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Register a new userDwarf spheroidal J-factors without priors: A likelihood-based analysis for indirect dark matter searches
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Line-of-sight integrals of the squared density, commonly called the J-factor, are essential for inferring dark matter annihilation signals. The J-factors of dark matter-dominated dwarf spheroidal satellite galaxies (dSphs) have typically been derived using Bayesian techniques, which for small data samples implies that a choice of priors constitutes a non-negligible systematic uncertainty. Here we report the development of a new fully frequentist approach to construct the profile likelihood of the J-factor. Using stellar kinematic data from several classical and ultra-faint dSphs, we derive the maximum likelihood value for the J-factor and its confidence intervals. We validate this method, in particular its bias and coverage, using simulated data from the Gaia Challenge. We find that the method possesses good statistical properties. The J-factors and their uncertainties are generally in good agreement with the Bayesian-derived values, with the largest deviations restricted to the systems with the smallest kinematic datasets. We discuss improvements, extensions, and future applications of this technique.
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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 $gamma$ and outer slope $beta$. 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.
For models in which dark matter annihilation is Sommerfeld-enhanced, the annihilation cross section increases at low relative velocities. Dwarf spheroidal galaxies (dSphs) have low characteristic dark matter particle velocities and are thus ideal candidates to study such models. In this paper we model the dark matter phase space of dSphs as isotropic and spherically-symmetric, and determine the $J$-factors for several of the most important targets for indirect dark matter searches. For Navarro-Frenk-White density profiles, we quantify the scatter in the $J$-factor arising from the astrophysical uncertainty in the dark matter potential. We show that, in Sommerfeld-enhanced models, the ordering of the most promising dSphs may be different relative to the standard case of velocity-independent cross sections. This result can have important implications for derived upper limits on the annihilation cross section, or on possible signals, from dSphs.
We calculate the effective $J$-factors, which determine the strength of indirect detection signals from dark matter annihilation, for 25 dwarf spheroidal galaxies (dSphs). We consider several well-motivated assumptions for the relative velocity dependence of the dark matter annihilation cross section: $sigma_A v$: $s$-wave (velocity independent), $p$-wave ($sigma_A v propto v^2$), $d$-wave ($sigma_A v propto v^4$), and Sommerfeld-enhancement in the Coulomb limit ($sigma_A v propto 1/v$). As a result we provide the largest and most updated sample of J-factors for velocity-dependent annihilation models. For each scenario, we use Fermi-LAT gamma-ray data to constrain the annihilation cross section. Due to the assumptions made in our gamma-ray data analysis, our bounds are comparable to previous bounds on both the $p$-wave and Sommerfeld-enhanced cross sections using dSphs. Our bounds on the $d$-wave cross section are the first such bounds using indirect detection data.
Dwarf spheroidal (dSph) galaxies are among the most promising targets for the indirect detection of dark matter (DM) from annihilation and/or decay products. Empirical estimates of their DM content - and hence the magnitudes of expected signals - rely on inferences from stellar-kinematic data. However, various kinematic analyses can give different results and it is not obvious which are most reliable. Using extensive sets of mock data of various sizes (mimicking ultra-faint and classical dSphs) and an MCMC engine, here we investigate biases, uncertainties, and limitations of analyses based on parametric solutions to the spherical Jeans equation. For a variety of functional forms for the tracer and DM density profiles, as well as the orbital anisotropy profile, we examine reliability of estimates for the astrophysical J- and D-factors for annihilation and decay, respectively. For large (N > 1000) stellar-kinematic samples typical of classical dSphs, errors tend to be dominated by systematics, which can be reduced through the use of sufficiently general and flexible functional forms. For small (N < 100) samples typical of ultrafaints, statistical uncertainties tend to dominate systematic errors and flexible models are less necessary. We define an optimal strategy that would mitigate sensitivity to priors and other aspects of analyses based on the spherical Jeans equation. We also find that the assumption of spherical symmetry can bias estimates of J (with the 95% credibility intervals not encompassing the true J-factor) when the object is mildly triaxial (axis ratios b/a = 0.8, c/a = 0.6). A concluding table summarises the typical error budget and biases for the different sample sizes considered.
This white paper describes the basic idea for indirect dark matter searches using antideuterons. Low energy antideuterons produced by dark matter annihilations/decays provide an attractive dark matter signature, due to the low astrophysical background. The current and future experiments have a strong potential to detect antideuterons from dark matter. They are complementary not only with each other, but also with other dark matter searches.
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