A Census of X-ray Millisecond Pulsars in Globular Clusters

We present a comprehensive census of X-ray millisecond pulsars (MSPs) in 29 Galactic globular clusters (GCs), including 68 MSPs with confirmed X-ray luminosities and 107 MSPs with X-ray upper limits. We compile previous X-ray studies of GC MSPs, and add new analyses of six MSPs (PSRs J1326$-$4728A, J1326$-$4728B, J1518$+$0204C, J1717$+$4308A, J1737$-$0314A, and J1807$-$2459A) discovered in five GCs. Their X-ray spectra are well described by a single blackbody model, a single power-law model, or a combination of them, with X-ray luminosities ranging from 1.9$\times$10$^{30}$ erg s$^{-1}$ to 8.3$\times$10$^{31}$ erg s$^{-1}$. We find that most detected X-ray MSPs have luminosities between $\sim 10^{30}$ erg s$^{-1}$ to $3 \times 10^{31}$ erg s$^{-1}$. Redback pulsars are a relatively bright MSP population with X-ray luminosities of $\sim2\times10^{31}$--$3\times10^{32}$ erg s$^{-1}$. Black widows show a bi-modal distribution in X-ray luminosities, with eclipsing black widows between $\sim 7\times10^{30}$ and $2\times10^{31}$ erg s$^{-1}$, while the two confirmed non-eclipsing black widows are much fainter, with $L_X$ of $1.5-3\times10^{30}$ erg s$^{-1}$, suggesting an intrinsic difference in the populations. We estimate the total number of MSPs in 36 GCs by considering the correlation between the number of MSPs and stellar encounter rate in GCs, and suggest that between 600--1500 MSPs exist in these 36 GCs. Finally, we estimate the number of X-ray detectable MSPs in the Galactic bulge, finding that 1--86 MSPs with $L_X > 10^{33}$ erg s$^{-1}$, and 20--900 MSPs with $L_X > 10^{32}$ erg s$^{-1}$, should be detectable there.