[astro-ph/0608407] A direct empirical proof of the existence of dark matter

 Authors: Douglas Clowe (1), Marusa Bradac (2), Anthony H. Gonzalez (3), Maxim Markevitch (4), Scott W. Randall (4), Christine Jones (4), Dennis Zaritsky (1) ((1) Steward Observatory, Tucson, (2) KIPAC, Stanford, (3) Department of Astronomy, Gainesville, (4) Abstract: We present new weak lensing observations of 1E0657-558 (z=0.296), a unique cluster merger, that enable a direct detection of dark matter, independent of assumptions regarding the nature of the gravitational force law. Due to the collision of two clusters, the dissipationless stellar component and the fluid-like X-ray emitting plasma are spatially segregated. By using both wide-field ground based images and HST/ACS images of the cluster cores, we create gravitational lensing maps which show that the gravitational potential does not trace the plasma distribution, the dominant baryonic mass component, but rather approximately traces the distribution of galaxies. An 8-sigma significance spatial offset of the center of the total mass from the center of the baryonic mass peaks cannot be explained with an alteration of the gravitational force law, and thus proves that the majority of the matter in the system is unseen. [PDF]  [PS]  [BibTex]  [Bookmark]

Discussion related to specific recent arXiv papers
Alex Nielsen
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[astro-ph/0608407] A direct empirical proof of the existence

These guys claim to directly compare the dark matter hypothesis with the modified gravity hypothesis and find that dark matter is to be prefered.

Their conclusion seems to rest on the assumption that that majority of the baryonic mass of a cluster is in the intracluster gas and not in the galaxies. I can't claim to be an expert in this, so does anyone know what the evidence is for this claim and whether it is entirely free of any assumptions regarding Newtonian gravity?

Scott Dodelson
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[astro-ph/0608407] A direct empirical proof of the existence

This seems like a pretty strong argument for dark matter. The X-Ray observations seem straightforward to interpret, so I've been looking at the lensing paper . On the one hand, numbers alone suggest you have to be careful interpreting the mass contours: there are 1900 background galaxies that are used to obtain info about 3600 pixels, so the S/N in each pixel is way less than 1. If you estimate that the average kappa in the regime of interest is of order 0.1, to get a 5-sigma detection of a particular mode, you need ~100 background galaxies to beat down shape noise, so you might expect that of order 20 modes are well measured.

And then there is the strong lensing data which -- as shown in Fig. 1 -- are centered on the two clusters. So maybe the strong lensing alone tells you where the mass is. Any strong lensing experts care to comment?

Their analysis, which they have tested against a number of simulations, is very iterative, so it would be difficult to assign any error matrix to the mass map. And also, there is the regularization function, which smooths the mass map but probably induces hellish correlations.

Bottom line: it seems like it would be hard to assign a statistical signifance to the result. Finally, see Eugene's comment about how this impacts TeVeS.

Tommy Anderberg
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Re: [astro-ph/0608407] A direct empirical proof of the exist

Scott Dodelson wrote:Finally, see Eugene's comment about how this impacts TeVeS.
I see several comments from him; I believe you mean this one:
Well, a cursory reading on the Angus et. al. (2006) paper cited by the Letter is rather interesting. In that paper, they show that you can actually construct multi-center mass distributions, with the lensing maps not projected onto the centers, in the TeVes framework. This has something to do with the complicated direct vector field interaction with metric.
(there's more, I'm quoting mainly because Cosmic Variance seems to come and go - overloaded maybe).

Arxiv: astro-ph/0606216, Can MOND take a bullet? Analytical comparisons of three versions of MOND beyond spherical symmetry

Addendum: something which I'd really like to see now is this comparison extended to include Moffat's Scalar-Tensor-Vector and Metric-Skew-Tensor Gravity (gr-qc/0608074).

Marusa Bradac
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[astro-ph/0608407] A direct empirical proof of the existence

Yes Scott, all you are saying is definitely true. And indeed, strong lensing alone gives you a pretty high significance of the positions of the mass peaks already. The reason why we do include weak lensing as well, is to get information for the mass distribution on the whole field and to be able to perform non-parametric reconstruction to start with (if you do the later with strong lensing only you need to inwoke strong priors).

