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

[hkyriazi]

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?

 

[Chalnoth]

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'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.

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?

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.

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?

Unfortunately I really doubt it.

 

[Chronos]

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.

 

[Chalnoth]

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.

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.

 

[Nabeshin]

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.

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).

 

[Vanadium 50]

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.

 

[Haelfix]

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:
http://arxiv.org/abs/astro-ph/0309300

 

[Chalnoth]

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).

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.

 

[juanrga]

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.)

Lots: MOND, AQUAL, PCG, TeVeS...

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?

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).

 

[twofish-quant]

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.)

http://arxiv.org/abs/1106.2476

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?

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.

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?

I don't know of any, but someone with sophomore undergraduate physics shouldn't have any problems writing one on their own.

 

[hkyriazi]

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.

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?

 

[hkyriazi]

http://arxiv.org/abs/1106.2476

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.

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 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.

I don't know of any, but someone with sophomore undergraduate physics shouldn't have any problems writing one on their own.

Well then, maybe I'll just have to hire one to do some simulations for me. {;-)

 

[twofish-quant]

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?

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.

Has anyone looked for such a hidden variable?

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.

 

[twofish-quant]

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.

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."

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.

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."

 

[Chronos]

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.

 

[Chalnoth]

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.

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.

 

[hkyriazi]

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.

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?

 

[hkyriazi]

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.

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.

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.

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

 

[Chalnoth]

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?

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.

 

[hkyriazi]

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.

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.

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.

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?

 

[Chalnoth]

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.

I just don't see a reason to do this. What problem is it supposed to solve, really? It certainly doesn't solve the issue of dark matter. And it has a number of problems in and of itself. For one, if you're going to modify gravity at short scales, you're going to run afoul of Solar System experiments which constrain short-distance gravity very tightly.

So I just see this idea as bringing up a whole host of problems without actually solving any of 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?

Not so much that. The problem is that as the central black hole absorbs matter, the matter it is absorbing belts out huge amounts of radiation (with nearly complete conversion of mass to energy). This causes black hole formation to "quench" as the outgoing radiation blows away the nearby matter, stopping it from feeding the black hole further. There are a lot of people right now trying very hard to understand the very complicated physics near black holes to get a handle on this issue.

 

[twofish-quant]

Was your misspelling of "phenomenological" an accident, or a jab at modified gravity theories? {;-)

It's because I can't spell. Also I think that the modified gravity people are doing good, solid work. It increasingly looks like they are wrong, but showing that a particular approach is wrong is good work.

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.

It actually isn't. One thing that research in modified gravity does to fit galaxy curve observations is to specifically *avoid* coming up with a specific models. It's a lot more efficient that way. The problem with dealing with one model at a time, is that it's inefficient because you spend months and years running numbers and you can only support or refute one model at a time, which makes things slow because there are *thousands* of possible models, and there is a possibility that you are dealing with some thing that has just not been observed.

Rather than focus on testing particular models, the MOND people are asking, based on the observation, what *types* of models are possible and what are not. If you can show that a particular *type* of model fits the data, at that point you can start look in detail about what could produce that type of model, but we just having reached that point yet.

So the MOND approach would be to vary the force of gravity and see how you have to vary gravity to fit the observations. They are *intentionally* not asking what could cause those variations, because it's only after you've shown that a particular *type* of variation fits, that you are in a position to do that.

You have particle physics people that are also playing a different game. We know that whatever theory of gravity exists that it has to look like GR at short distances and Newtonian physics at even shorter distances. Coming up with an original theory of gravity that does that is non-trivial.

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

I'm pretty sure that people have done that and have not found anything useful. There is something called publication bias. People only publish things that are interesting, and if you spend a month trying to fit gravity curves to characteristics of super-massive black holes, and you find nothing, then you file that under failed experiment and you don't publish. It's only if you find a correlation that you publish, and given that there is ton of research on this, and no one has reported anything, that looks to me like people just haven't gotten it to work. You can confirm this by going to conferences and having drinks and lunches with people that are working on this sort of thing, and they'll tell you about all of the non-publishable things that they've done.

Now I do vaguely remember that a few years ago there was some excitement when some groups reported some correlations with galaxy masses, but IIRC that disappeared once people started looking closely at the numbers.

One other thing is in doing research is that you must always consider the possibility that what you are working on just won't work. Trying to set things up so that you end up doing something useful even if it turns out that you are chasing wild geese and red herrings is part of research.

 

[twofish-quant]

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.

