On (minuscule) dark matter production in supernovae

Question

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.

Answer 1

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.

Answer 2

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.

Answer 3

Your line of thought is tempting and nice to read. But do not neglect that in particular the typical WIMP mass range 1...100GeV is highly challenged by direct dark matter experiments and also LHC: there are no signs, no hints, no clues. Only limits and non-observation. At the moment, the community is somehow moving away from the purely-WIMP-centered dark matter thinking:

There are uncounted models for dark matter with no consensus and no direct experimental evidence (again, only limits, and non-observation). That is not a trivial statement, any kind of relation of dark matter with respect to normal matter is tested, any kind of mass spectrum too. It doesn't really make sense to start here to list this in detail. There are good old weakly-interacting-massive-particles WIMPS, light dark matter, light mediators, dark sector, super-heavy, strangelets/baryonic, etc., etc. Most of the candidates are neutral, but some may even be milli-charged, some may interact electromagnetically, some via the weak or even strong force, or only gravitation. The currently probed mass spectrum reaches from fractions of eV to beyond TeV, with the GeV range (thus ~WIMP) becoming challenged most significantly by a lot of non-observations at direct dark matter experiments and LHC.

Thus, to your question: the amount of dark matter produced anywhere will depend mainly on two properties of the dark matter itself (which are 100% unknown):

1. how is it coupled to normal matter, how does it interact, and
2. what is its mass, since mass must be produced at minimum to create the particles.

The standard assumption of cosmology is that all relevant dark matter was formed in the big bang. Any potential production today (maybe in cosmic rays, supernova, AGNs, etc) will be minuscule and not significant/important. If the mass of dark matter turns out to be very high (~TeV or more) any production is basically IMPOSSIBLE today. There are basically no places in the universe where you could generate $\gg {\rm TeV}$ dark matter particles from non-thermal collisions (it is interesting to note that the actual high-energy universe is non-thermal, so your estimates could not be applied to this), or thermal energy (your own estimates above indicate that). Only ultra-high energy cosmic rays may theoretically play a role, but they are by themselves super-rare in the universe. If the mass of dark matter is $\ll {\rm eV}$ they can certainly be produced in hot-thermal or explosive events, but at the same time their mass will be very very small so the overall effect/mass still be negligible.

This doesn't really answer your question, but in my understanding it cannot be answered at this moment. This shouldn't stop you from following you estimates, but do not forget that there are major assumptions and uncertainties behind this.