Modelling the stellar soft-photon energy density profile of globular clusters

Abstract

Recent observations by the Fermi Large Area Telescope (LAT) and the High Energy Stereoscopic System (H.E.S.S.) have revealed globular clusters (GC) to be sources of high-energy (HE) and very-high-energy (VHE) gamma-rays. It has been suggested that the presence of large numbers of millisecond pulsars (MSPs) within these clusters may be either directly responsible for these gamma-ray fluxes through emission of pulsed curvature radiation, or indirectly through the injection of relativistic leptons into the cluster. These relativistic particles are plausibly re-accelerated in shocks, created by the collision of stellar winds, before interacting with the soft-photon radiation field set up by the stellar population of the host cluster. Inverse Compton (IC) scattering then produces gamma-radiation in the TeV band. In order to calculate the IC spectrum, an accurate profile for the energy density of the soft-photon field is required. We construct such a profile by deriving a radially-dependent expression for the stellar energy density, and then solve it numerically. As a next step, the average energy density values for three different regions of the cluster (demarcated by its core, half-mass, and tidal radii) are determined, which we consequently import into an existing radiation code to predict the TeV gamma-ray spectrum. As an application, we consider the case of Terzan 5, boasting a population of 34 radio MSPs, and compare our predicted spectrum with that measured by H.E.S.S.