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Disk Stability versus Dark Matter.
Accordingly to book "Galactic Dynamics" half of all the disk
galaxies contain bars (page 399). What I first try to understand are galaxies without a bar. A typical case is Sb galaxy NGC 2841 (page 392) and M31 (page 19) Andromeda Galaxy Accordingly to theory each of those galaxies contains a massive dark matter halo. This is explained because without this dark matter they would be unstable. I do not understand why dark matter is a prerequisite and a must, in order to make spiral galaxies stable. To state this different why cannot disks be stable without dark matter. In par 2.8 and 6.3 N body simulations are discussed. (As a side comment at page 372 , 373 a simulation of a spiral disc is shown. Only around t = 10 for a small period the simulation shows a bar which then disappears. is that not strange ?) I have also performed N body simulations. My initial configuration are N body situated in r concentric circles each with the same number of stars n. n*r = N The masses of the stars are selected such that all the N bodies are in equilibrium and that the speed of all the stars is identical. = flat rotation curve. However a different rotation curve is also possible. My simulation resembles the pictures of the galaxy in fig 6-25 at page 395. My simulation does not include dark matter and is IMO stable. In reality the simulation is not stable but that is clearly an accuracy issue. (there is also a second cause when N is small) My question is what is wrong with my simulation. I could have added an halo of dark matter but such a configuration would also be unstable, again only as a result of the accuracy issue. My question is how do you explain that dark matter in the form of an halo changes the disk stable from unstable to stable (while your initial condition is stable i.e. in equilibrium) For an explanation of the program and technical details see: http://users.pandora.be/nicvroom/progrm14.htm Nicolaas Vroom http://users.pandora.be/nicvroom/ |
#2
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Disk Stability MOND and Dark Matter.
In my previous posting I raised the question if
it is possible to simulate flat Galaxy rotation curves using Newton's Law. My answer is possitive. What is also interesting that no dark matter is required. A similar question can be raised related to MOND. For a copy of a program that simulates Galaxy Rotation curves using MOND See: http://users.pandora.be/nicvroom/prgmond.htm For a general discussion See: http://users.pandora.be/nicvroom/mond.htm Newton's Law is = G*M/r^2 MOND uses : a^2/a0 = G*M/r^2 One of the most striking results of Galaxy simulations using MOND is that they are much more stable than equivalent simulations using MOND. On the other hand in simulations strictly based on MOND no stars are ejected which is contrary to observations. Of course those simulations are wrong because at small distances Newton's Law should be used. This immediate raises some objections against MOND: At small scales Newton's Law applies and and large distances MOND with a certain range where a little bit of both can be used. This makes the whole MOND concept rather speculative. However there are more objections against MOND. Many rotation curves are flat or the speed decreases at larger distances. It is not possible to make such simulations using MOND. With MOND the speed increases or stays flat. (In the extreme case we have a BH in the center. The result is a complete flat rotation curve) Galaxy simulations should be based around the same baryonic mass. The problem is that the shape of such rotation curves are quite different. If you compare a galaxy with a flat rotation curve with a speed of 200 km/sec based on Newton's Law with a galaxy with the same mass distribution based on MOND than the speed increases from roughly 300 to 1500 km/sec. One solution is to decrease the universal constant a0. When you do that the shape of the rotation curve stays the same but speeds involved decrease. Again this makes the whole concept rather speculative. Ofcourse my simulations could be wrong. See also the discussion topic: "Barred galaxies mass distribution" in this newsgroup. Nicolaas Vroom http://users.pandora.be/nicvroom/ |
#3
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Disk Stability versus Dark Matter.
