Direct Ly $alpha$ imaging of intergalactic gas at $zsim2$ has recently revealed giant cosmological structures around quasars, e.g. the Slug Nebula (Cantalupo et al. 2014). Despite their high luminosity, the detection rate of such systems in narrow-band and spectroscopic surveys is less than 10%, possibly encoding crucial information on the distribution of gas around quasars and the quasar emission properties. In this study, we use the MUSE integral-field instrument to perform a blind survey for giant Ly $alpha$ nebulae around 17 bright radio-quiet quasars at $3<z<4$ that does not suffer from most of the limitations of previous surveys. After data reduction and analysis performed with specifically developed tools, we found that each quasar is surrounded by giant Ly $alpha$ nebulae with projected sizes larger than 100 physical kpc and, in some cases, extending up to 320 kpc. The circularly averaged surface brightness profiles of the nebulae appear very similar to each other despite their different morphologies and are consistent with power laws with slopes $approx-1.8$. The similarity between the properties of all these nebulae and the Slug Nebula suggests a similar origin for all systems and that a large fraction of gas around bright quasars could be in a relatively cold (T$sim$10$^4$K) and dense phase. In addition, our results imply that such gas is ubiquitous within at least 50 kpc from bright quasars at $3<z<4$ independently of the quasar emission opening angle, or extending up to 200 kpc for quasar isotropic emission.
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