Frontiers: Observational Signatures of Strong GravityAs we said a few lectures ago, general relativity is in a unique position among theoriesof fundamental interactions, because of the relative weakness of gravity. One can, for ex-ample, probe EM or strong/weak interactions using particle accelerators, and by this cantest the predictions of these theories in relatively extreme environments. But experimental,laboratory tests of GR predictions are limited to weak gravity. These include things like thegravitational redshift of light, light deflection by the Sun, delays of radio waves, and GRprecession of planets. However, GR corrections are typically of order M/r compared to theNewtonian predictions. This is very small in things to which we have access; for example,M/r ≈ 2 × 10−6for the Sun and M/r ≈ 10−9for the Earth. Even for signals from binarypulsars, it is their separation of ∼ 1011cm that matters, so again M/r ¿ 1.Therefore, many of the predictions of GR in strong gravity are untested experimentally.Since these predictions are used to model all black holes and neutron stars, the actualbehavior of gravity in these regimes is very important. Here’s an example. Suppose that blackholes are pseudo-Newtonian, in the sense that they have horizons but no ISCO. Therefore,gas will spiral in nearly circular orbits right down to the horizon, then get sucked in. Thismeans that they will release 50% of their mass-energy as they spiral. Ask class: how wouldwe use this, plus the Eddington luminosity, to estimate how long it would take a black holeto grow in mass? Since LEis the maximum luminosity of accretion, the maximum accretionrate is˙ME= LE/²c2, which is 3 × 1017g s−1(M/M¯), or 2.2 × 108yr for an e-folding time. Ifblack holes are originally formed with roughly stellar masses, ∼ 10− 100 M¯, then they needmore than 10 e-foldings to reach supermassive status. This would take 2-3 billion years, sowe wouldn’t expect any AGN at z > 4 − 5, even if the black holes all accrete at Eddington.This would pose problems. In contrast, with an ISCO the accretion efficiency is lower, sothere is no problem. Other consequences would be that one could no longer be sure aboutthe existence of black holes at all, if GR is dramatically wrong in the strong-gravity limit.In this lecture, then, we’ll talk about various possible and claimed signatures. You’ll geta chance to use your skeptical faculties to think about what might be problematic for theseclaims. That may sound purely negative, but it gives a better appreciation for the moresolid claims when these are encountered.Types of signaturesThe point, then, is to look for qualitatively new aspects of GR compared to Newtonianpredictions, and think of how these might be manifest in the data. Ask class: what aresome qualitatively new aspects of GR? ISCO, frame-dragging, horizon, epicyclic frequencies.Ask class: what are some ways they might imagine detecting effects due to these? Ingeneral, one has imaging, spectral, and timing information. How can these be used? WithStarship Enterprise-like resolution, one could think of imaging the event horizon of a blackhole, and seeing a variety of effects on background stars or the accretion disk that could becompared with predictions. Ask class: how can we estimate the angular resolution needed?We need to think of the largest angular scale that a black hole’s horizon could subtend. Firstguess: stellar-mass black hole. Typically about 10 M¯, so for Schwarzschild the horizon isabout 30 km across. The number in the Galaxy is probably around 108, so if the Galaxy hasa volume of (10 kpc)2×1 kpc, the average density of black holes is 10−3pc−3, so the nearestBH is probably 10 pc away. The angular size is then about 3 × 106/3 × 1019= 10−13rad,or about 2 × 10−8arcseconds. The black hole in the center of our Galaxy has a mass of3.5 × 106M¯and is 8 kpc distant, for an angle of 4 × 10−11rad, or 8 × 10−6arcseconds.These are really, really tiny, and probably out of reach for quite a while, although at slightlylarger scales VLBI might be able to do something.SpectraOur next try is spectra. Ask class: what kind of spectral signatures might reveal stronggravity effects? There are two types that have been suggested: line profiles or continuumspectra. We’ll start with continuum spectra to emphasize the need for line profiles!One type of continuum fit that attracted a lot of attention a few years ago was spectralfits to an accretion disk. A few lectures ago we discussed geometrically thin, optically thickdisks, and gave a rough derivation of their emission spectrum assuming that each annulusradiates as a blackbody, but with a temperature that depends on the radius and on the massaccretion rate. An idea dating to at least the mid-80s is that this may provide a signatureof the ISCO. Suppose, people argued, that one does a careful fit of the spectrum. Themodel parameters include things like the viewing angle, but more importantly include Rin,the innermost radius of the nearly circular flow, and the innermost radius of the significantemission. Black hole sources have varying mass accretion rates, but if Rinis the ISCO, itsvalue should remain constant. In a few sources this seemed to be the case, and some pressreleases were sent out indicating that the long sought after strong-gravity signature had beenseen.Ask class: what are some of the things that could go wrong here? One problem is thatthe fits are nonunique, to put it mildly. The real regions are more complicated, probably withhot coronae above the disk that reprocess radiation. Also, if you fool around with differentparameters you see that several of them are practically degenerate, meaning that you canchange Rinif you change the spin of the black hole or even the emissivity. Observationally,most sources have variable Rin, down to unphysical values such as 2 km, so this is not apromising direction. Incidentally, this type of fitting is still used by some researchers to inferother properties such as the spin of the black hole. I am highly dubious about this, becausethis is an even finer level of detail and cannot (at least at this time) be interpreted uniquely.One lesson that I think comes from this is that smooth continuum spectra are oftendifficult to interpret correctly. From an information-theoretic standpoint, they just don’tcontain that much information. Power laws, broad bumps, etc., can be produced by manymechanisms, so