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Ligo. What happened 1.3 billion years ago.
In Nature of 18 Februari 2016 at page 263 we read:
"Surprisingly Ligo's first detection dit not come from a binary neutron star system etc but from two large BH's. Both were of the order of 30 times the mass of the Sun. 'They are real astronomical beast'." My understanding is that BH's 30 times the size of the Sun are extremely small.See: https://en.wikipedia.org/wiki/List_o..._massive_stars See: https://en.wikipedia.org/wiki/List_o...ve_black_holes At page 262 we read: "Although the two BH's had probably been orbiting each other for millions of years LIGO began to pick up their waves only when they reached a a freq of 35 Hz. This frequency rapidly increased to 250 Hz." This sentence gives the impression that binary systems in general are stable configurations. So what happened. Simulations I have performed give the impression that for a binary system to merge generally speaking at least one object should increase in mass. For example comets which collide with the Sun will decrease the size of the solar system. This brings me to my question: Are we sure that this is really a binary system and is not a third object involved. See for example: http://users.telenet.be/nicvroom/VB%...0operation.htm Starting point of simulation is a binary star system. The standard configuration is that the masses are 1000, 1000 and 1. When you change this configuration to 1000, 500 and 50 you can investigate the influence the a relative large third object. In such a simulation you can get a configuration with average distance (radius) of 200 units, which changes in an elipse which shortest distance of 100 units. In the case of the BH you will get something like 36,29 and 3 Solar m. In this particular case I assume that the third object is rather small but it also could be a red giant which constantly transmit mass to the binary BH system Nicolaas Vroom |
#2
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Ligo. What happened 1.3 billion years ago.
In article , Nicolaas Vroom
writes: In Nature of 18 Februari 2016 at page 263 we read: "Surprisingly Ligo's first detection dit not come from a binary neutron star system etc but from two large BH's. Both were of the order of 30 times the mass of the Sun. 'They are real astronomical beast'." My understanding is that BH's 30 times the size of the Sun are extremely small.See: https://en.wikipedia.org/wiki/List_o..._massive_stars See: https://en.wikipedia.org/wiki/List_o...ve_black_holes The term "beast" here means large in mass, not in radius. At page 262 we read: "Although the two BH's had probably been orbiting each other for millions of years LIGO began to pick up their waves only when they reached a a freq of 35 Hz. This frequency rapidly increased to 250 Hz." This sentence gives the impression that binary systems in general are stable configurations. In general, yes, but they lose energy via gravitational waves. So what happened. Due to energy loss via gravitational waves, the orbits decayed until they merged. Simulations I have performed give the impression that for a binary system to merge generally speaking at least one object should increase in mass. For example comets which collide with the Sun will decrease the size of the solar system. Did you include energy loss via gravitational waves? This brings me to my question: Are we sure that this is really a binary system and is not a third object involved. Calculations are done for two merging objects and the comparison with observations is good. There is no hint of a third object. |
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Ligo. What happened 1.3 billion years ago.
Op zondag 28 februari 2016 08:28:43 UTC+1 schreef Phillip Helbig:
The term "beast" here means large in mass, not in radius. IMO the BH in the center of the Milkey Way is a beast, almight a small one compared with others. At page 262 we read: "Although the two BH's had probably been orbiting each other for millions of years LIGO began to pick up their waves only when they reached a a freq of 35 Hz. This frequency rapidly increased to 250 Hz." This sentence gives the impression that binary systems in general are stable configurations. In general, yes, but they lose energy via gravitational waves. Consider 3 different configurations: 1. A binary star system of 30 solar masses each. 2. A binary BH system of 30 solar masses each. 3. A one BH system of 60 solar masses. Consider as part of each system a star of 1 solar mass which rotates at a certain distance r from the Center of Gravity of each. Is it true that the speed v and the revolution time in each of these cases is identical? That being the case do you agree that the loss in gravitational energy in each case is the same? Gravitational energy loss implying gravitons? So what happened. This brings me to my question: Are we sure that this is really a binary system and is not a third object involved. Calculations are done for two merging objects and the comparison with observations is good. There is no hint of a third object. When an ordinary large star approaches a Binary Black Hole system it will evaporate (as a matter of saying). This process will increase the mass of the two BH's which will start to merge. Nicolaas Vroom |
#4
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Ligo. What happened 1.3 billion years ago.
