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BioSci
2006-Sep-22, 08:52 PM
A multi-part question:

1) Do we have good estimates of the production of neutrinos during the early stages of the big bang?

2) If such "primordial" neutrinos were produced - do we have estimates on their current speed? - would they no longer be traveling at relativistic speeds due to the expansion of space through which they would have traveled?

3) If such neutrinos are no longer traveling at relativistic speeds - would we be able to detect such slow neutrinos?

4) Could they contribute to the CDM?

antoniseb
2006-Sep-22, 09:19 PM
1. For some models we do, but we really have some gaps in our knowledge about the highest energy epochs.

2. Their current speed should be very close to 'c'.

3. If there were neutrinos traveling at speeds that bound them to galaxies and galaxy clusters, I'm not certain we'd be able to detect them with our current equipment.

4. Could they contribute to a substantial fraction of the CDM? Doubtful. That would be one heck of a lot of slow neutrinos. Also, think about this: if each neutrino has a rest mass of 100 micro-electron-volts, and each proton has a rest mass of 1 billion electron volts, and there is ten times as much dark matter as reactive matter, then each proton needed to essentially switch back and forth from proton to neutron 100 trillion times in the first femtosecond of the universe to create that many slow neutrinos.

BioSci
2006-Sep-22, 10:04 PM
Thanks for the answers!


then each proton needed to essentially switch back and forth from proton to neutron 100 trillion times in the first femtosecond of the universe to create that many slow neutrinos.

As one with mostly biological background - such a condition does not seem any less intuative than much of QM. :)

peteshimmon
2006-Sep-23, 12:03 AM
Good questions! Do not have any answers myself
but this might be the most accurate reply:)

Ken G
2006-Sep-23, 02:24 PM
2) If such "primordial" neutrinos were produced - do we have estimates on their current speed? - would they no longer be traveling at relativistic speeds due to the expansion of space through which they would have traveled?
antoniseb is right, the neutrinos would be considered "hot" dark matter, and should still be at least somewhat relativistic (i.e., travelling at near c) even after all that expansion. We can actually estimate their temperature, in eV. As the neutrinos are relativistic, they cool like photons, i.e., relatively quickly. But they should be even colder than the photons of today (which are at 2.7 K, or about 300 micro-eV), because there was a period when photons cooled like nonrelativistic gas, while matter dominated the energy density of the universe and photons were coupled to that gas prior to recombination. But that was a fairly short period-- the photons only cooled by a factor of 10 during that time. Since they would have cooled by a power 4/3 faster had they been left to their own druthers during that time, that means they would have cooled by another factor of 2. Also, neutrinos would have decoupled from matter prior to the recombination of hydrogen, which added more energy to the CMB photons that neutrinos would not have gotten. So as a rough guess, let's say the cosmic neutrinos are a factor 4 colder than cosmic photons.

If so, then cosmic neutrinos are at roughly 100 micro-eV. If this is much larger than their rest mass, then they are highly relativistic. antoniseb says that 100 micro-eV is a possible rest mass, so perhaps they are not so highly relativistic after all, but they are certainly not "slow"-- they must have a speed of the same order as light, so too fast to be bound by any galaxy, and therefore could not be CDM.

grav
2006-Sep-24, 04:01 PM
So as a rough guess, let's say the cosmic neutrinos are a factor 4 colder than cosmic photons.

I've been waiting for something like this. So are you saying that the effective cosmic neutrino temperature should be something like 2.7 K/4=.7 K? If it were actually about 2.7 K/[(3/5)/alpha]1/4=.9 K, or about a factor of 3 colder, then this might explain something I've been wondering about for quite a while. Could that be right?

Ken G
2006-Sep-24, 06:58 PM
If it were actually about 2.7 K/[(3/5)/alpha]1/4=.9 K, or about a factor of 3 colder, then this might explain something I've been wondering about for quite a while. Could that be right?