The significance of the peak positions is tested using bootstraping (and we bootstrap weak and in a sense also strong lensing catalogs - the later is done in a "poor man's" fashion though). Indeed, I get a headache even just by thinking about the correlation matrix in this case.

Hope this helps a bit. Marusa

Scott Dodelson
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[astro-ph/0608407] A direct empirical proof of the existence

Marusa,

Thanks very much for the comment, which is indeed very helpful.

One question about the strong lensing: is it true that the ACS fields are centered around the cluster and sub-cluster? Doesn't that mean that you're mmuch more likely to find multiply imaged objects around those regions? I.e., where you don't have such deep images, you probably are less sensitive to strong lensing, right? Does that somehow bias your mass model?

Thanks again for your help,
Scott

Douglas Clowe
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[astro-ph/0608407] A direct empirical proof of the existence

The HST data was in 2 pointings which covered the two clusters and the region in between (Marusa's paper has the entire HST field of view in the optical images, my paper uses the Magellan images which extend over a larger field). Most of the strong lensing, however, is also visible in the ground based images.

For the errors - the strong+weak algorithm in Marusa's paper does have the nasty correlation function as it's a maximum lkelihood type solution. For the weak lensing only reconstruction (the one in my paper), this is actually a direct solution made by taking derivates of the reduced shear field, combining them, and integrating using a von Neumann boundary condition to account for the limited field of view (Schneider 1995 is the appropriate place to look at it I think - I'm in a hotel currently driving between Tucson and Ohio, so can't look it up in my notes). You still get large changes in the shapes of the contours, particularly the outer contours, from the bootstrap samplings, but for the claimed detection that dark matter must exist the important thing is the centroid of the lensing derived mass peaks, and those are shown as the white contours in my paper.

Regarding the Angus paper - in TeVeS they showed that you could get some suppression of the lensing signal in the central peak of a 3 peak system, which they said might be enough to explain the 2004 lensing map. Our newer maps published in these papers have much tighter limits on what level of peak could exist centered on the gas, so it will be much harder to do this. Also, the Angus paper used a perfectly symmetric system which had dark matter in the outer peaks already (claimed it could be neutrinos, but had it peaked into cusps), just not as much dark matter as you'd need with Newtonian gravity. If you look at the figures in our papers, you'll see 1E0657 is not even close to being symmetric (the bigger cluster probably had ~4 times the mass of the bullet subcluster before the collision, has 2 seperate cores in galaxies (both of which have cD galaxies at the center), and the gas clouds are actually north of the line connecting the center of the main cluster with the subcluster).

We should soon be releasing models of the 3-D gas distribution, catalogs of color-selected likely cluster galaxies, and the lensing maps to anyone who wants them to test if the various modified gravity theories can reproduce the lensing, but I'll be incredibly suprised if any of them can do it without needing at least twice the mass in dark matter as is in the gas clouds.

edit - I should clarify that the strong lensing arcs are seen in the ground based data. The arclets (like the ones around the bullet subcluster) can mostly been seen as smudges in the ground based data, but you need the HST resolution to see that they are arclike in shape.

edit2 - to answer the original question, the X-ray gas mass can be calculated fairly simply when you have gas temperature and the x-ray luminosity (both of which the X-ray telescopes measure). You have to make a few assumptions regarding symmetry and the like, but the models are easily good to a factor of two and probably to 10-20% in most cases. The galaxy masses are calculated by taking the total optical light and multiplying by a given mass-to-light ratio calculated from population synthesis models or direct observations of the types of stars in various nearby galaxies. Again these are good to a factor of two or so. From this we got the 10:1 ratio of baryonic mass in the gas compared to the galaxies, and if you want to assume we got both wrong by a factor of two in exactly the wrong way, you'd still have 2.5:1 in favor of the gas.

Kate Land
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[astro-ph/0608407] A direct empirical proof of the existence

Hey,
I like the paper, and the result is fascinating. I have a couple of naive questions that I'd love to hear comments on:

1. How do we convert the last column in Table 2 ($\bar{\kappa}$) to an inferred dark matter' mass? This would be useful so to compare with the previous columns.

