The extended Ly α haloes (LAHs) have been found to be prevalent around high-redshift star-forming galaxies. However, the origin of the LAHs is still a subject of debate. The spatially resolved analysis of Ly α profiles provides an important diagnostic. We analyse the average spatial extent and spectral variation of the circumgalactic LAHs by stacking a sample of 155 Ly α emitters (LAEs) at redshifts of 3 < z < 4 in the MUSE Extremely Deep Field. Our analysis reveals that, with respect to the Ly α line of the…