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Our sample consists of continuum-faint (\u2212 15 \u2265 <jats:italic>M<\/jats:italic><jats:sub>UV<\/jats:sub> \u2265 \u221222) Ly<jats:italic>\u03b1<\/jats:italic> emitters (LAEs). Using a 2D, two-component (continuum-like and halo) decomposition of Ly<jats:italic>\u03b1<\/jats:italic> emission assuming circular exponential distributions, we measure scale lengths and luminosities of Ly<jats:italic>\u03b1<\/jats:italic> haloes. We find that 80% of our objects having reliable Ly<jats:italic>\u03b1<\/jats:italic> halo measurements show Ly<jats:italic>\u03b1<\/jats:italic> emission that is significantly more extended than the UV continuum detected by HST (by a factor \u22484 to &gt;20). The median exponential scale length of the Ly<jats:italic>\u03b1<\/jats:italic> haloes in our sample is \u22484.5 kpc with a few haloes exceeding 10 kpc. By comparing the maximal detected extent of the Ly<jats:italic>\u03b1<\/jats:italic> emission with the predicted dark matter halo virial radii of simulated galaxies, we show that the detected Ly<jats:italic>\u03b1<\/jats:italic> emission of our selected sample of Ly<jats:italic>\u03b1<\/jats:italic> emitters probes a significant portion of the cold circum-galactic medium of these galaxies (&gt;50% in average). This result therefore shows that there must be significant HI reservoirs in the circum-galactic medium and reinforces the idea that Ly<jats:italic>\u03b1<\/jats:italic> haloes are ubiquitous around high-redshift Ly<jats:italic>\u03b1<\/jats:italic> emitting galaxies. Our characterization of the Ly<jats:italic>\u03b1<\/jats:italic> haloes indicates that the majority of the Ly<jats:italic>\u03b1<\/jats:italic> flux comes from the halo (\u224865%) and that their scale lengths seem to be linked to the UV properties of the galaxies (sizes and magnitudes). We do not observe a significant Ly<jats:italic>\u03b1<\/jats:italic> halo size evolution with redshift, although our sample for <jats:italic>z<\/jats:italic>&gt; 5 is very small. We also explore the diversity of the Ly<jats:italic>\u03b1<\/jats:italic> line profiles in our sample and we find that the Ly<jats:italic>\u03b1<\/jats:italic> lines cover a large range of full width at half maximum (FWHM) from 118 to 512 km\u2009s<jats:sup>-1<\/jats:sup>. While the FWHM does not seem to be correlated to the Ly<jats:italic>\u03b1<\/jats:italic> scale length, most compact Ly<jats:italic>\u03b1<\/jats:italic> haloes and those that are not detected with high significance tend to have narrower Ly<jats:italic>\u03b1<\/jats:italic> profiles (&lt;350 km\u2009s<jats:sup>-1<\/jats:sup>). Finally, we investigate the origin of the extended Ly<jats:italic>\u03b1<\/jats:italic> emission but we conclude that our data do not allow us to disentangle the possible processes, i.e. scattering from star-forming regions, fluorescence, cooling radiation from cold gas accretion, and emission from satellite galaxies. <\/jats:p>","DOI":"10.1051\/0004-6361\/201731480","type":"journal-article","created":{"date-parts":[[2017,10,25]],"date-time":"2017-10-25T20:57:21Z","timestamp":1508965041000},"page":"A8","source":"Crossref","is-referenced-by-count":222,"title":["The MUSE <i>Hubble <\/i>Ultra Deep Field Survey"],"prefix":"10.1051","volume":"608","author":[{"given":"Floriane","family":"Leclercq","sequence":"first","affiliation":[]},{"given":"Roland","family":"Bacon","sequence":"additional","affiliation":[]},{"given":"Lutz","family":"Wisotzki","sequence":"additional","affiliation":[]},{"given":"Peter","family":"Mitchell","sequence":"additional","affiliation":[]},{"given":"Thibault","family":"Garel","sequence":"additional","affiliation":[]},{"given":"Anne","family":"Verhamme","sequence":"additional","affiliation":[]},{"given":"J\u00e9r\u00e9my","family":"Blaizot","sequence":"additional","affiliation":[]},{"given":"Takuya","family":"Hashimoto","sequence":"additional","affiliation":[]},{"given":"Edmund Christian","family":"Herenz","sequence":"additional","affiliation":[]},{"given":"Simon","family":"Conseil","sequence":"additional","affiliation":[]},{"given":"Sebastiano","family":"Cantalupo","sequence":"additional","affiliation":[]},{"given":"Hanae","family":"Inami","sequence":"additional","affiliation":[]},{"given":"Thierry","family":"Contini","sequence":"additional","affiliation":[]},{"given":"Johan","family":"Richard","sequence":"additional","affiliation":[]},{"given":"Michael","family":"Maseda","sequence":"additional","affiliation":[]},{"given":"Joop","family":"Schaye","sequence":"additional","affiliation":[]},{"given":"Raffaella Anna","family":"Marino","sequence":"additional","affiliation":[]},{"given":"Mohammad","family":"Akhlaghi","sequence":"additional","affiliation":[]},{"given":"Jarle","family":"Brinchmann","sequence":"additional","affiliation":[]},{"given":"Marcella","family":"Carollo","sequence":"additional","affiliation":[]}],"member":"250","published-online":{"date-parts":[[2017,11,29]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1088\/0067-0049\/220\/1\/1","volume":"220","author":"Akhlaghi","year":"2015","journal-title":"ApJS"},{"key":"R2","doi-asserted-by":"crossref","first-page":"L9","DOI":"10.1086\/505652","volume":"645","author":"Ando","year":"2006","journal-title":"ApJ"},{"key":"R3","doi-asserted-by":"crossref","first-page":"773508","DOI":"10.1117\/12.856027","volume":"7735","author":"Bacon","year":"2010","journal-title":"Proc. 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