"Nicolaas Vroom" wrote:
I have also performed N body simulations. My initial configuration are N body situated in r concentric circles each with the same number of stars n. n*r = N The masses of the stars are selected such that all the N bodies are in equilibrium and that the speed of all the stars is identical. = flat rotation curve. However a different rotation curve is also possible. My simulation does not include dark matter and is IMO stable. In reality the simulation is not stable but that is clearly an accuracy issue. (there is also a second cause when N is small) My question is what is wrong with my simulation. Well, first off you've created an artificial stability by making everything perfectly symmetrical. Make the masses vary randomly by 50%, the initial momentum vectors vary randomly by pi/50 in spherical coordinates, and the initial positions vary in 3 space by 5% of the radius, from the setup you have now, and see how long your simulation remains stable. You should soon be ejecting stars early and often. We know the existing galaxies eject stars, so we know that "stable" isn't an appropriate description of their _current_ conditions in any case. "Stable" is therefore the wrong thing to simulate if you want to investigate reality. Your simulation is likely to be unstable even _with_ a symmetric starting condition, not because of accuracy issues with 128 bit arithmetic, but because gravitational resonances of the various stars in the differently spinning adjacent orbits quickly push and pull stars out of circular alignment [but in your case only in the plane where they all commonly orbit because that's how you've started them going, so that there are no forces perpendicular to that orbital plane to perturb them from that plane]. Second off, you've ignored the whole reason dark matter is being posited: the stars in their existing orbits are _not_ in equilibrium, but without lots more mass holding them toward the center of the galaxy than is seen, would be flying outward until they found some stable orbit or else departed the galaxy. Third, the part I don't understand well, that proposed dark matter is described as a _halo_ rather than as an invisible point mass at the galaxy center, because it is only by being embedded inside part of the total dark matter mass, that the distribution of close to same speed orbits that we see, could exist. Quantum valeat. xanthian. |
#4
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Disk Stability versus Dark Matter.
Third, the part I don't understand well, that
proposed dark matter is described as a _halo_ rather than as an invisible point mass at the galaxy center, because it is only by being embedded inside part of the total dark matter mass, that the distribution of close to same speed orbits that we see, could exist. The reason astronomers postulate a roughly spherical halo of dark matter, rather than a thin disk of dark matter or a point mass of dark matter, is that thin, self-gravitating disks are unstable to perturbations. We would see many more "kinked" and "twisted" disks if the material were concentrated in a plane, rather than spread out in a roughly spherical form. |
#5
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Disk Stability versus Dark Matter.
"Kent Paul Dolan" schreef in bericht
... "Nicolaas Vroom" wrote: I have also performed N body simulations. My initial configuration are N body situated in r concentric circles each with the same number of stars n. n*r = N The masses of the stars are selected such that all the N bodies are in equilibrium and that the speed of all the stars is identical. = flat rotation curve. However a different rotation curve is also possible. My simulation does not include dark matter and is IMO stable. In reality the simulation is not stable but that is clearly an accuracy issue. (there is also a second cause when N is small) My question is what is wrong with my simulation. Well, first off you've created an artificial stability by making everything perfectly symmetrical. Make the masses vary randomly by 50%, the initial momentum vectors vary randomly by pi/50 in spherical coordinates, and the initial positions vary in 3 space by 5% of the radius, from the setup you have now, and see how long your simulation remains stable. You should soon be ejecting stars early and often. There are two issues: Is the galaxy stable versus Are there stars ejected. The fact that single stars are ejected does not mean that the galaxy as a whole is unstable. Yes it is true that the galaxy is symmetrical. This is inconflict with reality. But that is not so much an issue. The purpose of the exercise is to create in a simple manner stable galaxies starting with a given rotation curve. The result are mass values for each ring. Using those values in a the simulation I will observe that my galaxy maintains its shape. For example with 5 rings and 50 stars after an angle of 20 degrees the inner ring is still at a distance of 5800 and the speed is 200. No stars are ejected Now suppose that at the beginning of the simulation I keep the position and and the speed as calculated but I multiply each mass with 0.8 My simulation stays symmetric but after 20 degrees the distance of the inner has increased to 6205 and the speed decreased to 190. No stars are ejected. The important lesson is that this is not a stable galaxy. We know the existing galaxies eject stars, so we know that "stable" isn't an appropriate description of their _current_ conditions in any case. "Stable" is therefore the wrong thing to simulate if you want to investigate reality. The only thing I want to calculate what the total mass should be in each area of the galaxy, based on a given rotation curve. In a galaxy with 5 rings and 50 stars there are 250 of those areas. If the total mass in each area differs from this calculated value your galaxy for sure is unstable even