Millisecond Pulsars in Globular Clusters and Implications for the Galactic Center Gamma-Ray Excess

Abstract

We study the gamma-ray emission from millisecond pulsars within the Milky Way's globular cluster system in order to measure the luminosity function of this source population. We find that these pulsars have a mean luminosity of $\langle L_γ\rangle \sim (1-8)\times 10^{33}\, {\rm erg/s}$ (integrated between 0.1 and 100 GeV) and a log-normal width of $σ_L \sim 1.4-2.8$. If the Galactic Center Gamma-Ray Excess were produced by pulsars with similar characteristics, Fermi would have already detected $N \sim 17-37$ of these sources, whereas only three such pulsar candidates have been identified. We conclude that the excess gamma-ray emission can originate from pulsars only if they are significantly less bright, on average, than those observed within globular clusters or in the Galactic Plane. This poses a serious challenge for pulsar interpretations of the Galactic Center Gamma-Ray Excess.

Figures (7)

• Figure 1: The number of known millisecond pulsars in each of the 87 globular clusters considered in this study (those with $L_V > 10^5 \, L_{\odot}$ or $\Gamma_e > 0.01$) as a function of combinations of the stellar encounter rate, $\Gamma_e$, and visible luminosity, $L_V$ (in units of solar luminosities). Also shown are colored bands representing the predicted number of MSPs (68.27% and 95.45% containment) in each case, for selected values of $R_{\rm MSP}^{\rm Radio}$. The stellar encounter rate is normalized such that $\Gamma_e =1$ for NGC 104.
• Figure 2: The measured gamma-ray luminosities of the 87 globular clusters considered in this study (those with $L_V > 10^5 \, L_{\odot}$ or $\Gamma_e > 0.01$), compared to combinations of their stellar encounter rates and/or visible luminosities. As dark (light) grey bands, we show the 68.27% (95.45%) confidence interval predicted by the model for the the total gamma-ray luminosity. In each frame, we show the results that were obtained using the best-fit values for $\langle L_{\gamma} \rangle$, $\sigma_L$, $R_{\rm MSP}$, and/or $R'_{\rm MSP}$ (see Table \ref{['tab:param_constraints']}).
• Figure 3: Constraints on the MSP gamma-ray luminosity function parameters, after marginalizing over $R_{\rm MSP}$ and/or $R'_{\rm MSP}$. The best-fit point in each frame is shown as a dot, while the contours reflect the regions that are preferred at the levels of 1, 2 and 3$\sigma$ confidence.
• Figure 4: A comparison of the $2\sigma$ constraints on the MSP gamma-ray luminosity found in this study (for the best-fitting case of $\langle N_{\rm MSP}\rangle = R_{\rm MSP} \, \Gamma_e^{0.7} +R'_{\rm MSP} \, L_V$) to those published in previous studies of MSPs in the Galactic Plane. The luminosity function preferred by our analysis is in good agreement with those derived by Holst and Hooper Holst:2024fvb, and by Hooper and Mohlabeng Hooper:2016rap, but favor somewhat larger values for the average MSP luminosity than Ploeg et al.Ploeg:2017vai, or Bartels et al.Bartels:2018xom.
• Figure 5: The constraints on the MSP gamma-ray luminosity found in this study (shown for the case of $\langle N_{\rm MSP}\rangle = R_{\rm MSP}\, \Gamma_e^{0.7} +R'_{\rm MSP} \,L_V$), shown along with contours representing the number of Inner Galaxy MSPs that should appear in the Fermi source catalogs, $N_{\rm MSP}$, assuming that the Galactic Center Gamma-Ray Excess (GCE) is generated by MSPs Holst:2024fvb. As there are only three Inner Galaxy pulsars candidates in the 3PC, MSPs can generate the excess gamma-ray emission only if that source population consists of members that are significantly less luminous than those present in globular clusters.