Wednesday, April 15, 2015

Repulsive keV Dark Matter

The case for 2-10 keV mass dark matter has gotten a lot stronger in 2015.
First, as mentioned in the previous post, the Planck 2015 results significantly lowered the value of the optical depth for photon-electron scattering during reionization and significantly lowered the z-value at which reionization occurred. Effectively, this pushes back the time at which the first stars and galaxies formed, and therefore indirectly suggests that dark matter took longer to clump together than predicted by GeV cold dark matter theories. As can be seen in the last figure in that previous post, a lower value of optical depth is possible for thermal relics with rest masses of ~2-3 keV and is incompatible (at 1-2 sigma) with CDM theories.

Second, just today, it was announced that there is a good chance that dark matter is actually self-repulsive. (Of course, it's been know indirectly for awhile that dark matter is self-repulsive because there is a missing core of dark matter in the center of galaxies...which can be explained by fermion repulsion between identical particles.) The news today is that there appears to be repulsion between the dark matter halos in a 'slow collision.'  This should be contrasted with the lack of repulsion when two dark matter halos (such as in the Bullet Cluster) collide in a 'fast collision.'

So how do we reconcile all of this information?  Actual, the answer is quite simple.
Dark matter halos are made of Fermi particles of keV rest mass that are quantum degenerate when their density is high and non-degenerate when their density is low.

When two fermi degenerate halos of uncharged-particles collide with velocities much greater than their Fermi velocity, the clusters of particle pass right through each other. Pfenniger & Muccione calculated what would happen in collisions between Fermi particles (or we could imagine two degenerate halos...doesn't matter provided that we are talking about a degenerate halo of particles or a single particle.)
To quote Pfenniger & Muccione:  "An interesting aspect developed for example by Huang (1964, chap. 10), is that the first quantum correction to a classical perfect gas... caused purely by the bosonic or fermionic nature of the particles is mathematically equivalent to an particle-particle interaction potential:

φ(r) = −kT ∙ ln [1 ± exp (−2π r2 /  λdB2 )] ."

When going from a two-particle collision to a collision between 2 halos, the main difference is that the deBroglie wavelenth of the particle would be replaced by the effective degeneracy radius of the halo.
When the directed velocity is large compared with the thermal velocity of the cluster, then the Fermi clusters pass right through each other. The center of mass is nearly same as if these were classical particles. In other words, there would be no separation between the center of the dark matter mass and the center of the solar matter mass.


In the next case below, the directed velocity of the two particles (or clusters) is decreased 3-fold. In this case, there is some slight repulsion between clusters. In this case, there would be a slight separate between the center of the dark matter mass and the center of the non-dark matter mass because the solar matter mass will pass through unaffected by the DM collision (unless there was actually a solar-solar collision...however unlikely.)



Finally, in the last case, the directed velocity of the two particles (or clusters) is decreased a further 3-fold. In this case, the particles have the time to interact, and can actually gravitationally coalesce and entangle.


This means that we should expect the "cross section of interaction" to depend greatly on how quickly the dark matter clusters are colliding.


What's interesting is that Fermi repulsion can quantitatively explain why there was a separation in the Abell 3827 cluster between the center of mass of the stars and the center of mass of the dark matter halo. As the stars/halo were being gravitationally pulled towards the center of the galaxy cluster, the stars would feel gravitational attraction, but the dark matter halo would feel a combination of gravitational attraction and quantum degenerate self-repulsion from the dark matter in the center of the cluster. This means that the stars and dark matter would eventually start separating. Massey et al. 2015 measured a separation of  1.6+/-0.5 kpc between the stars and the dark matter, which likely means that there is some repulsive force between the dark matter that does not affect the stars.
It should be noted that the galaxies in this cluster are moving with velocities on the order of 200-300 km/s, where as in the Bullet Cluster, the galaxies are colliding with relative velocities on the order of 4500 km/s. (In other words, the Bullet Cluster is like Fig.4. above where as the collision in Abell 3827 is more similar to Fig.5. or Fig.6. above.)

It's easily to rule out most known and unknown forces of nature because the force would have to turn off in the "Bullet Cluster" limit of high relative directed velocity.

But here's the key to this argument:   one can calculate fairly easily the separation that one would expect due to the self-interaction, repulsive term. If there were no repulsion between the dark matter halos, then the separation between the center of the stars and center of the DM would be zero. If there were a constant acceleration difference, then the separation distance would be:

Separation = 0.5 * DeltaAcceleration * (Time)^2

Using the repulsion potential shown above and simplifying for the case of separation distance just below the degeneracy radius, the acceleration is approximately -0.2*kT/(Rest Mass_DM *EffectiveSeparationRadius.) This means that one could estimate the rest mass of the dark matter from the acceleration. The main problem here is that the Infall Time is unknown. Therefore, one can't estimate the mass of the dark matter without including large error bars.

