Hints of dark photon dark matter from observations and hydrodynamical simulations of the low-redshift Lyman-$\alpha$ forest

Recent work has suggested that an additional $\lesssim 6.9\mathrm{e}\mathrm{V}$ per baryon of heating in the intergalactic medium is needed to reconcile hydrodynamical simulations with Lyman-$\alpha$ forest absorption line widths at redshift $z\simeq 0.1$. Resonant conversion of dark photon dark matter into low frequency photons is a viable source of such heating. We perform the first hydrodynamical simulations including dark photon heating and show that dark photons with mass $m_{A^{\mathrm{\prime }}}\sim 8\times {10}^{-14}\mathrm{e}\mathrm{V}{\mathrm{c}}^{-2}$ and kinetic mixing $\epsilon \sim 5\times {10}^{-15}$ can alleviate the heating excess. A prediction of this model is a non-standard thermal history for underdense gas at $z\gtrsim 3$.