# Could Hawking radiation have a lot of neutrinos and dark matter?

Up till now I have thought that Hawking radiation would be mostly photons, since the temperatures are typically small. However, a comment on another question (thanks to John Doty) suggested that we should also consider other species of low rest mass. So my question is: could Hawking radiation have a large contingent of neutrinos? And could there be any other species of low mass?

As I understand it, the $$Z$$ mass measurement rules out further generations of neutrinos in the standard model, but presumably not further particles which don't interact with $$Z$$. Again, as I understand it, dark matter is thought to be largely 'cold', which suggests that if it is particles then they have high not low mass. But could there be a significant contingent of low mass particles?

We don't need to consider neutrinos in thermal radiation from ordinary matter, because their interactions are so weak, so they are not produced in anything like the same quantities as photons. But gravity being universal, I wonder whether Hawking neutrino radiation might have similar power to Hawking electromagnetic radiation, at least for small black holes whose temperature is above a few thousand kelvin, if we take neutrino mass as $$0.1$$ eV. That would be interesting, but perhaps it is ruled out by some argument coming from electroweak theory?

• Sep 6 at 11:51

Yes.

Hawking radiation is universal: the black hole is a modification of spacetime geometry, and the quantum fields, which manifest particles, are residents of that spacetime. Thus they are all affected by its presence (i.e. it "couples to" all those fields), and hence any and every physically possible particle can appear in the Hawking radiation from the black hole, at least supposing that all existent particles follow the laws of quantum field theory.

That said, that doesn't mean they are all emitted equally easily: for sufficiently massive particles, a suitably-hot black hole is needed or else the emission of the particle species in question is at the very least extraordinarily unlikely. This means that the black hole must be suitably small in mass, because the radiation temperature is inversely related to the black hole mass, and hence very massive particles will only be produced in the very last stages of the black hole's decay.

Hence, indeed dark matter will be emitted, but just when will depend on how massive dark matter particles are, or aren't, which is something we don't know yet as we haven't indisputably seen one. That said, the lightest (still unconfirmed) dark matter candidate is the axion, with projected masses of 10-1000 μeV. However, any present-day black hole we know of is so massive and thus "cold", that even this very light mass is still well above the typical particle energy available to it. All other proposed candidates are much heavier; and so the result is dark matter will with near-certainty not be emitted in significant quantities until the very late stages of the black hole's evolution (And neutrinos, by the way, are even heavier than axions, around $$10^5$$ μeV).

• To help quantify the fact that higher-mass particles contribute less to Hawking radiation, here's a quote from pages 4-5 in arXiv:1301.4995: "it seems most likely that there are no massless particles other than photons and gravitons..., and no massive particles of smaller rest-mass energy than $1.34 \times 10^{-10}$ eV. If this is indeed true, ...black holes of solar masses and above would radiate almost entirely photons and gravitons." Smaller black holes are hotter, which changes the numbers, but this example covers an important range of black hole sizes. Jun 22, 2021 at 0:00
• Just to underline: the question is about the relative rates or power in the contributions from different species, rather than the binary question of whether there is any at all. I think your answer is that the power for each species is similar if the temperature is above a threshold of order $mc^2 / k_B$ where $m$ is the rest mass of the species in question. Jun 22, 2021 at 8:58
• P.S. thanks for the comment on the axion too. Do you know if the range $10-1000\,\mu$eV is still heavy enough for such dark matter to be mostly "cold" now, in astronomical terms? Jun 22, 2021 at 9:01
• "The lightest (still unconfirmed) dark matter candidate is the axion, with projected masses of 10-1000 μeV." Ultralight axion-like particle dark matter candidates can have masses on the order of $~10^{-22}$ eV. These are often described as "fuzzy", "wave", or "scalar field" dark matter. They are cosmologically cold once the Hubble parameter becomes smaller than the mass in natural units. The interaction of such candidates with rotating black holes is one of the most promising means of constraining their mass, though I don't think this is related to Hawking radiation. Jun 22, 2021 at 9:29
• @Andrew Steane : It's lighter than neutrinos; so in fact you'd expect it to be "hot" (neutrinos are actually technically a "known" hot dark matter.). But it is "cold" because the formation mechanism results in it ending up as a Bose-Einstein condensate (axions are bosons). Jun 26, 2021 at 0:28

Yes. From this paper (Hooper, Krnjaic, McDermott: Dark Radiation and Superheavy Dark Matter from Black Hole Domination):

Unlike most other mechanisms for particle production, the process of Hawking evaporation generates particles democratically, producing all particle species regardless of their assigned charges or couplings. If there exist any stable particles without significant couplings to the Standard Model (SM), they would be produced through Hawking evaporation without subsequently thermalizing, but still contributing to the universe’s total energy density. This makes the evaporation of primordial black holes a particularly attractive mechanism for the production of both dark radiation and dark matter [77, 80