When did relic neutrinos cease being relativistic?

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Discussion Overview

The discussion centers on the transition of relic neutrinos from relativistic to non-relativistic speeds, particularly in relation to their decoupling from matter during nucleogenesis and the implications of their temperature and mass estimates over time. Participants explore theoretical aspects and implications of neutrino behavior in the early universe.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant states that relic neutrinos decoupled from matter around the time of nucleogenesis, suggesting their temperature was initially the same as that of matter and photons.
  • Another participant notes that the temperature of neutrinos should scale as (4/11)^(1/3) times that of photons, leading to a calculated neutrino temperature of approximately 1.945K based on the CMBR temperature.
  • There is a discussion about the estimated neutrino mass, with one participant referencing a mass of 0.32eV for the sum of three flavors, suggesting that neutrinos would transition from relativistic speeds around z~635, approximately 910k years after the Big Bang.
  • Another participant challenges the mass estimates, indicating that the numbers in the referenced paper might be on the high side compared to other estimates, and suggests that with a mass of 0.1eV, neutrinos would be slow today but still fast compared to gravitational wells of galaxies.
  • One participant expresses curiosity about the timing of the transition from "hot" to "cold" neutrinos and seeks confirmation on the validity of their estimation method, proposing that a mass of 0.01eV would shift the transition time to around 30 million years.
  • A later reply confirms the validity of the estimation method used by the participant seeking confirmation.

Areas of Agreement / Disagreement

Participants express differing views on the estimates of neutrino mass and temperature, with no consensus reached on the exact timing of the transition from relativistic to non-relativistic speeds. The discussion remains unresolved regarding the validity of the estimation methods and the implications of the mass estimates.

Contextual Notes

Participants highlight the dependence of their arguments on various mass estimates and the implications of temperature scaling, indicating that the discussion is limited by the assumptions made regarding these values.

GeorgeDishman
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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?
 
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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).
 
Thanks for the response.

mfb said:
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.
 
GeorgeDishman said:
and more importantly hoping someone will confirm if the method I've used to estimate the number is valid.
Sure.
 
Great, thank you.
 

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