Modelling the average spectrum expected from a population of gamma-ray globular clusters

Millisecond pulsars occur abundantly in globular clusters. They are expected to be responsible for several spectral components in the radio through gamma-ray waveband (e.g., involving synchrotron and inverse Compton emission), as have been seen by Radio Telescope Effelsberg, Chandra X-ray Observatory, Fermi Large Area Telescope, and the High Energy Stereoscopic System (H.E.S.S.) in the case of Terzan 5 (with fewer spectral components seen for other globular clusters). H.E.S.S. has recently performed a stacking analysis involving 15 non-detected globular clusters and obtained quite constraining average flux upper limits above 230 GeV. We present a model that assumes millisecond pulsars as sources of relativistic particles and predicts multi-wavelength emission from globular clusters. We apply this model to the population of clusters mentioned above to predict the average spectrum and compare this to the H.E.S.S. upper limits. Such comparison allows us to test whether the model is viable, leading to possible constraints on various average cluster parameters within this framework.