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Gravity and galaxy rotation curves: G vs. dynamics modifications?

  1. Oct 14, 2011 #1
    Three questions, all related.

    Firstly, I'm wondering what sort of modifications to Newtonian gravity were tried to explain the flatness of various galaxy rotation curves. (References, and especially a review, would be much appreciated. I haven't been able to find anything appropriate.)

    I assume having the gravitational "constant," G, increase with distance, was tried and found wanting, which led to Milgrom's notion of increased acceleration in low field strength environments (MOND). So, secondly, why is it that having the gravitational "constant" instead vary with distance (increasing, then decreasing and perhaps even becoming negative, i.e., giving rise to repulsive gravity over very long distances) doesn't work?

    Thirdly, are there any computer programs available on-line that would allow one easily to play with such changes to G and see what effect it would have on the rotation curves?
  2. jcsd
  3. Oct 15, 2011 #2


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    I'm not sure, unfortunately. However, two points:
    1. Galaxy rotation curves were only one of the first pieces of evidence for dark matter. Today we have a tremendous variety of evidence, so that it is not enough to simply fit galaxy rotation curves, you also have to fit galaxy cluster dynamics, gravitational lensing observations, the Cosmic Microwave Background, and other observations (The most stunning is the Bullet Cluster, described here).
    2. Galaxy rotation curves aren't actually flat. They vary quite a lot depending upon the ratio of dark matter to normal matter in the galaxy. Less massive galaxies tend to have far less normal matter, for example, because the normal matter is blown out of the small gravitational wells when the first stars form.

    The idea of having G change with distance doesn't make sense. G is a constant, let it be a constant. Just have it multiply something which depends upon distance instead.

    Unfortunately I really doubt it.
  4. Oct 15, 2011 #3


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    Numerical simulations are complex and require enormous computational power. Even models based on only a few thousand point particles is beyond the ability of most computers.
  5. Oct 15, 2011 #4


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    Well, that's true if you want to do a full simulation. It isn't nearly as difficult for just estimating a rotation curve given a density profile.
  6. Oct 15, 2011 #5


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    I wouldn't say that. The idea of a gravitational 'constant' which is actually a function of space is not too outlandish, and would be well motivated by scalar-tensor theories of gravitation. So if we're considering extensions to gravity, it certainly seems (at first glance) to be a plausible direction to head in. Unfortunately, as we know, once you actually do the calculations in a suitable scalar-tensor theory, you do not arrive at the right answer (given the constraints on the coupling parameter provided by solar system tests).
  7. Oct 15, 2011 #6

    Vanadium 50

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    Any theory that attempts to replace dark matter with modified gravity has to explain how you can have two galaxies with identical luminous matter distributions but different rotation curves.
  8. Oct 15, 2011 #7


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    There is nothing wrong a priori with promoting G to a field. Except that we know it cannot have varied very much over the age of the universe (alternatively quasar constraints are pretty limiting), which rules out physics that looks like power laws, or anything like that. So at most you would be looking at very slow, logarithmic growth functions.

    The only obvious physics that can possibly do that, would be to appeal to massless scalar fields. However, these are really quite nasty for phenomenology as they would then be extremely difficult to see why they don't show up in searches for new long range forces in nature, as well as potential violations of the equivalence principle, which has been tested to high accuracy (solar system tests).

    You could, perhaps give the field a very small mass, but then you have to explain where it comes from, and why it is so technically unnatural..

    In any event, the idea doesn't really work with one possible caveat. It is perhaps possible for a so called chameleon field to evade many of these constraints, and there is an industry to that effect:
  9. Oct 15, 2011 #8


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    My point was that if you have an equation of the form:

    F(r) = G f(r)

    Then it doesn't make any sense to consider something else of the form:

    F(r) = G(r) f(r)

    Instead, just wrap the radial dependence into the function f(r).

    Edit: of course, there are other ideas that allow G to vary, but not in the way that hkyriazi is suggesting.
  10. Oct 15, 2011 #9
    Lots: MOND, AQUAL, PCG, TeVeS...

    The observed flatness is not distance related but acceleration related. Therein that MOND maintains G constant and introduces the Milgrom constant a_0, which splits Newtonian (a>>a_0) from non-Newtonian regimes (a<<a_0).
  11. Oct 19, 2011 #10

    If you have one galaxy, it will work quite nicely. The trouble is that what ends up happening is that in order for this to work, you end up having to have different laws of gravity for each different galaxy, and this seems weird. If you could come up with a rule that says, give me this galaxy, and I'll be able to tell you law of gravity for that galaxy, it might make more sense, but no one has been able to do it.