But just for the fun of it, let's pick a middle ground case. Let's pick the middle value for the separation (1.6 kpc) and let's pick a middle ground value for the infall time of 300 million years. (According to Massey et al. , reasonable values for the infall time would be between 20 million years and 1000 million years, so 300 million years is a roughly intermediate value.) This means that the repulsive acceleration between the galaxies would have to be approximately 10^-12  m/s^2. This is a really small repulsion compared with accelerations on Earth.
So, now, let's estimate the dark matter rest mass such that self-repulsion matches this acceleration using the simplification above, i.e. the repulsive acceleration is approximately -0.2*kT/(Rest Mass_DM * EffectiveSeparationRadius.)   And let's note that the EffectiveSeparationRadius is a function of Rest Mass because in the limit of GeV dark matter particle, the EffectiveSeparationRadius becomes infinite and there is no acceleration term.
To do this calculation, let's also assume that the dark matter has a temperature of 1.4 K. (i.e. slightly colder than the photons in the CMB due to the lack of re-heating during e+/e- annihilation.)

Using this assumption, I calculated a repulsive acceleration of 10^-12  m/s^2 when the rest mass of the dark matter particle is 8 keV. However, it should be noted that by picking a different infall time or a higher or lower separation distance, it's quite easy to obtain values of the that rest mass of the dark matter particle any where from 1 keV to 40 keV. In order to become more precise, we need to know the infall time, the separation, and the temperature to much greater accuracy.

My point here is simply to note that self-repulsive Fermi dark matter particles with rest masses on the order of 2-20 keV can provide the required acceleration to create a sizable separation between the center of mass of the stars and the center of mass of the dark matter, but only when the galaxies are moving slow enough that self-repulsion can turn on. In the case of high directed velocity, the dark matter in the galaxies would pass right by each other.

We could redo the calculation above and estimate the rest mass of the dark matter particle, such that the directed velocity of the galaxy (~200 km/s) is only a few times greater than the thermal velocity. (Repulsion will occur as the directed velocity becomes comparable to the thermal velocity because there will be overlap in the wave function due to the limited number of position-momentum spaces available.) At a temperature of 1.4 K, the  thermal velocity of a 8 keV rest mass dark matter particle is 52 km/s. Hence, the collision would be roughly between the collisions listed above in Fig.4. and Fig.5. A 40 keV rest mass dark matter particle has a thermal velocity of 23 km/s. This means that the collision is effectively classical (i.e. there is effectively no collision at all.)
For a 1 keV rest mass, the thermal velocity is roughly 147 km/s, and we can see that there would be significant interaction between the dark matter halos if they only have a directed velocity difference of ~200 km/s. So, we can see that once again, we are led to conclude that we need dark matter particle on the order 2-20 keV in order to obtain any appreciable (but not too large) self-repulsion. (And nicely, the repulsion goes away for this 2-20 keV rest mass dark matter halo when the collision velocity between the halos is 4500 km/s, as in the Bullet Cluster.)

So, let's know set back.  GeV Cold Dark matter has been effectively ruled out for the following reasons:
(a) Clumps too much in the center of galaxies
(b) Over-predicts the number of dwarf satellite galaxies within the Milky Way
(c) Predicts a value of the optical scatter depth during reionization that is too large
(d) Can't explain the separation between the stars and the dark matter in the Abell 3827 cluster.

Axion dark matter does an even worse job than Cold Dark Matter because it completely over-predicts the dark matter mass in the center of galaxies, and once again, can't explain the separation between the stars and the dark matter in the Abell 3827 cluster. In fact, axion dark matter might predict that there would be separation in the opposite direction (i.e. that the dark matter would be attracted even more than the stars to the center of the cluster.)
And I won't even go into MOND because MOND theories are completely incompatible with (a) Bullet Cluster, (b) Abell 3827, and (c) Planck...and likely many more data sets. Dark matter is required in order to explain the clumpiness in the CMB. MOND theories can't explain the clumpiness in the CMB as seen by WMAP/Planck/etc...

In summary:   Dark matter is real; it likely has a rest mass in the range of 2-20 keV; and my guess is that it's a resonantly produced, non-thermal species with a rest mass of ~6-8 keV (which means that it can act like a 3 keV thermal relic as far as quantum degeneracy calcs at small scales and act like a 20 keV thermal relic as far as thermal velocity at large scale...which is exactly what is required to both explain large-scale BAO data and the small scale galaxy rotation curves.)


If only we could find such a particle...or perhaps we already have... (Boyarsky et al. and Bulbul et al.)

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