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

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 ?-rays. We examine their detectability by present and future ?-ray observatories. The key innovative features of our analysis are as follows: (i) we take into account the angular size of the dSphs; while nearby objects have higher ?-ray flux, their larger angular extent can make them less attractive targets for background-dominated instruments; (ii) we derive DM profiles and the astrophysical J-factor (which parametrizes the expected ?-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 subclumps; (iii) we use a Markov chain Monte Carlo technique to marginalize over unknown parameters and determine the sensitivity of our derived J-factors to both model and measurement uncertainties; and (iv) we use simulated DM profiles to demonstrate that our J-factor determinations recover the correct solution within our quoted uncertainties. Our key findings are as follows: (i) subclumps in the dSphs do not usefully boost the signal; (ii) the sensitivity of atmospheric Cherenkov telescopes to dSphs within similar to 20 kpc with cored haloes can be up to similar to 50 times worse than when estimated assuming them to be point-like. Even for the satellite-borne Fermi-Large Area Telescope (Fermi-LAT), the sensitivity is significantly degraded on the relevant angular scales for long exposures; hence, it is vital to consider the angular 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 DM cusp slope 0 <= gamma prior <= 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 alpha(c) = 2r(h)/d (where rh is the half-light radius and d is the distance from the dwarf) and we estimate the corresponding sensitivity of gamma-ray observatories; (v) the 'classical' dSphs can be grouped into three categories: 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); and (vi) observations of classical dSphs with the Fermi-LAT integrated over the mission lifetime are more promising than observations with the planned Cherenkov Telescope Array for DM particle mass less than or similar to 700 GeV. However, even the Fermi-LAT will not have sufficient integrated signal from the classical dwarfs to detect DM in the 'vanilla' Minimal Supersymmetric Standard Model. Both the Galactic Centre and the 'ultrafaint' dwarfs are likely to be better targets and will be considered in future work.