Bullet Cluster and MOND

Question

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?

Answer 1

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.

Answer 2

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.

Answer 3

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.

Answer 4

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.