A population of gamma-ray emitting globular clusters seen with the Fermi
  Large Area Telescope
  Globular clusters with their large populations of millisecond pulsars (MSPs)
are believed to be potential emitters of high-energy gamma-ray emission. Our
goal is to constrain the millisecond pulsar populations in globular clusters
from analysis of gamma-ray observations. We use 546 days of continuous
sky-survey observations obtained with the Large Area Telescope aboard the Fermi
Gamma-ray Space Telescope to study the gamma-ray emission towards 13 globular
clusters. Steady point-like high-energy gamma-ray emission has been
significantly detected towards 8 globular clusters. Five of them (47 Tucanae,
Omega Cen, NGC 6388, Terzan 5, and M 28) show hard spectral power indices $(0.7
< \Gamma <1.4)$ and clear evidence for an exponential cut-off in the range
1.0-2.6 GeV, which is the characteristic signature of magnetospheric emission
from MSPs. Three of them (M 62, NGC 6440 and NGC 6652) also show hard spectral
indices $(1.0 < \Gamma < 1.7)$, however the presence of an exponential cut-off
can not be unambiguously established. Three of them (Omega Cen, NGC 6388, NGC
6652) have no known radio or X-ray MSPs yet still exhibit MSP spectral
properties. From the observed gamma-ray luminosities, we estimate the total
number of MSPs that is expected to be present in these globular clusters. We
show that our estimates of the MSP population correlate with the stellar
encounter rate and we estimate 2600-4700 MSPs in Galactic globular clusters,
commensurate with previous estimates. The observation of high-energy gamma-ray
emission from a globular cluster thus provides a reliable independent method to
assess their millisecond pulsar populations that can be used to make
constraints on the original neutron star X-ray binary population, essential for
understanding the importance of binary systems in slowing the inevitable core
collapse of globular clusters.
