We report the detection of extended Lyman-alpha (Lya) haloes around 145 individual star-forming galaxies at redshifts 3<z<6 in the Hubble Ultra Deep Field observed with the Multi-Unit Spectroscopic Explorer at ESO-VLT. Our sample consists of continuum-faint (-15> M_{UV}> -22) Lya emitters (LAEs). Using a 2D, two-component decomposition of Lya emission assuming circular exponential distributions, we measure scale lengths and luminosities of Lya haloes. We find that 80% of our objects having reliable Lya halo measurements show Lya emission that is significantly more extended than the UV continuum detected by HST (by a factor ~4 to >20). The median exponential scale length of the Lya haloes in our sample is ~4.5 kpc. By comparing the maximal detected extent of the Lya emission with the predicted dark matter halo virial radii of simulated galaxies, we show that the detected Lya emission of our selected sample of LAEs probes a significant portion of the cold circum-galactic medium (CGM) of these galaxies (>50% in average). This result shows that there must be significant HI reservoirs in the CGM and reinforces the idea that Lya haloes are ubiquitous around high-redshift Lya emitting galaxies. Our characterization of the Lya haloes indicates that the majority of the Lya flux comes from the halo (~65%) and that their scale lengths seem to be linked to the UV properties of the galaxies. We do not observe a significant Lya halo size evolution with redshift. We also find that the Lya lines cover a large range of full width at half maximum (FWHM) from 118 to 512 km/s. While the FWHM does not seem to be correlated to the Lya scale length, most compact Lya haloes and those that are not detected with high significance tend to have narrower Lya profiles. Finally, we investigate the origin of the extended Lya emission but we conclude that our data do not allow us to disentangle the possible processes.
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