The volume fraction of ionized intergalactic gas at redshift z=6.5

The observed number density of Ly alpha sources implies a minimum volume of the intergalactic medium that must be ionized, in order to allow the Ly alpha photons to escape attenuation. We estimate this volume by assigning to each Lya emitter the minimum ionized bubble that would allow half its Ly alpha photons to escape. This implies a lower limit to the ionized gas volume fraction of 20%-50% at z = 6.5. This is a lower limit in two ways: First, we conservatively assume that the Ly alpha sources seen (at a relatively bright flux limit) are the only ones present, and second, we assume the smallest ionized bubble volume that will allow the photons to escape. This limit is completely independent of what ionizing photon sources produced the bubbles. Deeper Ly alpha surveys are possible with present technology and can strengthen these limits by detecting a higher density of Ly alpha galaxies.