark Mass at the Galactic Center: M ~ 4x106 M (inferred from stellar motions)

16. Stellar Dynamics at the Galactic Center Schodel et al. (2002)MBH=4.00.2106 M

17. Radio Source at the GC: Sagittarius A* • There is a compact radio source, Sagittarius A* (Sgr A*) located at the Galactic Center • Very Long Baseline Interferometer (VLBI) observations place an exquisitely tight limit on the velocity ofSgr A*: -0.4  0.9 km s-1(Reid & Brunthaler 2004) • Brownian motion analysis suggests a mass of at least105M i.e. Sgr A* is the BH candidate

18. Nearly all the motion is in longitude, due to the orbital motion of the Sun Small motion in latitude is entirely consistent with the Sun’s peculiar velocity

19. Luminosity and Spectrum of Sgr A* • Sgr A* is a rather dim source with a luminosity of ~1036 erg/s • Most of the emission is in the sub-mm • Is this radiation from the accretion flow or from the surface? Sub mm

20. SgrA* is Ultra-Compact • Radio VLBI images show that Sgr A* is extremely compact (Shen et al. 2005; Doeleman et al. 2008; Fish et al. 2010) • Size ~ few RS • From the observed radio flux, estimated brightness temperature is TB  1010 K • This means that the radiating gas has a temperature: T TB > 1010 K

21. Brightness Temperature TB • TB is the temperature at which a blackbody would emit the same flux at a given wavelength as that observed • If the source is truly a blackbody, TB directly gives the temperature of the object • If not, then • temperature of the object is larger: T > TB • optically thin emission (semi-transparent)

22. A Surface Will Emit Blackbody Radiation • Any astrophysical object that has been accreting for a long time (~1010 years) will be in steady state and will radiate from its surface very nearly as a blackbody • Because • Steady state thermal equilibrium (T) • Optically thick (opaque) blackbody (T)

23. Radio/Submm Radiation Must Be From the Accretion Disk • Blackbody emission from optically thick gas at temperature T TB > 1010 K would peak in -rays (and would outshine the universe!!): L = 4R2T4 ~ 1062 erg/s • Sgr A*is definitely not doing this!! • Therefore, the radiation from Sgr A* must be emitted by gas that is optically thin in IR/X-rays/-rays • This radiation cannot be from the “surface” of Sgr A* • It must be from the (optically thin) accretion flow

24. Luminosity and Spectrum of Sgr A* Sub mm

25. Is There Any “Surface” Emission from Sgr A*? • The surface luminosity is expected to be LsurfLacc (very likely LsurfLacc ) • Since we know Lacc ~ 1036 erg/s, we expect: Lsurf 1036 erg/s (or even  1036 erg/s) • For typical radii of Sgr A*’s “surface” the radiation is predicted to come out in the IR • But there is no sign of this radiation!!

26. Based on Broderick & Narayan (2006) All four IR bands have flux limits well below the predicted flux even though model predictions are very conservative (e.g., assume radiatively efficient). Therefore,Sgr A*cannot have a surface, i.e., it must be a BH

27. Summary of the Argument • Sgr A*=dark object at the Gal. Center • The observed sub-mm emission in Sgr A*is definitely from the accretion flow, not from the surface of the compact object • If Sgr A* has a surface we expect at least ~1036 erg/s from the surface • This should come out in the IR • Measured limits are far below prediction • Therefore, Sgr A* cannot have a surface

28. Does the Argument Survive in Strong Gravity? • In some very unusual models of compact stars (e.g., gravastar, dark energy star), it is possible to have a surface close to the Event Horizon: R* = 2M + R, R  2M • Extreme relativistic effects, e.g., largegravitational redshifts,are expected • Can this hide the surface emission? NO!!

29. Radiation May Take Forever to Get Out • The extra delay relative to the Newtonian case is TINY • At most it is ~ 1 hr(forR ~ Planck scale!) --- no big deal • Unless R/Rstar~ exp[-1016] !!

30. Gravitational Redshift Will Kill the Emission • Looks serious, especially if redshift is large • But energy has to be conserved, and it is easy to show that this argument is false

31. Radiation Does Not have a Blackbody Spectrum • If R < 3GM/c2 = (3/2)RS, then some rays from the surface are bent back and return to the surface

32. For large redshift, there is only a tiny hole for radiation to escape • Even though surface “looks” convex in Schwarzschild coordinates, it is actually highly concave in terms of photon geodesics! • In fact, it is the perfect textbook example of a blackbody: a furnace with a pinhole! • Therefore, the larger the redshift, the closer the emission will be to blackbody! BB radn Furnace =

33. Particle Emission • Could the emission come out in dark particles? • Surface emission is thermal – so we expect a (nearly) perfect blackbodyspectrum • Only photons,and particles with mc2 < kT(neutrinos), will reach infinity • (At surface, TlocT many other particles) • Allowing for three types ofneutrinos, the observed photon luminosity is reduced by 16/29 (Broderick & Narayan 2007) – no big deal

34. One Key Assumption • We do make one key assumption • We assume that the radio/sub-mm radiation is produced by accretion • Hence, one way out of an Event Horizon is to say that Sgr A* is powered by something other than accretion • Then where is the accretion luminosity?

35. Let us Accept that Sgr A* and Other Astrophysical BH Candidates have no Surfaces • Does this prove that these objects have Event Horizons and aretruly BHs? • Not really – there are other options • However, they are even more bizarre!

36. Wormholes • Damour & Solodukhin (2007) • Wormholes can “look” just like BHs • Accreting gas falls and then bounces back • If bounce-back time is long enough, then cannot distinguish a Wormhole from a BH • But it requires:   exp[-1015] (!!) • Is such an extreme value reasonable? • Could accreted mass modify the solution?

37. Naked Singularities (Joshi) • E.g., Kerr solution with a*>1 (super-spinars): Bambi & Freese (2009), Bambi et al. (2009, 2010,…) • Q: Are naked singularities consistent with the lack of “surface radiation”? • If we can see down to the singularity, we might expect to observe continued emission from gas right down to the center • In this case the object will be very bright…

38. Summary • A variety of strong astrophysical arguments indicate that astrophysical BH candidates have no surface • No surface emission seen in Sgr A* • Each argument by itself is pretty strong • The combined evidence is Super-Strong • Our BHs must have Event Horizons • Unless wormholes, naked singularities?!