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Apparently the Bullet Cluster is some slam-dunk proof of ΛCDM. The argument seems to be that most (>90%) of the baryonic mass in these clusters is in the form of X-ray emitting gas. Therefore the gravity lensing should follow the gas. However, I can't find any references for the basic assumption about the gas to total baryonic mass ratio (that didn't already assume a ΛCDM model) . Can anyone provide the background?

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    $\begingroup$ Why do you think it is an assumption rather than an estimation based on (a) the X-ray luminosity (that depends on the gas density) and (b) measuring the distribution of the gas from its X-ray behaviour that tells you something about the gravitating mass distribution (and total mass) and (c) measuring the motions of the galaxies and (d) gravitational lensing which tells you about all the gravitating mass? $\endgroup$ – Rob Jeffries Oct 3 '15 at 17:09
  • $\begingroup$ (a) (b) because I've yet to find a reference on this subject that didn't assume DM made up 90% of the rest of the mass of the Bullet Cluster (c) the motions of the Bullet Cluster fail the criteria for a Virialized Mass (there's no way they can be time averaged due to the recent collision) (d) I accept the gravitational lensing part of the argument. $\endgroup$ – Donald Airey Oct 3 '15 at 17:58
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    $\begingroup$ To avoid wasting peoples' time, it would be helpful if your question included a brief summary of why the obvious technique of using the optically thin X-rays to estimate an emission measure and then using this and the volume of the gas to estimate its mass, is deemed unacceptable. $\endgroup$ – Rob Jeffries Oct 3 '15 at 23:17
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The first paper I looked at (Paraficz et al. 2012) explains that the hot gas mass is determined from X-ray observations. The X-ray flux from an optically thin gas depends on the square of the gas density multiplied by its volume [Specifically: $f_x = A(T) n_{e}^2 V/4\pi d^2$, where $A(T)$ is the known radiative cooling function and $T$ comes from the X-ray spectrum, $V$ the volume, $n_e$ the electron number density and $d$ the distance.] - if you can measure $f_x$ then estimate the volume you get the density and also the gas mass. Some details for the analysis of the Chandra X-ray observations of the Bullet cluster are found in Close et al. (2006), including how they model the geometry of the various components. They conclude that their gas mass estimate is good to 10 per cent.

The masses of individual galaxies are estimated by modelling their luminosities through Faber-Jackson or (for spirals) Tully-Fisher scaling relations (see also here). These give the total galaxy mass, which would include dark matter. To estimate just the baryonic mass one just uses the mass to luminosity ratio for stellar material under the assumption that most of the baryonic matter is stars (a small correction could be made for gas, dust etc).

It is on this basis that it is claimed that the X-ray emitting gas contains a similar amount of mass to that associated with individual galaxies. If those galaxies have non-baryonic dark matter halos that dominate their total mass (which seems likely unless they have extraordinarily low luminosity to mass ratios) then I think this leads to the claim that about 90 per cent of the baryonic mass is in the X-ray emitting gas. If one is sceptical of dark matter and don't trust the FJ and TF scaling relations, then I guess you just take the luminosity of the individual galaxies, convert that to a stellar mass, and you would arrive at more-or-less the same number.

For the Bullet Cluster, gravitational lensing then reveals that the galaxies plus hot gas only represents 20 per cent of the total cluster mass (9 per cent in hot gas, 11 per cent in galaxies) and thus that 89 per cent of the total mass is not in galaxies and that only a small fraction of this is in the form of a hot baryonic gas.

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  • $\begingroup$ "The X-ray flux from an optically thin gas depends on the square of the gas density multiplied by its volume - if you can then estimate the volume you get the density and also the gas mass" I don't see the connection. How did you get the gas density? You know the luminosity density, but just like stars, there's going to be an M/L relation. The only thing close to an M/L relation for a gas is the ideal gas law. $\endgroup$ – Donald Airey Oct 5 '15 at 3:08
  • $\begingroup$ @DonaldRoyAirey see edit. A hot gas emits bremsstrahlung. The emissivity is a weak fn of T and can be calculated. So there is a straightforward relationship. $\endgroup$ – Rob Jeffries Oct 5 '15 at 5:55
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ΛCDM doesn't enter into the Bullet Cluster. What we have is the following accounting:

  • We can measure the mass of the hot intracluster medium. This gas is millions of kelvins and thus glowing predictably in X-rays. By measuring X-ray emissions, we know how much gas there is. Call this $M_\mathrm{gas}$.
  • We can measure the mass of stars in galaxies. This is done by measuring the total light output and using our models for how luminous stars are as a function of mass. Call this $M_\mathrm{stars}$. Note $M_\mathrm{stars} \ll M_\mathrm{gas}$.
  • We can measure the total gravitational mass via lensing. The more light is bent, the more stuff must be bending the light. Call this $M_\mathrm{tot}$.

