On the Sizes of Ionized Bubbles Around Galaxies During the Reionization Epoch. The Spectral Shapes of the Lyα Emission from Galaxies

We develop a new method to determine the distance between a high-redshift galaxy and a foreground screen of atomic hydrogen. In a partially neutral universe, and assuming spherical symmetry, this equates to the radius of an ionized “bubble” ( R B ) surrounding the galaxy. The method requires an observed Ly α equivalent width, its velocity offset from systemic, and an input Ly α profile for which we adopt scaled versions of the profiles observed in low- z galaxies. We demonstrate the technique in a sample of 23 galaxies at z > 6, including 8 at z = 7.2–10.6 recently observed with JWST. Our model estimates the emergent Ly α properties and the foreground distance to the absorbing intergalactic medium. We find that galaxies at z > 7.5 occupy smaller bubbles (∼0.5–1 pMpc) than those at lower z . With a relationship that is secure at 99% confidence, we empirically demonstrate the growth of ionized regions during the reionization epoch for the first time. We independently estimate the upper limit on the Strömgren radii ( R S ), and derive the escape fraction of ionizing photons ( f esc LyC ) from the ratio of R B / R S , deriving a median value of 5%, which, on average, represents the lower end of the photon budget necessary for reionization.