Possible constraints on dark matter particle mass

Although there is very good indirect evidence for the existence of dark matter, it’s an understatement to say that actual detection of dark matter particles has not been easy. Recent research results from two different teams that both studied gamma rays from dwarf galaxy neighbors of the Milky Way provide an illustration of the difficulty.

Both studies are based on the hypothesis that dark matter consists largely of “WIMPs” (Weakly Interacting Massive Particles). If existing indirect evidence for dark matter can be explained by modifications to the theory of gravity (so dark matter doesn’t actually exist), or if it exists in some form other than WIMPs, then the results of these studies are consistent with either possibility, but otherwise provide no additional information.

A further assumption of the WIMP hypothesis is that WIMPs are Majorana fermions. This is true, at least, if WIMPs are supersymmetric neutralinos. What this means is that WIMPs are their own antiparticles, and hence they are annihilated in any collision with another of their kind.

This annihilation can occur in different ways or “channels”, in which different types of known antiparticle pairs are created, such as b and anti-b mesons or τ+ leptons. These particles subsequently decay and produce gamma rays, which the Fermi Gamma-ray Space Telescope is designed to detect. The latest research shows that gamma-ray emissions that can be detected, from 7 to 10 dwarf satellite galaxies of the Milky Way, are not significantly higher than expected background emissions. Consequently, if indeed dark matter consists of WIMPs, then the individual particles must have masses above some lower bounds.

The reasoning is based on the “cross section“, or probabilility, for interactions in specific “channels” to occur. If WIMPs make up most of existing dark matter, then some channels can be ruled out entirely, based on observed gamma-ray emissions. This is because the amount of dark matter that must exist to account for observed gravitational effects is known with reasonable confidence.

The larger the cross section for some channel then the smaller will be the number of WIMPs needed to result in the observed (essentially zero) amount (above background) of gamma radiation from the dwarf galaxies studied. As it happens, in all but two plausible channels, the cross section is too large for there to be enough WIMPs of any possible mass to account for the expected total mass of dark matter.

The two channels that may have small enough cross sections involve b mesons and τ leptons. Here there is the opposite problem. For any given WIMP mass, you can compute (a range of) the numbers you need to account for the expected amount of dark matter. If WIMP mass is too low, then the numbers required will be so large that the number of annihilations, and hence gamma radiation, will be higher than is observed (above background). Only by going to higher mass, and lower particle numbers, is it possible to match both expected total mass and observed radiation.

The main uncertainty involves how much mass of dark matter each dwarf galaxy contains and hence what level of gamma radiation is expected. Approximate numbers for the total mass can be calculated, but they give a certain range of reasonable values. This leads to a range of masses that WIMPs must have.

The channel with the smallest cross section involves b mesons. In that case, the range of minimal masses that a WIMP must have to account for the range of total dark matter mass expected runs from 19 GeV up to 240 GeV, with the most likely value around 40 GeV. For the τ lepton channel, with a slightly larger cross section (fewer particles required), the range of minimal WIMP mass is from 13 GeV to 80 GeV, with 19 GeV most likely. These figures are from one of the studies (Geringer-Sameth and Koushiaiappas [GK]). The other study (Fermi-LAT Collaboration [FC]) had roughly similar numbers.

The two studies just reported used similar, fairly standard methods to estimate the total amount of dark matter in each of the dwarf galaxies. The main difference between the two studies lies in how the amount of background gamma radiation was estimated.

One study [GK] took the straightforward approach of simply using measurements of gamma radiation outside of, but close to, the various galaxies, excluding specific known sources. These measured values were assumed to extend to the area covered by the dwarf galaxies themselves. The other study [FC] used more elaborate theoretical techniques to estimate the gamma-ray background.

The net result from both studies is that the lack of a gamma-ray flux significantly above the expected background rules out low masses (below ~30 GeV) for WIMPs consisting of Majorana fermions. The main uncertainty results from uncertain estimates of total dark matter content in the galaxies studied, but that only leads to a range with limited lower end of possible minimal values for dark matter WIMP masses. This is not an especially confining mass limit, since there’s very little theory that would rule out neutralino WIMPS with masses of 1000 GeV or more.

In a separate investigation that also used the Fermi Gamma-ray Space Telescope, a different type of possible evidence for dark matter was apparently ruled out. This concerned previous tentative reports of unexpectedly large numbers of positrons in cosmic rays that seemed to originate from the central region of the Milky Way. This research, however, did not place specific limits on the nature or masses of possible dark matter particles.