I'm not seeing how this is going to affect galaxy rotation curves since the big differences are nowhere near the central supermassive black hole.

Also once you start putting in specific scenarios, you get sidetracked into irrelevant discussions. If you assert that the galaxy rotation curves are doing to differences in supermassive black holes, then you end up spending years learning and arguing about the physics of black holes. If you just assert that the there is unknown factor X that changes gravity fields, which might be black holes or something different, then you don't get into arguments about black holes.

You'll have to spend two years or so learning about the details of galaxy rotation curves. If you argue that this due to some difference in gravity due supermassive black holes, then you'll have to spend several more years learning about the physics of black holes and more years learning getting yourself the point that you can make decent quantum gravity arguments. If your position is "I don't know what is causing any of this" then you can focus on one part of the problem.

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?

No clue. We really have no idea how galaxies form so that you can at this point make up any story you want. The problem at this point is not coming up with new scenarios. In the absence of data, you can let your imagination go wild and make up anything. The hard part is to show that certain things *can't* happen.

 

[Lino]

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.

Vanadium50, do you know of a good article / paper / example of this (two galaxies with identical luminous matter distributions but different rotation curves) that I could follow up on?

Regards,

Noel.

 

[hkyriazi]

I just don't see a reason to do this. What problem is it supposed to solve, really? It certainly doesn't solve the issue of dark matter. And it has a number of problems in and of itself. For one, if you're going to modify gravity at short scales, you're going to run afoul of Solar System experiments which constrain short-distance gravity very tightly.

So I just see this idea as bringing up a whole host of problems without actually solving any of them.

I guess you're right, though I'm not sure why you don't think it could solve at least the galaxy rotation curve portion of the dark matter problem. And, I'm not proposing any modification of gravity at short distances. But, even though much stronger long-distance gravity (from super-massive black holes) could help explain the galaxy rotation curves, as soon as strong "near gravity" mass (in regular stars) starts to disappear from the galaxy center, into the super-massive black hole, the remaining stars near the galaxy center would start moving away in their orbits (due to the apparent drop in mass, i.e., weaker "near gravity"). On the other hand, maybe that could help explain some of the erratic ("random") motions of stars in some galaxy central bulges.

I should add that, in the gravity model I'm pursuing, even ordinary mass has a slowly increasing influence as r increases on the galaxy scale (decreasing and going negative at even longer distances), so galaxies without super-massive black holes could also exhibit exhibit somewhat flat rotation curves. The black hole wrinkle simply may help explain the rotation curve differences between galaxies of apparently similar sizes and masses. (My apologies for being somewhat obtuse about this.)

Not so much that. The problem is that as the central black hole absorbs matter, the matter it is absorbing belts out huge amounts of radiation (with nearly complete conversion of mass to energy). This causes black hole formation to "quench" as the outgoing radiation blows away the nearby matter, stopping it from feeding the black hole further. There are a lot of people right now trying very hard to understand the very complicated physics near black holes to get a handle on this issue.

I see. Thanks!

 

[hkyriazi]

I'm not seeing how this is going to affect galaxy rotation curves since the big differences are nowhere near the central supermassive black hole.

See previous response to Chalnoth. (The idea is that G - or a new variable that modifies G in the equation - isn't a constant, but increases greatly with r, before decreasing and going negative.)

Also once you start putting in specific scenarios, you get sidetracked into irrelevant discussions. If you assert that the galaxy rotation curves are doing to differences in supermassive black holes, then you end up spending years learning and arguing about the physics of black holes. If you just assert that the there is unknown factor X that changes gravity fields, which might be black holes or something different, then you don't get into arguments about black holes.

You'll have to spend two years or so learning about the details of galaxy rotation curves. If you argue that this due to some difference in gravity due supermassive black holes, then you'll have to spend several more years learning about the physics of black holes and more years learning getting yourself the point that you can make decent quantum gravity arguments. If your position is "I don't know what is causing any of this" then you can focus on one part of the problem.

Point well taken, but not applicable to me at the moment, as I have no intention - or ability, really - of spending years specializing in galaxy rotation curves and trying to categorize galaxies on the basis of their black hole masses. I'm working on a specific theory of gravity. I just want to know whether I'll have to punt on the dark matter issue, or whether there's an opportunity for a Hail Mary pass into the end zone, or at least getting a first down. And, I'd certainly want to know if the data tell me the theory is a definite "no go."