when there are no ejections. Your simulation is likely to be unstable even _with_ a symmetric starting condition, not because of accuracy issues with 128 bit arithmetic, but because gravitational resonances of the various stars in the differently spinning adjacent orbits quickly push and pull stars out of circular alignment [but in your case only in the plane where they all commonly orbit because that's how you've started them going, so that there are no forces perpendicular to that orbital plane to perturb them from that plane]. The initial position is symmetric. Generally speaking each star in each ring should feel the same force and move in the same direction and the result should be a new symmetrical situation. This does not happen. The reason is accuracy with 128 bit arithmatic. (If you study MOND that is much less of an issue) Second off, you've ignored the whole reason dark matter is being posited: the stars in their existing orbits are _not_ in equilibrium, but without lots more mass holding them toward the center of the galaxy than is seen, would be flying outward until they found some stable orbit or else departed the galaxy. I have not ignored that. Starting point is a measured galaxy rotation curve GRC You also should tell me what based on measured light density and based on the M/L function what the calculated Mass distribution is and what total mass MtotC is. The object of the program is to calculate based on the GRC the total mass of the galaxy MtotS that is stable. If MtotL is smaller that MtotS than you know for sure that there is not enough visible mass to have a stable galaxy. The solution is to predict Dark Matter A different solution is MOND. IMO the difference between MtotS and MtotC is small. Are we sure that we cannot solve this discrapency by introducing Pluto sized objects in the disc? Third, the part I don't understand well, that proposed dark matter is described as a _halo_ rather than as an invisible point mass at the galaxy center, because it is only by being embedded inside part of the total dark matter mass, that the distribution of close to same speed orbits that we see, could exist. Which such a point mass in the center i.e a hugh black hole you cannot solve the discrepancy between MtotC and MtotS i.e. you cannot make the rotation curve flat. Quantum valeat. xanthian. Nicolaas Vroom http://users.pandora.be/nicvroom/ |
#6
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Disk Stability MOND and Dark Matter.
"Nicolaas Vroom" schreef in bericht
... A similar question can be raised related to MOND. For a copy of a program that simulates Galaxy Rotation curves using MOND See: http://users.pandora.be/nicvroom/prgmond.htm For a general discussion See: http://users.pandora.be/nicvroom/mond.htm Newton's Law is = G*M/r^2 MOND uses : a^2/a0 = G*M/r^2 One of the most striking results of Galaxy simulations using MOND is that they are much more stable than equivalent simulations using MOND. I would like remark that this are simulations with MOND only. If Newton is added over small distances than the picture changes. On the other hand in simulations strictly based on MOND no stars are ejected which is contrary to observations. Of course those simulations are wrong because at small distances Newton's Law should be used. This immediate raises some objections against MOND: At small scales Newton's Law applies and and large distances MOND with a certain range where a little bit of both can be used. This makes the whole MOND concept rather speculative. However there are more objections against MOND. Many rotation curves are flat or the speed decreases at larger distances. It is not possible to make such simulations using MOND. With MOND the speed increases or stays flat. (In the extreme case we have a BH in the center. The result is a complete flat rotation curve) ppt # 9 at the following url http://www.slac.stanford.edu/exp/gla...y_mar16_06.ppt shows 30 rotation curves ppt # 11 shows an 15 rotation curves. At some of those at larger distances the speed is decreasing. IMO which MOND such simulations are not possible. Galaxy simulations should be based around the same baryonic mass. The problem is that the shape of such rotation curves are quite different. If you compare a galaxy with a flat rotation curve with a speed of 200 km/sec based on Newton's Law with a galaxy with the same mass distribution based on MOND than the speed increases from roughly 300 to 1500 km/sec. This is also a problem with the above mentioned 45 rotation curves. The amount of baryonic mass is missing for each. Only with that data you can verify the claims made with MOND. One solution is to decrease the universal constant a0. When you do that the shape of the rotation curve stays the same but speeds involved decrease. Again this makes the whole concept rather speculative. Ofcourse my simulations could be wrong. A comparison with Newton versus MOND often starts with a rotation curve. With the aid of my program you can calculate with for example 10 rings and 50 stars (500) the mass involved to support a stable galaxy. The results show that the amount with MOND is smaller than with Newton. Perform the same simulation but now with 50 rings and 80 stars (4000). The results show is that the amount of mass with Newton stays approximate the same but with MOND decreases roughly with a factor 10. If you make the simulation based on star sized particles than the differences are almost gargantuan. This same problem is also discussed in the article by Chris Mihos: http://www.astro.umd.edu/~ssm/mond/mondnbody.ps IMO this is a serious issue. I would like to know how the people responsible for the 45 rotation curves coped with that issue. See also the discussion topic: "Barred galaxies mass distribution" in this newsgroup. Nicolaas Vroom http://users.pandora.be/nicvroom/ |
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