Dark matter decays or annihilations that produce linelike spectra may be smoking-gun signals. However, even such distinctive signatures can be mimicked by astrophysical or instrumental causes. We show that velocity spectroscopy-the measurement of energy shifts induced by relative motion of source and observer-can separate these three causes with minimal theoretical uncertainties. The principal obstacle has been energy resolution, but upcoming experiments will have the precision needed. As an example, we show that the imminent Astro-H mission can use Milky Way observations to separate possible causes of the 3.5-keV line. We discuss other applications.
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