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 Lyα equivalent width, its velocity offset from systemic, and an input Lyα 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 Lyα 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.