Nicolaas Vroom wrote:
Consider 3 different configurations: 1. A binary star system of 30 solar masses each. 2. A binary BH system of 30 solar masses each. 3. A one BH system of 60 solar masses. Let me first answer your questions for cases 1 and 2; here the issues are quite clear-cut: Is it true that the speed v and the revolution time in each of these cases is identical? That being the case do you agree that the loss in gravitational energy in each case is the same? Gravitational energy loss implying gravitons? The speed v and the orbital period, and the rate of gravitational-radiation emission, all depend on the distance between the two bodies. If that distance is the same between cases 1 and 2, then apart from tidal effects (which are only important for very close-in binaries -- they fall off rapidly with orbital separation), cases 1 and 2 will have identical orbital speeds, periods, and gravitational-radiation emission. Consider as part of each system a star of 1 solar mass which rotates at a certain distance r from the Center of Gravity of each. If the 1-solar-mass star orbits at a distance that is *not* very much larger than the distance between the two 30-solar-mass objects (say, in very round numbers, less than 1000 times the distance between the two 30-solar-mass objects), then even in Newtonian gravity the 1-solar-mass star will feel a different gravitational potential between cases 1/2 and 3, which will lead to slightly different long-term orbital evolution of the 1-solar-mass star. See, for example, https://en.wikipedia.org/wiki/Kozai_mechanism But if the 1-solar-mass star orbits at a distance that is much larger than the distance between the two 30-solar-mass objects, then there will be relatively little difference in the 1-solar-mass-star's orbit between cases 1/2 and 3. Again, cases 1 and 2 will be essentially identical, but case 3 will differ a bit even at the Newtonian level. Adding relativistic effects doesn't change this picture much. This brings me to my question: Are we sure that this is really a binary system and is not a third object involved. By the customary standards of "proof" in astrophysics, yes, we're sure that there is not a dynamically-significant 3rd object. That is, we can model the system very nicely as a binary system, so Occham's razor (actually Russell's teapot, https://en.wikipedia.org/wiki/Russell%27s_teapot) argues against hypothesizing a 3rd undetectable object which doesn't significantly influence the dynamics of the two detectable objects. The basic binary-system analysis is pretty simple: The observed gravitational-wave signal is sinusoidal, and it sweeps up ("chirps") in frequency and amplitude simultaneously. It was first observed above the detector noise at a frequency of around 35 Hz and ended at a frequency of around 250 Hz (*not* limited by detector noise, i.e., if it had kept on chirping up to still-higher frequencies it should have been detectable). The frequency, frequency-chirp rate (i.e. d frequency/d time), and amplitude increase rate (i.e., d amplitude/d time) are all measurable. And they agree exactly with what general relativity predicts for the decay of a close binary system (in this phase of the analysis, it doesn't matter whether the objects are black holes or something else), and there is no other known source which produces such a signal. For this sort of binary system the gravitational-wave signal is *twice* the orbital frequency (there are two complete gravitational-wave cycles per orbit), so the orbital frequency is around 17.5 Hz when the system is first observed, chirping up to around 125 Hz. Assuming that the bodies can't orbit faster than the speed of light, an orbital frequency of 125 orbits/second limits the radius of the orbit to no more than about 380 km. From the overall amplitude of the gravitational-wave signal we know the total mass of the system (a bit over 60 solar masses). So... what sorts of objects which can have a total mass of 60 solar masses and which can get to within 400 km of each other *without* physically colliding (which would lead to quite different gravitational-wave signals that what are observed)? The answer is that the only known objects which could do this are black holes. [Neutron stars are also be compact enough to get within 400 km without colliding... but neutron stars can't exceed about 3 solar masses ("the Chandresekhar limit").] The "icing on the cake" is that after the gravitational-wave signal peaks in amplitude, it rises sharply in frequency and decays rapidly (exponentially) in amplitude. This is (to within the -- sadly rather large -- experimental errors) precisely the pattern you would expect from a black hole which has just formed from a black-hole collision, i.e., a black hole which is not in its equilibrium shape: the newly formed (deformed) black hole "rings down" and settles into its equilibrium shape, and these "ringdown" oscillations have specific frequencies and decay rates. The observed frequency and decay rate of the final part of the observed