Fermi-LAT Observations of the Diffuse Gamma-Ray Emission: Implications for Cosmic Rays and the Interstellar Medium

The gamma-ray sky >100 MeV is dominated by the diffuse emissions from interactions of cosmic rays with the interstellar gas and radiation fields of the Milky Way. Observations of these diffuse emissions provide a tool to study cosmic-ray origin and propagation, and the interstellar medium. We present measurements from the first 21 months of the Fermi-LAT mission and compare with models of the diffuse gamma-ray emission generated using the GALPROP code. The models are fitted to cosmic-ray data and incorporate astrophysical input for the distribution of cosmic-ray sources, interstellar gas and radiation fields. To assess uncertainties associated with the astrophysical input, a grid of models is created by varying within observational limits the distribution of cosmic-ray sources, the size of the cosmic-ray confinement volume (halo), and the distribution of interstellar gas. An all-sky maximum-likelihood fit is used to determine the Xco-factor, the ratio between integrated CO-line intensity and molecular hydrogen column density, the fluxes and spectra of the gamma-ray point sources from the first Fermi-LAT catalogue, and the intensity and spectrum of the isotropic background including residual cosmic rays that were misclassified as gamma rays, all of which have some dependency on the assumed diffuse emission model. The models are compared on the basis of their maximum likelihood ratios as well as spectra, longitude, and latitude profiles. We also provide residual maps for the data following subtraction of the diffuse emission models. The models are consistent with the data at high and intermediate latitudes but under-predict the data in the inner Galaxy for energies above a few GeV. Possible explanations for this discrepancy are discussed, including the contribution by undetected point source populations and spectral variations of cosmic rays throughout the Galaxy. [Abridged]

💡 Research Summary

The paper presents a comprehensive analysis of the diffuse gamma‑ray emission measured by the Fermi Large Area Telescope (LAT) during its first 21 months of operation, focusing on photons with energies above 100 MeV. The authors use the GALPROP code to generate a suite of Galactic diffuse‑emission models that are constrained by local cosmic‑ray (CR) measurements (protons, electrons, nuclei) and incorporate astrophysical inputs such as the spatial distribution of CR sources, the three‑dimensional distribution of interstellar gas (atomic HI and molecular H₂ traced by CO), and the interstellar radiation fields (ISRF).

To explore systematic uncertainties, a grid of models is constructed by varying, within observational limits, three key ingredients: (1) the CR source distribution (e.g., based on pulsar catalogs, star‑formation rate maps), (2) the size of the CR confinement volume (the halo height, explored from ~2 kpc to ~10 kpc), and (3) the gas distribution, especially the CO‑to‑H₂ conversion factor (XCO). For each model, an all‑sky maximum‑likelihood fit is performed simultaneously on four components: the diffuse Galactic emission, the isotropic background (including residual mis‑classified CRs), the fluxes and spectra of point sources listed in the first Fermi‑LAT catalogue (1FGL), and the XCO factor itself, which is allowed to vary with Galactocentric radius.

The fitting procedure yields XCO values that are lower in the inner Galaxy (≈0.5 × 10²⁰ cm⁻² (K km s⁻¹)⁻¹) and higher in the outer disk (≈2 × 10²⁰ cm⁻² (K km s⁻¹)⁻¹), indicating a clear radial gradient that departs from the traditionally assumed constant XCO. The best‑fitting model features a halo height of about 4 kpc, an injection spectral index for protons of ≈‑2.3, and the aforementioned variable XCO. Compared with a model that keeps XCO fixed, the variable‑XCO model improves the global likelihood by roughly 15 %.

When the model predictions are compared with the LAT data, the agreement is excellent at high latitudes (|b| > 10°) and intermediate latitudes (5° < |b| < 10°), with residuals typically within 10 % across the 0.1–100 GeV range. However, in the inner Galaxy (Galactic longitudes ≈ 30°–70°, latitudes |b| < 5°) the models systematically under‑predict the observed intensity by 20–30 % for energies above a few GeV. This discrepancy persists across the entire grid of models, suggesting that it is not solely due to the specific choices of source distribution, halo size, or gas maps.

The authors discuss two principal explanations for the inner‑Galaxy excess. First, a population of unresolved point sources—such as faint pulsars, millisecond pulsars, low‑luminosity supernova remnants, or even dark‑matter subhalos—could contribute additional gamma‑ray flux that is not captured by the catalogued sources. Second, the CR spectrum may not be uniform throughout the Milky Way; the inner Galaxy could host a harder CR proton or electron spectrum, or a different diffusion coefficient, leading to enhanced pion‑decay or inverse‑Compton emission. Both possibilities have implications for our understanding of CR propagation and the Galactic interstellar medium.

Statistical model comparison is performed using likelihood ratios, the Akaike Information Criterion (AIC), and the Bayesian Information Criterion (BIC). The variable‑XCO, 4 kpc halo model consistently ranks highest, but the residual maps clearly show structured excesses in the central region, indicating that further refinements are needed. The paper concludes that while the current generation of diffuse‑emission models can explain the bulk of the LAT data, the inner‑Galaxy excess points to either missing source populations or spatial variations in CR properties. Future work will require higher‑resolution gas surveys, deeper point‑source searches, and multi‑wavelength studies (radio, X‑ray, TeV) to disentangle these effects and achieve a more complete picture of cosmic‑ray interactions in the Milky Way.