This leads to the following problem: $M_\mathrm{gas} + M_\mathrm{stars} \ll M_\mathrm{tot}$. There are really only two solutions to the problem:

  1. At least one of our mass measurements is way off. This includes having bad data and also having bad theories with which to interpret the data and extract a mass.
  2. There is another category of mass that we haven't accounted for.

Option (1) is the sort of thing that jumps out the first time a strange measurement arises. But the data has been checked a lot, and we're not using anything too fancy to get at the masses. In particular, ΛCDM doesn't enter into the calculations. This leaves (2).

The only question then is "Is the missing mass normal baryons that are by chance hard to detect, or is it non-baryonic material (that is thus naturally hard to detect electromagnetically)?" The real strength of the Bullet Cluster are the following additional observations:

  • The accounted for gas mass $M_\mathrm{gas}$ is consistent with a fluid that experiences pressure. In particular, even as galaxies pass though each other in a cluster collision, the surrounding gas clouds will collide and stop in the middle.
  • The distribution of $M_\mathrm{tot}$ is different from that of $M_\mathrm{gas}$. In particular, it seems to match up with $M_\mathrm{stars}$. That is, the missing mass is behaving as a pressureless fluid.

Such a large amount of baryons in the gas phase could not be pressureless; they would collide with each other as the clusters collided. Stars are pressureless baryons at these scales (again, stars essentially never collide with each other, even as galaxies collide), but we can't think of any way to have so much mass tied up in stars without a significant boost to the galaxies' luminosities. Once you have a star's worth of material in one place, it's going to shine like a star.

On the other hand, we could say there appears to be some non-baryonic matter in the system, with a mass about five times that of the observed baryons. It turns out this is exactly the amount of non-baryonic matter needed in ΛCDM to explain BAOs and the CMB power spectrum. It is the remarkable agreement of the ΛCDM cosmological model with the independent Bullet Cluster observations (as well as galactic rotation curves and the kinematics of galaxies in clusters) that leads many to trust in the existence of dark matter.

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  • $\begingroup$ No, you are missing the point entirely. You can't measure the gas directly. You can measure the temperature and make a profile of the brightness. You cannot connect the temperature with a mass because there are dozens of unknowns: what is heating the gas? how long has it been cooling? Please provide some sort of paper that explains how the mass of the gas in the bullet cluster is determined (that isn't built on a house of cards of assumption). $\endgroup$ – Donald Airey Oct 3 '15 at 22:18
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    $\begingroup$ @DonaldRoyAirey If I see a certain number of X-ray photons from a gas of a certain volume, then I can calculate the electron density of that gas, which then leads, without any assumptions about dark matter, to the mass of the X-ray emitting gas. The only place I see that requires a minor assumption about $\Lambda$CDM is in the assumed cosmology that tells you how big the bullet cluster is - ie the volume. As it is not very high redshift, this is not very important. $\endgroup$ – Rob Jeffries Oct 3 '15 at 23:06
  • $\begingroup$ All you know is the surface density. Without de-projection, you don't know the actual 3D density. We've got some pretty good science behind a Sersic or de Vaucouleurs profile, but I'm missing the part where we know the volume of a bow-shaped shock-wave based on the surface profile. I'd appreciate it if you can make the connection. $\endgroup$ – Donald Airey Oct 4 '15 at 0:33
  • $\begingroup$ @DonaldRoyAirey You are correct to point out that there are inherent uncertainties in deprojecting 2D X-ray maps, but this is how it is done, and answers your question (without any assumptions about $\Lambda$CDM). If you now wish to shift the focus of your scepticism to another aspect of the process (the assumptions used to estimate gas masses from X-ray observations) then you should ask a different question. $\endgroup$ – Rob Jeffries Oct 4 '15 at 7:59
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It offers strong evidence that the unaccounted for mass (assuming a missing mass type scenario) behaves more like the stars (i.e. like a collision-less gas) than it does like the accounted for gas and dust (which exhibit a degree of viscosity).

On the other hand, if you're trying to develop a MOND like theory it leaves you trying to argue that the correction terms to the behavior of gravity are different for the the stars than they are for the viscous gas and dust, despite the two distributions having roughly the same linear scale.

I don't suppose non-dark-matter theories are completely sunk by this one observation but the naturalness (something I have gotten the feeling drives at least some of the interest in avoiding dark matter) starts to look a little strained.

