6. The Bullet Cluster and galaxy clusters in modified-gravity theories

This is our second post on the topic of the Bullet Cluster and galaxy clusters in general. Here you can find the first part: “But the Bullet Cluster …“, in which we argue that it can not be used to proof the Dark Matter Hypothesis. The third and last part, about an ‘anti Bullet Cluster’, will be published in a few days.

Modified gravity theories do well on galaxy scales. Even Ethan Siegel accepts that they are better than Dark Matter at these small scales. But can they cope with the Bullet-Cluster observations? Ethan says no. Let us explain why this statement is wrong.

As mentioned before, the relative velocities of the two galaxy clusters are too fast to be consistent with the standard cosmological framework. In theories of modified gravity, in contrast, high relative velocities of galaxy clusters occur because the effective gravitational acceleration is stronger. And this does take into account that there is less mass because there is no dark matter. The increase in acceleration out-weighs this. High impact velocities naturally occur in MOND, as Angus and McGaugh (2008) have shown, while Moffat and Toth (2010) were able to resolve the infall-velocity issue using MOG.

Thus, there is at least one problem on galaxy cluster scales where modified gravity theories do better than Dark Matter. They not only convincingly triumph on the small scales (as even Ethan Siegal submits to and as is demonstrated scientifically in our research paper). Seen this way, one can just as well use the Bullet Cluster as an example against the Cold Dark Matter Hypothesis.

But how to explain the missing mass in galaxy clusters? It can not all be in hot gas because of the observed offset between the lensing mass and the gas emission in the Bullet Cluster. Assuming the validity of Newtonian Dynamics, the mass missing in clusters of galaxies is about a factor of 4 more than what can be seen in luminous galaxies and gas. Life is made much easier in Modified Newtonian Dynamics (MOND) as Sanders (1999) has shown, because in MOND less mass can produce the same acceleration. This reduces the factor of missing mass to only two times the visible mass. This amount of missing mass might be found in neutrinos, or it might not even be real: a factor of two is not much in astronomy. And a systematically larger mass may be obtained through biases hitherto not taken into account.

We know that neutrinos oscillate, therefore they must have a mass. That mass is small. This makes them a form of hot dark matter that we most definitely know to exist. In order to explain the oscillations, particle physics even predicts the existence of more massive, sterile neutrinos, which only interact by gravity. If they exist they might be massive enough to account for the missing mass in galaxy clusters in MOND (and they can fit the first three acoustic peaks in the CMB).

For Moffat’s theory of Modified Gravity (MOG) the situation is different still: Analyzing the Bullet Cluster, Brownstein and Moffat (2007) realized that in MOG, no Dark Matter is needed at all:

“Using Modified Gravity (MOG) theory, the ‘normal’ matter in the Bullet Cluster is enough to account for the observed gravitational lensing effect.”

So, please, do not say the Bullet Cluster or the high speeds of galaxies in clusters kill all alternative gravity theories. They don’t. In fact, they might just be arguments for non-Newtonian gravity.

by Anton Ippendorf, Pavel Kroupa and Marcel Pawlowski (04.08.2010): “The Bullet Cluster and galaxy clusters in modified-gravity theories” in “The Dark Matter Crisis – the rise and fall of a cosmological hypothesis” on SciLog. See the overview of topics in  The Dark Matter Crisis.

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