gravitational-wave signal nicely match (to within those error bars I mentioned) the calculated frequency and decay rate of a distorted black hole ringing down to an equilibrium state (described by the Kerr metric). From that final "ringdown" signal we can estimate the mass of the final black hole (the ringdown frequencies scale as 1/mass), and this mass comes out to be significantly *less* than the sum of the two inspiraling black holes -- a bit over 3 solar masses less, in fact. That's just what you'd expect from merging black holes -- that 3 solar masses corresponds to just the expected-from-general-relativity energy radiated in gravitational waves from a black hole collision of this type. So overall, this is a pretty well-constrained system, and a model based purely on general relativity + the known detector noise spectrum fits the signal beautifully. Of course, it could be that some other system -- one for which noone has yet done a detailed (relativistic-gravity) simulation -- would fit the data equally well. Until these alternatives are simulated in detail (which probably takes years of research, plus large supercomputer simulations), we won't know. What is clear is that this system was observed at a fairly modest signal-to-noise ratio, and that the observations lasted for only a short time ( 1 second). Longer and/or higher-signal-to-noise-ratio observations would (will) allow more stringent tests of whether general relativity alone (still) suffices to accurately model the observed signals. Finally, if you're interested in the details of how the LIGO data is analyzed (the various steps that lie between the raw detector data and the curves you see in the published papers), I second Steve Willner's recommendation There's a tutorial on LIGO data processing at https://losc.ligo.org/s/events/GW150..._tutorial.html From a quick look it seems to be an excellent tutorial. -- -- "Jonathan Thornburg [remove -animal to reply]" Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA currently visiting colleagues in Europe (at one of the institutions closely involved in the LIGO data analysis, in fact) "There was of course no way of knowing whether you were being watched at any given moment. How often, or on what system, the Thought Police plugged in on any individual wire was guesswork. It was even conceivable that they watched everybody all the time." -- George Orwell, "1984" |
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Ligo. What happened 1.3 billion years ago.
Nicolaas Vroom asked:
This brings me to my question: Are we sure that this is really a binary system and is not a third object involved. I replied: By the customary standards of "proof" in astrophysics, yes, we're sure that there is not a dynamically-significant 3rd object. [[...]] The basic binary-system analysis is pretty simple: The observed gravitational-wave signal is sinusoidal, and it sweeps up ("chirps") in frequency and amplitude simultaneously. [[...]] The frequency, frequency-chirp rate (i.e. d frequency/d time), and amplitude increase rate (i.e., d amplitude/d time) are all measurable. And they agree exactly with what general relativity predicts for the decay of a close binary system [[...]] and there is no other known source which produces such a signal. Overall, I'd say the case that this is a binary-something-or-other decay/merger is very very strong -- the "chirp" signal is very characteristic of such a system, and I can't think of (and don't recall ever seeing a published proposal for) any other way to get such a "chirp". The case that the two pre-merger objects were (already) both black holes is somewhat less strong. The data rule out any extended bodies (they would physically collide much earlier than black holes), but if you imagine some sort of exotic object (gravastar, boson star, etc etc) it *might* be possible to fit the data adequately (i.e., to within the finite signal/noise available). The case that the post-merger object is a black hole is also moderately strong. The data are consistent with the "ringing" of a black hole as it relaxes to an equilibrium state, but the signal/noise of this part of the data is modest. The challenge for any alternative hypothesis would be to (quantitative) match the observed frequency and decay rate of the ringing (which do nicely match those predicted for a black hole). Overall, as astrophysics observations go, this is pretty watertight. But of course, observations of more systems and/or observations with higher signal/noise will more tightly constrain our models. -- -- "Jonathan Thornburg [remove -animal to reply]" Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA "There was of course no way of knowing whether you were being watched at any given moment. How often, or on what system, the Thought Police plugged in on any individual wire was guesswork. It was even conceivable that they watched everybody all the time." -- George Orwell, "1984" |
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Ligo. What happened 1.3 billion years ago.
