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

[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.

 

[twofish-quant]

But, even though much stronger long-distance gravity (from super-massive black holes) could help explain the galaxy rotation curves

It's an easier problem if instead of saying

"stronger long-distance gravity (from super-massive black holes) could help explain the galaxy rotation curves"

you ask

"Can stronger long-distance gravity (from any reason) could help explain the galaxy rotation curves?"

It turns out that you run into lots of problems. The big one is that the shape of the gravity that you need in order to explain rotation curves is different for different types of galaxies. Now if it turns out that all your rotation curves have the same shape but they have different strengths, then you can try to argue that there is one hidden parameter that influences everything, and then you can try to match that with something.

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").

Except that gravity doesn't disappear when you drop it into a black hole. If it did, then you've changed the rules of gravity, and once you've done that, then it becomes questionable whether black holes exists at all. Also, if you assert that "gravity just behaves differently" then why complicate things by talking about supermassive black holes.

Again, it's better if you try to be "scenario independent". You start by asking "suppose I remove mass from the center of the galaxy for whatever reason, does this match what I'm seeing?" You spend a year coming trying to answer the question. If yes, you dig further and ask what could be causing the change. If not (and I think people have figured out that this won't work), then you try something else.

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.

You really need to read up on the MOND literature. There are a ton of papers out there that describe the gravity models that might work and those that don't. But if supermassive black holes don't matter, then why bring them up?

Also, what you really want to do is to kill a theory. A theory that says that galaxy rotation curves are caused by supermassive black holes is a "better" theory than one that says "well sometimes supermassive black holes are important and sometimes not." It's "better" because you can show it's false. I have a galaxy without a supermassive black hole and weird galaxy rotation curves, the theory is wrong. That's good.

I'm a theorist. My job isn't to come up with theories that are correct. My job is to come up with theories that are testable. A theory that is "provable wrong" is often a lot better than one that is "vacuously correct." So what I do is to come up with models, and then tell people to observe X, Y, and Z. If it turns out that by observing X, Y, and Z you can show that the model is dead wrong, that's good.

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.)

Except that it's possible that galaxies that have similar size and masses have similar sized black holes. Or not.

The problem that you have here is that gravity is a local theory. You have objects A, B, and C. If you change the way that A affects C, then it's going to have observable effects on B. Now you can argue that our theories of gravity are wrong, and if you have three objects in a row, then A can change the behavior of C without having effects on B.

That's fine, but you are going to have your hands full enough defining your theory of gravity that you don't shouldn't even worry about black holes.

 

[twofish-quant]

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.

Actually you are. The mathematicians have worked this out and if you are suggesting that G changes with r over some range then it turns out that this is the same as saying that gravitational mass is different than inertial mass. (And there are dozens if not hundreds of papers on that topic.)

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).

No they can't. The problem is that if dark matter is in the form of compact objects, then every now and then, one is going to move in front of a background object and the gravity of the compact object is going to cause the background object to "wink".

So you calculate the number of compact objects you need, look for them, and you see nothing.

The technical term for these objects are MACHO's (MAssive Compact Halo Objects). It got this name because the alternative model for dark matter are WIMP's (Weakly Interacting Massive Particles). 100% MACHO theories are dead, because you can show that the fact that we haven't seen them means that they can't account for all of the dark matter. You might still get away with an N% MACHO theory, but as time passes and you see nothing, N goes down.

 

[twofish-quant]

I'm still trying to grasp why models that have G (or a new but equivalent function) increasing with r fail.

The problem is that you end up with different gravity functions for different galaxies, which is weird. If you can come up with an explanation that will work, but no one has come up with one that works.

Also if you have different forms of gravity for different galaxies, you end up with all sorts of headaches. If gravity is different in different galaxies, then why do the stars look the same? What happens at the boundaries between galaxies? Why are the different "zones" galaxies? Let's suppose G is very different at long distances, and it's the same at short distances. Then what happens at middle distances?

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.

But then you run into what I call the "bag of marbles" problem. Suppose gravity behaves differently for different masses. OK. Gravity behaves the same for a marble. It behaves differently for a galaxy. What happens if you put together a bag of marbles? Does it behave according to the small object rule or the big object rule?

The other problem is that we've been able to see and map dark matter with gravitational lensing.

 

[hkyriazi]

The problem is that you end up with different gravity functions for different galaxies, which is weird. If you can come up with an explanation that will work, but no one has come up with one that works.

That's the whole question - why does one necessarily end up with different gravity functions? In my response of Oct26-11 09:16 am I tried to present my understanding of the reason why (and why Milgrom's MOND, on the other hand, seems to work much better -though not perhaps as well as the dark matter idea), to see if my understanding was correct. I'm not sure whether your "bag of marbles" example was meant to refute the changing G idea, or MOND, or something else. I'm simply trying to understand exactly why MOND is so much better than a changing G. Of course it makes no sense to have different G functions for different galaxies, as you pointed out. I'm asking about it here because I thought I could get an answer much quicker than by trying to read through years of MOND articles (the Scientific American article by Milgrom - "Does Dark Matter Really Exist?" from 2002 didn't do it for me).

The other problem is that we've been able to see and map dark matter with gravitational lensing.

Other than cases where the gravitational lens mass has been shown not to correlate with the visible mass, is there something about the gravitational lens data that supports the dark matter idea? I get the feeling there's something major I don't understand about this data. I understand your point about MACHOs causing winking, but does that mean that such winking has been seen for black holes - possibly being major evidence for their existence?