    I don't know of any, but someone with sophomore undergraduate physics shouldn't have any problems writing one on their own.
  12. Oct 21, 2011 #11
    Is it possible that one of the galaxies in question has a super-massive black hole, whose dense core matter is altered in such a way that it exhibits a different variation of G with distance (or another variable we'll create that varies with r, as we leave G a constant, as Chalnoth suggests), while the other galaxy does not have such a super-massive black hole, leading to the different rotation curves? Has anyone looked for such a hidden variable?
  13. Oct 21, 2011 #12
    Wow! A 300-page review! From browsing through it, it seems rather over my head. But, I appreciate your calling it to my attention nonetheless.

    I mentioned, in response to Vanadium 50, the possibility of super-massive black holes being a hidden variable. The jury's out on whether that can fly or not.

    Well then, maybe I'll just have to hire one to do some simulations for me. {;-)
  14. Oct 21, 2011 #13
    Yes, it's possible. I don't think it's likely, but it's possible.

    The hard part in science in situations where you don't have much data is not trying to think of things that are possible. When you have no data, then anything is possible. The hard part is showing through data and theoretical argument that certain things are not possible.

    If you suggest that the value of G might be different in different galaxies, that's not a paper. Now if you can come up with an experiment that gives you limits to how much G can vary between galaxies, then that's a paper.

    Most of the modified gravity proposes are phenomenonlogical, which is to say that you don't have a specific model in mind. You have a general formula and you try to fit the data to the formula. The trouble is that if you assume enough hidden variables, then anything will fit.

    So you assume that the rotation curves are caused by mystery variable X. Now if it turned out that all of the galaxies at the same type of mystery variable X, then you might be on to something, but we haven't seen that.
  15. Oct 21, 2011 #14
    There have been hundreds/probably thousands of papers on this topic. People have spent entire careers working on modified gravity models. The reason this matters is that it's unlikely that you've thought of something that hasn't been thought of before.

    Also if you assume that the central black hole is different, that doesn't explain the weird part of the rotation curve which is near the edge of the galaxy. The rotation curves near the center of the galaxy seem "non-weird."

    Again, there are thousands of papers on this topic. The jury is "probably not." The big problem is that you'd expect if that it was due to weird gravity, you'd expect some pattern. Blue galaxies have more/less G than red galaxies or something else like that. No one has come up with a pattern.

    The other problem is that we can see the supermassive black hole in our galaxy and it looks normal. There are stars orbiting near a 4 million solar mass BH, that we can see moving, and there is no weird G effect.

    The big problem is that if you assert that G is changing that you really have explained nothing. "Some weird unknown unexplained change in G, is not that much more explanation than some weird unknown, unexplained thing."
  16. Oct 21, 2011 #15


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    Setterfield physics is my short answer. Even MOND sometimes needs dark matter injections to work. Given MOND was motivated by the desire to get rid of dark matter, this is a curious situation.
  17. Oct 21, 2011 #16


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    The central black hole is no more than a couple percent the mass of the galaxy, typically much much less than that. So while it can have effects on the galaxy as a whole, its gravitational impact is almost negligible when you're any noticeable distance from the center of the galaxy.
  18. Oct 21, 2011 #17
    Granted, but is there any direct evidence that when super-massive black holes are growing, lots of the mass of the contributing (falling in) stars doesn't become invisible at relatively near distances? In other words, is all of the evidence of the mass of super-massive black holes inferred from the gravitational behavior of its near neighbors, and mightn't their relatively low mass be more illusion than reality?
  19. Oct 21, 2011 #18
    Was your misspelling of "phenomenological" an accident, or a jab at modified gravity theories? {;-) In any case, good points. In my case, I do have a specific model in mind, but that's beside the point at the moment.

    Yes, and I'm wondering if anyone has looked at the presence of super-massive black holes as that mystery variable.
  20. Oct 21, 2011 #19


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    This doesn't make any sense to me at all. Their mass is inferred from their gravity. I don't see how this can be an illusion.

    But what's more, we currently have a very hard time explaining why these central black holes sometimes get as big as they do. Proposing that they're actually bigger would make that theoretical problem dramatically worse.
  21. Oct 21, 2011 #20
    What I meant was that their "near gravity" effects might be much less than their "far gravity" ones, due to a hypothetical, gravity-altering change in the structure of the mass that fell into them.

    Is the idea here that, with the current thinking about how galaxies typically evolve (given the heterogeneous distribution after the Big Bang, inferred from the CMBR temperature's fine structure), there shouldn't or wouldn't be so much mass near the center, to allow such super-massive black holes to form?
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