The Fundamental Plane of Gamma-ray Globular Clusters

We have investigated the properties of a group of $γ$-ray emitting globular clusters (GCs) which have recently been uncovered in our Galaxy. By correlating the observed $γ$-ray luminosities $L_γ$ with various cluster properties, we probe the origin of the high energy photons from these GCs. We report $L_γ$ is positively correlated with the encounter rate $Γ_{c}$ and the metalicity $\left[{\rm Fe/H}\right]$ which place an intimate link between the gamma-ray emission and the millisecond pulsar population. We also find a tendency that $L_γ$ increase with the energy densities of the soft photon at the cluster location. Furthermore, the two-dimensional regression analysis suggests that $L_γ$, soft photon densities, and $Γ_{c}$/$\left[{\rm Fe/H}\right]$ possibly span fundamental planes which potentially provide better predictions for the $γ$-ray properties of GCs.

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