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#11
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Black hole mass-sigma correlation
Hans Aberg wrote:
Only approximately, as there is a GR correction showing that they will in fact slowly drop into the center (due to emission of "gravity waves"). This is also why this development is so exiting: As GR, unlike Newtonian physics, predicts that the galaxy mass should drop into the center, one would think that the belief that there are black holes at the centers of the galaxies should have come along very early, but in fact it took a long time. Now there are even formulas for telling the size of that black hole mass. This effect should be completely negligible compared to other effects taking place in a galaxy, such as the transport of angular momentum by the spiral arms, which may let some of the material in the galactic disc drift inwards while angular momentum is transported outwards, and the scattering of stars against giant molecular clouds. There may be even more dramatic effects taking place during the formation of a galaxy, and as far as we can tell today the black holes at the centers of the galaxies form early in the life of the galaxies. Angular momentum loss through the emission of gravitational waves can be important in the evolution of close binaries though, and provides a perfect explanation for the timings of the double pulsar PSR 1916+13. Ulf Torkelsson [Mod. note: reformatted to 80 characters per line -- mjh] |
#12
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Black hole mass-sigma correlation
Hans Aberg wrote:
I am not an expert at GR computations, but my intuition about it was that sufficiently massive objects will emit those gravitational waves. Thus, other forces may be stronger in the short term, but unless there is some outward push by some non-gravitational forces, say solar winds from the stars or the like, in the long term, mass should drop into the center. For the general relativistic deviations from Newtonian gravity to become dominating we need to have (GM/c^2)/L to be of order unity. For a galaxy with a mass of 10^(12) solar masses GM/c^2 is of the order of 10^(12) km, and the galaxy has a size of 10 kpc, which is 10^(16) km, so you can forget general relativity on the scale of individual galaxies. Assuming that there is a black hole of 10^8 solar masses at the center of the galaxy we see that you need to get within 10^8 km of that before general relativity becomes really important, that is about the distance between the Earth and the Sun. The damping time scale of the orbit due to gravitational radiation is L/c (L/(GM/c^2))^3, see for instance Shapiro, S. L., Teukolsky, S. A., 1983, Black holes, white dwarfs, and neutron stars, John Wiley & Sons, New York, which for our galaxy is 10^(17) years. This BBC World program described a theory explaining the black hole mass-sigma correlation in terms of a black hole formed even before the galaxy had formed. It suggested that this was in reality the quasars, galaxies in very early formation, emitting radiation from the black hole. The idea was that this black hole should then stop feeding. Right, but keep in mind that this radiation is formed in the gas that is accreting onto the black hole, and the process is essentially one described by classical hydrodynamics. The exception being if the black hole is rotating, in which case there is a theoretical possibility to tap the black hole of its rotational energy. In the latter case you need to do relativistic (magneto)hydrodynamics in a Kerr metric. However, this program also presented some even later research, suggesting that the black hole is feeding also in later stages of the galaxy life. In addition, I have vague memory of research a few years ago suggesting that our Milky Way black hole is feeding, even swallowing up some stars, and it should be in its middle age. Therefore, taking those circumstantial pieces of evidence into account, it might perhaps be the case that the galaxy center black holes are feeding a lot more than those facts you are mentioning suggest. Actually the accretion rate onto the black hole in the centre of the Milky Way is quite low for the moment, definitely much lower than in an ordinary active galaxy or quasar, see for instance Mezger, P. G., Duschl, W. J., Zylka, R., 1996, The Galactic Center: a laboratory for AGN?, Ann. Rev. Astron. & Astrophys., 7, 289 My guess is that such observations have in the past been used in order to confirm GR. Actually the observations of PSR 1916+13 are still the only observations showing that gravitational waves are generated. Ulf Torkelsson [Mod. note: quoted text trimmed -- mjh.] |
#13
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Black hole mass-sigma correlation
Hans Aberg wrote:
I am not an expert at GR computations, but my intuition about it was that sufficiently massive objects will emit those gravitational waves. Thus, other forces may be stronger in the short term, but unless there is some outward push by some non-gravitational forces, say solar winds from the stars or the like, in the long term, mass should drop into the center. For the general relativistic deviations from Newtonian gravity to become dominating we need to have (GM/c^2)/L to be of order unity. For a galaxy with a mass of 10^(12) solar masses GM/c^2 is of the order of 10^(12) km, and the galaxy has a size of 10 kpc, which is 10^(16) km, so you can forget general relativity on the scale of individual galaxies. Assuming that there is a black hole of 10^8 solar masses at the center of the galaxy we see that you need to get within 10^8 km of that before general relativity becomes really important, that is about the distance between the Earth and the Sun. The damping time scale of the orbit due to gravitational radiation is L/c (L/(GM/c^2))^3, see for instance Shapiro, S. L., Teukolsky, S. A., 1983, Black holes, white dwarfs, and neutron stars, John Wiley & Sons, New York, which for our galaxy is 10^(17) years. This BBC World program described a theory explaining the black hole mass-sigma correlation in terms of a black hole formed even before the galaxy had formed. It suggested that this was in reality the quasars, galaxies in very early formation, emitting radiation from the black hole. The idea was that this black hole should then stop feeding. Right, but keep in mind that this radiation is formed in the gas that is accreting onto the black hole, and the process is essentially one described by classical hydrodynamics. The exception being if the black hole is rotating, in which case there is a theoretical possibility to tap the black hole of its rotational energy. In the latter case you need to do relativistic (magneto)hydrodynamics in a Kerr metric. However, this program also presented some even later research, suggesting that the black hole is feeding also in later stages of the galaxy life. In addition, I have vague memory of research a few years ago suggesting that our Milky Way black hole is feeding, even swallowing up some stars, and it should be in its middle age. Therefore, taking those circumstantial pieces of evidence into account, it might perhaps be the case that the galaxy center black holes are feeding a lot more than those facts you are mentioning suggest. Actually the accretion rate onto the black hole in the centre of the Milky Way is quite low for the moment, definitely much lower than in an ordinary active galaxy or quasar, see for instance Mezger, P. G., Duschl, W. J., Zylka, R., 1996, The Galactic Center: a laboratory for AGN?, Ann. Rev. Astron. & Astrophys., 7, 289 My guess is that such observations have in the past been used in order to confirm GR. Actually the observations of PSR 1916+13 are still the only observations showing that gravitational waves are generated. Ulf Torkelsson [Mod. note: quoted text trimmed -- mjh.] |
#14
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Black hole mass-sigma correlation
Hans Aberg wrote:
However, it depends on how that 1983 formula was derived: Perhaps it makes some approximations about heavy objects moving in orbit in order to filtrate out GR effects. It is just a simple order of magnitude estimate to check whether gravitational radiation is relevant in these circumstances and it is not. If mass is spread over an area, then one may have to integrate over the matter distribution to find more accurate GR corrections. Perhaps this gains some magnitudes in the GR corrections. Then it might the case that more significant amounts of matter drops into the center. Yes, much more matter drops into the center in the beginning because of a pure Newtonian effect called free fall. The reason that not all the matter drops into the center is due to another Newtonian effect called conservation of angular momentum. There is no need to invoke relativistic complications to understand this. By the standards of this development, this paper is should be old. I do not remember exactly what they said on the BBC Horizon program, but I got the impression that they said that one thought the Milky Way(?) center black hole should be stable (i.e., non-feeding), but now they had some evidence that it was not so. I got the impression that these results are more recent than the observational verification of the black hole mass-sigma correlation. No, the existence of a black hole at the center of our galaxy was discussed already in the seventies, and in the nineties it was clear that the accretion rate onto this black hole is actually quite small, though not negligible, compared to that of active galaxies. The black hole mass-sigma correlation is fresher than that, but they are in accordance with each other. Ulf Torkelsson [Mod. note: quoted text trimmed, reformatted, &c -- mjh.] |
#15
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Black hole mass-sigma correlation
Hans Aberg wrote:
However, it depends on how that 1983 formula was derived: Perhaps it makes some approximations about heavy objects moving in orbit in order to filtrate out GR effects. It is just a simple order of magnitude estimate to check whether gravitational radiation is relevant in these circumstances and it is not. If mass is spread over an area, then one may have to integrate over the matter distribution to find more accurate GR corrections. Perhaps this gains some magnitudes in the GR corrections. Then it might the case that more significant amounts of matter drops into the center. Yes, much more matter drops into the center in the beginning because of a pure Newtonian effect called free fall. The reason that not all the matter drops into the center is due to another Newtonian effect called conservation of angular momentum. There is no need to invoke relativistic complications to understand this. By the standards of this development, this paper is should be old. I do not remember exactly what they said on the BBC Horizon program, but I got the impression that they said that one thought the Milky Way(?) center black hole should be stable (i.e., non-feeding), but now they had some evidence that it was not so. I got the impression that these results are more recent than the observational verification of the black hole mass-sigma correlation. No, the existence of a black hole at the center of our galaxy was discussed already in the seventies, and in the nineties it was clear that the accretion rate onto this black hole is actually quite small, though not negligible, compared to that of active galaxies. The black hole mass-sigma correlation is fresher than that, but they are in accordance with each other. Ulf Torkelsson [Mod. note: quoted text trimmed, reformatted, &c -- mjh.] |