Nicolaas Vroom asked:
This brings me to my question: Are we sure that this is really a binary system and is not a third object involved. I replied: By the customary standards of "proof" in astrophysics, yes, we're sure that there is not a dynamically-significant 3rd object. That is, we can model the system very nicely as a binary system, so Occham's razor (actually Russell's teapot, https://en.wikipedia.org/wiki/Russell%27s_teapot) argues against hypothesizing a 3rd undetectable object which doesn't significantly influence the dynamics of the two detectable objects. I should also add that we can only rule out a 3rd object if (roughly speaking) that 3rd object is massive and close to the binary. If the 3rd object is low-mass enough and/or far enough away from the binary, its effect wouldn't be detectable. For *this* system (GW150914), and for almost any other system observed by a ground-based gravitational-wave detector, our bounds on a possible 3rd object will be very poor, because (roughly speaking) these bounds scale as the square of the observation time, and for this system the observation time is very short ( 0.1 seconds). However, for inspirals observed over multi-year timescales by (future) pulsar-timing-array or space-based gravitational-wave detectors, interesting observations of, or constrinats on, supermassive "3rd-object" black holes are possible. Yunes, Miller, and I analysed this case a few years ago: Yunes, Miller, and Thornburg Phys. Rev. D 83, 044030 (2011) DOI: 10.1103/PhysRevD.83.044030 arXiv:1010.1721 Abstract: Extreme mass ratio inspirals, in which a stellar-mass object merges with a supermassive black hole, are prime sources for space-based gravitational wave detectors because they will facilitate tests of strong gravity and probe the spacetime around rotating compact objects. In the last few years of such inspirals, the total phase is in the millions of radians and details of the waveforms are sensitive to small perturbations. We show that one potentially detectable perturbation is the presence of a second supermassive black hole within a few tenths of a parsec. The acceleration produced by the perturber on the extreme mass-ratio system produces a steady drift that causes the waveform to deviate systematically from that of an isolated system. If the perturber is a few tenths of a parsec from the extreme-mass ratio system (plausible in as many as a few percent of cases) higher derivatives of motion might also be detectable. In that case, the mass and distance of the perturber can be derived independently, which would allow a new probe of merger dynamics. -- -- "Jonathan Thornburg [remove -animal to reply]" Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA "There was of course no way of knowing whether you were being watched at any given moment. How often, or on what system, the Thought Police plugged in on any individual wire was guesswork. It was even conceivable that they watched everybody all the time." -- George Orwell, "1984" |
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Ligo. What happened 1.3 billion years ago.
In article ,
"Jonathan Thornburg [remove -animal to reply]" writes: From the overall amplitude of the gravitational-wave signal we know the total mass of the system (a bit over 60 solar masses). How is that possible without knowing the distance? I thought the masses came from detailed fitting to the waveform, but I am no expert in this business. -- Help keep our newsgroup healthy; please don't feed the trolls. Steve Willner Phone 617-495-7123 Cambridge, MA 02138 USA |
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Ligo. What happened 1.3 billion years ago.
I wrote:
From the overall amplitude of the gravitational-wave signal we know the total mass of the system (a bit over 60 solar masses). Steve Willner asked: How is that possible without knowing the distance? I thought the masses came from detailed fitting to the waveform, but I am no expert in this business. In fact, fitting the waveform gives both the masses *and* the distance (and the orbital inclination too)! I think this was first realised by @article{Schutz-1986, author = "Bernard F. Schutz", title = "Determining the {H}ubble constant from gravitational wave observations", journal = "Nature", year = 1986, month = "September 25", volume = 323, pages = "310--311", doi = "10.1038/323310a0", ADScite = "http://adsabs.harvard.edu/abs/1986Natur.323..310S", } The basic idea is pretty simple: Suppose we have a "compact" binary system, i.e., one where the two bodies can be approximated as point masses (i.e., tidal effects are negligible). In practice, this is an excellent approximation for black holes or neutron stars until shortly before the actual merger. And let's also assume that the binary orbit is roughly circular (we expect gravitational wave emission to damp out any significant eccentricity well before the system is observable by LIGO et al, so this is a reasonable assumption). The observed gravitational-wave (GW) signal is a "chirp", a sinusoid which sweeps up in frequency and amplitude as the binary spirals closer together. To lowest post-Newtonian order, the "chirp rate" $\dot{f} := df/dt$ (where $f$ is the instantaneous GW frequency) turns out to depend on the binary masses $m_1$ and $m_2$ only through a particular combination, known as the "chirp mass", $\mathcal{M} := (m_1 m_2)^{3/5} / (m_1 + m_2)^{1/5}$. So, measuring $f$ and $\dot{f}$ (which -- apart from cosmological redshifts -- can be done without knowing the source's distance) suffices to determine the chirp mass. [The orbital inclination can be determined from the linear-vs-circular polarization of the GW signal; a more detailed analysis is needed to get the individual masses $m_1$ and $m_2$.] But -- and this is the remarkable part -- it turns out that the total GW "absolute magnitude" (signal amplitude at some fidicual frequency as measured at some fiducial luminosity distance) depends on $m_1$ and $m_2$ only through that *same* combination, the chirp mass. So knowing the chirp mass lets us calculate the GW "absolute magnitude". In other words, compact-binary GW signals are "standard candles" in the usual astronomical sense. (We often say "standard sirens" because (for ground-based detectors like LIGO) the frequencies involved are in the audio band.) Combining this with the observed signal amplitude then lets us calculate the (luminosity) distance to the source, in the usual astronomical way. [Note that GW detectors measure signal *amplitude*, not power, so there's a 1/r falloff with luminosity distance, not a 1/r^2. This is good because it means a fractor-of-10 reduction in detector noise gives a factor-of-10 increase in the maximum distance at which a given source can be detected, i.e., and factor-of-1000 increase in the volume of space within which we can detect such sources. This (a factor of 10 reduction in detector noise) is roughly the improvement between the initial LIGO/Virgo detectors and their current "advanced" versions.] -- -- "Jonathan Thornburg [remove -animal to reply]" Dept of Astronomy & IUCSS, Indiana University, Bloomington, Indiana, USA "There was of course no way of knowing whether you were being watched at any given moment. How often, or on what system, the Thought Police plugged in on any individual wire was guesswork. It was even conceivable that they watched everybody all the time." -- George Orwell, "1984" |
#9
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Ligo. What happened 1.3 billion years ago.
