Where is the fuzz? Undetected Lyman alpha nebulae around QSOs at z~2.3

We observed a small sample of 5 radio-quiet QSOs with integral field spectroscopy to search for possible extended emission in the Ly$\alpha$ line. We subtracted the QSO point sources using a simple PSF self-calibration technique that takes advantage of the simultaneous availability of spatial and spectral information. In 4 of the 5 objects we find no significant traces of extended Ly$\alpha$ emission beyond the contribution of the QSO nuclei itself, while in UM 247 there is evidence for a weak and spatially quite compact excess in the Ly$\alpha$ line at several kpc outside the nucleus. For all objects in our sample we estimated detection limits for extended, smoothly distributed Ly$\alpha$ emission by adding fake nebulosities into the datacubes and trying to recover them after PSF subtraction. Our observations are consistent with other studies showing that giant Ly$\alpha$ nebulae such as those found recently around some quasars are very rare. Ly$\alpha$ fuzz around typical radio-quiet QSOs is fainter, less extended and is therefore much harder to detect. The faintness of these structures is consistent with the idea that radio-quiet QSOs typically reside in dark matter haloes of modest masses.