#16
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Black hole mass-sigma correlation
In article , Ulf Torkelsson
wrote: However, it depends on how that 1983 formula was derived: Perhaps it makes some approximations about heavy objects moving in orbit in order to filtrate out GR effects. It is just a simple order of magnitude estimate to check whether gravitational radiation is relevant in these circumstances and it is not. My worry is that Newtonian 1/r forces are very special mathematically, making formulas line up very nicely, making angular momentum around different points independent. GR has some compensations thrown in, so it could be that one has to take the interactions of the different components into account in order to get better GR correction. If mass is spread over an area, then one may have to integrate over the matter distribution to find more accurate GR corrections. Perhaps this gains some magnitudes in the GR corrections. Then it might the case that more significant amounts of matter drops into the center. Yes, much more matter drops into the center in the beginning because of a pure Newtonian effect called free fall. The reason that not all the matter drops into the center is due to another Newtonian effect called conservation of angular momentum. There is no need to invoke relativistic complications to understand this. If some large cloud already has angular momentum, why should mass drop into the center? It does not happen with the planets in orbit. By the standards of this development, this paper is should be old. I do not remember exactly what they said on the BBC Horizon program, but I got the impression that they said that one thought the Milky Way(?) center black hole should be stable (i.e., non-feeding), but now they had some evidence that it was not so. I got the impression that these results are more recent than the observational verification of the black hole mass-sigma correlation. No, the existence of a black hole at the center of our galaxy was discussed already in the seventies, and in the nineties it was clear that the accretion rate onto this black hole is actually quite small, though not negligible, compared to that of active galaxies. The black hole mass-sigma correlation is fresher than that, but they are in accordance with each other. You must have misunderstood what I said: The program said that one thought that the black hole accretion rate was low, in seeming accordance with the model that seems to explain the black hole mass-sigma correlation. But some research later then the discovery of the black hole mass-sigma correlation suggested otherwise, namely that it might in fact be higher, at a rate not explainable by this theory. It was mentioned at the very end of that program. The comment did not have anything to do with the history of the discussion of that there should be a black hole there. Hans Aberg |
#17
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Black hole mass-sigma correlation
In article , Ulf Torkelsson
wrote: However, it depends on how that 1983 formula was derived: Perhaps it makes some approximations about heavy objects moving in orbit in order to filtrate out GR effects. It is just a simple order of magnitude estimate to check whether gravitational radiation is relevant in these circumstances and it is not. My worry is that Newtonian 1/r forces are very special mathematically, making formulas line up very nicely, making angular momentum around different points independent. GR has some compensations thrown in, so it could be that one has to take the interactions of the different components into account in order to get better GR correction. If mass is spread over an area, then one may have to integrate over the matter distribution to find more accurate GR corrections. Perhaps this gains some magnitudes in the GR corrections. Then it might the case that more significant amounts of matter drops into the center. Yes, much more matter drops into the center in the beginning because of a pure Newtonian effect called free fall. The reason that not all the matter drops into the center is due to another Newtonian effect called conservation of angular momentum. There is no need to invoke relativistic complications to understand this. If some large cloud already has angular momentum, why should mass drop into the center? It does not happen with the planets in orbit. By the standards of this development, this paper is should be old. I do not remember exactly what they said on the BBC Horizon program, but I got the impression that they said that one thought the Milky Way(?) center black hole should be stable (i.e., non-feeding), but now they had some evidence that it was not so. I got the impression that these results are more recent than the observational verification of the black hole mass-sigma correlation. No, the existence of a black hole at the center of our galaxy was discussed already in the seventies, and in the nineties it was clear that the accretion rate onto this black hole is actually quite small, though not negligible, compared to that of active galaxies. The black hole mass-sigma correlation is fresher than that, but they are in accordance with each other. You must have misunderstood what I said: The program said that one thought that the black hole accretion rate was low, in seeming accordance with the model that seems to explain the black hole mass-sigma correlation. But some research later then the discovery of the black hole mass-sigma correlation suggested otherwise, namely that it might in fact be higher, at a rate not explainable by this theory. It was mentioned at the very end of that program. The comment did not have anything to do with the history of the discussion of that there should be a black hole there. Hans Aberg |
