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.

## 11 comments:

Cool!

To me it's kind of funny how usually in astronomy, the issue is how the interstellar medium interferes with photons, through their interactions with all the charged particles out there, but for these kinds of experiments, the issue might be how the interstellar medium interferes with charged particles, through their interactions with all the photons out there. It's like the hero and the villain of the story have traded places.

A note: you have "the, the" in the last paragraph.

Could primordial black holes be a source of excess positrons?

Hi there,

to be honest, I don't understand why all this is a hint to a purely secondary origin of the positron fraction.

The only conclusion I draw from the paper you mention (and the updated version 1305.1324) is the following: the rise is

compatiblewith purely secondary production, if one doesn't make any assumptions about energy losses.But the mere fact that it is possible to place an upper limit on a quantity compatible with the data does

notmean that the data can be explained by the underlying model (here the secondary production). In other words, I think obviously there are a lot of theories out there for which it is possible to find very conservative upper limits compatible with the AMS-02 data.To really support the secondary origin of the positron fraction, I would like to see a concrete, well-motivated model for propagation/energy losses, which can really explain the rise of the fraction, instead of just placing an upper limit compatible with the data.

So, They dropped the positron cooling (which must be there) and they call this simple (wrong) model as "upper-limit". Ok, it is a real upper limit because the cooling will pull down the positron fraction. They also claim it's model-independent but it's not, because propagation effects are still there (btw they are even less understood than the cooling), in fact they use a very crude propagation model with very bad fit to the B/C ratio, to fix alpha.

Finally, they claim that whatever is below their curve will support the scenario, no matter the spectral shape. No matter if the AMS data increase with energy, in clear contradiction with any secondary-production scenario. Cool, eh?!

" This allows the collaboration to conclude that the positron fraction has a maximum and starts to decrease at high energies :] "

They haven't shown the data above 500 GeV.

But... It doesn't mean they haven't looked at them.

What, nothing about BICEP? Come on, Jester, gloat a little. You earned it!

Thank you Jester for this nice summary. However, if you choose to emphasize a work that states "But maybe primary positron sources are not needed at all?", you should be cautious. This work is based on a very questionable assumption: radiative losses are neglected. While this is correct for cosmic-ray nuclei, it is well known for decades that this cannot be the case for e+e-, because of the very efficient synchrotron and inverse Compton processes (see the seminal works of Ginzburg & Syrovatskii in the 60's, or all available textbooks, for instance Berezinskii's, Longair's, or Schlickeiser's). And as far as I understand, electrodynamics has not been ruled out yet ;-).It is not because they are ignorant that the majority of high-energy astrophysiciscts expert in the domain believe that this large positron fraction is a serious hint for primary positrons. Pulsar winds and SNRs are indeed the best candidates, which are demonstrated to exist around there. Now, it is also true that it is hard to make predictions from first principles, but come on, since the effect is local (see for example Shen ApJL 162, L181, 1970, or Aharonian et al 1995, etc.), and since these sources are macroscopic, you can hardly blame the experts for that ... There is no shame in not controlling things as long as one does not look for exotic signals there ... and it is well known that nobody does ;-) (as it is the case for channels strongly polluted with QCD background at the LHC).

I can smell an elephant in the room.

To clarify: I don't think they *assume* that radiative cooling can be neglected. They merely say that the situation with no cooling represents a robust upper limit for the secondary positron flux. I find it intriguing that the positron flux measured by AMS asymptotes to that upper limit. This does not prove the positrons are secondary, but for primary positrons of whatever origin it would have to be a weird coincidence than the (in principle arbitrary) local flux falls close to that value.

Now, assuming the positrons are secondary, one has to conclude that cooling is small above 100 GeV. That is indeed challenging to understand in terms of an underlying propagation model. But there's no robust proof either that t_cooling < t_escape in any sensible physical propagation model.

I don't understand this cooling time argument. I would imagine the processes that "cool" electrons act exactly the same way on positrons. So why would the _fraction_ of positrons change with energy?

I think most of the electrons are produced from primary sources, therefore propagation effects are different for the two.

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