As this question, or something close to it, comes up often, in various sections of BAUT, I thought it would be a good idea to have a thread devoted to it.

First, some words on scope. This thread is primarily about the sets of observations, done by astronomers and others, which have lead to the idea of dark matter being fully accepted by the astronomical community. Of necessity, some theory will also need to be covered, particularly General Relativity and Newtonian dynamics.

Two classes of 'dark matter' are somewhat tangential to this thread - 'hot dark matter' ('dark matter' which is, or was, moving at relativistic speeds; neutrinos are an example), and 'baryonic dark matter' (or 'ordinary matter' - atoms and molecules and ions of H, He, ..., whether in the form of plasma, gas, dust, or bigger clumps that does not emit detectable electromagnetic radiation; this also includes baryonic matter in the form of white dwarfs or neutron stars).

Recently, a good, popular-level book on DM has been published by Springer-Praxis "In Search of Dark Matter", Ken Freeman and Geoff McNamara (ISBN 0-387-27616-5).

First of all, CDM was proposed to explain the rotation curves of spiral galaxies.

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Any day you wake up on "the right side of the dirt" is a good day.

T. Anderson

CDM is needed for a bunch of reasons, this is an incomplete list:
1) to get the gravity right in spiral galaxies, as Kaptain K already pointed out
2) to get the gravity right in clusters of galaxies, as inferred from their motions
3) to get enough gravity for 1 and 2 above without messing up the observed fractions of light nuclei that were formed early in the Big Bang
4) to get a flat universe (in comoving coordinates) as expected from inflation. Even if you don't accept inflation, the fact that it is near flat would be spectacularly suprising if it wasn't virtually exactly flat.
5) to explain how galaxies were able to form from a nearly homogeneous matter distribution (baryonic matter alone could not have caused galaxies to form so quickly).
6) to avoid altering the theory of gravity, a very successful theory with excellent axiomatic underpinnings, with something completely ad hoc that so far has not proved to be promising.
7) to allow the possibility that not all matter interacts with light, which otherwise would be a very photon-ocentric view of the universe just because we have eyes.

Non-baryonic dark matter is needed due to, for instance, graviational lensing surveys show that baryonic MACHOs aren't numerous enough, and other studies finding that baryonic WIMPs aren't numerous enough to account for the necessary DM to agree with Ken G's list above.

I don't understand it well enough to explain it -- perhaps someone can step in here with a clear explanation -- but apparently specific information can be drawn from careful measurements of the CMBR to enable the following conclusion:
This statement comes from the Conclusion section of the Wilkinson Microwave Anisotropy Probe (WMAP) Three Year Results: Implications for Cosmology.

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Everyone is entitled to his own opinion, but not his own facts.

Nereid said, "'hot dark matter' ('dark matter' which is, or was, moving at relativistic speeds; neutrinos are an example)"

I was under the impression that neutrinos have mass, is that correct? (and do we know how much mass? As much as an electron? Less?) Assuming that they do have mass, I must infer that by "relativistic speeds" you mean speeds approaching, but not reaching, c. Is that correct? I just want to make sure I`m clear on this...

Maybe, maybe not. The latest data strongly indicate that (at least) two of the three "flavors" of neutrinos may have mass.
Very much less. Data so far only set upper limits and these limits are a very small fraction of the mass of an electron.
Yes.

__________________
Any day you wake up on "the right side of the dirt" is a good day.

T. Anderson

This is probably a bizarre question, and I`m not trying to go off into woo-woo-land, but maybe someone could help me out with the following (and of course, disabuse me of any misconceptions I may be harboring). Photons have no mass, and travel at c, which is the fastest possible speed. Objects with mass are prohibited from ever reaching c, but would any massless particle (assuming others are found) necessarily move at c, or could massless particles possibly move slower in their own frame? (I understand that photons can be made to go slower than c in our frame, but in their own, they are still moving at c, right?) If so, do we have any idea why some massless particles would move at different speeds than others?

