Measuring the properties of reionised bubbles with resolved Lyman alpha spectra

Identifying and characterising reionised bubbles enables us to track both their size distribution, which depends on the primary ionising sources, and the relationship between reionisation and galaxy evolution. We demonstrate that spectrally resolved $z\gtrsim6$ Lyman-alpha (Ly$\alpha$) emission can constrain properties of reionised regions. Specifically, the distant from a source to a neutral region sets the minimum observable Ly$\alpha$ velocity offset from systemic. Detection of flux on the blue side of the Ly$\alpha$ resonance implies the source resides in a large, sufficiently ionised region that photons can escape without significant resonant absorption, and thus constrains both the sizes of and the residual neutral fractions within ionised bubbles. We estimate the extent of the region around galaxies which is optically thin to blue Ly$\alpha$ photons, analogous to quasar proximity zones, as a function of the source's ionising photon output and surrounding gas density. This optically thin region is typically $\lesssim 0.3$ pMpc in radius (allowing transmission of flux $\gtrsim -250$ km s$^{-1}$), $\lesssim 20$% of the distance to the neutral region. In a proof-of-concept, we demonstrate the $z\approx6.6$ galaxy COLA1 -- with a blue Ly$\alpha$ peak -- likely resides in an ionised region $>0.7$ pMpc, with residual neutral fraction $<10^{-5.5}$. To ionise its own proximity zone we infer COLA1 has a high ionising photon escape fraction ($f_{\mathrm{esc}}>0.50$), relatively steep UV slope ($\beta < -1.79$), and low line-of-sight gas density ($\sim0.5\times$ the cosmic mean), suggesting it is a rare, underdense line-of-sight.