Stellar Neutrino production

[Ariphaos]

So, I do some math and, from raw fusion, it would seem that stars release anywhere from ~1% (proton-proton dominates) to about ~30% (high-temperature CNO) of their energy as neutrinos.

Wikipedia claims that the solar energy output in neutrinos is in fact 2%, citing these neutrino graphs, but that doesn't seem to be what the source is saying at all. Most other sources I find simply say 1%.

On the other hand, researching it, I did find various papers discussing pair annihilation, plasma neutrinos, photo neutrinos, etc.. It's quite enlightening as I didn't know neutrinos were made by these methods, however they only give energy loss in terms of temperature and density, per cubic centimeter. Problem being that since fusion occurs in a shell (at least for stars I'm worrying about for this) and this sort of "Something special happens to an electron" loss would occur throughout the star - it's not enough to cheat and try to work out how much a given cubic centimeter at a given temperature and density would lose normally to fusion. Just looking at the high temp/pressure lines is rather suggestive of stars actually going supernova because of this energy loss.

Is anyone aware of any estimated neutrino production rates as a percentage of their luminous output for hypothetical stars, taking this into account? At least pre-supernova, anyway.

[starslayer]

No, I don't, but they should be out there... somewhere. This shouldn't be particularly difficult to calculate, though. There are published density and temperature profiles for stars of all kinds floating around out there, and from that it's simple numerical integration to figure out the neutrino production and the resulting energy losses since you have the production rates. Fusion could be fairly easily and accurately approximated as a sharp cutoff between different fusion regions, though you could include the fusion rates as a function of density, temperature, and composition if you really felt like it. Kippenhahn and Weigert could be very helpful for you, depending on how much you already know about stellar structure and evolution. It's basically the Bible of stellar evolution, but it's about $80 new on Amazon and a little out of date on some stuff by now.

Anyway, stars do not go supernova from neutrino losses. Pair production instability can result in supernovae for extremely massive stars, but the cores usually don't get hot enough (temperatures above ~109 K) for significant pair production to occur. There have been some noises made about electron capture supernovae at the extreme low mass end of the SN range (~8 Msun), but that doesn't rely on neutrinos either so far as I am aware. But I don't really know much about them or how they work, so I could very well be wrong. Normal CCSN produce tons of neutrinos as part of the collapse to a neutron star, and neutrinos are very important there (the core becomes opaque to neutrinos!), but the initial loss of pressure support is from the complete loss of degeneracy pressure support in the iron core and processes like photodisintegration of iron, which also does not depend on neutrinos.

I haven't done the calculations myself either, but I'm pretty sure fusion neutrinos dominate over the other processes for most, if not all, stars. I'd interested to hear what you find.

As an aside, what kind of stars are you looking at? I might be able to help a bit more if I knew more specifically what of stuff/objects you need this for.

[Ariphaos]

Well it looks like it's highly dependent on the metallicity of the star in question, so giving a general answer, outside of possibly of low mass stars, is probably not very sound. On the other hand I'm mostly looking for a range rather than specific values. I did find one document covering a .6 solar mass white dwarf, but it didn't give any totaled equation, though I might have just missed it.

Let's see. Solar energy production in layers - more general equations might be better but we can use the 10MK line and correlate them.

Joules per second per kilogram at this boundary at 10.1 MK is given as .0016, or about 16 ergs per gram per second.
Joules per second per cubic meter at the same is given as 6.9, giving us a density of 4.3 grams per cubic centimeter, 69 ergs per c^3.

I'm not sure how to properly read the graphs in this paper - how ρ/µe (density divided by mean molecular weight per electron) factors specifically. I'm guessing that this is primarily to compensate for increasing numbers of neutrons.

This paper has some better graphs covering this temperature and density range, though its purpose is different. Total energy loss due to these processes is 10^-8 to 10^-7 ergs per second per cubic centimeter. Fairly safe to say that it isn't significant at the 10 megakelvin range, at least outside of white dwarfs, which look like they would have some notable cooling by this method (on the order of 1-2 watts or so per cubic meter).

Once neon burning starts, it looks like pair annihilation is carrying away ~10^12 ergs per second per cubic centimeter. Of course the star is not long for the Universe at this point, but I'd be surprised if that isn't at least a noticeable part of its energy output. Or even for a star simply undergoing carbon burning.

Not looking at stars about to go boom, though.

Would need to find some similar data for stars with core temps around 100 megaKelvin, though, to get an idea of whether or not it's significant at those ranges. May also need to find something else covering high densities for pair annihilation neutrinos at this point - as the second paper shows, it's also pretty insignificant at 10^7 Kelvin, but at 10^8 kelvin we're actually getting nearly 10 erg/second/cc losses at densities of 10 grams/cc. (Edit: For Helium-4 at this density)

[Surlethe]

Is there not a section or chapter on this in BOB? I can check this afternoon.

[starslayer]

The Orange Bible? Possible, but K&W go over some of it in fairly excruciating detail, and cover the rest well.

Xeriar, I'll get back to you sometime next week; I've got a bunch of stuff all landing at once on me right now.

[Ariphaos]

BOB?

Equations I'm finding on the Internet for 'rough approximations' seem to have some rather generous interpretations of rough... linear density model gives a central density of about ~5.6 grams/cm^3 for the Sun. Quadratic is even worse (!?) Essentially defines central density to be 2.5x average density.

[Surlethe]

The Big Orange Book.