#18
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Black hole mass-sigma correlation
Hans Aberg wrote:
My worry is that Newtonian 1/r forces are very special mathematically, making formulas line up very nicely, making angular momentum around different points independent. GR has some compensations thrown in, so it could be that one has to take the interactions of the different components into account in order to get better GR correction. The order of magnitude estimate that I was using is based on GR. There are no gravitational waves in Newtonian gravity theory. Apart from that the differences between GR and Newtonian physics is small as long as GM/(c^2 r) is small. If some large cloud already has angular momentum, why should mass drop into the center? It does not happen with the planets in orbit. The difference between a gas cloud and the planets is that different parts of the gas cloud are interacting with each other through hydrodynamic forces. Thus the angular momentum can be re-distributed within the gas cloud allowing some parts of the cloud to gain most of the angular momentum, while other gas elements fall to the center of the cloud. Ulf Torkelsson [Mod. note: quoted text trimmed and posting reformatted, again -- mjh] |
#19
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Black hole mass-sigma correlation
Hans Aberg wrote:
My worry is that Newtonian 1/r forces are very special mathematically, making formulas line up very nicely, making angular momentum around different points independent. GR has some compensations thrown in, so it could be that one has to take the interactions of the different components into account in order to get better GR correction. The order of magnitude estimate that I was using is based on GR. There are no gravitational waves in Newtonian gravity theory. Apart from that the differences between GR and Newtonian physics is small as long as GM/(c^2 r) is small. If some large cloud already has angular momentum, why should mass drop into the center? It does not happen with the planets in orbit. The difference between a gas cloud and the planets is that different parts of the gas cloud are interacting with each other through hydrodynamic forces. Thus the angular momentum can be re-distributed within the gas cloud allowing some parts of the cloud to gain most of the angular momentum, while other gas elements fall to the center of the cloud. Ulf Torkelsson [Mod. note: quoted text trimmed and posting reformatted, again -- mjh] |
#20
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Black hole mass-sigma correlation
In article , Ulf Torkelsson
wrote: My worry is that Newtonian 1/r forces are very special mathematically, making formulas line up very nicely, making angular momentum around different points independent. GR has some compensations thrown in, so it could be that one has to take the interactions of the different components into account in order to get better GR correction. The order of magnitude estimate that I was using is based on GR. Sure, that was clear from your posts. There are no gravitational waves in Newtonian gravity theory. And this is, of course the reason one wants to put in GR corrections. Apart from that the differences between GR and Newtonian physics is small as long as GM/(c^2 r) is small. What might make a difference in the magnitude of this smallness is that it may behave differently when just considering say two point masses, or a large distribution of mass where individual components may emit gravitational waves by mutual GR interaction (not just against the center mass). In picture, this difference might be like the difference between planets and a gas, with GR influences replacing gas hydrodynamic forces. If the paper you quoted with the rough GR estimate does not do that latter thing, integrating over the GR corrections, then that might be one thing to look up before writing off GR influences as wholly negligible. -- Especially, if there is someone out there doing observations that might suggest that the Milky Way black hole feeding rate is in fact higher than explainable by the suggested the black hole mass-sigma correlation model, the latter which only derives from Newtonian physics. The most important thing, though, would be to pin down the feeding rate of the Milky Way black hole. But if it eventually turns out to be higher than earlier research suggested, and you are positively sure that there is an estimate that once and for all rules out all GR effects, what should cause it? -- The alternative explanation (to that of GR waves) would be that there is some gas that for some reason is loosing its angular momentum. Hans Aberg |
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