The results presented in Table 7 show no statistically significant evidence of any preferential clustering of galaxies of one type about those of another for any of the pairs of samples investigated. In particular, there is no evidence of any association of the faint blue galaxies about candidate luminous galaxies.
The candidate -faint blue galaxy study found galaxy-galaxy separations in the 10 to 60 arcsec range, using 13 candidates. The predicted number for a random distribution of blue galaxies was This gives an excess number of separations of in this range, equivalent to an overdensity of blue galaxies per candidate.
galaxies having B to would lie at redshifts of to 0.36, adopting K-corrections appropriate to Sab galaxies (Driver et al. 1994), and zero cosmological constant. At a typical redshift of a 60 arcsec angular radius about the galaxy corresponds to a physical radius of 330 kpc (the expected limit for potential merging victims, as discussed in Sect. 2). Thus a sigma upper limit of 1.9 blue galaxies within this region corresponds to a projected mean excess density of 5.6 Mpc
It is informative to compare this limit with the predicted number of dwarf galaxies of all colours within the 330 kpc radius, having similar magnitudes to the blue galaxies, which would be given by the local galaxy population extrapolated to The B to apparent magnitude limits for the faint blue galaxy sample corresponds to to at for K-corrections typical of dwarf irregulars, or to if they are dwarf ellipticals. In either case, using the Efstathiou et al. (1988) local parameterisation of the Schechter luminosity function (with a faint end slope ), the number density of conventional (having the properties of the local population) dwarf galaxies of all colours passing the apparent magnitude selection test of the faint blue galaxies is predicted to be in the absence of evolution after applying a volume scaling. A steeper faint end of the galaxy luminosity function, with would increase this by a factor of as would a rescaling of the luminosity function to fit the galaxy counts at (see e.g. Metcalfe et al. 1995; Glazebrook et al. 1995c).
From Phillipps (1985a, b) and Phillipps & Shanks (1987a) we see that the expected projected excess number density of galaxies within an angular radius corresponding to a projected physical separation s from a galaxy is related to the amplitude of the correlation function by
where is the index of the spatial two-point correlation function is a constant ( for ), and is the integral of the galaxy luminosity function between the two absolute magnitude limits of the sample. Assuming a number density of faint blue galaxies equal to that of a conventional (local, no evolution, with only density scaling) galaxy population at the upper limit on the clustering amplitude is then for a standard flat luminosity function or for a slightly steeper one or one with a higher normalisation. If the faint blue galaxies actually have a higher space density (e.g. Phillipps & Driver 1995; Driver et al., 1995b), then their clustering amplitude drops correspondingly. In any of these cases there is certainly no evidence for strong clustering of the faint blue galaxies about primaries: the numbers observed are consistent with (or more likely less than) the numbers expected for galaxies with 'average' clustering ( Mpc; see e.g. Peebles 1980). The limit for the cross-correlation would be consistent with the low clustering amplitude seen for the faint blue galaxies themselves (see e.g. Efstathiou et al. 1991; Roukema & Peterson 1994). In particular, Brainerd et al. (1995) find that their data at () are consistent with Similar results are implied by the work of Couch, Jurcevic & Boyle (1993) and Roche et al. (1993). Brainerd et al. conclude that the clustering evolution that would be needed if the faint blue galaxies (or rather, their present day descendents) had the same correlation function as 'normal' giants is physically implausible, and prefer to identify them with a weakly clustered component (perhaps dwarf irregulars, see e.g., Thuan et al. 1991, Santiago & da Costa 1990). This is certainly consistent with our finding of very weak clustering of the faint blue population about giants, too (for redshifts around 0.2 to 0.4). Using HST data, Burkey et al. (1994) have found relatively few close companions around field galaxies at to Recently, Le Fèvre et al. (1996) have used redshift data to show that magnitude galaxies at redshifts exhibit weak spatial clustering, consistent with these results.
The study of the clustering between the other samples of galaxies reveals no evidence of correlations within the estimated errors. It should be noted that the contamination of the samples of faint galaxies by stars (estimated in Table 5) should not affect the results of Table 7. The presence of a random population of images in any galaxy sample will not affect the overdensity in excess of a random distribution found within 60 arcsec of other galaxy. The only effect of star contamination will be to increase the errors present in the overdensities; as the total number of images in the samples - including stars - have been used in the error calculations of Sect. 7 and Table 6, these results are unaffected.
Studies of the angular two-point correlation function of galaxies at faint magnitudes find an amplitude smaller than that for brighter magnitudes (e.g. Efstathiou et al. 1991; Neuschaefer et al. 1991; Roche et al. 1993). Adopting an amplitude of the correlation function of at an angular separation of for B to galaxies (see the review of Efstathiou 1995), and an angular dependence of predicts an excess of 1.7% faint galaxies about other faint galaxies in the to separation range. This compares with the observed under density of for the faint blue galaxies of the current study.
© European Southern Observatory (ESO) 1997
Online publication: July 3, 1998