5. The clustering of faint blue galaxies around L* galaxies
It should be possible to test the hypothesis that the faint blue galaxies are in reality dwarfs associated with giant galaxies if a sample of candidate giants can be identified on the basis of their observed photometric properties. We can then test the clustering of the blue galaxies around them. Magnitude-limited samples tend to select galaxies having luminosities close to for galaxies with properties comparable with the local population (e.g. Schechter 1976). Even for their dwarf-rich model of galaxy populations, Driver et al. (1994a) have shown that magnitude-limited samples of galaxies are likely to be dominated by giants (with intrinsic luminosities close to of the Schechter luminosity function) for B ; only at fainter magnitudes do they predict that dwarfs become increasingly important. A more conservative field galaxy luminosity function, without a sharp turn-up in the numbers of dwarfs, would predict giant domination to even fainter magnitudes. That galaxies in the B to magnitude range are dominated by objects is confirmed from the results of redshifts surveys (e.g. Broadhurst et al. 1988). Expecting samples of galaxies brighter than (at least) B to be rich in giant galaxies, we select candidate galaxies on the basis of magnitude and colour.
A simple measure of the clustering of a sample of objects about a central point is the excess over random statistics of the objects within a particular distance of the centre (e.g. Yee & Green 1987; Longair & Seldner 1979; Aragón-Salamanca et al. 1993). Such a method is consistent with the use of the two-point angular correlation function (Phillipps & Shanks 1987a, b). Note that here we are not concerned about detecting an average excess over some overall random background; rather we are interested in the distribution of one specific set of galaxies about another specific set. We therefore do not need to consider the intricacies of data-data, data-random or random-random pairs (e.g. Landy & Szalay 1993), but simply calculate the numbers of faint blue galaxies in concentric annuli of constant thickness centred on the candidate objects and compare these with the corresponding results for randomly distributed points.
5.1. Selecting samples of galaxies
We choose to select a sample of candidate galaxies using a B magnitude range of 1.5 mag. extending to the B approximate limit of giant domination of the observed galaxy population. We further constrain the sample by imposing limits in The no-evolution model of galaxy colours used in Driver et al. (1994a) provides the mean as a function of B magnitude for Sa giants (cf. Coleman et al. 1980). We set a red limit for the candidate sample at redder than this locus to allow for photometric errors and to take some account of a distribution of galaxy properties, e.g. from E to Sc. If present, evolutionary effects would produce galaxies bluer than these colours. We define a locus in the - B plane accounting for evolution of the stellar populations by introducing the blueing effects of Bruzual's (1983) models of spiral bulges and elliptical galaxies on the Driver et al. Sa giant model. A blue limit bluer than this evolution model is used for the candidate selection. The resultant sample contained 17 photometrically-selected images. For an cosmological model, these galaxies are expected to lie at redshifts of to 0.4 (cf. Koo & Kron 1992). Throughout this paper a Hubble Constant of is used.
Star-galaxy classification was attempted in order to reject star images from the sample of candidate galaxies. Stars are likely to form a significant fraction of objects having the magnitudes of the candidate sample and the images are sufficiently bright that image classification can be attempted. Following Jones et al. (1991), we used plots of the image central intensity against R magnitude, and of the area above the detection isophotal threshold against R magnitude for each data frame. Stellar loci were identified for each plot. The images of interest were classified according to their displacement from the appropriate stellar locus. The images were labelled as being stars, galaxies or having uncertain classifications, the process being performed independently for the central intensity and image area graphs. An overall classification was achieved through a comparison of the results of the intensity and area methods, and by visual inspection to reject merged or confused images. An object was regarded as a suitable galaxy if it appeared visually to be a single image and if it had received a galaxy classification under the automated tests, either through two unambiguous galaxy classifications or one galaxy and one uncertain result. Of the 17 objects in the original sample, 13 passed the star/galaxy tests. These 13 images formed the sample of candidate galaxies for the present study.
The sample of faint blue galaxies was selected using an apparent magnitude range of B to these limits are fainter than the equivalent ones for the candidate objects. The adopted colour limits were to An additional criterion was imposed that the galaxies (of all four fields) lay within the predicted selection limit of the 1991 February 15 field (see Table 1); it is to be expected that photometric results outside this limit are unreliable due to the low signals involved. This limit is shown in the colour-magnitude diagram in Fig. 3.
