A New Constraint on the Escape Fraction in Distant Galaxies Using γ-Ray Burst Afterglow Spectroscopy

We describe a new method to measure the escape fraction f esc of ionizing radiation from distant star-forming galaxies using the afterglow spectra of long-duration γ-ray bursts (GRBs). Optical spectra of GRB afterglows allow us to evaluate the optical depth of the host ISM, according to the neutral hydrogen column density N (H I) observed along the sight lines toward the star-forming regions where the GRBs are found. Different from previous efforts in searching for faint, transmitted Lyman continuum photons, our method is not subject to background subtraction uncertainties and does not require prior knowledge of either the spectral shape of the host galaxy population or the IGM Lyα forest absorption along these GRB sight lines. Because most GRBs occur in sub- L * galaxies, our study also offers the first constraint on f esc for distant low-mass galaxies that dominate the cosmic luminosity density. We have compiled a sample of 28 GRBs at redshift z ≳ 2 for which the underlying N (H I) values in the host ISM are known. These GRBs together offer a statistical sampling of the integrated optical depth to ionizing photons along random sight lines from star-forming regions in the host galaxies, and allow us to estimate the mean escape fraction ⟨ f esc ⟩ averaged over different viewing angles. We find ⟨ f esc ⟩ = 0.02 ± 0.02 and place a 95% c.l. upper limit ⟨ f esc ⟩ ≤ 0.075 for these hosts. We discuss possible biases of our approach and implications of the result. Finally, we propose to extend this technique for measuring ⟨ f esc ⟩ at z ~ 0.2 using spectra of core-collapse supernovae.