We search for evidence of diffuse Ly \alpha emission from extended neutral hydrogen surrounding Ly \alpha emitting galaxies ( LAEs ) using deep narrow-band images of the Extended Chandra Deep Field South .
By stacking the profiles of 187 LAEs at z = 2.06 , 241 LAEs at z = 3.10 , and 179 LAEs at z = 3.12 , and carefully performing low-surface brightness photometry , we obtain mean surface brightness maps that reach 9.9 , 8.7 , and 6.2 \times 10 ^ { -19 } ergs cm ^ { -2 } s ^ { -1 } arcsec ^ { -2 } in the emission line .
We undertake a thorough investigation of systematic uncertainties in our surface brightness measurements , and find that our limits are 5–10 times larger than would be expected from Poisson background fluctuations ; these uncertainties are often underestimated in the literature .
At z \sim 3.1 , we find evidence for extended halos with small scale lengths of 5–8 kpc in some , but not all of our sub-samples .
We demonstrate that sub-samples of LAEs with low equivalent widths and brighter continuum magnitudes are more likely to possess such halos .
At z \sim 2.1 , we find no evidence of extended Ly \alpha emission down to our detection limits .
Through Monte-Carlo simulations , we also show that we would have detected large diffuse LAE halos if they were present in our data sets .
We compare these findings to other measurements in the literature , and discuss possible instrumental and astrophysical reasons for the discrepancies .