STATISTICAL DETERMINATION OF THE PROFILES OF HICKSONS COMPACT-GROUPS

We present a method to determine the density profiles of galaxy groups , based on the study of the average autocorrelation function of galaxy members. Only information on the relative distances of galaxy members is needed in this method. This circumvents the delicate problem of de termining the centre of the group. By means of Monte-Carlo simulations , we show that this method is capable of recovering the mean profile o f such systems, even in the case of poor statistics (low numbers of gr oups and of galaxies per group). We have applied this method to a samp le of 42 compact groups from Hickson's catalog. The comparison of the data to Monte-Carlo simulations shows that it is not necessary to resc ale the sizes of the groups in order to apply the method, which would be a source of uncertainty. We show that the distributions of intergal actic separations in Hickson's compact groups are compatible with a un ique modified Hubble profile, for which the best fit yields a slope be ta = 1.4 and a core radius r(c) = 18h(-1) kpc. We present the regions of the (r(c),beta) plane where we are not forced to reject the null hy pothesis at different confidence levels. Hickson's groups are very com pact structures. A lensing analysis shows that three Hickson compact g roups are good candidates for strong lensing, if their optical velocit y dispersions are not spurriously large due to interlopers.