 

[Chalnoth]

I guess you're right, though I'm not sure why you don't think it could solve at least the galaxy rotation curve portion of the dark matter problem. And, I'm not proposing any modification of gravity at short distances.

But you are, because you're supposing that the "true" gravitation of a large black hole is larger than we think. That requires significant modification of gravity at short distances to provide this "masking" you're talking about.

More to the point, a single source of gravity at the center of the galaxy would produce exactly the opposite effect that we see: it would produce steeper rotation curves, not shallower ones.

Anyway, the central black holes do have profound effects on galaxy formation, but not because of their gravity. They have profound effects because when matter is falling into them, they are stupidly-bright light sources, so much that they have profound effects upon the gas in the galaxy. It is generally believed that the behavior of the galactic nucleus is a significant factor in whether a galaxy forms into a spiral or elliptical shape, because it has such a tremendous effect upon the gas in the galaxy while it is absorbing matter.

But their gravity is just way, way too small to have much of an impact. Once you move more than a short distance from the galactic center, the stars near the galactic center are more massive than the black hole. And that effect only drops as you move further out. To suppose otherwise requires a massive violation of the equivalence principle, and in a completely strange way.

I should add that, in the gravity model I'm pursuing, even ordinary mass has a slowly increasing influence as r increases on the galaxy scale (decreasing and going negative at even longer distances), so galaxies without super-massive black holes could also exhibit exhibit somewhat flat rotation curves. The black hole wrinkle simply may help explain the rotation curve differences between galaxies of apparently similar sizes and masses. (My apologies for being somewhat obtuse about this.)

Galaxies, however, are the worst possible place to look for explanations of dark matter. The problem there is that galaxies are horribly complicated, making it terribly easy to deceive yourself. Galaxy clusters, being larger, tend to be much cleaner observations. The Bullet Cluster is particularly striking evidence:
http://blogs.discovermagazine.com/cosmicvariance/2006/08/21/dark-matter-exists/

It is fundamentally impossible to explain the Bullet Cluster by simply changing the scaling relation of gravity, because the collision that occurred there separated the normal matter from the dark matter.

Even more powerful evidence, to me, is found in the Cosmic Microwave Background, but that is much harder to get a handle on than the Bullet Cluster.

 

[Vanadium 50]

Vanadium50, do you know of a good article / paper / example of this (two galaxies with identical luminous matter distributions but different rotation curves) that I could follow up on?

Well, the Milky Way is dark-matter poor, even by spiral standards. I don't know of a good review article, but the terms you might look up are "dark matter rich/poor" galaxies and "light to mass ratio".

The black hole wrinkle simply may help explain the rotation curve differences between galaxies of apparently similar sizes and masses. (My apologies for being

You do realize that a supermassive black hole contains only a tiny fraction of a galaxy's mass. For the Milky Way, it's 6 parts per million.

 

[hkyriazi]

But you are, because you're supposing that the "true" gravitation of a large black hole is larger than we think. That requires significant modification of gravity at short distances to provide this "masking" you're talking about.

Oops. This is embarrassing. I was confused. Sorry! For now at least, let's drop the idea that black holes might be a hidden variable in the galaxy rotation curve data.

More to the point, a single source of gravity at the center of the galaxy would produce exactly the opposite effect that we see: it would produce steeper rotation curves, not shallower ones.

I see your point - it's better to have the matter distributed throughout the galactic disk (or ellipse) if you want to have velocity stay nearly flat as r increases. And even if G of all of that evenly scattered matter were to increase many fold as r increases to 50,000 LY or so, it still could explain, at most, the rotation curves of galaxies of one size, but not all sizes. Is that right?

But their gravity is just way, way too small to have much of an impact. Once you move more than a short distance from the galactic center, the stars near the galactic center are more massive than the black hole. And that effect only drops as you move further out. To suppose otherwise requires a massive violation of the equivalence principle, and in a completely strange way.

Could you elaborate on this equivalence principle violation? I wasn't suggesting that gravitational mass is different than inertial mass, simply that G might increase with r over some range.

Galaxies, however, are the worst possible place to look for explanations of dark matter. The problem there is that galaxies are horribly complicated, making it terribly easy to deceive yourself. Galaxy clusters, being larger, tend to be much cleaner observations. The Bullet Cluster is particularly striking evidence:
http://blogs.discovermagazine.com/cosmicvariance/2006/08/21/dark-matter-exists/

It is fundamentally impossible to explain the Bullet Cluster by simply changing the scaling relation of gravity, because the collision that occurred there separated the normal matter from the dark matter.

