Title:The AMIGA sample of isolated galaxies. V. Quantification of the isolation

Abstract: The AMIGA project aims to build a well defined and statistically significant reference sample of isolated galaxies in order to estimate the environmental effects on the formation and evolution of galaxies. The goal of this paper is to provide a measure of the environment of the isolated galaxies in the AMIGA sample, quantifying the influence of the candidate neighbours identified in our previous work and their potential effects on the evolution of the primary galaxies. Here we provide a quantification of the isolation degree of the galaxies in this sample. Our starting sample is the Catalogue of Isolated Galaxies (CIG). We used two parameters to estimate the influence exerted by the neighbour galaxies on the CIG galaxy: the local number density of neighbour galaxies and the tidal strength affecting the CIG galaxy. We show that both parameters together provide a comprehensive picture of the environment. For comparison, those parameters have also been derived for galaxies in denser environments such as triplets, groups and clusters. The CIG galaxies show a continuous spectrum of isolation, as quantified by the two parameters, from very isolated to interacting. The fraction of CIG galaxies whose properties are expected to be influenced by the environment is however low (159 out of 950 galaxies). The isolated parameters derived for the comparsion samples gave higher values than for the CIG and we found clear differences for the average values of the 4 samples considered, proving the sensitivity of these parameters. The environment of the galaxies in the CIG has been characterised, using two complementary parameters quantifying the isolation degree, the local number density of the neighbour galaxies and the tidal forces affecting the isolated galaxies. (Abridged)