Abstract
Gamma-ray experiments seeking to detect evidence of dark matter annihilation in dwarf spheroidal galaxies require knowledge of the distribution of dark matter within these systems. We analyze the effects of flattening on the annihilation (J) and decay (D) factors of dwarf spheroidal galaxies with both analytic and numerical methods. Flattening has two consequences: first, there is a geometric effect as the squeezing (or stretching) of the dark matter distribution enhances (or diminishes) the J-factor; second, the line of sight velocity dispersion of stars must hold up the flattened baryonic component in the flattened dark matter halo. We provide analytic formulae and a simple numerical approach to estimate the correction to the J- and D-factors required over simple spherical modeling. The formulae are validated with a series of equilibrium models of flattened stellar distributions embedded in flattened dark-matter distributions. We compute corrections to the J- and D-factors for the Milky Way dwarf spheroidal galaxies under the assumption that they are all prolate or all oblate and find that the hierarchy of J-factors for the dwarf spheroidals is slightly altered (typical correction factors for an ellipticity of $0.4$ are $0.75$ for the oblate case and $1.6$ for the prolate case). We demonstrate that spherical estimates of the D-factors are very insensitive to the flattening and introduce uncertainties significantly less than the uncertainties in the D-factors from the other observables for all the dwarf spheroidals (for example, ${}^{+10\mathrm{\,percent}}_{-3\mathrm{\,percent}}$ for a typical ellipticity of $0.4$). We conclude by investigating the spread in correction factors produced by triaxial figures and provide uncertainties in the J-factors for the dwarf spheroidals using different physically-motivated assumptions for their intrinsic shape and axis alignments. (abridged)
Highlights
In recent years, gamma-ray observations of Milky Way dwarf spheroidal galaxies have led to great strides in sensitivity to dark matter annihilation
We have presented corrections to the J- and D-factors based on the assumption that the dwarf spheroidal galaxies (dSphs) are prolate or oblate figures with axes aligned with the line of sight
The ultrafaint dSphs have many fewer baryons than the classical dwarfs so it is anticipated that feedback effects have a weaker effect on the shape of the dark matter distribution in the ultrafaints
Summary
Gamma-ray observations of Milky Way dwarf spheroidal galaxies (dSphs) have led to great strides in sensitivity to dark matter annihilation. The dark halos of the ultrafaints are expected to be more highly flattened than those of the classical dSphs, as it is known that baryonic feedback effects drive the dark matter distribution towards sphericity [32,33]. The ultrafaints have such a puny baryonic content that pure dissipationless simulations [34,35], which find strongly triaxial and nearly prolate dark halos, may be a much better guide to the true shape. VII we summarize our findings and discuss possible implications for the claimed signal from Reticulum II in light of our work
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