I really wasn't interested in dark matter so much as exploring the ability of altered Newtonian gravity to explain the galaxy rotation curves and galactic cluster data. I'd read the reports on the Bullet Cluster before, and wondered whether the super-massive black holes inside the clusters' galaxies might have enough "hidden" mass to fill the role of the supposed cloud of dark matter (vs. the seemingly more massive gas clouds).

Even more powerful evidence, to me, is found in the Cosmic Microwave Background, but that is much harder to get a handle on than the Bullet Cluster.

You mean the fine spatial structure of the CMBR's temperature variations?

I'm very sleepy. Sorry if some of this is gibberish. I'll re-read tomorrow.

 

[Chalnoth]

Could you elaborate on this equivalence principle violation? I wasn't suggesting that gravitational mass is different than inertial mass, simply that G might increase with r over some range.

Another way of stating the equivalence principle is that all sorts of mass gravitate in the same way. What you are proposing here would require the mass of a central black hole to gravitate in a fundamentally different way from the masses of stars.

You mean the fine spatial structure of the CMBR's temperature variations?

I wouldn't say fine structure. Structure, yes, but not fine structure. Basically, before the CMB was emitted, normal matter interacted strongly with photons. This means that normal matter experienced pressure, so that when it fell into a gravitational potential well, it would tend to bounce back out. Dark matter, on the other hand, doesn't interact with photons (or much of anything else), so it doesn't bounce: it just falls into gravitational potential wells and stays there.

The relationship between bouncing/not bouncing can be seen by looking at what is known as the power spectrum (which is the size of fluctuations as a function of wavelength, with longer wavelengths on the right, shorter wavelengths on the left):
http://lambda.gsfc.nasa.gov/product...nyear/powspectra/images/med/dl7_f01_PPT_M.png

The first peak that you see is the largest wavelength for which matter has had time to fall into gravitational potential wells. The second peak is the matter that fell in, but bounced back. The third peak comes from matter that has had time to fall in, bounce back, then fall in again.

There is an overall decreasing trend to the peaks due to how the CMB was emitted, but there is also a distinct difference between the even and odd-numbered peaks. This difference is driven by how much of the matter bounces, and how much doesn't. So we can calculate very accurately the ratio of normal matter to dark matter by examining the ratio of these peaks.

This test is particularly nice because before the CMB was emitted, there simply wasn't any structure in the universe. There were no stars, no galaxies, no black holes. Matter was extremely smoothly-distributed, to one part in one hundred thousand. And yet we see the signature of dark matter showing up clear as day.

 

[Lino]

Thanks Vanadium50.

 

[hkyriazi]

I wouldn't say fine structure. Structure, yes, but not fine structure. Basically, before the CMB was emitted, normal matter interacted strongly with photons. This means that normal matter experienced pressure, so that when it fell into a gravitational potential well, it would tend to bounce back out. Dark matter, on the other hand, doesn't interact with photons (or much of anything else), so it doesn't bounce: it just falls into gravitational potential wells and stays there.

The relationship between bouncing/not bouncing can be seen by looking at what is known as the power spectrum (which is the size of fluctuations as a function of wavelength, with longer wavelengths on the right, shorter wavelengths on the left):
http://lambda.gsfc.nasa.gov/product...nyear/powspectra/images/med/dl7_f01_PPT_M.png

The first peak that you see is the largest wavelength for which matter has had time to fall into gravitational potential wells. The second peak is the matter that fell in, but bounced back. The third peak comes from matter that has had time to fall in, bounce back, then fall in again.

There is an overall decreasing trend to the peaks due to how the CMB was emitted, but there is also a distinct difference between the even and odd-numbered peaks. This difference is driven by how much of the matter bounces, and how much doesn't. So we can calculate very accurately the ratio of normal matter to dark matter by examining the ratio of these peaks.

Thanks. Very interesting - I wasn't aware of this strong, and independent, evidence for dark matter. I'd seen those plots before, but the things they were plotting on the axes were so derived that I couldn't make heads or tails of them. I see that peaks 2 and 4 are abnormally small compared to trend established by 1 and 3.

So, is there no actual spatial structure of the temperature variations plotted here? We're just plotting the size of the variation (at different points in the sky - taking only the max and min, at wherever nearby region they appear?) vs. wavelength? I'm just trying to grasp the physical significance of the plot, and relate it to your narrative about bouncing/not bouncing. What I'm thinking is that the 1st peak represents some sort of rectified/normalized Doppler shift of light emanating from normal and dark matter falling into some mass, the 2nd peak is a similar shift of light emanating from the normal matter bouncing out, etc.

