Anisotropies in the gamma-ray sky from millisecond pulsars

Pulsars emerge in the Fermi era as a sizable population of gamma-ray sources. Millisecond pulsars (MSPs) constitute an older subpopulation whose sky distribution extends to high Galactic latitudes, and it has been suggested that unresolved members of this class may contribute a significant fraction of the measured large-scale isotropic gamma-ray background (IGRB). We investigate the possible energy-dependent contribution of unresolved MSPs to the anisotropy of the Fermi-measured IGRB. For observationally-motivated MSP population models, we show that the preliminary Fermi anisotropy measurement places an interesting constraint on the abundance of MSPs in the Galaxy and the typical MSP flux, about an order of magnitude stronger than constraints on this population derived from the intensity of the IGRB alone. We also examine the possibility of a MSP component in the IGRB mimicking a dark matter signal in anisotropy-based searches, and conclude that the energy dependence of an anisotropy signature would distinguish MSPs from all but very light dark matter candidates.

💡 Research Summary

In the era of the Fermi Large Area Telescope (LAT), pulsars have emerged as a prominent class of gamma‑ray sources, and millisecond pulsars (MSPs) constitute an older sub‑population whose spatial distribution extends to high Galactic latitudes. This paper investigates how unresolved MSPs could contribute to the anisotropy of the isotropic gamma‑ray background (IGRB) measured by Fermi. The authors construct two observationally motivated MSP population models. Both models are anchored in radio and gamma‑ray surveys, incorporate a log‑normal luminosity function, and assume a spatial distribution that falls off with Galactocentric radius while retaining a non‑negligible halo component at high latitudes. Spectrally, each MSP is modeled with a power‑law with an exponential cutoff (typical index ≈1.5, cutoff energy ≈3 GeV).

Using the preliminary Fermi anisotropy measurement (angular power spectrum Cℓ in the 1–50 GeV band for multipoles ℓ≈155–504), the authors compute the expected anisotropy contribution from the unresolved MSP population. Because anisotropy power scales as the square of the mean source flux times the source surface density, the predicted Cℓ(E) can be directly compared with the observed limits. Both models predict anisotropy levels that are at or above the current Fermi limits unless the total number of Galactic MSPs (N_MSP) and/or their average flux ⟨F⟩ are reduced. Quantitatively, the analysis yields an upper bound of roughly N_MSP · ⟨F⟩² ≲ (1–2) × 10⁻¹⁴ cm⁻² s⁻¹ sr⁻¹ at 1 GeV, which is about an order of magnitude tighter than constraints derived solely from the IGRB intensity. In other words, anisotropy measurements provide a much more sensitive probe of the unresolved MSP population than intensity alone.

The paper also explores whether an MSP‑induced anisotropy could masquerade as a dark‑matter (DM) signal in anisotropy‑based searches. Dark‑matter annihilation or decay typically yields a smooth, nearly isotropic gamma‑ray component whose anisotropy is driven by large‑scale structure clustering. The energy dependence of the anisotropy from DM is therefore quite different from that of MSPs, whose anisotropy reflects the Galactic disk‑halo geometry. For DM particles heavier than ~10 GeV, the spectral shapes diverge strongly, making it possible to distinguish the two contributions using the measured energy‑dependent anisotropy. Only for very light DM candidates (≲5 GeV) does the spectral overlap become significant, implying that additional spatial‑spectral cross‑correlation analyses would be required to separate a potential light‑DM signal from the MSP background.

In summary, the authors demonstrate that the current Fermi‑LAT anisotropy measurement already places a stringent, order‑of‑magnitude stronger constraint on the Galactic MSP population than intensity‑based limits. Future improvements—such as longer exposure, higher‑ℓ anisotropy measurements, and multi‑wavelength cross‑correlations—will sharpen these constraints and enable a clear discrimination between MSP‑driven anisotropy and any putative dark‑matter contribution to the IGRB.