On the sizes of ionized bubbles around the highest redshift galaxies. Spectral shapes of the Lyman-alpha emission from galaxies

Abstract: 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 a ionized 'bubble' (R_B) surrounding the galaxy. The method requires an observed Lya equivalent width, its velocity offset from systemic, and an input Lya 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 eight at z = 7.2 - 10.6 recently observed with JWST. Our model estimates the emergent Lya properties, and the foreground distance to the absorbing IGM. 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 Str\"omgren radii (R_S), and derive the escape fraction of ionizing photons budget necessary for reionization.