The Fundamental Plane of Gamma-ray Globular Clusters

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