On a related note, does anyone know why c is what it is, and not faster or slower? Why that specific speed?

What's "the great attractor" ? Can this be explained in terms of non-baryonic DM ?

The great attractor is probably a very massive galaxy cluster located where we can't see it behind Milky Way dust clouds. It is the explanation for why relatively local galaxies are having their velocities changed in that general direction.

There isn't a specific physical reason that it couldn't be explained by a large collection of purely non-baryonic dark matter, but so far we haven't ever seen something like that, so the odds seem pretty low.

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Forming opinions as we speak

All massless particles move at c in a vacuum, relative to any observer. Were this not so, contradictions with the fundamental postulates of relativity would appear. Maybe those postulates are wong, but they haven't let us down yet. Also note that it isn't true that photons move at c in their own frame, anything is at rest in its own frame if it has a frame, which massless particles do not (no observations can be made from the frame of a photon, so it is not an allowable frame for doing physics). Finally, the question of why c is what it is is very profound, and I have no idea the answer, except to say that there are basically three possibilities. Either c=infinite, which would do violence with the principle of cause and effect (causes and effects could happen at the same time), or c=0, which would not allow anything to cause anything else, or c is somewhere in between, which allows for an interesting universe that acts like ours. The value of "somewhere in between" seems pretty arbitrary, but it is important that it is a very fast speed relative to our daily experience. Were this not so, even cavemen would have attained some level of understanding of relativity. Why is it such a fast speed relative to our experience? I've no idea.

<<The great attractor is probably a very massive galaxy cluster located where we can't see it behind Milky Way dust clouds. >>

Where I was coming from was, if there's some unexplained huge mass in intergalactic space that we can't see, and if that is being explained by baryonic matter, how do we know in the depths of the universe there aren't super-great attractors, or indeed large numbers of difficult-to-detect minor great attractors?

However, you seem to be saying it's just a line of sight problem, if we could see past our own milky way dust clouds, we'd be able to see it.

Has anyone checked through distant galactic vectors to check for other great attractors?

The problem is that for great distances, all we have are radial (line of sight) vectors. Any translational (perpendicular to line of sight) vectors are to small to show up, given our instrument accuracy and time of measurement.

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Any day you wake up on "the right side of the dirt" is a good day.

T. Anderson

KenG said, "Also note that it isn't true that photons move at c in their own frame, anything is at rest in its own frame if it has a frame, which massless particles do not (no observations can be made from the frame of a photon, so it is not an allowable frame for doing physics)."

d`oh. Thanks, I`m trying to learn to use the terminology correctly.

See the tutorial "Anisotrpies in the CMB", from Wayne Hu. The basic idea is that the height of the 2nd acoustic peak, relative to the first acoustic peak, depends on the scattering of CMB photons due to matter. The height of that peak as observed implies that there should be much less mass in the universe than is implied by observed gravity. Hence, there must be more mass, but the mass must not scatter CMB photons. But any baryonic matter must scatter CMB photons. So, the missing mass cannot be baryonic.

As somebody else already pointed out, you can come to a similar conclusion, based on gravitational lensing.

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The point of philosophy is to start with something so simple as not to seem worth stating, and to end with something so paradoxical that no one will believe it. -- Bertrand Russell

No worries, you're doing fine so far.

The observational evidence for (cold, non-baryonic) dark matter can be grouped under the following headings (in the order I propose to address them):

- rich clusters (radial velocity dispersion of member galaxies, the Sunyaez-Zel'dovich effect, (strong) gravitational lensing, X-ray observations)

- galaxy halos (weak lensing, derived orbits of luminous objects in or just outside)

- (spiral) galaxy rotation curves

- CDM in, and near, the Milky Way (really a subset of galaxy rotation curves, but because it's so local, I'll treat it separately)

- poor clusters, galaxy groups (radial velocity dispersions, derived orbits of luminous objects in or near)

- large-scale structure and the CMB (observations provide indirect support for CDM).

