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UMD ASTR 680 - Evidence for BH: Orbits and Stellar Sources

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Evidence for BH: Orbits and Stellar SourcesStar motions in galactic centersOne set of observations, which has had promise for years but has only come into itsown in the past decade, is the observation of star motions in the centers of galaxies. Oneexpects that the most massive things will settle into the centers of galaxies by gravitationalinteractions, so it is reasonable to look for black holes there. If the hole is not accretingactively, its presence can be sensed by the motion of stars near it. In particular, if manystars are m oving rapidly in ways that are consistent with an orbit, then by determinationof their velocity and their radius of orbit one can infer the mass interior to them. This issomething that has plenty of potential hazards. For example, the motion had better bedue to the gravity of the central mass(es), and not something else. About 15 years agothere was a press release announcing the discovery of a 1011M⊙black hole in the center ofone galaxy, but the authors had to retract when it was discovered that they were actuallylooking at the center of two galaxies merging; the high velocities were ballistic, not orbital!However, many examples have by this time been found, particularly with telescopesor techniques that allow excellent angular resolution, so one can look at many individualstars as close as possible to the central object. For our own Galaxy, individual stellar orbitscoming as close as 40-60 AU from the Galactic center indicate that there is a mass of about3.5× 106M⊙interior to those radii. This implies a mass density of at least 3× 1016M⊙pc−3.However, in principle one could imagine placing stars in that region, and there would be asurprisingly large amount of space available; equally spaced, the typical volume available toa 1 M⊙star would be about 0.25 AU3, which is about 500,000 times the volume of the Sun.Ask class: therefore, what is the real issue here?If you tried to put normal stars in that volume, you’d see them; several million solarluminosities wouldn’t be missed by observers. However, you could put stellar remnants inthat region, e.g., white dwarfs or especially neutron stars, and they would be too dim tosee. Sin ce neutron stars are really tiny (10 km radius, or another factor of 3 × 1014smallerin volume than the Sun), they wouldn ’t be colliding with each other! We therefore haveto be a little more sophisticated. It turns out that in such a small volume, if you populatethe region with stellar-mass objects, their mutual gravitational perturbations would flingeach other out of the region or cause other dynamical catastrophes in a matter of tens ofthousands of years, which is a blink of the astrophysical eye. You could try to put d arkmatter there in the form of elementary particles, but then stars moving into and out of thatregion would kick the particles out and sink in, so that doesn’t work. Some people haveproposed exotic solutions such as boson stars or fermion stars, but no specific ideas of thistype work and it must be said that any such objects would be a lot more exotic than blackholes!For more discussion of these issues, you might take a look at (*modest cough*) Miller,M. C. 2006, MNRAS, 367, L32Black holes in binariesThe above is enough to demonstrate that black holes must exist. However,complementary (and in some ways more convincing) evidence exists from the study ofX-ray binaries. In many cases one sees X-rays coming from a region that contains a visiblestar that is orbiting around something not evident in optical. Ask class: do they knowwhat needs to be measured to get a constraint on the mass? One can measure the periodP of the orbit and the radial velocity v1along the line of sight of the visible companion inits orbit. Here the “1” indicates that the visible object is labeled 1 (the invisible object islabeled 2). From these observables and Kepler’s third law one can calculate an importantquantity called the “mass function”,f(M1, M2, i) =P v312πG=(M2sin i)3(M1+ M2)2. (1)Here M1is the mass of the visible star 1, M2is the mass of the invisible star 2, and i is th einclination angle of the orbital axis relative to the line of sight (e.g., i = 0 for face-on, i = 90for edge-on). You can convince yourself that the minimum mass of the unseen star is just f,which occurs for M1= 0 and i = 90. Th erefore, from just these two measured parameters,it is possible to get a lower limit on the mass of the unseen object. Extremely generalconsiderations (the assumption that GR is the correct theory of gravity!) indicate thatneither a neutron star nor any other object with a surface that is supported by degeneracypressure can have a gravitational mass more than 3 M⊙(the real limit is probably closer to2 M⊙). Therefore, if f > 3 M⊙, you’ve got a black hole. This is the case for > 20 sourcesin the Galaxy. Incidentally, there are some systems where one can say something aboutthe inclination angle i (mainly by modeling the variation in the optical light curve as thedistorted star orbits around). For those, one can get fairly precise estimates of the blackhole mass. The examples in which f > 3 M⊙all have companions with low masses, unlikebetter-known candidates such as Cyg X-1. Ask class: why would it be easier to get massestimates when the hole has a low-mass companion? Because the companion is movedaround more by the gravity of the black hole. For higher-mass stars, the mass functionis typically low because M1> M2. Uncertainties in the true mass of the companion thenmake rigorous identification of the black hole very difficult if not impossible. There are alsosignificant differences between accretion onto a black hole from a low-mass or a high-masscompanion. We will now investigate them.Accretion from a low-mass companionIf the companion is a low-mass star, then it has few innate processes by which it losesmass. Mass transfer therefore happens when the star evolves or spirals close enough to theblack hole that the star’s radius exceeds the radius of its Roche lobe (that is, the matterbecomes gravitationally unbound with respect to the companion, and hence flows over tothe black hole). Ask class: would the mass that makes its way to the black hole thereforehave high or low angular momentum? High. Ask class: so, what happens to the mass asit spirals in? An accretion disk forms, as we’ve discussed previously. The long evolutionarytimes of low-mass stars means that this kind of accretion can continue for


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UMD ASTR 680 - Evidence for BH: Orbits and Stellar Sources

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