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Simple J-factors and D-factors for indirect dark matter detection

Published version
Peer-reviewed

Type

Article

Change log

Authors

Evans, NW 
Sanders, JL 
Geringer-Sameth, A 

Abstract

J-factors (or D-factors) describe the distribution of dark matter in an astrophysical system and determine the strength of the signal provided by annihilating (or decaying) dark matter respectively. We provide simple analytic formulae to calculate the J-factors for spherical cusps obeying the empirical relationship between enclosed mass, velocity dispersion and half-light radius. We extend the calculation to the spherical Navarro-Frenk-White (NFW) model, and demonstrate that our new formulae give accurate results in comparison to more elaborate Jeans models driven by Markov Chain Monte Carlo methods. Of the known ultrafaint dwarf spheroidals, we show that Ursa Major II, Reticulum II, Tucana II and Horologium I have the largest J-factors and so provide the most promising candidates for indirect dark matter detection experiments. Amongst the classical dwarfs, Draco, Sculptor and Ursa Minor have the highest J-factors. We show that the behaviour of the J-factor as a function of integration angle can be inferred for general dark halo models with inner slope γ and outer slope β. The central and asymptotic behaviour of the J-factor curves are derived as a function of the dark halo properties. Finally, we show that models obeying the empirical relation on enclosed mass and velocity dispersion have J-factors that are most robust at the integration angle equal to the projected half-light radius of the dSph divided by heliocentric distance. For most of our results, we give the extension to the D-factor which is appropriate for the decaying dark matter picture.

Description

Keywords

astro-ph.GA, astro-ph.GA, astro-ph.CO, astro-ph.HE

Journal Title

Physical Review D

Conference Name

Journal ISSN

2470-0010
2470-0029

Volume Title

93

Publisher

American Physical Society (APS)

Rights

Publisher's own licence
Sponsorship
Science and Technology Facilities Council (ST/K000985/1)
Science and Technology Facilities Council (ST/N000927/1)