My calculation was quite rough, so yes, it could be only a factor of 3 colder. However, be advised that better calculations do exist, based on cosmological models that have growing observational support, so you might want to check with those to see what the neutrino temperature is really expected to be. As it has never actually been observed, it is rather difficult to distinguish between opposing theories of neutrino temperature, and it might even depend on the neutrino rest mass.

grav
2006-Sep-24, 08:20 PM
My calculation was quite rough, so yes, it could be only a factor of 3 colder. However, be advised that better calculations do exist, based on cosmological models that have growing observational support, so you might want to check with those to see what the neutrino temperature is really expected to be. As it has never actually been observed, it is rather difficult to distinguish between opposing theories of neutrino temperature, and it might even depend on the neutrino rest mass.
Thanks, Ken. I appreciate it. :)

Cougar
2006-Sep-25, 01:27 AM
1) Do we have good estimates of the production of neutrinos during the early stages of the big bang?
As our models become more and more constrained, we should be getting to a pretty good estimate. According to Weinberg's The First Three Minutes, which in some areas is undoubtedly out of date, having been written in 1977, there is "something like" 1 billion neutrinos and antineutrinos for every nuclear particle in the universe.


2) If such "primordial" neutrinos were produced - do we have estimates on their current speed? - would they no longer be traveling at relativistic speeds due to the expansion of space through which they would have traveled?As mentioned, I think they're still going very close to "c". Their wavelengths have simply expanded in proportion to the size of the universe.


3) If such neutrinos are no longer traveling at relativistic speeds - would we be able to detect such slow neutrinos?
I don't know that there's any such thing as a slow neutrino. They are (finally) detectable, but only via their weak force interaction. (See Super-K in Japan.)


4) Could they contribute to the CDM?
They are considered Hot Dark Matter. Even though there are so many of them, their mass is so tiny that they don't contribute much.

Weinberg: After the universe became transparent to neutrinos (at about 10 billion degrees K), the electrons and positrons began to annihilate, heating the photons but not the neutrinos. Hence their present temperature is a little less than that of the photons.... After the annihilation process is over, the photon temperature is higher than the neutrino temperature by a factor of.... 1.401.

Again, these are not exactly current figures, but at least Weinberg shows that these things can be calculated very rigorously.

Ken G
2006-Sep-25, 03:31 PM
Weinberg: After the universe became transparent to neutrinos (at about 10 billion degrees K), the electrons and positrons began to annihilate, heating the photons but not the neutrinos. Hence their present temperature is a little less than that of the photons.... After the annihilation process is over, the photon temperature is higher than the neutrino temperature by a factor of.... 1.401.

And note that this is only one contribution to that factor of roughly 4 that I outlined above. It's a rough figure because a real calculation would require a full cosmological model.

trinitree88
2006-Sep-27, 12:19 AM
[QUOTE=Cougar;831959]As our models become more and more constrained, we should be getting to a pretty good estimate. According to Weinberg's The First Three Minutes, which in some areas is undoubtedly out of date, having been written in 1977, there is "something like" 1 billion neutrinos and antineutrinos for every nuclear particle in the universe.

As mentioned, I think they're still going very close to "c". Their wavelengths have simply expanded in proportion to the size of the universe.


I don't know that there's any such thing as a slow neutrino. They are (finally) detectable, but only via their weak force interaction. (See Super-K in Japan.)


Cougar:snippet: If neutrinos have mass then they are indistinguishable from anti-neutrinos in other reference frames. But if they are massless, then a billion neutrinos and antineutrinos for every nuclear particle has a consequence...they can annihilate each other without violating conservation laws. Chance intersections of very low, but non-vanishing cross-sections can lead to total annihilation.
It is interesting to note that below the threshold annihilation energy of 1.022 Mev for electron/positron pairs, only two possibilities exist...Z0/anti-Z0, or photons. The photons should appear as an all pervasive "fog" of black-body-like, low temperature, radiation, of unknown origin, appearing in horn antennae in New Jersey and elsewhere, except that those found coming from proximate vicinity of the Local Bubble should have a distinct axisymmetric dipole matching the sun's magnetic field orientation because of the extended polarization effect on iron needles left in the Local Bubble by past supernovae ejecta. (Dwek) It will be interesting to see this polarization flip when the sun's field does....which will be soon. A first rate theory predicts.:shifty: :eek: :dance: Ciao. Pete.

