We present the median surface brightness profiles of diffuse Ly α haloes (LAHs) around star-forming galaxies by stacking 155 spectroscopically confirmed Ly α emitters (LAEs) at 3 < z < 4 in the MUSE Extremely Deep Field (MXDF) with a median Ly α luminosity of L Ly α ≈ 10 41.1 erg s −1 . After correcting for a systematic surface brightness offset we identified in the data cube, we detect extended Ly α emission out to a distance of ≈270 kpc. The median Ly α surface-brightness profile shows a power-law decrease in the inner 20 kpc and a possible flattening trend at a greater distance. This shape is similar for LAEs with different Ly α luminosities, but the normalisation of the surface-brightness profile increases with luminosity. At distances over 50 kpc, we observe a strong overlap of adjacent LAHs, and the Ly α surface brightness is dominated by the LAHs of nearby LAEs. We find no clear evidence of redshift evolution of the observed Ly α profiles when comparing with samples at 4 < z < 5 and 5 < z < 6. Our results are consistent with a scenario in which the inner 20 kpc of the LAH is powered by star formation in the central galaxy, while the LAH beyond a radius of 50 kpc is dominated by photons from surrounding galaxies.
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