On (minuscule) dark matter production in supernovae

It is believed that dark matter is made of particles, which interact with matter only weakly and gravitationally. One common candidate for dark matter are so called WIMPs. WIMPs, specifically, are heavy and may be their own antiparticles.

And as any other particles dark matter particles can be produced at sufficiently high energies. The mass of dark matter particles is unknown, but is estimated to be of order $1$-$100 \textrm{GeV}$, which corresponds to temperatures of $T_{DM}\approx 10^{13}$-$10^{15}\textrm{K}$, at which these particles may be expected to be produced.

Such enormous temperatures are barely attainable in any reasonable astrophysical processes, but say in core-collapse supernovae newly formed core has temperatures of $T_{SN,after}\approx 10^{11}\textrm{K}$, and probably more during the collapse phase. Then a crude estimate would suggest that the amount of dark matter produced is $M_{DM}\approx e^{-T_{DM}/T_{SN,max}}M_\odot$. Or, in number form $\log_{10}(M_{DM}/\textrm{kg})=30.3-0.43(T_{DM}/T_{SN})$. This means that at $T_{SN}=1.4\cdot 10^{-2}T_{DM}$ the amount of dark matter produced during a supernova will be around one kilogram. Such temperatures are fairly reachable for $1 \textrm{GeV}$ DM particles. So one can optimistically expect few kilograms of dark matter produced per supernova.

Now the question. What is a typical dark matter production in core-collapse supernovae? A good answer, I imagine, would be a more robust expansion on the existing estimate. Any constructive comments are welcome.

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The most favoured WIMPS at the moment are probably neutralinos, see http://en.wikipedia.org/wiki/Neutralino

These particles are purely hypothetical at the moment. The mass estimates in the above Wikipedia article for the lightest neutralino range between 10 and 10,000 GeV, meaning that the production rates in SNs will be much lower than with an assumed 1 GeV. Higher production rates should have already been detected at LHC.

Hence from the non-detection (in the form of energy loss) of WIMPS at LHC an estimate of an upper bound of the production rates in SNs should be possible.

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I would still be curious to know such an estimate. Is it a few particles, or is it a nanogram that we might expect, or is it even anywhere above macroscales? One other point hindering the production, except for the expected energy range, is of course due to the reaction crossections. They can be also rather low. –  Alexey Bobrick Jan 6 '14 at 20:28
@AlexeyBobrick One hypotheses is, that DM WIMPS are decay products of heavier particles. SNs may reach much higher energies than LHC, up to about 10e19 eV. If the production of WIMPS goes that way, high energy cosmic particles may be an additional source of information. That's some hope I can give for DM production in SNs, despite lack at LHC. I hesitate to supply numbers, because there exist too many unconfirmed hypotheses. All may be wrong. –  Gerald Jan 6 '14 at 21:03
true, and it is model dependent of course. However, even a rough estimate for some particular model would be interesting. Note also, that 1) the most energetic cosmic rays are most likely not produced in supernovae, 2) it is thermal, not the bulk motion, which matters for reactions. –  Alexey Bobrick Jan 6 '14 at 21:48
The most energetic observed cosmic rays are thought to be produced at a "nearby" black hole, which is still to be confirmed. But if so, this might also occur at supernovae collapsing to a black hole, although a good correlation between GRBs (which might be associated with SNs) and high energy CRs couldn't been confirmed thus far. High energy cosmic rays are restricted in their travel by blue-shifted cosmic microwave background and associated energy loss. The current ideas of the formation of WIMPs, as far as I can anticipate, tend towards decay of heavier particles. –  Gerald Jan 6 '14 at 23:30
... roughly like the decay of nucleons produce neutrinos. A direct production of neutralinos with a mass below 100 GeV looks rather unlikely or at least very rare, rarer than Higgs particles. One can now guess the weight of particles, which decay into neutralinos or other WIMPS, and look for the probabilities, that theses energies occur in SNs. Now this has to be multiplied with a guessed reaction cross-section. A hypothetical decay to WIMPs should then be straightforward. But here we have a sequence of assumptions which will multiply up uncertainties. –  Gerald Jan 6 '14 at 23:40

There are several types of supernova and ways that the core can collapse. Lets take an extreme case in which gamma-ray photodisintegration destroys all of the heavy elements (Si, Fe and Ni, etc) and breaks them all up into protons, neutrons and electrons. Each nucleus releases all of its binding energy, about 9 MeV per nucleon mass or 0.9% of the rest mass. Most of the energy, I believe, comes out in the form of relativistic neutrinos (the rest in kinetic energy of the protons, neutrons, and electrons). So, an upper limit is that 0.9% of the mass of the core ends up in neutrinos. The rest mass of the neutrinos is much less, but the relativistic mass is probably the more relevant number.

Only a small fraction of closure density ($\Omega$) is in stars, $\Omega_{stars}$ = 0.0027 (Fukugita & Peebles, 2004), about 7% of mass in stars goes into supernova, ~10% is in core-collapse, 0.9% comes out in relativistic neutrinos. So altogether $\Omega$ in hot dark matter from SN is less than 0.0027*0.07*0.1*0.009, roughly speaking.

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