Monday, September 22, 2014

A simple explanation behind AMS' electron+positron flux power law?

Aside from tweets about the latest, not so interesting, and inconclusive Planck paper on the dust and polarized CMB, Francis Emulenews Villatoro tweeted the following suggestive graphs to his 7,000+ Twitter followers:

The newest data from the Alpha Magnetic Spectrometer are fully compatible with the positron flux curve resulting from an annihilating lighter than \(1\TeV\) dark matter particle. But the steep drop itself hasn't been seen yet (the AMS' dark matter discovery is one seminar away but it may always be so in the future LOL) and the power-law description seems really accurate and attractive.

What if neither dirty pulsars nor dark matter is the cause of these curves? All of those who claim to love simple explanations and who sometimes feel annoyed that physics has gotten too complicated are invited to think about the question.

The fact at this moment seems to be that above the energy \(30\GeV\) and perhaps up to \(430\GeV\) or much higher, the positrons represent \(0.15\) of the total electron+positron flux. Moreover, this flux itself depends on the energy via a simple power law:\[

\Phi(e^- + e^+) = C \cdot E^\gamma

\] where the exponent \(\gamma\) has a pretty well-defined value.

Apparently, things work very well in that rather long interval if the exponent (spectral index) is\[

\gamma= -3.170 \pm 0.008 \pm 0.008

\] The first part of the error unifies the systematic and statistical error; the other one is from the energy scale errors. At any rate, the exponent is literally between \(-3.18\) and \(-3.16\), quite some lunch for numerologists.

My question for the numerologist and simple ingenious armchair physicist (and others!) reading this blog is: what in the Universe may produce such a power law for the positron and electron flux, with this bizarre negative exponent?

The thermal radiation is no good if the temperature \(kT\) is below those \(30\GeV\): you would get an exponential decrease. You may think about the thermal radiation in some decoupled component of the Universe whose temperature is huge, above \(430\GeV\), but then you will get something like \(\gamma=0\) or a nearby integer instead of the strange, large, and fractional negative constant.

You may continue by thinking about some sources distributed according to this power law, for example microscopic (but I mean much heavier than the Planck mass!) black holes. Such Hawking-radiating black holes might emit as many positrons as electrons so it doesn't look great but ignore this problem – there may be selective conversion to electrons because of some extra dirty effects, or enhanced annihilation of positrons.

If you want the Hawking radiation to have energy between \(30\) and \(430\GeV\), what is the radius and size of the black hole? How many black holes like that do you need to get the right power law? What will be their mass density needed to obtain the observed flux? Is this mass density compatible with the basic data about the energy density that we know?

Now, if that theory can pass all your tests, you also need the number of smaller i.e. lighter i.e. hotter microscopic black holes (those emitting higher-energy radiation) to be larger. Can you explain why the small black holes should dominate in this way? May the exponent \(-3.17\) appear in this way? Can you get this dominance of smaller black holes in the process of their gradual merger? Or thanks to the reduction of their sizes during evaporation?

I am looking forward to your solutions – with numbers and somewhat solid arguments. You can do it! ;-)

A completely different explanation: the high-energy electrons and positrons could arise from some form of "multiple decoupling events" in the very high-energy sector of the world that isn't in thermal equilibrium with everything else. Can you propose a convincing model about the moments of decoupling and the corresponding temperature that would produce such high-energy particles?


  1. Lumo,

    Have you seen Jester's response? What do you think of the positron excess as being due to secondary particles from intergalactic gamma rays?

  2. that would galactic gamma rays stuck in the galactic magnetic field.

  3. Lubos, the black hole scenario naturally produces a flux (dN/dE) tail of E^(-3). The form of dM/dt from the Hawking radiation gives this high energy tail regardless of formation mechanism. Probably slightly steeper than E^(-3) due to intermediate decays in the Hawking emitted species contributing to the total positron output. Doing a back-of-the-envelope estimate the AMS flux at 100 GeV looks consistent with my black number density constraints from 100 MeV so other PBH limits wouldn't rule the idea out. No problem with the electron flux so long as the observed electron flux is greater than the positron flux. The mass of a 100 GeV black hole is about 10^8 kg.

  4. I have no experience with indirect products of intergalactic gamma rays and no intuition for that, so I have no idea why Jester would befriend exactly this new explanation as his pet explanation. It looks to me he searches for the most dull-sounding, most mundane, most frustrating, and ultimately least likely explanation one could think of. But maybe I am wrong. Of course it can be what he says.

  5. Excellent, Jane, you're the winner! Too bad I didn't prepare a prize.

    Do you also agree that the 100-GeV-massed black holes have a Hawking lifetime comparable to a year only?

  6. The 100 GeV black hole with last about 6 days. But that's not a problem: if astrophysical populations of such small black holes exist, they will have a number density per unit mass interval of dn/dM goes as M^2 independent of formation mechanism (again this comes from the Hawking dM/dt for an individual black hole). So as the present ones at 100 GeV complete their evaporation lifetimes, the 100 GeV distribution will be replenished (by those who are slightly cooler than 100 GeV today but will reach 100 GeV 6 days from now) and the E^(-3) tail will be maintained.

  7. that is "Thank you".