Dark matter or pulsars? AMS hints it's neither.

Yesterday AMS-02 updated their measurement of cosmic-ray positron and electron fluxes. The newly published data extend to positron energies 500 GeV, compared to 350 GeV in the previous release. The central value of the positron fraction in the highest energy bin is one third of the error bar lower than the central value of the next-to-highestbin.  This allows the collaboration to conclude that the positron fraction has a maximum and starts to decrease at high energies :]  The sloppy presentation and unnecessary hype obscures the fact that AMS actually found something non-trivial.  Namely, it is interesting that the positron fraction, after a sharp rise between 10 and 200 GeV, seems to plateau at higher energies at the value around 15%.  This sort of behavior, although not expected by popular models of cosmic ray propagation, was actually predicted a few years ago, well before AMS was launched.  

Before I get to the point, let's have a brief summary. In 2008 the PAMELA experiment observed a steep rise of the cosmic ray positron fraction between 10 and 100 GeV. Positrons are routinely produced by scattering of high energy cosmic rays (secondary production), but the rise was not predicted by models of cosmic ray propagations. This prompted speculations of another (primary) source of positrons: from pulsars, supernovae or other astrophysical objects, to  dark matter annihilation. The dark matter explanation is unlikely for many reasons. On the theoretical side, the large annihilation cross section required is difficult to achieve, and it is difficult to produce a large flux of positrons without producing an excess of antiprotons at the same time. In particular, the MSSM neutralino entertained in the last AMS paper certainly cannot fit the cosmic-ray data for these reasons. When theoretical obstacles are overcome by skillful model building, constraints from gamma ray and radio observations disfavor the relevant parameter space. Even if these constraints are dismissed due to large astrophysical uncertainties, the models poorly fit the shape the electron and positron spectrum observed by PAMELA, AMS, and FERMI (see the addendum of this paper for a recent discussion). Pulsars, on the other hand, are a plausible but handwaving explanation: we know they are all around and we know they produce electron-positron pairs in the magnetosphere, but we cannot calculate the spectrum from first principles.

But maybe primary positron sources are not needed at all? The old paper by Katz et al. proposes a different approach. Rather than starting with a particular propagation model, it assumes the high-energy positrons observed by PAMELA are secondary, and attempts to deduce from the data the parameters controlling the propagation of cosmic rays. The logic is based on two premises. Firstly, while production of cosmic rays in our galaxy contains many unknowns, the production of different particles is strongly correlated, with the relative ratios depending on nuclear cross sections that are measurable in laboratories. Secondly, different particles propagate in the magnetic field of the galaxy in the same way, depending only on their rigidity (momentum divided by charge). Thus, from an observed flux of one particle, one can predict the production rate of other particles. This approach is quite successful in predicting the cosmic antiproton flux based on the observed boron flux. For positrons, the story is more complicated because of large energy losses (cooling) due to synchrotron and inverse-Compton processes. However, in this case one can make the  exercise of computing the positron flux assuming no losses at all. The result correspond to roughly 20% positron fraction above 100 GeV. Since in the real world cooling can only suppress the positron flux, the value computed assuming no cooling represents an upper bound on the positron fraction.

Now, at lower energies, the observed positron flux is a factor of a few below the upper bound. This is already intriguing, as hypothetical primary positrons could in principle have an arbitrary flux,  orders of magnitude larger or smaller than this upper bound. The rise observed by PAMELA can be interpreted that the suppression due to cooling decreases as positron energy increases. This is not implausible: the suppression depends on the interplay of the cooling time and mean propagation time of positrons, both of which are unknown functions of energy. Once the cooling time exceeds the propagation time the suppression factor is completely gone. In such a case the positron fraction should saturate the upper limit. This is what seems to be happening at the energies 200-500 GeV probed by AMS, as can be seen in the plot. Already the previous AMS data were consistent with this picture, and the latest update only strengthens it.

So, it may be that the mystery of cosmic ray positrons has a simple down-to-galactic-disc explanation. If further observations show the positron flux climbing  above the upper limit or dropping suddenly, then the secondary production hypothesis would be invalidated. But, for the moment, the AMS data seems to be consistent with no primary sources, just assuming that the cooling time of positrons is shorter than predicted by the state-of-the-art propagation models. So, instead of dark matter, AMS might have discovered models of cosmic-ray propagation need a fix. That's less spectacular, but still worthwhile.

Thanks to Kfir for the plot and explanations.