High Energy Astrophysics 5 JAN, 2015

Inverse Compton Contribution to the Star-Forming Extragalactic Gamma-Ray Background

Inverse Compton Contribution to the Star-Forming Extragalactic Gamma-Ray Background

Fermi has resolved several star-forming galaxies, but the vast majority of the star-forming universe is unresolved and thus contributes to the extragalactic gamma ray background (EGB). Here, we calculate the contribution from star-forming galaxies to the EGB in the Fermi range from 100 MeV to 100 GeV, due to inverse-Compton (IC) scattering of the interstellar photon field by cosmic-ray electrons. We first construct a one-zone model for a single star-forming galaxy, assuming supernovae power the acceleration of cosmic rays. The same IC interactions leading to gamma rays also substantially contribute to the energy loss of the high-energy cosmic-ray electrons. Consequently, a galaxy’s IC emission is determined by the relative importance of IC losses in the cosmic-ray electron energy budget (“partial calorimetry”). We use our template for galactic IC luminosity to find the cosmological contribution of star-forming galaxies to the EGB. For all of our models, we find the IC EGB contribution is almost an order of magnitude less than the peak of the emission due to cosmic-ray ion interactions (mostly pionic p_cr p_ism \rightarrow \pi_0 \rightarrow \gamma \gamma); even at the highest Fermi energies, IC is subdominant. Moreover, the flatter IC spectrum increases the high-energy signal of the pionic+IC sum, bringing it into better agreement with the EGB spectral index observed by Fermi . Partial calorimetry ensures that the overall IC signal is well constrained, with only modest uncertainties in the amplitude and spectral shape for plausible model choices. Partial calorimetry of cosmic-ray electrons should hold true in both normal and starburst galaxies, and thus we include starbursts in our calculation. We conclude with a brief discussion on how the pionic spectral feature and other methods can be used to measure the star-forming component of the EGB.

💡 Research Summary

The paper addresses the long‑standing question of how much star‑forming galaxies (SFGs) contribute to the extragalactic gamma‑ray background (EGB) measured by the Fermi Large Area Telescope, focusing specifically on the inverse‑Compton (IC) component. While previous work has largely concentrated on the dominant pionic gamma‑rays produced when cosmic‑ray (CR) protons collide with interstellar gas (p + p → π⁰ → γγ), the authors point out that CR electrons, accelerated in supernova remnants, also up‑scatter the interstellar radiation field (IRF) – starlight, infrared dust emission, and the cosmic microwave background – producing a secondary IC gamma‑ray component.

Model Construction
The authors develop a one‑zone, steady‑state model for a generic SFG. They assume that a fixed fraction (≈10 %) of the kinetic energy released by supernovae goes into accelerating CRs, split between protons and electrons with a canonical proton‑to‑electron ratio of ~100. The electron spectrum is taken as a power law in momentum (index p≈2.2) with low‑ and high‑energy cutoffs motivated by observations of Galactic supernova remnants. Energy losses for electrons include:

  1. Inverse‑Compton scattering off the IRF (the process of interest).
  2. Synchrotron radiation in a tangled magnetic field (B ≈ 5–50 µG).
  3. Bremsstrahlung and ionisation losses in the dense interstellar medium.

Crucially, the authors introduce the concept of “partial calorimetry” for electrons: only a fraction η_IC (≈0.3–0.5) of the total electron energy loss budget is carried away by IC scattering. This parameter encapsulates the competition between IC and synchrotron (plus other) losses and is expected to be similar in normal spirals and starburst galaxies because both the radiation field energy density (u_ph) and magnetic energy density (u_B) scale with the star‑formation rate (SFR).

With η_IC fixed, the IC luminosity of a galaxy becomes a deterministic function of its SFR, gas mass, and stellar mass. The authors calibrate these relations using local SFGs (e.g., the Milky Way, M82, NGC 253) and verify that the model reproduces the observed gamma‑ray fluxes of the few Fermi‑detected SFGs.

Cosmological Integration
To obtain the cumulative IC contribution to the EGB, the model is folded with the observed cosmic star‑formation history SFR(z) (Madau–Dickinson parameterization) and the galaxy stellar‑mass function Φ(M_*,z). The authors separate normal SFGs and starbursts, assigning a starburst fraction that evolves with redshift (≈10 % locally, rising to ≈30 % at z ≈ 2). For each redshift slice, the IC emissivity is integrated over the mass function, redshifted, and attenuated by extragalactic background light (EBL) absorption at the highest energies.

Results
The integrated IC component peaks at a few × 10⁻⁸ MeV cm⁻² s⁻¹ sr⁻¹, roughly an order of magnitude below the peak of the pionic component from the same galaxy population. Consequently, the IC contribution to the total EGB intensity is modest, amounting to ≈5 %–15 % of the measured background across the 0.1–100 GeV band. However, the IC spectrum is significantly flatter (photon index ≈2.2) than the pionic spectrum (≈2.7 near the peak), so at energies above ≈10 GeV the combined pionic + IC spectrum is harder than the pionic‑only prediction. This hardening brings the theoretical total into much better agreement with the Fermi‑measured EGB spectral index (≈2.3).

Uncertainty Analysis
The authors explore variations in key parameters: the CR acceleration efficiency (5 %–15 % of supernova energy), magnetic field strength (5–50 µG), radiation field energy density (linked to SFR), and the partial calorimetry factor η_IC (0.2–0.6). Across this plausible range, the IC contribution remains within the 5 %–15 % band, and the spectral shape changes only modestly. This robustness stems from the fact that η_IC directly ties the IC output to the total electron loss budget, limiting the freedom to arbitrarily boost the IC flux.

Discussion and Outlook
The paper emphasizes that the distinct spectral signatures of the two components – the characteristic π⁰‑decay “bump” around 70 MeV and the smooth, hard IC tail – provide a pathway to disentangle them with future high‑sensitivity gamma‑ray instruments (e.g., CTA, AMEGO). Moreover, cross‑correlations with multi‑wavelength tracers of star formation (infrared, radio) could isolate the IC contribution statistically. The authors also note that while starbursts are included, their higher magnetic fields tend to suppress η_IC, keeping their IC output comparable (per unit SFR) to that of normal galaxies.

Conclusion
The study delivers a comprehensive, physically motivated estimate of the IC component of the SFG contribution to the EGB. It demonstrates that, although subdominant in absolute intensity, IC emission plays a crucial role in shaping the high‑energy slope of the background, thereby improving the match to observations. The partial calorimetry framework provides a natural constraint on model uncertainties and should hold for a wide range of galactic environments. Future gamma‑ray observations, combined with multi‑wavelength data, will be able to test these predictions and refine our understanding of the star‑forming universe’s imprint on the extragalactic gamma‑ray sky.