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Ana Vasile
Joined: 26 Mar 2006 Posts: 25 Affiliation: Institute for Space Sciences

Posted: June 25 2013 


Dear all,
I am having trouble understanding the sterile neutrino analysis performed in CosmoMC March 2013 (Planck 2013 results).
More specifically:
In CMB_Cls_simple.f90 what is the physical significance of the comparison: If Ω_{ν}h^{2} > Ω_{ν}h^{2}_{sterile} (or else ...)?
CMB_Cls_simple.f90
Code:  if (CMB%omnuh2>CMB%omnuh2_sterile) then
neff_massive_standard = num_massive_neutrinos*default_nnu/3
P%Num_Nu_Massive = num_massive_neutrinos
P%Nu_mass_eigenstates=P%Nu_mass_eigenstates+1
if (CMB%nnu > neff_massive_standard) then
P%Num_Nu_Massless = CMB%nnu  neff_massive_standard
else
P%Num_Nu_Massless = 0
neff_massive_standard=CMB%nnu
end if
P%Nu_mass_degeneracies(P%Nu_mass_eigenstates) = neff_massive_standard
P%Nu_mass_fractions(P%Nu_mass_eigenstates) = (CMB%omnuh2CMB%omnuh2_sterile)/CMB%omnuh2
else
neff_massive_standard=0
end if

Moreover, the case when Ω_{ν}h^{2} > Ω_{ν}h^{2}_{sterile} seems to be valid all the time when a sterile neutrino is included, since in Params_CMB.f90, Ω_{ν}h^{2}_{sterile} has been added to Ω_{ν}h^{2}
Params_CMB.f90:
Code:  CMB%omnuh2 = CMB%omnuh2 + CMB%omnuh2_sterile 
I would really appreciate some help to better understand the physics behind this.
Thank you,
Ana 

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Antony Lewis
Joined: 23 Sep 2004 Posts: 1351 Affiliation: University of Sussex

Posted: June 25 2013 


Given the values of the total neutrino density, sterile density and total N_{eff} it is trying to assign values to the standard neutrinos. By default the standard netrinos are assumed to have standard thermal history (i.e. heated slightly at electronpositron annihilation, so N_{eff} = 3.046/3 per species). And the analysis assumes that the standard neutrinos have the minimal hierarchy, so there's one eigenstate with 0.06eV mass (so Ω_{nu} h^{2} is greater than just the sterile contribution). The steriles are assumed not to be heated at electronpositron annihilation.
The noninteger N_{eff} (slight heating) of massive neutrinos is handled by assignining it to the eigenstate degeneracy parameter: one eigenstate with noninteger degeneracy factor is equivalent to changing N_{eff} because everything is a function of m/T. 

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Ana Vasile
Joined: 26 Mar 2006 Posts: 25 Affiliation: Institute for Space Sciences

Posted: June 25 2013 


Thanks Antony! 

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