Dark matter profiles and annihilation in dwarf spheroidal ga laxies: prospectives for present and future -ray observatories I. The classical dSphs

Due to their large dynamical mass-to-light ratios, dwarf spheroidal galaxies (dSphs) are promising targets for the indirect detection of dark matter (DM) in γ-rays. We examine their detectability by present and future γ-ray observatories. The key innovative features of our analysis are: (i) We take into account the angular size of the dSphs; while nearby objects have higher γ ray flux, their larger angular extent can make them less attra ctive targets for background-dominated instruments. (ii) We derive DM profil es and the astrophysical J -factor (which parameterises the expected γ-ray flux, independently of the choice of DM particle model) for the classical dSphs directly from photometric and kinematic data. We assume very little about the DM profile, modelling this as a smooth split- power law distribution, with and without sub-clumps. (iii) We use a Markov Chain Monte Carlo (MCMC) technique to marginalise over unknown parameters and determine the sensitivity of our derived J -factors to both model and measurement uncertainties. (iv) We use simulated DM profiles to demonstrate that our J -factor determinations recover the correct solution withi n our quoted uncertainties. Our key findings are: (i) Sub-clumps in the dSphs do not usefully boost the signal; (ii) The sensitivity of atmospheric Cherenkov telescopes to dSphs within � 20 kpc with cored halos can be up to �50 times worse than when estimated assuming them to be point-like. Even for the satellite-borne Fermi-LAT the sensitivity is significa ntly degraded on the relevant angular scales for long exposures, hence it is vital to consider the a ngular extent of the dSphs when selecting targets; (iii) No DM profile has been ruled out by current data, but using a prior on the inner dark matter cusp slope 0 6 γprior 6 1 provides J -factor estimates accurate to a factor of a few if an appropriate angular scale is chosen; (iv ) The J -factor is best constrained at a critical integration angle αc = 2rhalf/d (where rhalf is the half light radius and d is the distance to the dwarf) and we estimate the corresponding sensitivity of γ-ray observatories; (v) The ‘classical’ dSphs can be grouped into three categori es: well-constrained and promising (Ursa Minor, Sculptor, and Draco), well-constrained but less promising (Carina, Fornax, and Leo I), and poorly constrained (Sextans and Leo II); (vi) Observations of classical dSphs with Fermi-LAT integrated over the mission lifetime are more promising than observations with the planned Cherenkov Telescope Array for DM particle mass . 700 GeV. However, even Fermi-LAT will not have sufficient integrated signal from the classical dwarfs to detect DM in the ‘vanilla’ Minimal Supersymmetric Standard Model. Bo th the Galactic centre and the ‘ultra-faint’ dwarfs are likely to be better targets and wil l be considered in future work.