Neutrino mass limit from galaxy cluster number density evolution

Measurements of the evolution with redshift of the number density of massive galaxy clusters are used to constrain the energy density of massive neutrinos and so the sum of neutrino masses $\sum _{}^{}{m}_{\nu }$. We consider a spatially flat cosmological model with cosmological constant, cold dark matter, baryonic matter, and massive neutrinos. Accounting for the uncertainties in the measurements of the relevant cosmological parameters we obtain a limit of $\sum _{}^{}{m}_{\nu }<2.4\mathrm{eV}$ (95% C.L.).

Figure 1

The curves show the number density evolution of massive clusters ($M>8\times {10}^{14}{h}^{-1}{M}_{\odot }$) for models in which the sum of neutrino masses $\sum _{}^{}{m}_{\nu }=0$, 2, 3.2 eV (from bottom to top). The other five parameters ${\Omega }_M$, ${\Omega }_b$, ${\sigma }_8$, $n$, and $h$ are set at the center of the scan interval. The crosses show the observational data of Eq. (4) in four redshifts bins with $1\mathrm{\text{−}}\sigma$ Poisson error bars.

Figure 2

Variation of cluster number density evolution $N(M>8\times {10}^{14}{h}^{-1}{M}_{\odot },z)$ as a function of ${\sigma }_8$ with parameters kept at the same values as in Fig. 1 except for ${\sigma }_8$ which is varied and $\sum _{}^{}{m}_{\nu }$ which is kept at zero. The observational data are the same as those shown in Fig. 1.

Figure 3

The marginalized (integrated) likelihood $\mathcal{L}/{\mathcal{L}}_{\max }$ as a function of $\sum _{}^{}{m}_{\nu }$, accounting for the observational uncertainties in ${\Omega }_M$, ${\Omega }_b$, ${\sigma }_8$, $n$, and $h$. The shaded region is excluded at 95% confidence level. The likelihood function has been scaled for display purposes to a value of one at $\sum _{}^{}{m}_{\nu }=0$.

Figure 4

The curves show the two-dimensional likelihood in $({\sigma }_8,\sum _{}^{}{m}_{\nu })$. The continuous line is the $2\mathrm{\text{−}}\sigma$ contour and the dashed line is the $1\mathrm{\text{−}}\sigma$ contour. Lower values of ${\sigma }_8$ favor a higher neutrino mass; for example, at ${\sigma }_8=0.77$ the most likely neutrino mass value is $\sum _{}^{}{m}_{\nu }=1.3\mathrm{eV}$ (also see Ref. 45, 46) whereas at high ${\sigma }_8$ values only upper limits on $\sum _{}^{}{m}_{\nu }$ apply.