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We argue that the decomposition of gamma-ray maps in spherical harmonics is asensitive tool to study dark matter (DM) annihilation or decay in the mainGalactic halo of the Milky Way. Using the spherical harmonic decomposition in awindow excluding the Galactic plane, we show for one year of Fermi data thatadding a spherical template (such as a line-of-sight DM annihilation profile)to an astrophysical background significantly reduces chi^2 of the fit to thedata. In some energy bins the significance of this DM-like fraction is abovethree sigma. This can be viewed as a hint of DM annihilation signal, althoughastrophysical sources cannot be ruled out at this moment. We use the derived DMfraction as a conservative upper limit on DM annihilation signal. In the caseof bb-bar annihilation channel the limits are about a factor of two lessconstraining than the limits from dwarf galaxies. The uncertainty of our methodis dominated by systematics related to modeling the astrophysical background.We show that with one year of Fermi data the statistical sensitivity would besufficient to detect DM annihilation with thermal freeze out cross section formasses below 100 GeV.

Spherical harmonics analysis of Fermi gamma-ray data and the Galactic dark matter halo