How many neutrinos are produced by the Sun in a second? What happens to neutrinos after they are emitted? IIRC, they are captured in some kinds of beta radiation, but I also know that interactions are vanishingly rare, at least on Earth. The reason this came up was that my son wanted to know how many neutrinos there were in the entire universe.
Thanks,
Rob
Googling produced some vague results - one site gave a figure of 2*10[sup]38[/sup].
If my calculations are correct, that’s something like 100 kg of neutrinos per second.
Your son would probably enjoy this neutrino “what if” from Randall, I think it’s my favorite:
Wikipedia gives solar neutrino flux at the earth’s surface around 10^11/m^2/s
1 A.U. = 1.5x10^11m
Area of sphere radius 1 A.U. (4πr^2) = 10^23m^2
So total solar neutrino output 10^38/s, in agreement with Xema’s number
(Orders of magnitude, I think if you do it properly, a 2* does come out)
I was trying to figure out the total number of neutrinos emitted since the Big Bang was greater or less that googol. My back-of-the-envelope questions are around 10^82, but that is based on 10^22 stars in the universe all emitting 10^38 neutrinos/sec for 10^22 seconds. That leaves out neutrino flux before the stelliferous era, supernovae, etc.
So, neutrinos. There are four interactions (think “forces,” but at least two of the four have no classical analogue) in quantum theory: gravity, electromagnetic, weak, and strong. Gravity is the familiar one, and it’s almost always not an issue at the quantum scale because the masses involved are so small. The electromagnetic is, at the macroscopic, qualitative level, about what you’d expect: Particles have a positive or negative or zero charge; the interaction pulls particles oppositely-charged particles together, pushes like-charged particles apart, and ignores chargeless particles. The strong force only deals with particles that have a color charge, which are just quarks and gluons.
That leaves the weak interaction. That interaction can change particles into other particles. The classical example is, as you mentioned, beta decay. There, a neutron decays into a proton, emitting an electron (which was called a beta particle at one point), and a neutrino. It’s important to note that the neutrino wasn’t anywhere the process to begin with. Neutrons and protons are composites of quarks and don’t ‘contain’ neutrinos; the latter are spontaneously created as part of the process. In particular, there isn’t a fixed, conserved number of neutrinos in the universe; it varies over time. (Of course, it’s not like anyone is deliberately controlling the sources or sinks of neutrinos, so we can estimate how many there are at any given time.)
The weak interaction is, as its name implies, weak. It’s the only one of the four interactions that the neutrino participates in to any degree. Its mass is extremely low even by particle physics standards, so the gravitational effect is almost always negligible; it has no electrical charge, so it doesn’t participate in the electromagnetic interaction; and it has no color charge, so it doesn’t participate in the strong interaction. We therefore usually only detect neutrinos as a result of other processes, where we can infer their existence by, for example, conservation of momentum.
A couple of factors that might change the numbers.
Recent Hubble findings indicate that there are 2 trillion galaxies in the universe, 10 times more than previously thought.
The number of stars probably has not been consistent over time. The Sun is a third generation star. Earlier generations had much hotter stars than lived for far shorter times. I don’t know the neutrino emission of a very hot star. Would it emit more neutrinos? Would that counter a lifespan in the millions rather than billions of years?
For that matter, the Sun may be called an “average” star but its not median or modal. Smaller, longer-lived dwarves outnumber it. I can’t find any good numbers in my brief search, though.
My guess is that your simplifications are off by a considerable number of orders of magnitude. But I’m going to let you do the work. 
For archival purposes, note there’s a typo here. This should be per cm^2 rather than per m^2. (Riemann’s calculation used the correct value.)
For this question in particular, the number of neutrinos in the universe is overwhelmingly dominated by those left over from the early universe. There are about 350 relic cosmic neutrinos in every cubic centimeter of space. These are the neutrino analogues to the perhaps more familiar cosmic microwave background.
And that really is every cubic centimeter of space, even way out in the vast voids (which most of the universe is). But at our location right near the sun, the volume density of neutrinos from the sun is still only 1% of the relic neutrino density.
The total number of neutrinos in the observable universe is in the ballpark of 10[sup]89[/sup], all due to the relic neutrinos.
10[sup]22[/sup] seconds is a long time.
A star that goes supernova emits most of its neutrinos during its death throes (versus during the course of its regular burning). And, early stars tended to go supernova. Thus, the count of neutrinos from the full history of stars is dominated by those neutrinos emitted by the full history of supernovae – the so-called “diffuse supernova neutrino background”, or DSNB. The DSNB density is about a trillionth of the relic neutrino density.
