## 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 Ωνh2 > Ωνh2sterile (or else ...)?

CMB_Cls_simple.f90

Code: Select allp>

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 Ωνh2 > Ωνh2sterile seems to be valid all the time when a sterile neutrino is included, since in Params_CMB.f90, Ωνh2sterile has been added to Ωνh2

Params_CMB.f90:

Code: Select allp>

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: 1352
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 Neff 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 Neff = 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 Ωnu h2 is greater than just the sterile contribution). The steriles are assumed not to be heated at electron-positron annihilation.

The non-integer Neff (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 Neff because everything is a function of m/T.

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

Thanks Antony!