Indirect Dark Matter Detection from Dwarf Satellites: Joint Expectations from Astrophysics and Supersymmetry

TL;DR

This paper develops a comprehensive framework to predict gamma-ray flux from neutralino annihilation in Milky Way dwarf spheroidal galaxies by integrating CJSSM- and kinematic-derived dark matter halo models with a Bayesian CMSSM parameter scan. It introduces an analytic boost factor from halo substructure and demonstrates that the boost is highly sensitive to the extrapolated concentration-mass relation down to the minimum halo mass $m_{min}$, found to lie in $10^{-9}$–$10^{-6}\,M_{\odot}$. Using two well-studied dwarfs, Draco and Segue 1, the study shows that optimistic PL extrapolations can yield average boosts of ~20, making a $\sim$20% chance of detecting a $E>1$ GeV gamma-ray signal from Draco with Fermi after ~5 years at $S/N>3$. The work highlights the critical role of priors and halo physics uncertainties, provides a method to jointly propagate particle physics and astrophysical uncertainties, and suggests stacking multiple dwarfs could enhance discovery prospects.

Abstract

We present a general methodology for determining the gamma-ray flux from annihilation of dark matter particles in Milky Way satellite galaxies, focusing on two promising satellites as examples: Segue 1 and Draco. We use the SuperBayeS code to explore the best-fitting regions of the Constrained Minimal Supersymmetric Standard Model (CMSSM) parameter space, and an independent MCMC analysis of the dark matter halo properties of the satellites using published radial velocities. We present a formalism for determining the boost from halo substructure in these galaxies and show that its value depends strongly on the extrapolation of the concentration-mass (c(M)) relation for CDM subhalos down to the minimum possible mass. We show that the preferred region for this minimum halo mass within the CMSSM with neutralino dark matter is ~10^-9-10^-6 solar masses. For the boost model where the observed power-law c(M) relation is extrapolated down to the minimum halo mass we find average boosts of about 20, while the Bullock et al (2001) c(M) model results in boosts of order unity. We estimate that for the power-law c(M) boost model and photon energies greater than a GeV, the Fermi space-telescope has about 20% chance of detecting a dark matter annihilation signal from Draco with signal-to-noise greater than 3 after about 5 years of observation.

Figures (15)

• Figure 1: Posterior probability distribution for the mass within 30 pc for Segue 1( left panel) and the mass within 300 pc for Segue 1 ( right panel). The four curves in each panel assume different Bayesian priors: a uniform prior in $V_{\rm max}^{-3}$ (black, solid) $V_{\rm max}^{-2}$ (red, dashed), $V_{\rm max}^{-1}$ (green, dot-dashed), and $\ln(V_{\rm max})$ (blue, dotted). The prior distributions are truncated at $V_{\rm max} = 3$km s$^{-1}$ as described in the text. Increasing negative powers of $V_{\rm max}$ causes the posterior to be more "biased" toward lower mass solutions. As a result, the posterior corresponding to these different priors differ.
• Figure 2: Posterior probability distribution for the mass within 300 pc for Draco. The four curves in each panel assume different Bayesian priors: a uniform prior in $V_{\rm max}^{-3}$ (black, solid) $V_{\rm max}^{-2}$ (red, dashed), $V_{\rm max}^{-1}$ (green, dot-dashed), and $\ln(V_{\rm max})$ (blue, dotted). The prior distributions are truncated at $V_{\rm max} = 3$km s$^{-1}$ as described in the text. Note that the trend in mass within 300 pc with prior reverses here compared to the case in Figure \ref{['fig:prioreffect_seg']}. This traces back in part to the fact that the mass is best constrained near twice the half-light radius SKB07. For Draco, 300 pc is within the half-light radius and when the CDM $r_{\rm max}$-- $V_{\rm max}$ prior is imposed, lower $V_{\rm max}$ halos are forced, on average, to be more concentrated at 300 pc. In Figure \ref{['fig:prioreffect_seg']}, 300 pc is beyond the half-light radius of Segue 1, and priors that favor larger $V_{\rm max}$ give larger extrapolated masses.
• Figure 3: Posterior probability distribution for the mass within 300 pc for Segue 1, assuming an isotropic velocity distribution (the magenta dot-dot-dot-dashed line) and the model in eq:beta (black solid line). Both curves assume a uniform prior in $V_{\rm max}^{-3}$. Both curves assume a uniform prior in $V_{\rm max}^{-3}$ with an imposed cutoff below $V_{\rm max} = 3$ km s$^{-1}$.
• Figure 4: Posterior probability for m$_{\rm min}$ in the CMSSM, assuming flat priors and employing all available constraints.
• Figure 5: Left: Halo concentration versus halo mass for our PL model (solid black line) and the B01 model (dashed red line). Right: The boost for an $M = 10^8 M_\odot$ halo that results from the PL model (solid black) (using eq:boostans) and the B01 (dashed red) concentration models. Note that both of these concentration-mass models are consistent with current simulations.