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.
