Searching for dark matter in X-rays: how to check the dark matter origin of a spectral feature

A signal from decaying dark matter (DM) can be unambiguously distinguished from spectral features of astrophysical or instrumental origin by studying its spatial distribution. We demonstrate this approach by examining the recent claim of Loewenstein and Kusenko regarding the possible DM origin of the 2.5 keV line in Chandra observations of the Milky Way satellite known as Willman 1. Our conservative strategy is to adopt, among reasonable mass estimates derived here and in the literature, a relatively large dark mass for Willman 1 and relatively small dark masses for the comparison objects. In light of the large uncertainty in the actual DM content of Willman 1, this strategy provides minimum exclusion limits on the DM origin of the reported signal. We analyse archival observations by XMM-Newton of M31 and Fornax dwarf spheroidal galaxy (dSph) and Chandra observations of Sculptor dSph. By performing a conservative analysis of X-ray spectra, we show the absence of a DM decay line with parameters consistent with those of Loewenstein and Kusenko. For M31, the observations of the regions between 10 and 20 kpc from the centre, where the uncertainties in the DM distribution are minimal, make a strong exclusion at the level above 10σ. The Fornax dSph provides a ~3.3σ exclusion instead of a predicted 4σ detection, and the Sculptor dSph provides a 3σ exclusion instead of a predicted 2.5σ detection. The observations of the central region of M31 (1-3 kpc off-centre) are inconsistent with having a DM decay line at more than 20σ if one takes the most conservative among the best physically motivated models. The minimal estimate for the amount of DM in the central 40 kpc of M31 is provided by the model of Corbelli et al., assuming the stellar disc's mass to light ratio ~8 and almost constant DM density within a core of 28 kpc. Even in this case one gets an exclusion at 5.7σ from central region of M31, whereas modelling all processed data from M31 and Fornax produces more than 14σ exclusion. Therefore, despite possible systematic uncertainties, we exclude the possibility that the spectral feature at ~2.5 keV found in Loewenstein and Kusenko is a DM decay line. We conclude, however, that the search for DM decay line, although demanding prolonged (up to 1 Ms) observations of well-studied dSphs, M31 outskirts and other similar objects, is rather promising, as the nature of a possible signal can be checked. An (expected) non-observation of a DM decay signal in the planned observations of Willman 1 should not discourage further dedicated observations.