## Sterile neutrino in Planck 2013 analysis

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

### Sterile neutrino in Planck 2013 analysis

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 \Omega_{\nu}h^2 > \Omega_{\nu}h^2_{sterile} (or else ...)?

CMB_Cls_simple.f90

Code: Select all

if &#40;CMB%omnuh2>CMB%omnuh2_sterile&#41; 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 &#40;CMB%nnu > neff_massive_standard&#41; 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&#40;P%Nu_mass_eigenstates&#41; = neff_massive_standard
P%Nu_mass_fractions&#40;P%Nu_mass_eigenstates&#41; = &#40;CMB%omnuh2-CMB%omnuh2_sterile&#41;/CMB%omnuh2
else
neff_massive_standard=0
end if

Moreover, the case when \Omega_{\nu}h^2 > \Omega_{\nu}h^2_{sterile} seems to be valid all the time when a sterile neutrino is included, since in Params_CMB.f90, \Omega_{\nu}h^2_{sterile} has been added to \Omega_{\nu}h^2

Params_CMB.f90:

Code: Select all

CMB%omnuh2 = CMB%omnuh2 + CMB%omnuh2_sterile

I would really appreciate some help to better understand the physics behind this.

Thank you,

Ana

Antony Lewis
Posts: 1812
Joined: September 23 2004
Affiliation: University of Sussex
Contact:

### Re: Sterile neutrino in Planck 2013 analysis

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 electron-positron 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 \Omega_nu h^2 is greater than just the sterile contribution). The steriles are assumed not to be heated at electron-positron annihilation.

The non-integer N_eff (slight heating) of massive neutrinos is handled by assignining it to the eigenstate degeneracy parameter: one eigenstate with non-integer degeneracy factor is equivalent to changing N_eff because everything is a function of m/T.

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

Thanks Antony!