If I have missed significant set of observations, that provide direct evidence of CDM, please add.

I don't think of it as significant, but I've seen a paper or two that attribute several observations to neutralino self-annihilation. These don't demand dark matter, and are still very questionable, but they include:
- excess heat emitted by the gas giants
- positrons coming from the center of the galaxy

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Forming opinions as we speak

There is also the related issue of observations that suggest the dark matter cannot be baryonic. An example of that is observations of the outputs of cosmic nucleosynthesis, the light element ratios.

Just to be clear - you intend to show how these provide evidence that the DM must be collisionless CDM specifically? As opposed to Warm DM, Self interacting DM, baryonic DM ... ?

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"The scientist who asks the right question reconnoiters a new patch of the unknown, and may, with luck, bring it within the constricted but expanding boundaries of the known."

~Timothy Ferris (The Red Limit) 1982

Observations interpreted in the context of the expectations of specific theory. The observations themselves do not rule out baryonic DM. Rather, cosmic nucleosynthesis in combination with the observed light element abundances is inconsistent with the DM being entirely baryonic. If observations in the future should show that in fact the DM is baryonic, then that would contradict our models of nucleosynthesis. Of course it is probably quite unlikely that the DM would turn out to be baryonic - the only reasonably viable baryonic DM candidate that is not absolutely ruled out would be molecular hydrogen (Pfenniger&Combes 1994).

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"The scientist who asks the right question reconnoiters a new patch of the unknown, and may, with luck, bring it within the constricted but expanding boundaries of the known."

~Timothy Ferris (The Red Limit) 1982

All observations are interpreted in the context of the expectations of some theory, the issue is whether the observations are needed to help confirm the theory or if the theory is already on a strong enough foundation that you can use it to draw other inferences. I'd say the theories of nucleosynthesis and general relativity are in the latter category, so it is acceptable to consider light element abundances to be observational constraints on baryonic densities. There are always a few details to hammer out, and big surprises are also possible, but what else is new.

Sidney van den Bergh's 1999 Review (The Early History of Dark Matter) gives the landmark Zwicky paper as "Zwicky, F. 1933, Helvetica Phys. Acta, 6, 110", four years before the 1937 ApJ paper most folk remember (On the Masses of Nebulae and of Clusters of Nebulae, Astrophysical Journal 86, 217 - PDF).

Nevermind, in the 1937 paper Zwicky not only introduces an application of the virial theorem as a means of estimating the mass in a (rich) cluster, but also gravitational lensing (he also discusses rotation curves in spirals!).

This 'virial theorem' method continues to be used, and provides an estimate of the mass in individual (rich) clusters. Naturally, it comes with caveats (for example, the cluster must be 'dynamically relaxed', or close to it), so corroboration of these cluster mass estimates, obtained from the application of methods using quite different physics, would be nice.

So, what is the 'virial theorem' method?

Observationally, one obtains the redshifts of as many galaxies - in the cluster of one's desire - as possible. The dispersion of these redshifts (crudely, the value of the standard deviation of the distribution of redshifts) is related to the (total) mass of the cluster, via the virial theorem.

Of course, the estimate depends upon Newtonian gravity - if galaxies in rich clusters don't respect Newton, then the virial theorem won't work (the difference between GR and Newton, in this domain, wrt the virial theorem, is trivial).

The kicker is, as Zwicky found for the Coma cluster, that there's (apparently) far more mass in the cluster than you'd expect, simply by 'counting (optical) photons' - i.e. from the kinds of stars that we know and love, from our observations of our own Milky Way galaxy.

So, where is all the 'missing mass'? Is it (all) 'non-baryonic, dark matter'?

Stay tuned!

Yes.