Geringer-Sameth, A., & Koushiappas, S. (2011). Exclusion of Canonical Weakly Interacting Massive Particles by Joint Analysis of Milky Way Dwarf Galaxies with Data from the Fermi Gamma-Ray Space Telescope Physical Review Letters, 107 (24) DOI: 10.1103/PhysRevLett.107.241303

Ackermann, M., Ajello, M., Albert, A., Atwood, W., Baldini, L., Ballet, J., Barbiellini, G., Bastieri, D., Bechtol, K., Bellazzini, R., Berenji, B., Blandford, R., Bloom, E., Bonamente, E., Borgland, A., Bregeon, J., Brigida, M., Bruel, P., Buehler, R., Burnett, T., Buson, S., Caliandro, G., Cameron, R., Cañadas, B., Caraveo, P., Casandjian, J., Cecchi, C., Charles, E., Chekhtman, A., Chiang, J., Ciprini, S., Claus, R., Cohen-Tanugi, J., Conrad, J., Cutini, S., de Angelis, A., de Palma, F., Dermer, C., Digel, S., do Couto e Silva, E., Drell, P., Drlica-Wagner, A., Falletti, L., Favuzzi, C., Fegan, S., Ferrara, E., Fukazawa, Y., Funk, S., Fusco, P., Gargano, F., Gasparrini, D., Gehrels, N., Germani, S., Giglietto, N., Giordano, F., Giroletti, M., Glanzman, T., Godfrey, G., Grenier, I., Guiriec, S., Gustafsson, M., Hadasch, D., Hayashida, M., Hays, E., Hughes, R., Jeltema, T., Jóhannesson, G., Johnson, R., Johnson, A., Kamae, T., Katagiri, H., Kataoka, J., Knödlseder, J., Kuss, M., Lande, J., Latronico, L., Lionetto, A., Llena Garde, M., Longo, F., Loparco, F., Lott, B., Lovellette, M., Lubrano, P., Madejski, G., Mazziotta, M., McEnery, J., Mehault, J., Michelson, P., Mitthumsiri, W., Mizuno, T., Monte, C., Monzani, M., Morselli, A., Moskalenko, I., Murgia, S., Naumann-Godo, M., Norris, J., Nuss, E., Ohsugi, T., Okumura, A., Omodei, N., Orlando, E., Ormes, J., Ozaki, M., Paneque, D., Parent, D., Pesce-Rollins, M., Pierbattista, M., Piron, F., Pivato, G., Porter, T., Profumo, S., Rainò, S., Razzano, M., Reimer, A., Reimer, O., Ritz, S., Roth, M., Sadrozinski, H., Sbarra, C., Scargle, J., Schalk, T., Sgrò, C., Siskind, E., Spandre, G., Spinelli, P., Strigari, L., Suson, D., Tajima, H., Takahashi, H., Tanaka, T., Thayer, J., Thayer, J., Thompson, D., Tibaldo, L., Tinivella, M., Torres, D., Troja, E., Uchiyama, Y., Vandenbroucke, J., Vasileiou, V., Vianello, G., Vitale, V., Waite, A., Wang, P., Winer, B., Wood, K., Wood, M., Yang, Z., Zimmer, S., Kaplinghat, M., Martinez, G., & , . (2011). Constraining Dark Matter Models from a Combined Analysis of Milky Way Satellites with the Fermi Large Area Telescope Physical Review Letters, 107 (24) DOI: 10.1103/PhysRevLett.107.241302

Further reading:

Physicists set strongest limit on mass of dark matter

Latest Fermi studies find no trace of dark matter

Strongest limit set on dark matter’s mass

Gamma Rays Carry No Trace of Dark Matter

New Twist in the Search for Dark Matter

Dark matter particles may be heavyweights after all

Fermi Observations of Dwarf Galaxies Provide New Insights on Dark Matter

Exclusion of Canonical Weakly Interacting Massive Particles by Joint Analysis of Milky Way Dwarf Galaxies with Data from the Fermi Gamma-Ray Space TelescopearXiv.org

Constraining Dark Matter Models from a Combined Analysis of Milky Way Satellites with the Fermi Large Area TelescopearXiv.org

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