# "Thermal" neutrino generation?

• I
Consider the Sun. It radiates energy by generating EM radiation. However, Sun is not transparent to EM, and therefore energy can only escape from the surface using this mechanism. Hot plasma below the surface generates and absorbs gazillions of photons, but they are "trapped" there.

But EM is just one side of electroweak force. In particular, every EM process mediated by photons has a counterpart mediated by Z-boson.

So I suddenly realized that "hot plasma below Sun's surface" ought to also generate virtual Z-bosons as well (with vastly lower probability than photons). And unlike photons, Z-bosons can transform back not to electrons, but neutrinos. And _those_ particles are not trapped!

So, Sun should be radiating these "thermally" generated neutrinos from its entire volume, not just its surface. In fact, not only virtual Z-bosons contribute, W-bosons should as well: e- => nu + W- => nu + e- + anti-nu.

(As usual, these processes are possible, just like analogous photonic processes, only in the presence of other particles, to satisfy energy and momentum conservation. Freely traveling electrons do not spontaneously emit light, or Z-bosons. Electrons in Suns plasma can.)

Since I never read any scientific discussions about stars emitting "thermal neutrinos", I suppose the probability is so low that even the advantage of radiating from the entire volume does not make this process noticeable in energy balance?

Alternatively, do I miss something and these processes are not allowed?

Orodruin
Staff Emeritus
Homework Helper
Gold Member
2021 Award
The weak force is called weak for a reason. The mass of the Z-boson should suppress your interaction rate by a factor of ##E^4G_F^2##, where ##E## is the typical energy involved. For a temperature corresponding to the Sun's core, this is a factor roughly ##10^{-34}## relative to photon interactions.

Does Urca process depend on the availability of suitable beta radioactive nuclei, or are any neutrinos emitted directly from thermal Z neutrinos?
Also, can hot sources like supernova cores and young neutron stars only emit electron and antielectron neutrinos, which only later oscillate to mu, antimu, tau and antitau neutrinos, or can any mu, tau, antimu and antitau neutrinos form directly from thermal virtual Z bosons?

mfb
Mentor
Also, can hot sources like supernova cores and young neutron stars only emit electron and antielectron neutrinos, which only later oscillate to mu, antimu, tau and antitau neutrinos, or can any mu, tau, antimu and antitau neutrinos form directly from thermal virtual Z bosons?
The Z couples equally to all neutrino types.

For neutron stars neutrinos contribute a lot to initial cooling - with a couple of different processes.

The weak force is called weak for a reason. The mass of the Z-boson should suppress your interaction rate by a factor of ##E^4G_F^2##, where ##E## is the typical energy involved. For a temperature corresponding to the Sun's core, this is a factor roughly ##10^{-34}## relative to photon interactions.

Thanks for some numbers.

Using photons (and convection), energy from the Sun's core needs on the order of a million year to cross about ~1 light second distance from the core to surface (where it can finally escape). That's less efficient than neutrinos on the order of 3*10^13.
Combining with your number, Sun's thermal neutrino luminosity is ~10^-20 of the "photonic" one.

Orodruin
Staff Emeritus
Homework Helper
Gold Member
2021 Award
Don't take the number too seriously. It is sort of only an upper bound. In fact, you do not have the same thermal interactions with Zs as you do with photons. The photon gas is kept in approximate local thermal equilibrium by reactions that absorb or emit a photon. In the case of the Z, there is not enough energy to produce an on-shell Z and so you need to add an additional vertex to actually go to neutrinos. What would be more relevant to look at would be the neutrino production rates. You then essentially have two options:
1. Production via ##p+e \to n + \nu_e##. Since the Sun's core temperature is lower than the mass difference, this is strongly Boltzmann suppressed.
2. Production via dressing electron-electron interactions with a Fermi vertex emitting a neutrino-antineutrino pair. You would have a final 4-body phase space rather than the 3-body phase space for photon production and the suppression with energy should be based on the momentum transfer.
The conclusion must be that thermal neutrino production is way too slow to play any sort of role in terms of cooling the stellar core.

You can compare this to what happens in a supernova, where thermal neutrino production plays a significant role. Supernova cores are dense enough to be opaque to neutrinos and so just like a star has a photosphere, a supernova has a neutrino sphere. A major part of the energy from a core collapse supernova is emitted in the form of neutrinos.

mfb
Mentor
What is wrong with the process ##e+\gamma \to e +Z^*(\nu\nu)##? It has a huge suppression from the energy scale, which also means the neutrinos won't follow a proper thermal spectrum, but it can produce some neutrinos at quite low energies. On the other hand: There are also fusion reactions that produce low energy neutrinos by random chance. Probably much more than the other processes.

Orodruin
Staff Emeritus
Homework Helper
Gold Member
2021 Award
What is wrong with the process ##e+\gamma \to e +Z^*(\nu\nu)##?
What is wrong with it is that I missed it so early in the morning due to not thinking enough of the photon gas.
When thinking of photons I only thought about processes changing the photon number, since it varies with temperature.

It has a huge suppression from the energy scale, which also means the neutrinos won't follow a proper thermal spectrum, but it can produce some neutrinos at quite low energies.

Agreed. One might argue whether or not being produced by the interactions of thermal components it should be called thermal production or not. I agree that it will not have a thermal spectrum, but it should be suppressed by the momentum transfer all the same.