Sunday, July 27, 2014

The Case for keV Dark Matter

As I've mentioned before in previous posts, the case for GeV Cold Dark Matter is becoming weaker and weaker every day. However, that doesn't seem to stop people who work in this field from defending their theories and attacking Warm Dark Matter.
That's fine, but for those of you who actually care about understanding how the universe works. We need to move on and actually analyze what the data is suggesting.
So, here's a list of what we know:

(1) Dark matter is real, and it's roughly 25% (+/-3%) of the universe. We can detect it "directly" through gravitational lensing and "indirectly" from the CMB spectra. Dark Matter is not an artifact due to Modified Newtonian Dynamics (i.e. MOND) because the location of dark matter is not 100% correlated with the location of normal matter. The Bullet Cluster is an excellent example of this, but there are many many more examples of this phenomena. When galaxies collide, the normal matter of doesn't always follow the dark matter and the dark matter doesn't immediately clump together. This is one of many signs that dark matter is not GeV rest mass particles, but rather is quantum degenerate fermions with rest mass in the low keV range.

(2) Dark Matter particles can't have a rest mass less than 1 eV (or else they would be relativistic when universe first de-ionized.) Because a keV dark matter particle is non-relativistic when electrons and protons recombine, a keV dark matter particle only affects the "effective number of Relativistic Particles" (i.e the Neff in the CMB) with a contribution of roughly 0.03. This is well within the error bars for Neff, which was measured by Planck+BAO to be 3.30+/-0.27. When you include data from Big Bang Nucleosynthesis, the allowed range for Neff remains pretty much the same. This means that a keV sterile neutrino is completely compatible with data from the Planck satellite to within 1 sigma uncertainty on Neff.

(3) If Dark Matter particles are Fermions, then their rest mass can't be less than ~ 2 keV because the mass density would be too low to explain experimental data on dark matter density in dwarf galaxies. (de Vega and Sanchez 2013)

(4) Using the Lyman Alpha Forest data in the early universe, there are constraints on the rest mass of dark matter particles. The exact cut-off depends on the allowed uncertainty (i.e. 1 sigma, 2 sigma, 3 sigma, 5 sigma) and on the model assumptions about the particle. The most recent best-fit-value I found for dark matter using Lyman Alpha Forest data was listed as 33 keV in Table II of Viel et al. 2013. The 1 sigma range was 8 keV to infinite rest mass (i.e. no constraint on the high end), and the 2 sigma range was 3.3 keV to infinite rest mass. What's interesting is that the best fit through the data was a keV rest mass dark matter particle...not a GeV rest mass dark matter particle. One way of explaining this is that a GeV dark matter particle would over-predict the Density Perturbations, whereas a 10-100 keV particle is a better fit through the data. For example, in the plot below of the Power Spectrum P(k) vs. wavenumber (k)  (where larger wavenumber means smaller length scales), the Cold Dark Matter line is well above the data points for the Lyman Alpha Forest (and this was known even back in 2002.) More recent data confirms that the data is better fit with a 33 keV particle than with a GeV scale particle.

The reason I find this funny is that the Lyman Alpha Forest had been used by proponents of GeV Dark Matter to fend off proponents of Warm Dark Matter. Ah, how the tides turn. While Lyman Alpha Forest Data can't rule out GeV Dark Matter, it is now suggesting that Dark Matter is Warm  (i.e. in the keV scale.)

(5) If a GeV Dark Matter particle obtains its mass from the Higgs Boson (like it appears that the tau lepton and the bottom quark do), then we can rule out the mass of the particle from ~ GeV to half the rest mass of the Higgs Boson. The reason is that the branching ratios of the Higgs Boson are proportional to the rest mass of the Fermion. In other words, we would have indirectly detected Dark Matter particles at CERN if they had rest masses on the order of ~1-62 GeV. In addition, if the dark matter particle were 10-1000 GeV we would have likely detected it in detectors looking for WIMPS. As such, the range 1-1000 GeV is effectively ruled out for dark matter particles. (See plot from Aad et al. in PRL 23 May 2014)