So are there any neutrino sinks? I imagine crossing the event horizon of a black hole does it.
And there must be some reversed analogue of beta decay, right?
That would be Electron Capture. Of course it almost always emits a neutrino, rather than absorbing an antineutrino.
I don’t think the total mass and #stars estimates changed. It’s more galaxies, but smaller.
eta: yup, just found Phil Plait’s article on it
Any process which can produce a neutrino can also absorb a neutrino, by running in reverse. It’s pretty rare for it to happen, but then, photon sinks are already pretty rare. There’s an awful lot of empty in space.
Okay. Question time. How are these far more numerous neutrinos not detected by the neutrino detectors that measure the Sun’s output (as well as the odd supernova neutrino)?
Mostly anti-neutrinos? Too low of energy to trigger the reactions the detectors are based on? Something else?
Are there any real measurements of this background neutrino noise or is at all calculated?
The reversal of beta decay (n –> p + e + anti-nu) that you’re after moves the (anti)neutrino on the left-hand side of the reaction, as either:
nu + n –> p + e[sup]-[/sup]
or
anti-nu + p –> n + e[sup]+[/sup]
The latter is often called “inverse beta decay”, but the former where the incoming particle is a neutrino or either case when the incoming flavor is not electron flavor would not be called inverse beta decay. The more all-inclusive name is quasi-elastic scattering.
But as Chronos notes, there just isn’t enough stuff out in the emptiness of space to have neutrino sinks.
The relic neutrinos are all redshifted to very low energies and thus have a very low cross section (i.e., very low interaction rate). They have not been detected. For the most promising detection method, the first step will be to measure neutrino mass directly in a lab (also not yet done), as there are strong ties between that measurement and the experimental signature of relic neutrinos.
The diffuse supernova neutrino background has also not yet been detected, but the experimental sensitivities are just a hair’s width away from reaching the levels needed, according to current estimates of the flux. The trouble here is experimental backgrounds from other local sources of neutrinos (the sun, cosmic ray interactions in the atmosphere) and from radiological backgrounds (particularly those produced continuously by cosmic rays passing through the detector).
I should note that there are measurements of the relic neutrinos insofar as they need to be there for cosmological data to make any sense given our current understanding of cosmology. Fits to cosmological observations yield a measure of the neutrino masses and of the number of neutrino species. But seeing a relic neutrino directly interacting in a detector hasn’t happened yet (and likely won’t for some time. It’s a very difficult measurement.)
In fact, last I heard, the cosmological data provided the tightest upper bound on neutrino mass. Though that may well have changed since: There are several different sorts of experiments/observations which bound the neutrino mass, and all of them give answers in the same ballpark.
That’s right. Cosmological data limits the sum of the masses of the three neutrinos to less than 0.2 eV. There is a lab measurement that limits a different quantity (the effective electron neutrino mass, which involves the masses and the elements of the neutrino mixing matrix) to less than 2 eV. In the next five years or so this latter limit could be reduced to 0.2 eV via the KATRIN experiment. There are other experimental approaches in the works, but as for current upper limits, those are the only competitive ones on the books.
(The next most competitive limit actually comes from the difference in travel times for neutrinos versus photons from supernova 1987a.)
As an aside: it’s a good thing these reactions occur, because otherwise we wouldn’t be able to detect neutrinos at all. One of the earliest neutrino detectors used the top reaction with the neutrons in chlorine atoms; when the neutrinos hit the chlorine atom, they turned into argon, and trace amounts of argon gas could then be measured in the detector. Contemporary experiments of this type look for the light emitted by the electron that is created. But detecting an interaction where (for example) the neutrino just bounced off of a baryon and didn’t actually change its flavor would be damn near impossible.
This interaction type is detected routinely. This so-called “neutral current” interaction was central to definitively establishing neutrino oscillations using solar neutrinos. This is because neutral current interactions happen equally well for all three neutrino flavors whereas charged current scattering (where the neutrino turns into its charged lepton partner) only occurs for solar electron neutrinos since they otherwise don’t have enough energy to make a muon or tau. The 2015-Nobel-Prize-sharing experiment SNO measured the total solar neutrino flux via neutral current interactions and the electron-flavor-only neutrino flux via charged current interactions and showed that some of the flux was indeed in other flavors while the total flux matched solar modeling. (They also measured a third interaction type – neutrino-on-electron elastic scattering – which has different properties from either of the above.)