When did relic neutrinos cease being relativistic?

[GeorgeDishman]

Relic neutrinos decoupled from matter around the time of nucleogenesis so had the same temperature as matter and photons at that time. Photons decoupled much later, after electron/positron annihilation which heated the photons slightly so thereafter neutrino temperature should be (4/11)^(1/3) times that of the photons. The CMBR is at 2.725K so the neutrinos should be at 1.945K or equivalently 1.676*10^-4eV. See pages 14 & 15 of:

http://darkuniverse.uni-hd.de/pub/Main/WinterSchool08Slides/CosmologicalNeutrinos.pdf

That temperature scales as (1+z).

The latest estimate of neutrino mass is 0.32eV for the sum of the three flavours or 0.11eV each.

http://arxiv.org/abs/1308.5870v2

That suggests their energy would be comparable to their mass at z~635 which is around 910k years. Obviously the change would be slow but am I right in thinking that time would be roughly when the neutrinos transitioned from relativistic speeds if the estimated masses are correct?

 

[mfb]

They just get slower and slower over time. Also note that the temperature just gives the average energy.
The numbers in that paper are on the high side compared to other estimates. With a mass of .1 eV they would be slow today, yes (but still fast compared to gravitational wells of galaxies).

 

[GeorgeDishman]

Thanks for the response.

They just get slower and slower over time. Also note that the temperature just gives the average energy.

Yes, that's why I noted it would not be an abrupt change.

The numbers in that paper are on the high side compared to other estimates.

Super-Kamiokande results suggest there is one pair with a difference of at least 0.04eV so if the others are much less, the average would be around 0.013eV so less than an order of magnitude lower ;-)

http://en.wikipedia.org/wiki/Neutrino#cite_note-49

With a mass of .1 eV they would be slow today, yes (but still fast compared to gravitational wells of galaxies).

It is generally accepted that they should be "cold" today but were "hot" at the time of recombination (378k years), I'm just curious when the transition would be roughly, and more importantly hoping someone will confirm if the method I've used to estimate the number is valid. Using a mass of 0.01eV moves the time to around 30M years if the method is correct.

 

[mfb]

and more importantly hoping someone will confirm if the method I've used to estimate the number is valid.

Sure.

 

[GeorgeDishman]

Great, thank you.