We statistically study the physical properties of a sample of narrow absorption line (NAL) systems looking for empirical evidences to distinguish between intrinsic and intervening NALs without taking into account any a priori definition or velocity cut-off. We analyze the spectra of 100 quasars with 3.5 < z$rm_{em}$ < 4.5, observed with X-shooter/VLT in the context of the XQ-100 Legacy Survey. We detect a $sim$ 8 $sigma$ excess in the number density of absorbers within 10,000 km/s of the quasar emission redshift with respect to the random occurrence of NALs. This excess does not show a dependence on the quasar bolometric luminosity and it is not due to the redshift evolution of NALs. It extends far beyond the standard 5000 km/s cut-off traditionally defined for associated absorption lines. We propose to modify this definition, extending the threshold to 10,000 km/s when also weak absorbers (equivalent width < 0.2 AA) are considered. We infer NV is the ion that better traces the effects of the quasar ionization field, offering the best statistical tool to identify intrinsic systems. Following this criterion we estimate that the fraction of quasars in our sample hosting an intrinsic NAL system is 33 percent. Lastly, we compare the properties of the material along the quasar line of sight, derived from our sample, with results based on close quasar pairs investigating the transverse direction. We find a deficiency of cool gas (traced by CII) along the line of sight associated with the quasar host galaxy, in contrast with what is observed in the transverse direction.
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