RussT
2006-Sep-27, 12:33 AM
Why do we think that the sun 'makes' neutrino's and how does it do it?

trinitree88
2006-Oct-01, 12:18 AM
Why do we think that the sun 'makes' neutrino's and how does it do it?

RussT. If you start with hydrogen, with a single proton, and a single electron, then in order to make helium, with two protons, and two neutrons...you have to convert some of those protons into neutrons.
Consider a "free" neutron produced in a nuclear reactor. After a short half-life....~ 1000 sec, it decays. It produces a proton, an electron , and an electron-type antineutrino. This is an energetically favorable decay. "Free" neutrons are unstable. The rest mass of the proton is less than the rest mass of the neutron. In radioactive decay schemes, that generally makes them favorable.
However, it is possible to reverse the process...convert a proton into a neutron. This requires an input of energy. For fusion to occur, the time, temperature (read as ...avg. kinetic energy of collision), and density must meet certain minimal criteria. When this happens, collisions between protons knock out positrons(read as ...create a W+...that decays into a positron and a neutrino). The neutron can then bind with a proton to make deuterium...two of these can fuse to release energy, and make helium. The net effect is a release of energy in the formation of helium nuclei....the release of neutrinos, and formation of helium. (two of the positrons produced annihilate two electrons in a spate of gamma rays)...so four protiums eventually make one helium atom. Neat trick. Nitsche pas?
The Sudbury Neutrino Observatory has confirmed that the musings of Hans Bethe, and later, John N. Bahcall, are true as expected. :shifty: Pete.

RussT
2006-Oct-01, 10:27 PM
RussT. If you start with hydrogen, with a single proton, and a single electron, then in order to make helium, with two protons, and two neutrons...you have to convert some of those protons into neutrons.
Consider a "free" neutron produced in a nuclear reactor. After a short half-life....~ 1000 sec, it decays. It produces a proton, an electron , and an electron-type antineutrino. This is an energetically favorable decay. "Free" neutrons are unstable. The rest mass of the proton is less than the rest mass of the neutron. In radioactive decay schemes, that generally makes them favorable.
However, it is possible to reverse the process...convert a proton into a neutron. This requires an input of energy. For fusion to occur, the time, temperature (read as ...avg. kinetic energy of collision), and density must meet certain minimal criteria. When this happens, collisions between protons knock out positrons(read as ...create a W+...that decays into a positron and a neutrino). The neutron can then bind with a proton to make deuterium...two of these can fuse to release energy, and make helium. The net effect is a release of energy in the formation of helium nuclei....the release of neutrinos, and formation of helium. (two of the positrons produced annihilate two electrons in a spate of gamma rays)...so four protiums eventually make one helium atom. Neat trick. Nitsche pas?
The Sudbury Neutrino Observatory has confirmed that the musings of Hans Bethe, and later, John N. Bahcall, are true as expected. :shifty: Pete.

Thanks, and as usual, your indepth knowledge of these processes according to current understanding is enviable.

[If neutrinos have mass then they are indistinguishable from anti-neutrinos in other reference frames.]

Above you said this. If neutrinos do have a Planck mass, could you go into a little more detail on what this would mean?

jlhredshift
2006-Oct-03, 02:39 PM
Thanks, and as usual, your indepth knowledge of these processes according to current understanding is enviable.

[If neutrinos have mass then they are indistinguishable from anti-neutrinos in other reference frames.]

Above you said this. If neutrinos do have a Planck mass, could you go into a little more detail on what this would mean?

