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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 validpossibility. In this paper we investigate the potential of the cosmic shearpower spectrum to constrain such a mixed (hot plus cold) DM scenario with twoadditional free parameters, the hot-to-total DM fraction ($f_{\rm hdm}$) andthe thermal mass of the hot component ($m_{\rm hdm}$). Running a Bayesianinference analysis for both the Kilo-Degree Survey cosmic shear data (KiDS) aswell as the Cosmic Microwave Background (CMB) temperature and polarisation datafrom Planck, we derive new constraints for the mixed DM scenario. We find a 95per 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 $m_{\rm hdm}\sim200$ eVremain unconstrained by the data. Next to providing limits, we investigate thepotential of mixed DM to address the clustering (or $S_8$) tension betweenlensing and the CMB. We find a reduction of the 2D ($\Omega_m - S_8$) tensionfrom 2.9$\sigma$ to 1.6$\sigma$ when going from a pure cold DM to a mixed DMscenario. When computing the 1D gaussian tension on $S_8$ the improvement ismilder, from 2.4$\sigma$ to 2.0$\sigma$.

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