2. Extending on the previous comments about most of the baryonic mass being in the gas, rather than the galaxies, by 10:1. If one calculates the galactic baryonic mass by summing the optical light, how much of a problem are brown dwarfs and super massive black holes expected to be?

3. Putting these two comments together - how much heavier would the galaxies need to be to explain the observations without Dark Matter (or any other option...)?

Cheers, Kate

Douglas Clowe
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Re: [astro-ph/0608407] A direct empirical proof of the exist

Kate Land wrote: 1. How do we convert the last column in Table 2 ($\bar{\kappa}$) to an inferred dark matter' mass? This would be useful so to compare with the previous columns.
multiply $\bar{\kappa}$ by 2.85e9 to get M_solar/kpc^2, then by $\pi r^2$ to get mass. We're also working on a paper to which have more mass estimates from a variety of methods, including total mass estimates for the cluster and for the two components seperately. Note that this mass is only true for a WMAP cosmology with Newtonian gravity.
2. Extending on the previous comments about most of the baryonic mass being in the gas, rather than the galaxies, by 10:1. If one calculates the galactic baryonic mass by summing the optical light, how much of a problem are brown dwarfs and super massive black holes expected to be?
The super massive black holes shouldn't be much of a problem, the ones at the centers of the galaxies are only 0.01% of the baryonic mass in stars for the galaxies as a whole (from memory, might be off by a factor of 10), and I don't know of any observations of supermassive blackholes elsewhere in a galaxy except in recent mergers. Brown dwarfs will certainly raise the M/L ratio, but again you'd need an extremely large number of them (probably more than are allowed by the micro-lensing surveys) to significantly alter the results. You can also hide a lot of stars in the inter-galactic light which we wouldn't be taking into account, and that's what the factor of 2 that I was quoting in the rough error is from - some estimates are that there are as many stars between the galaxies in clusters as there are in the galaxies.
3. Putting these two comments together - how much heavier would the galaxies need to be to explain the observations without Dark Matter (or any other option...)?
You'd need to increase the mass of the galaxies to make up for any dark matter you want to take away. So at least a 10 fold increase to get the galaxies to a similar mass with the gas, and then several more fold after that depending on how much extra mass you need around the galaxies to explain the peak positions.

The only real way to get around the dark matter is something like the central peak suppression from Angus et al, but you need a huge suppression factor. After that, you then have to explain how the 10% of the total baryons left in the galaxy compoent (up it to 20-30% if you want to get the upper limit on the galactic mass without using lots of supermassive black holes in the outer haloes, etc) can produce the same amount of lensing as normal clusters with the same amount of galactic mass but with the gas mixed in, and more lensing than clusters with the same baryonic mass mixed between galaxies and gas.

Simon DeDeo
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[astro-ph/0608407] A direct empirical proof of the existence

"You can also hide a lot of stars in the inter-galactic light which we wouldn't be taking into account, and that's what the factor of 2 that I was quoting in the rough error is from - some estimates are that there are as many stars between the galaxies in clusters as there are in the galaxies."

Curious, and never heard this before; where is a good place to read up on the debate? Are these stars expelled from galaxies, or do they form in situ?

karel van acoleyen
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[astro-ph/0608407] A direct empirical proof of the existence

Hi,

Does anybody know if there exist data for galaxyclusters that are at similar distances to each other, but that have NOT (yet) collided. I guess this could settle the issue of modified gravity versus dark matter for clusters, since for the modified gravity case we would expect to find a similar picture with an offset between the inferred dark matter distributions (using ordinary gravity) and the luminous matter distributions, whereas if it is really dark matter, it should still be centred around the luminous matter.

Douglas Clowe
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Re: [astro-ph/0608407] A direct empirical proof of the exist

Simon DeDeo wrote:"You can also hide a lot of stars in the inter-galactic light which we wouldn't be taking into account, and that's what the factor of 2 that I was quoting in the rough error is from - some estimates are that there are as many stars between the galaxies in clusters as there are in the galaxies."

Curious, and never heard this before; where is a good place to read up on the debate? Are these stars expelled from galaxies, or do they form in situ?
A good place to start is Gonzalez, Zabludoff, and Zaritsky, 2005, ApJ, 618, 195 (note that it's not the first paper, just the one that I remember - in part because they're collaborators on this and other projects).