Here..Here.. enviable indeed.

And where do we stand currently on the shortage of neutrinos from the sun and their transformation enroute to our detectors?

RussT
2006-Oct-05, 09:35 AM
Trinitree88;

Even with all that praise, it seems he didn't want to answer these. LOL:D

I am sure that they just snuck by him:lol:

[Above you said this. If neutrinos have mass then they are indistinguishable from anti-neutrinos in other reference frames.]

[could you go into a little more detail on what this would mean?]

[And where do we stand currently on the shortage of neutrinos from the sun and their transformation enroute to our detectors?]

RussT
2006-Oct-06, 09:49 AM
Ah, You already answered this. It was in my 'space' thread though.

Quote:
Originally Posted by RussT
Correct me if I am wrong here Ken, but since we know that what ever 'space' is made of, it does not interact with baryonic matter, then it is irrelavent to the 2 body velocities.



RussT. Don't wash out the neutrino sea, here. Astromark is incorrect in saying that space is nothing, and empty. If the proponents of massive neutrinos turn out to be correct, then they must be subluminal or we are mandated to trash The Special Theory of Relativity. Saving the STR would give a limiting velocity to those neutrinos making up the "sea" (earlier work,not by grav). That would be the "third velocity" KenG mentions here.
On the other hand if neutrinos are massless and travel at c (as allowed by the experimental data so far...there are only upper bounds on possible masses), they make up a boson gas which expands if "space" is expanding. An adiabatic expansion in an invariant neutrino sea would require that they redshift. That would lead to a time-varying value of G, Cavendish's determination of the universal gravitational constant. But, there are two competing effects here:
1. stellar fusion, radioactive beta decays, and supernovae add continuously to the relative abundances of the "sea" neutrinos...inhomogeneously.
2. "sea" neutrinos can also interact via the three branches of the weak current, the W+, W-, and the neutral current ..or Z0. In so doing they can lose energy and momentum, back to the visible baryonic universe.
It is interesting to note that the effects of GR are adequately modeled by concommittent simultaneous changes in the ambient neutrino sea flux. A day night oscillation in the SNO solar Be-8 flux is directly attributable to the "non-interacting neutrinos" interacting in the Earth-mass passage on their way to SNO...(Sudbury Neutrino Observatory).
Perhaps it is worth noting here that as you pile up mass in a region, and allow greater neutrino scattering, redshifting those coming through("neutrino sea" term precedes "neutrino medium" by decades here)....an ever increasing density in the same sphere will ultimately redshift out nearly all the incoming energy. Appearing as photons and phonons...the temperature rises here. But doubling the mass again will not double the incoming/outgoing gradient. Consequently, you can't stop more than all of them, and an expected change in the local gravitational field is Non-Newtonian. For extended systems, like giant galaxies, the bulge will contain far more mass than you would otherwise infer from the Keplerian motion of it's inner orbits, and it would fall off (MOND) style in a non-Keplerian mode. The "excess" more "wheel-like" velocities of remote stars is not unexpected here; it is non-Keplerian.
Further, it makes a clear and testable prediction. The measured value of big "G" from a Cavendish experiment,is time varying over perihelion and aphelion in Earth's orbit, but perhaps (unfortunately) far more noticeable in Mar's. Perhaps, like the parity effects of Lee and Yang....nobody has ever looked? Pete.

This has some very interesting content, (why do I have to read your stuff 2 or 3 time to get it?), so again the same envie comment as above.



an ever increasing density in the same sphere will ultimately redshift out nearly all the incoming energy.

Could this possibly mean that there was no 'real' energy coming in, in the first place?



If the proponents of massive neutrinos turn out to be correct, then they must be subluminal or we are mandated to trash The Special Theory of Relativity. Saving the STR would give a limiting velocity to those neutrinos making up the "sea" (earlier work,not by grav). That would be the "third velocity" KenG mentions here.

And isn't this exactly what I have been trying to get the answer to?