High-resolution X-ray spectrometers onboard suborbital sounding rockets can search for dark matter candidates that produce X-ray lines, such as decaying keV-scale sterile neutrinos. Even with exposure times and effective areas far smaller than XMM-Newton and Chandra observations, high-resolution, wide field-of-view observations with sounding rockets have competitive sensitivity to decaying sterile neutrinos. We analyze a subset of the 2011 observation by the X-ray Quantum Calorimeter instrument centered on Galactic coordinates l = 165, b = -5 with an effective exposure of 106 seconds, obtaining a limit on the sterile neutrino mixing angle of sin^2(2 theta) < 7.2e-10 at 95% CL for a 7 keV neutrino. Better sensitivity at the level of sin^2(2 theta) ~ 2.1e-11 at 95% CL for a 7 keV neutrino is achievable with future 300-second observations of the galactic center by the Micro-X instrument, providing a definitive test of the sterile neutrino interpretation of the reported 3.56 keV excess from galaxy clusters.
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