In general these are thought to be mostly stars stripped out of galaxies in the clusters, either during the infall process or as they're transiting the core.
Karel van Acoleyen wrote:Does anybody know if there exist data for galaxyclusters that are at similar distances to each other, but that have NOT (yet) collided. I guess this could settle the issue of modified gravity versus dark matter for clusters, since for the modified gravity case we would expect to find a similar picture with an offset between the inferred dark matter distributions (using ordinary gravity) and the luminous matter distributions, whereas if it is really dark matter, it should still be centred around the luminous matter.
There are a couple that are known (or at least suspected) cases with gravitational lensing measurements:
The A222-223 system (Dietrich et al, 2005, A&A, 440, 453)
A901-902 (Kaiser et al 2000, Gray et al 2002).
Problem is because they likely haven't interacted yet, we don't have any knowledge of how much of the redshift difference is physical distance and how much is velocity moving toward each other.

Tommy Anderberg
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[astro-ph/0608407] A direct empirical proof of the existence

Everybody interested has probably already seen it, but for completeness and future reference, Angus et al have a new paper out,

astro-ph/0609125: On the Law of Gravity, the Mass of Neutrinos and the Proof of Dark Matter

which basically says "that don't impress me much": the combination of MOND and 2 eV neutrinos is shown to fit the bullet cluster (this time without the objectionable cusps), leading to the conclusion (page 4):
The bullet cluster thus poses nothing new to the MOND paradigm, noticing that the current best attempt to explain WMAP data with relativistic MOND also invokes 2 eV neutrinos (Skordis et al. 2006).

Douglas Clowe
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[astro-ph/0608407] A direct empirical proof of the existence

Yes, but you failed to mention that they need a minimum of 2.4 times more dark matter than baryonic matter, they just claim that with MOND you can use 2 eV neutrinos to get that amount (which i think also assumes the maximum relic neutrino density possible).

Also, if you look in their table 2, they use less gas in the MOND fits than the GR fit, with the gas mass calculated by assuming a certain gas profile (which turns out to be too centrally peaked - much lower gas mass than is present at the 180 kpc radius, higher within 100 kpc, which is part of why they're also picking up seperate lensing peaks for the gas in all of their gravity models) and scaling the total mass to get a good fit to the contours published in the letter. The gas mass is calculated in a gravity-independent manner from the Chandra data, so it really can't be lowered unless you assume that you can put the gas in thin, dense shells instead of filling the cluster volume (and keep them in those shells for 100 million years after the passthrough event).

I don't think it is the final word in whether MOND can model the cluster as they're going to be attempting to model it using the observed gas distrtribution instead of the assumed profile. They also need to test if the amount of neturino mass they need in the peak is consistent with the shear profile at large radius (which they couldn't do in this paper as I wasn't able to fit it into my letter) and the x-ray temperature at large radius (which might turn out to be impossible to model due to shock heating of the gas, something we need to look at).

Kate Land
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[astro-ph/0608407] A direct empirical proof of the existence

multiply by 2.85e9 to get M_{solar}/kpc^2, then by \pi r^2 to get mass
Thanks for that. So from my calculations, around the galaxies you are observing a ratio of about 6:1 for dark matter (inferred from $\bar{\kappa}$) to (visible) baryons.

Would we not expect a high ratio than this in LCDM?

I thought it was usually 10:1 for galaxies, and higher for larger objects such as clusters.

Cheers, Kate

Douglas Clowe
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Re: [astro-ph/0608407] A direct empirical proof of the exist

From the WMAP 3 year results, $\Omega_m h^2 = 0.127, \Omega_b h^2 = 0.0223$ so a ratio of 5.7:1. You can raise this ratio in galaxies by using supergalactic winds to blow out baryons, but clusters should be right around the mean value. The 3 year results seem to be coming in a little bit low compared to other methods, but 8:1 would probably still be an upper limit - the CMB guru's could probably give us a better range of allowable ratios.

In the very centers of the clusters you would actually expect a lower ratio, as the baryons can collapse more than the dark matter due to interactions and cooling.