 

[Chalnoth]

Thanks. Very interesting - I wasn't aware of this strong, and independent, evidence for dark matter. I'd seen those plots before, but the things they were plotting on the axes were so derived that I couldn't make heads or tails of them. I see that peaks 2 and 4 are abnormally small compared to trend established by 1 and 3.

So, is there no actual spatial structure of the temperature variations plotted here? We're just plotting the size of the variation (at different points in the sky - taking only the max and min, at wherever nearby region they appear?) vs. wavelength? I'm just trying to grasp the physical significance of the plot, and relate it to your narrative about bouncing/not bouncing. What I'm thinking is that the 1st peak represents some sort of rectified/normalized Doppler shift of light emanating from normal and dark matter falling into some mass, the 2nd peak is a similar shift of light emanating from the normal matter bouncing out, etc.

This plot is a plot of the typical amount of temperature variation as a function of angular size across the sky. And yes, as far as we can tell, there is no spatial structure in that the waves are completely independent and random but with an average amplitude that depends upon wavelength. There are a number of theories which predict these waves would be correlated somewhat, but so far no such correlations have been found (some have been claimed at large angular scales, but they aren't statistically significant).

Just in case you were interested in how this kind of plot is developed, a simple sketch is the following.

First, you take the spherical harmonic transform of the sky:

$$m(\theta, \phi) \to a_{\ell m}$$

This is somewhat similar to a Fourier transform, if you're familiar with those, except it is performed on the surface of a sphere. This transformation, by the way, preserves all of the information in the original temperature map. You're just representing it as a function of wavelength ($\ell$) and direction on the sky ($m$) instead of as a function of spatial location. If you're interested in the nitty gritty details, see the Wikipedia page here:
http://en.wikipedia.org/wiki/Spherical_harmonics

Once this transformation is done, the power spectrum is simply given by:

$$C_\ell = \frac{1}{2\ell+1}\sum_{m=-\ell)^\ell a_{\ell m}a_{\ell m}^*$$

That is to say, the power spectrum $C_\ell$ is the average of the amplitudes of the waves for a given wavelength ($\ell$).

 

[hkyriazi]

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).

I'm still trying to grasp why models that have G (or a new but equivalent function) increasing with r fail. Does the dependence with r fail for galaxies of one size but different mass densities? Likewise, does it fail for galaxies of various sizes but the same mass density? Does making it work for anyone galaxy always lead to failure for explaining galactic cluster dynamics?

I suppose that Milgrom's MOND model success implies that in Newtonian regimes (reasonably high mass density regions), no modification is necessary, and is thus actually contraindicated. And, depending upon the particular galaxy's mass density, the non-Newtonian regime could start at greatly varying distances, indicating that distance isn't the relevant factor.

Is that a reasonable answer to my original question #2?

 

[hkyriazi]

This plot is a plot of the typical amount of temperature variation as a function of angular size across the sky. And yes, as far as we can tell, there is no spatial structure in that the waves are completely independent and random but with an average amplitude that depends upon wavelength. There are a number of theories which predict these waves would be correlated somewhat, but so far no such correlations have been found (some have been claimed at large angular scales, but they aren't statistically significant).

Just in case you were interested in how this kind of plot is developed, a simple sketch is the following.

First, you take the spherical harmonic transform of the sky:

$$m(\theta, \phi) \to a_{\ell m}$$

This is somewhat similar to a Fourier transform, if you're familiar with those, except it is performed on the surface of a sphere. This transformation, by the way, preserves all of the information in the original temperature map. You're just representing it as a function of wavelength ($\ell$) and direction on the sky ($m$) instead of as a function of spatial location. If you're interested in the nitty gritty details, see the Wikipedia page here:
http://en.wikipedia.org/wiki/Spherical_harmonics

Once this transformation is done, the power spectrum is simply given by:

$$C_\ell = \frac{1}{2\ell+1}\sum_{m=-\ell)^\ell a_{\ell m}a_{\ell m}^*$$

That is to say, the power spectrum $C_\ell$ is the average of the amplitudes of the waves for a given wavelength ($\ell$).

Thanks, Chalnoth. Fourier analysis is about the only higher math that I do understand, so your explanation helps a bit - a lot, actually, in the sense that I now realize those harmonics are not intuitive, and that I have lots to learn about them.