Joint constraints on thermal relic dark matter from strong gravitational lensing, the Lyman-$\alpha$ forest, and Milky Way satellites

We derive joint constraints on the warm dark matter (WDM) half-mode scale by combining the analyses of a selection of astrophysical probes: strong gravitational lensing with extended sources, the Lyman-$\alpha$ forest, and the number of luminous satellites in the Milky Way. We derive an upper limit of $\lambda_{\rm hm}=0.089{\rm~Mpc~h^{-1} }$ at the 95 per cent confidence level, which we show to be stable for a broad range of prior choices. Assuming a Planck cosmology and that WDM particles are thermal relics, this corresponds to an upper limit on the half-mode mass of $M_{\rm hm }< 3 \times 10^{7} {\rm~M_{\odot}~h^{-1}}$, and a lower limit on the particle mass of $m_{\rm th }> 6.048 {\rm~keV}$, both at the 95 per cent confidence level. We find that models with $\lambda_{\rm hm}> 0.223 {\rm~Mpc~h^{-1} }$ (corresponding to $m_{\rm th }> 2.552 {\rm~keV}$ and $M_{\rm hm }< 4.8 \times 10^{8} {\rm~M_{\odot}~h^{-1}}$) are ruled out with respect to the maximum likelihood model by a factor $\leq 1/20$. For lepton asymmetries $L_6>10$, we rule out the $7.1 {\rm~keV}$ sterile neutrino dark matter model, which presents a possible explanation to the unidentified $3.55 {\rm~keV}$ line in the Milky Way and clusters of galaxies. The inferred 95 percentiles suggest that we further rule out the ETHOS-4 model of self-interacting DM. Our results highlight the importance of extending the current constraints to lower half-mode scales. We address important sources of systematic errors and provide prospects for how the constraints of these probes can be improved upon in the future.