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  • $\begingroup$ Please, I hear the same thing on nearly every post I've read: it proves that DM follows light. Why does following the light prove anything? Do we know exactly how much matter is in the gas in a cluster? I could see this being evidence of something if we knew for certain that 90% of the cluster mass was gas. $\endgroup$ – Donald Airey Oct 3 '15 at 2:00
  • $\begingroup$ Then google it. I used "gas to stars ratio". That turned up this poster on the first page of links. It seems to say that for the sampled clusters gas out-massed stars by a factor of 5-10. But notice that it also implies the the Baryonic total is in the 10-17% of total mass (again, assuming a DM scenario). $\endgroup$ – dmckee Oct 3 '15 at 2:29
  • $\begingroup$ Ah, adding "cluster" to the search terms helps some more. There is also astr.ua.edu/keel/galaxies/icm.html (from 2009, apparently) which is again, going with 90% of the mass not in galaxies. $\endgroup$ – dmckee Oct 3 '15 at 2:33
  • $\begingroup$ Sorry, more questions than answers here. The first post suggests ranges of 10-15% of gas to total mass. If that's the case, why does it prove anything that the gravity lense follows the other 90% of the mass? The second paper - I dunno - maybe I missed something. He says 90% is made up of gas and I totally missed the part where he re-wrote the Virial Theorem or came up with an alternative. $\endgroup$ – Donald Airey Oct 3 '15 at 3:11
  • $\begingroup$ No the first post suggest that known Baryonic matter is 10-15%, but only 10-20% of the Baryonic matter is stars. That is that roughly 2% of the total mass is stars. And yes, this is all predicated on the existence of some kind of dark matter. $\endgroup$ – dmckee Oct 3 '15 at 3:45
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MOND does extremely well for spiral galaxies ($10^{10}-10^{12} M_0)$ in calculating with the measured tangential velocity as a function of radius. MOND has one constant $a_0=2 \times 10^{-8}{{cm}\over{sec^2}}$ used for all galaxies and uses the measured baryonic inside the radius for which the velocity is being calculated. MOND yields the baryonic Tully-Fisher relation which is in spooky agreement with the flattening velocity versus baryonic mass.

MOND also explains the dispersion velocity of the stars seen in dwarf galaxies ($10^6 - 10^9 M_0$), in elliptical galaxies, and possibly in isolated globular clusters ($10^3-10^5 M_0$).

MOND is said to fail in clusters of galaxies ($10^{13}-10^{15}M_0$) because it predicts an invisible missing mass that is about equal to the visible mass of the cluster. The visible mass is measured by x-rays to be ~90% gas and by light ~10% stars. Newton predicts missing mass ("Dark Matter") that is ~100 times the visible mass of the cluster.

Furthermore, the Bullet Cluster mass contours from weak gravitational lensing of background galaxies encompass a region with no visible mass (except the stars which are a minority of the visible mass). The gas got stopped in the collision. Clearly there is non-interacting "dark matter" in the Bullet Cluster.

However,if you fill up the phase space of a galactic cluster (out to ~megaparsec, 1000 km/sec) with a Fermi Dirac distribution of neutrinos (3 generations) and all the neutrinos have ~1-2 eV mass, then this would explain the MOND predicted invisible missing mass. This is below the present measured electron neutrino mass limit of 2.2 eV. KATRIN will soon begin a more sensitive mass measurement down to .2 eV. CMBR measurements with the DM paradigm strongly disfavor such a large neutrino mass. There is some chance KATRIN's results will be exciting.

You also point out that the collision velocity of the two clusters is very large (~3000 km/sec as determined by the observed gas shock). If you just let the two at rest clusters (with all their Newton inferred DM) fall together under Newton gravity from infinity, they would pick up <2000 km/sec collision velocity. Thus the initial gas clouds that formed the clusters must start with a large velocity pointing at each other. This is an improbable event which will make $\Lambda CDM$ progressively more unlikely if more high collisional velocity pairs of clusters are found. The MOND force law, which is stronger than Newton at large radii, predicts the large collision velocity.

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  • $\begingroup$ Are you saying that neutrinos are slow enough to be captured by the mass of a galaxy cluster? $\endgroup$ – Peter Shor Oct 3 '15 at 16:20
  • $\begingroup$ @Peter: The present wisdom is that warm dark matter (eg: 1 eV neutrinos) would delay/prevent structure formation in the early universe. However, the MOND force law is stronger than Newton and warm dark matter may well be needed to slow down structure formation. As for how these neutrinos would eventually get trapped in the Fermi-Dirac distribution of a galactic cluster. Good point. I don't know. Will think about it. $\endgroup$ – Gary Godfrey Oct 3 '15 at 17:11
  • $\begingroup$ @Gary - "The visible mass is measured by x-rays to be ~90% gas and by light ~10% stars." I'm looking for a reference for this that doesn't assume a ΛCDM model. $\endgroup$ – Donald Airey Oct 3 '15 at 18:08
  • $\begingroup$ @GaryGodfrey - Again, I'm not sure how you came to this number (90%), but Ota & al studied 79 clusters and came up with a ratio of roughly %20. astro.isas.jaxa.jp/~ota/Cluster_Catalog_files/om04_aa_all.pdf $\endgroup$ – Donald Airey Oct 4 '15 at 1:18
  • $\begingroup$ @DonaldRoyAirey Ota et al find the average gas to total mass is 20 per cent. The value for the bullet cluster is a little lower. No assumptions about $\Lambda$CDM required for this. $\endgroup$ – Rob Jeffries Oct 4 '15 at 7:30

protected by Qmechanic Oct 3 '15 at 21:58

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