Op zaterdag 5 maart 2016 10:32:33 UTC+1 schreef Jonathan Thornburg:
Nicolaas Vroom wrote: Consider 3 different configurations: 1. A binary star system of 30 solar masses each. 2. A binary BH system of 30 solar masses each. 3. A one BH system of 60 solar masses. But if the 1-solar-mass star orbits at a distance that is much larger than the distance between the two 30-solar-mass objects, then there will be relatively little difference in the 1-solar-mass-star's orbit between cases 1/2 and 3. Again, cases 1 and 2 will be essentially identical, but case 3 will differ a bit even at the Newtonian level. Thanks for all your time and efforts There exists also a fourth case: a one star system of 60 solar masses. What you are saying if the 1-solar-mass object is at a far enough distance it is very difficult to distinquish between the 4 cases. The issue is how you distinquish between 3 and 4. (one BH versus 1 star) To study what the influence of a third object could be I have written a program in VB 5.0. See http://users.telenet.be/nicvroom/VB%...0operation.htm In this program (Newton's Law) I make a difference between three cases: 1 BH and a light ray, 2 BH's and 3 BH's. With 3 BH's I mean: a binary BH system and a third large star. The idea behind the simulation is that the 2 BH's revolve around each other and that the initial angle varies. BH#3 always enters from the right. What the url shows are the results of 36 simulations with the mass of BH #3 resp 5 and 10 solar masses. The idea behind the simulation is that when the speed of BH#3 becomes larger than 300000 km/sec the BH "evaporates" and slowly merges with either BH1 or BH2. The result will be that the two BH will start to spiral together. But in none of these cases the 2 BH's will also merge. When you use mass of BH3 = 12 and Phi = 40 the speed of BH2 will increase also above 300000 km/sec implying more or less the same as what LIGO has detected. The frequency change is from 33 to 88 Hz. Unfortunate the url does not work well on a ipad. Nicolaas Vroom |
#10
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Ligo. What happened 1.3 billion years ago.
Op donderdag 10 maart 2016 09:33:32 UTC+1 schreef Nicolaas Vroom:
Op zaterdag 5 maart 2016 10:32:33 UTC+1 schreef Jonathan Thornburg: Nicolaas Vroom wrote: Consider 3 different configurations: 1. A binary star system of 30 solar masses each. 2. A binary BH system of 30 solar masses each. 3. A one BH system of 60 solar masses. The following is an interesting article: https://astronomynow.com/2016/03/11/...ve-black-hole/ "Clocking the rotation rate of a supermassive black hole" The article discusses a Binary Blackhole system of two large BH's The primary BH is 18 billion sm. The second a mere 150 million sm. (Also see Scientific American May 2016: "the orbital period is getting shorter because the the system is losing energy as it emits gravitational waves") The articles are interesting because the primary BH also contains a massive accretion disc. The secondary BH goes through this accretion disc at intervals of 12 years. My understanding is that as a result of this passing through the secondary BH will increase in mass and thereby comming closer to the primary BH. The final result will be that the two could merge. The accretion disc of the primary BH is also interesting because be this could be left overs of previous encounters with stars or small BH's which collided with the primary BH. These collisions will increase the mass of the primary BH which can also be a reason why the secondary BH closely approaches the primary BH. Nicolaas Vroom |
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