Modeling the Extragalactic Background Light from Stars and Dust

The extragalactic background light (EBL) from the far infrared through the visible and extending into the ultraviolet is thought to be dominated by starlight, either through direct emission or through absorption and reradiation by dust. This is the most important energy range for absorbing $\g$-rays from distant sources such as blazars and gamma-ray bursts and producing electron positron pairs. In previous work we presented EBL models in the optical through ultraviolet by consistently taking into account the star formation rate (SFR), initial mass function (IMF) and dust extinction, and treating stars on the main sequence as blackbodies. This technique is extended to include post-main sequence stars and reprocessing of starlight by dust. In our simple model, the total energy absorbed by dust is assumed to be re-emitted as three blackbodies in the infrared, one at 40 K representing warm, large dust grains, one at 70 K representing hot, small dust grains, and one at 450 K representing polycyclic aromatic hydrocarbons. We find our best fit model combining the Hopkins and Beacom SFR using the Cole et al. parameterization with the Baldry and Glazebrook IMF agrees with available luminosity density data at a variety of redshifts. Our resulting EBL energy density is quite close to the lower limits from galaxy counts and in some cases below the lower limits, and agrees fairly well with other recent EBL models shortward of about 5 $\mu$m. Deabsorbing TeV $\g$-ray spectra of various blazars with our EBL model gives results consistent with simple shock acceleration theory. We also find that the universe should be optically thin to $\g$-rays with energies less than 20 GeV.

💡 Research Summary

This paper presents a comprehensive, semi-analytic model for calculating the extragalactic background light (EBL) from the far-infrared to the ultraviolet, based on the fundamental sources of emission: stars and dust. The EBL, a diffuse cosmic radiation field, is crucial for absorbing very high-energy gamma-rays from distant sources like blazars through photon-photon pair production.

The authors extend their previous work (RDF09), which modeled starlight by treating main-sequence stars as blackbodies and integrating over a stellar initial mass function (IMF) and a cosmic star formation rate (SFR) density. The key advancements in this work are the inclusion of post-main-sequence stellar evolution (using the analytic formulae of Eggleton et al. 1989) and a self-consistent treatment of dust reprocessing.

The model operates in two stages. First, the comoving luminosity density from stars is calculated. The fraction of starlight that escapes galaxies without being absorbed by dust (f_esc) is taken from empirical fits. The remaining fraction is assumed to be absorbed by interstellar dust. Second, the energy absorbed by dust is re-radiated in the infrared as a sum of three blackbody components, representing: warm large grains (40 K), hot small grains (70 K), and polycyclic aromatic hydrocarbons or PAHs (450 K). The fractional energy distribution (f_n) among these components and their temperatures are treated as free parameters, tuned to match local infrared luminosity density data.

The final EBL energy density at the present epoch (z=0) is obtained by integrating the total (stellar + dust) luminosity density over the entire cosmic history, accounting for cosmological redshift and dilution.

The main numerical results are derived by testing different combinations of IMFs (e.g., Salpeter, Baldry & Glazebrook) and SFRs (e.g., Hopkins & Beacom). The model combining the Hopkins & Beacom SFR with the Baldry & Glazebrook IMF provides the best agreement with available luminosity density data across a range of redshifts (z=0 to z~2). The resulting EBL spectrum shows the characteristic double-peak structure: a “stellar” peak near 1 micron and a “dust” peak near 100 microns. The predicted EBL intensity is close to, and in some cases below, the strict lower limits derived from galaxy counts, and agrees well with other recent EBL models at wavelengths shortward of about 5 microns.

The paper then applies this EBL model to astrophysical phenomenology. By “de-absorbing” the observed TeV gamma-ray spectra of several distant blazars (i.e., removing the calculated EBL absorption effect), the derived intrinsic spectra are found to be consistent with predictions from simple shock acceleration theory, validating the model’s utility. A critical finding from calculating the optical depth for gamma-gamma absorption is that the universe should be optically thin to gamma-rays with energies below approximately 20 GeV for all redshifts. This implies that absorption by the EBL is negligible for gamma-rays in this energy range, allowing instruments like Fermi-LAT to observe distant sources without this particular form of attenuation.

In conclusion, the study demonstrates that a relatively simple, physically motivated model integrating stellar evolution and dust reprocessing can successfully reproduce key observational constraints on the EBL. The model serves as a practical tool for interpreting very high-energy gamma-ray observations and places important constraints on the opacity of the universe to gamma-rays. The authors acknowledge remaining uncertainties, particularly in the dust model parameters and the IMF at high redshifts, suggesting directions for future refinement.