Anticipating the XRISM search for the decay of resonantly produced sterile neutrino dark matter

The sterile neutrino ($N_1$) features in multiple extensions of the standard model and is a compelling dark matter candidate, especially as the decay of $N_1$ with mass $m_{\mathrm{s}}=7.1\mathrm{k}\mathrm{e}\mathrm{V}$ is a possible source for the unexplained $3.55\mathrm{k}\mathrm{e}\mathrm{V}$ X-ray line reported in galaxy clusters. This particle will be accessible to the XRISM X-ray mission over the next 12 months. We revisit the physics behind $N_1$ and the uncertainty in its parameters. We compare predictions for the $m_s=7.1\mathrm{k}\mathrm{e}\mathrm{V}$ $N_1$ mixing angle, ${\sin }^2(2\theta )$, and half-mode mass, $M_{\mathrm{h}\mathrm{m}}$, as described in the $\nu$MSM standard model extension to existing X-ray observations and structure formation constraints. The strongest available constraints rule out $N_1$ as a dark matter candidate, and a more optimistic reading of the data prefers ${\sin }^2(2\theta )=5\times {10}^{-11}$ and $M_{\mathrm{h}\mathrm{m}}=3.5\times {10}^8{M}_{\odot }$. We highlight that the most promising upcoming opportunity for a detection is to find a line of velocity dispersion $\sim 500{\mathrm{k}\mathrm{m}\mathrm{s}}^{-1}$ in the Virgo cluster with XRISM, and then draw up a list of future objects of study to determine: (i) whether the line is from dark matter generally, and (ii) if from dark matter, whether that candidate is indeed $N_1$.