Likely detection of gamma-ray pulsations of PSR~J1717+4308A in NGC~6341 and implication of the gamma-ray millisecond pulsars in globular clusters

We report our analysis results for the globular cluster (GC) NGC~6341 (M92), as a millisecond pulsar (MSP) J1717$+$4308A has recently been reported found in this GC. The data used are from the Large Area Telescope onboard the {\it Fermi Gamma-ray Space Telescope (Fermi)}. We detect $\gamma$-ray pulsations of the MSP at a $4.4\sigma$ confidence level (the corresponding weighted H-test value is $\sim$28.4). This MSP, the fourth $\gamma$-ray pulsar found in a GC, does not have significant off-pulse emission and has $\gamma$-ray luminosity and efficiency $1.3\times10^{34}$\,erg\,s$^{-1}$ and 1.7\% respectively. In order to have a clear view on the properties of the known GC $\gamma$-ray MSPs, we re-analyze the \fermi\ LAT data for the other three ones. These four MSPs share the properties of either having high $\dot{E}$ ($\sim 10^{36}$\,erg\,s$^{-1}$) or being in the GCs that contain only limited numbers of known MSPs. In addition, we find that PSRs~J1823$-$3021A and B1821$-$24, in NGC~6624 and NGC~6626 respectively, have detectable off-pulse $\gamma$-ray emission and PSR J1835$-$3259B in NGC~6652 does not. Using the obtained off-pulse spectra or spectral upper limits, we constrain the numbers of other MSPs in the four GCs. The results are consistent with the numbers of the radio pulsars reported in them. While at least in NGC~6624 and NGC~6626, the contribution of other MSPs to their observed $\gamma$-ray emission can not be ignored, our study indicates that the presence of a bright MSP could be the dominant factor for whether a GC is detectable at $\gamma$-rays or not.