Constraining Hot Dark Matter Sub-Species with Weak Lensing and the Cosmic Microwave Background Radiation

Although it is well known that the bulk of dark matter (DM) has to be cold, the existence of an additional sub-dominant, hot species remains a valid possibility. In this paper we investigate the potential of the cosmic shear power spectrum to constrain such a mixed (hot plus cold) DM scenario with two additional free parameters, the hot-to-total DM fraction ($f_{\rm hdm}$) and the thermal mass of the hot component ($m_{\rm hdm}$). Running a Bayesian inference analysis for both the Kilo-Degree Survey cosmic shear data (KiDS) as well as the Cosmic Microwave Background (CMB) temperature and polarisation data from Planck, we derive new constraints for the mixed DM scenario. We find a 95 per cent confidence limit of $f_{\rm hdm}<0.08$ for a very hot species of $m_{\rm hdm}\leq20$ eV. This constraint is weakened to $f_{\rm hdm}<0.25$ for $m_{\rm hdm}\leq80$ eV. Scenarios with masses above $m_{\rm hdm}\sim200$ eV remain unconstrained by the data. Next to providing limits, we investigate the potential of mixed DM to address the clustering (or $S_8$) tension between lensing and the CMB. We find a reduction of the 2D ($\Omega_m - S_8$) tension from 2.9$\sigma$ to 1.6$\sigma$ when going from a pure cold DM to a mixed DM scenario. When computing the 1D gaussian tension on $S_8$ the improvement is milder, from 2.4$\sigma$ to 2.0$\sigma$.