(6) GeV Dark Matter would clump together in the center of galaxies. There is nothing to stop GeV Dark Matter from clumping together. This is the well known "Cuspy Core Problem" of GeV dark matter, and it also shows up as a problem with estimating the number and size of dwarf galaxies.
What solves these problems and keeps dark matter from clumping is the Fermi Exclusion Principle, which states that only 1 Fermi particle can fill any position-momentum level. As mentioned above, the Fermi exclusion principle sets a lower limit of ~1-2 keV for dark matter in order to explain the actual density of dark matter in dward galaxies. But the principle also helps to explain why the density of dark matter is not cuspy in the center of galaxies, provided that the mass of the dark matter particle is in the range of 1-10 keV. Below is a comparison (from de Vega et al. 2014 that compares observational data for the density of dark matter in galaxies vs. theory for quantum degenerate dark matter with a rest mass around 2 keV.) Notice that the theory matches the observational data quite well at small radius. GeV dark matter would tend to clump up at the center and could in no way match the data. However, it should be noted that I was unable to determine after reading the entire paper what rest mass was actually used in the simulations. This is a major oversight on their part, and I hope that it gets corrected shortly. The point is that a ~2 keV dark matter particle does a pretty good job of reproducing the actual distribution of dark matter in a wide variety of different types of galaxies.

So, let me summary the points above:

*Lyman Alpha Forest Data points to a 10-100 keV dark matter particle  (Viel et al. 2013)
*Sub-halo counts point to a 6-12 keV dark matter particle  (Horiuchi et al.,)
*Dwarf Galaxies point to a 1-4 keV dark matter particle   (F.A. Kamada and J.E. Papastergis, as well as de Vega and Sanchez 2013 and de Vega et al. 2014 )
*Planck results suggest that the rest mass is >10 eV, and best fit in the ~keV range to explain Neff slightly greater than 3.  (Planck Collaboration: Cosmological Parameters)

There is now no data specifically pointing to GeV dark matter particles.

So, the only problem appears to be the fact that some research suggests a rest mass of 10-100 keV and some research suggests a rest mass of 1-4 keV range. But there is an range between 4-10 keV which might be compatible with all data (when including uncertainty and when treating dark matter as a fermion.)
Note that there have been some recent papers that try to rule out dark matter with mass greater than or equal to 4 keV. However, one should be very careful when reading papers written by proponents of GeV dark matter who try to model keV dark matter. Such GeV proponents often fail to include the quantum nature of keV particles and forget to model them as a quantum degenerate fermion. Such authors often make claims ruling out Warm Dark Matter, but this is an over-reach because they are not correctly modeling keV dark matter. (For example, see

So, I am in no way claiming to know what is the exact rest mass of dark matter (in fact it might be composed of multiple different rest mass species.) While this X-ray emission at 3.55 keV might be suggesting a 7.1 keV matter particle, I think that we should keep an open mind and see where the astrophysics data leads us.
With that having been said, I think that we should be using Warm Dark Matter as our "standard model" and including the rest mass of the dark matter particle as a variable. It has always seemed strange to me that Planck researchers didn't include the rest mass of the dark matter particle as a free variable in its model. They had all sorts of variables, but failed to include the mass of the dark matter as a variable. This seems like a major mistake. The group looked into whether dark energy was constant, but failed to analyze their data to determine the mass of the dark matter.

What I would be interested in learning is what is the best-fit (and 1,2 sigma range) for the rest mass of the dark matter particle given all of the following experimental constraints:
CMB (WMAP, Planck), Lyman Alpha Forest (MIKE, HIRES), BigBangNucleosynthesis, Baryon Acoustic Oscillations, Sub-halo counts around large galaxies, and dark matter profiles within galaxies.

So far, I have yet to see a research paper that includes all of these experimental data sets at the same time. (Please let me know if I'm mistaken here.) What I've seen is some people looking at the small scale and some people looking at the big scale, but nothing that covers the whole range and determines what is the rest mass of the dark matter particle that best fits all of the known data.

To end this post, I'd like to mention that the 2014 Warm Dark Matter Conference in Paris recently ended. I did not attend the conference, but  I wish that I had. Here's the link to the site with the presentations from the conference. In the next few weeks, I'll write a post summarizing any key news finding/results.


  1. well put. I'm surprised there aren't any comments on this. Do you know of any good structure formation simulations using WDM which treats it as quantum degenerate fermions?

  2. Anjali,
    I have yet to find any papers in which the authors do full simulations of structure formation when assuming quantum degenerate fermionic WDM. The closest is the de Vega manuscript, which was updated in Nov 2014 after the announcement of a possible 7.1 keV sterile neutrino from X-ray data by Bulbul et al. in late 2014.
    Also, note that I've updated this post, and a new summary can be found here:

  3. Great. Will have a look, thanks.

  4. Anjali,
    It looks like there's now a paper doing just what we described (structure formation simulations with warm dark matter in which the fermion dark matter can be quantum degenerate as small scales/high density.)
    "Structure formation in warm dark matter cosmologies Top-Bottom Upside-Down"
    Paduroiu et al.

    I've only skimmed the paper so far. I'll likely create an entire post devoted to this paper, some time in the next few weeks.