Though, since we're doing science here, "must be" is a little too strong, and 'collisionless', 'cold', and 'non-baryonic' will, of course, be appropriately defined (and constrained).

And the primary thrust is 'dark matter' - i.e. mass which neither emits nor absorbs electromagnetic radiation, in the relevant wavebands, to the established observational limits.

I agree "must be" is too strong. But you said that you are going to show that the DM is non-baryonic CDM. That is not the same thing as showing that there is an observational basis for the existence of DM. I just wanted to make sure I knew whether you are going to show that the DM is non-baryonic CDM.

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"The scientist who asks the right question reconnoiters a new patch of the unknown, and may, with luck, bring it within the constricted but expanding boundaries of the known."

~Timothy Ferris (The Red Limit) 1982

I agree with this. My only caveat is that sometimes researchers may forget that the census of baryonic matter is another test of nucleosynthesis. If observations showed that molecular hydrogen (for example) existed in sufficient amounts to cover the DM budget, that would contradict the current predictions of nucleosynthesis theory.

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"The scientist who asks the right question reconnoiters a new patch of the unknown, and may, with luck, bring it within the constricted but expanding boundaries of the known."

~Timothy Ferris (The Red Limit) 1982

That is true, sometimes you can go a long way on a wrong theory before you realize that it just isn't working as well as you thought it did. It can be pretty hard to let go sometimes, as Galileo discovered! If there's a significant problem with nucleosynthesis, it will be a bottleneck in cosmology for a pretty long time, I'd expect.

Among the many HST images which APOD has used, more than once, this one of Abell 2218 (taken Jan. 11 to 13, 2000 by the veteran WFPC2) has featured thrice, and its predecessor twice.

A quick count turns up some ~20 APODs showing (strong) gravitational lensing of (background) objects by (foreground) clusters (some are repeats).

Gravitational lensing is an example of the bending of light by mass, predicted by Einstein's GR, and its first observation - during a solar eclipse (stars 'near' the Sun were just where they were predicted to be*) - received widespread publicity.

These "luminous arcs" were first written up by Roger Lynds and Vahé Petrosian, in 1989 (though they were announced three years earlier).

Under favourable circumstances, the distorted images of the background object(s) can be used to reconstruct the 'gravitational lens' - if you assume light bends per Einstein's GR, from you can 'work backwards' to make a 'map' of the distribution of the mass doing the lensing.

CL0024+1654 is a good example. This page gives a popular account of how the reconstruction works (I've seen a better account, but can't find it just now); here is the preprint of the paper giving the full details (it was published, but you need a subscription; I don't think there's any significant difference between the preprint and the published paper).

This is, of course, both an independent corroboration of the 'Zwicky virial theorem' observations (covered in post #24), as well as an advance - for at least some rich clusters, a detailed 'mass map' can be made**.

For the purposes of this thread, the result is the same - most of the mass in these rich clusters is not in the galaxies, but in the space between them; and it is more concentrated towards the centre than the edges.

Clearly, there is a lot more mass in these clusters than meets the 'optical' eye.

Are there other ways to 'weigh' such clusters?

And how to tell whether the invisible stuff is made of baryons?

Stay tuned!

*The data were, in fact, quite marginal; the error bars much too large to rule out 'Newtonian' bending. Subsequent observations, in many wavebands, of bending by many objects, have all been consistent with GR, and (so far) no alternatives have come even close to matching the (good) data.
**Searching with ADS or Google Scholar, for the rich clusters featured in APODs (such as Abell 2218, Abell 1689, and CL0024+1654) is fun - there are hundreds of papers on these objects, many on reconstructing mass maps!

... is in the Sky&Telescope, December 2004 issue: "Cosmology with Galaxy Clusters", by Megan Donahue (p32).

It covers all the methods I will/have discuss(ed) re rich clusters - virial theorem, gravitational lensing, the SZE, the baryonic content of galaxies, and X-ray observations (in two aspects - total mass, and baryonic content).