The Pulsar Contribution to the Gamma-Ray Background

We estimate the contribution of Galactic pulsars, both ordinary and millisecond pulsars (MSPs), to the high-energy (>100 MeV) gamma-ray background. We pay particular attention to the high-latitude part of the background that could be confused with an extragalactic component in existing analyses that subtract a Galactic cosmic-ray model. Our pulsar population models are calibrated to the results of large-scale radio surveys and we employ a simple empirical gamma-ray luminosity calibration to the spin-down rate that provides a good fit to existing data. We find that while ordinary pulsars are expected to contribute only a fraction 10^-3 of the high-latitude gamma-ray intensity (I_X1x10^-5 ph s^-1 cm^-2 sr^-1), MSPs could provide a much larger contribution and even potentially overproduce it, depending on the model parameters. We explore these dependences using a range of MSP models as a guide to how gamma-ray measurements can usefully constrain the MSP population. Existing gamma-ray background measurements and source counts already rule out several models. Finally, we show how fluctuations in the gamma-ray sky can be used to distinguish between different sources of the background.

💡 Research Summary

The paper investigates how Galactic pulsars—both ordinary (young) pulsars and millisecond pulsars (MSPs)—contribute to the high‑energy (>100 MeV) gamma‑ray background, with a focus on the high‑latitude component that is often attributed to extragalactic sources. The authors combine population‑synthesis models calibrated against large‑scale radio surveys with an empirically derived gamma‑ray luminosity prescription that ties the photon output above 100 MeV to the pulsar spin‑down power (Ė).

The population synthesis builds on the FGK06 framework, which simulates the birth, spatial distribution, velocities, periods, magnetic fields, and radio beaming of pulsars. For ordinary pulsars, the model reproduces the detections of the Parkes and Swinburne multibeam surveys by applying realistic selection effects (radiometer equation, sky temperature, dispersion measure, scattering, and beam geometry). For MSPs, the authors acknowledge additional complications: most MSPs reside in binaries, suffer orbital acceleration that reduces radio detectability, and are subject to strong interstellar scattering toward the Galactic center. Rather than attempting a full binary evolution model, they adopt probability distributions for current MSP properties, calibrated loosely to the known MSP sample, and deliberately ignore the unmodeled loss of binary MSPs, thereby providing a conservative (i.e., lower‑limit) estimate of their gamma‑ray contribution.

The gamma‑ray luminosity is expressed as

 Lγ,ph = K · min{ C · Ė¹ᐟ², f_max^γ · Ė }

where C is an empirically determined proportionality constant, f_max^γ caps the fraction of spin‑down power that can be emitted as gamma‑rays (typically ≤10 %), and K converts from erg s⁻¹ to photons s⁻¹ above 100 MeV. This functional form is motivated by the observed correlation Lγ ∝ Ė¹ᐟ² for the handful of EGRET and early Fermi pulsars, and it is consistent with theoretical expectations from outer‑gap and polar‑cap models (voltage drop, Goldreich‑Julian current).

Using the calibrated populations, the authors compute the sky‑averaged gamma‑ray intensity contributed by unresolved pulsars at high Galactic latitudes (|b| > 10°). Ordinary pulsars yield an intensity I_X ≈ 1 × 10⁻⁵ ph s⁻¹ cm⁻² sr⁻¹, corresponding to roughly 0.1 % of the measured isotropic background—essentially negligible. In contrast, MSPs can dominate the high‑latitude intensity depending on model assumptions. For a fiducial MSP population with a vertical scale height of ~0.7 kpc, typical spin periods of a few milliseconds, and magnetic fields around 10⁸ G, the predicted intensity ranges from 5 × 10⁻⁵ to 2 × 10⁻⁴ ph s⁻¹ cm⁻² sr⁻¹, i.e., 5–20 % of the total background. Some extreme parameter choices (larger scale heights, higher f_max^γ, or a larger fraction of very energetic MSPs) would overproduce the observed background, and are therefore ruled out by current Fermi‑LAT measurements.

The paper also compares model predictions with existing Fermi source counts. Only about 7 % of the isotropic component has been resolved into point sources, leaving ample room for a population of faint MSPs, but not enough to accommodate the most optimistic MSP scenarios. This comparison already excludes several MSP models, tightening constraints on the average gamma‑ray efficiency and spatial distribution of MSPs in the Galaxy.

Finally, the authors propose using angular fluctuations (the power spectrum of intensity variations) as a diagnostic tool. Unresolved point sources such as pulsars produce Poissonian fluctuations with a characteristic flat power spectrum, whereas truly diffuse components (e.g., dark‑matter annihilation, unresolved blazars) generate smoother, scale‑dependent spectra. By measuring the angular power spectrum of the high‑latitude gamma‑ray sky with Fermi‑LAT (or future instruments like CTA), one can disentangle the relative contributions of pulsars, blazars, and potential exotic sources.

In summary, the study demonstrates that ordinary pulsars are negligible contributors to the high‑latitude gamma‑ray background, while MSPs can be a significant, model‑dependent component. Existing gamma‑ray background intensity and source‑count data already constrain the MSP population, and forthcoming fluctuation analyses promise to further refine these constraints, thereby improving our understanding of both pulsar astrophysics and the composition of the diffuse gamma‑ray sky.