No star/galaxy classification was attempted for the faint blue sample; at these faint magnitudes and blue colours the sample of images is dominated by galaxies, as is evident from a comparison of the star count predictions of Bahcall & Soneira (1980) with standard galaxy number counts. Indeed, at these faint magnitudes it becomes very difficult to distinguish galaxies from stars given the small image sizes compared with the seeing discs. To illustrate this point more fully, the numbers of stars expected in the faint blue galaxy samples in the four fields were computed by modelling star number counts. Using a program written and provided by Dr. G. Gilmore (briefly discussed in Gilmore 1984), star densities were computed across the (B-V) - V colour-magnitude diagram for each field by integrating the stellar populations along the sight. The three-component Gilmore-Reid-Wyse model of the Galaxy was adopted (Gilmore et al. 1989; Gilmore et al. 1990). Converting to the - B colour-magnitude diagram and integrating the predicted star densities over magnitude and colour provides estimates of the numbers of stars in the faint blue galaxy samples in each of the four fields. In all cases these are small, between 1 and 4 stars, as a result of the colour index limits of the sample being bluer than the majority of the main sequence stars of the (old) Galactic halo and thick disc. Due to incompleteness of the samples and to photometric errors, it is expected that the numbers of stars observed in the faint blue sample in each field will be smaller than the estimated numbers of stars present. We therefore choose to express the star contamination as a fraction of the total number of images present, taking the total numbers of images from the deep observations of Metcalfe et al. (1995) which are complete in all the regions of the - B colour-magnitude diagram of the photometrically selected samples used here. We predict a star contamination of the faint blue galaxy samples of between and in the four fields; these results are presented in full in Table 5. The presence of such small numbers of stars will not significantly affect conclusions about the clustering of the faint blue galaxies.
The faint blue galaxy sample contains 152 objects over all four fields. Because of the different K-corrections, the magnitude limits of the and blue galaxy samples are displaced typically by in absolute B magnitude. The luminosities of the faint blue galaxies, if at the same distances as the objects, would be in the range to typically Fig. 3 shows the sample regions in the colour-magnitude diagram. Although the adopted selection criteria should produce a well-defined sample of blue galaxies, incompleteness in the R band catalogue for the less deep fields may bias the samples against the most extreme blue galaxies, possibly reducing the sensitivity of the results to the most extreme colour changes induced by galaxy interactions.
5.2. The statistics of the separations between the blue and galaxies
The separations between each of the candidate and blue galaxies were computed for the four fields from their R band centroid coordinates. The R band observations tend to be deeper than the B band data on account of the greater efficiency of the Hitchhiker camera at red wavelengths than blue; the R band positional data were therefore used in preference to the B band. A total of 525 separations were obtained. Fig. 4 presents a histogram of the separations between the faint blue and candidate galaxies summed over all four data frames. The deviation of the observed separation distribution from an ideal linear relation is due to the finite area of the data frames. An assessment of any excess density of blue galaxies around objects demands that the histogram of separations for random distributions of galaxies is known.
Monte Carlo simulations were used to model randomly distributed faint blue galaxies across the four data frames. This approach enables the effect of the finite areas of the data frames to be accounted for in detail. In order to overcome the statistical errors associated with small samples, faint galaxies were distributed across each frame and the separations between these and the 13 observed galaxies were computed. The distributions of separations for each of the four frames were normalised and added according to the number of separations from the observational data for each frame. The resultant distribution may be compared directly with the equivalent observational results; both histograms are shown in Fig. 4.
To investigate whether there is an overdensity of faint blue galaxies in the vicinity of candidates, the number of separations between the two samples observed in the 10 to 60 arcsec range relative to the total number of separations were compared with the Monte Carlo simulations. The results are presented in Table 2. The observed results are clearly consistent with no observed overdensity of blue galaxies around candidates on scales smaller than 1 arcmin compared with the entire 0-5 arcmin range.
Table 2. Observational results for the association of faint blue galaxies with candidate galaxies
5.3. The detection of faint images in the vicinity of brighter galaxies
A potential problem which complicates the interpretation of the results of Table 2 is that of a failure to detect faint galaxy images in the close vicinity of brighter galaxies (cf. Turner et al. 1993). At small separations galaxy images might become merged at the limiting detection isophote and the pixels of the fainter image might be included with those of the brighter object during the compilation of the image catalogue. A selective loss of faint galaxy images at small separations could conceal the presence of a genuine excess of faint blue galaxies around the candidate objects.
The 13 galaxies of the sample have image areas above the detection threshold corresponding to mean radii in the range 2.8 to 5.3 arcsec. The images of the 152 blue galaxies have mean total radii typically in the range 0.7 to 1.7 arcsec. It is therefore to be expected that galaxy-galaxy separations of 10 arcsec and greater will not be significantly affected by the merging of images. At a typical redshift of an apparent angular separation of 10 arcsec corresponds to a transverse physical separation of 55 kpc (for and zero cosmological constant).
To test this in greater detail, simulations were performed of the detection of faint images in the vicinity of example candidate images. The May 1993 R band data frame was selected for the study, being the least deep of the available R band observations. The frame has 4 candidate galaxies from the sample of Sect. 5.1. They have magnitudes in the range to Faint blue galaxies were represented by circularly-symmetric gaussian light profiles having full-widths at half-maximum intensity equal to the measured seeing. The central intensities were selected to give a total magnitude of typical of the faint blue sample. The blue galaxies were added to the observed R band data frame, one at a time, and the image detection process of Sect. 4 applied to the frame. The image catalogue was inspected to determine whether the artificial blue galaxy had been detected as a distinct image, whether it was merged with the galaxy, or whether it was merged with another nearby galaxy. Faint blue galaxies were placed at distances of 5.0, 7.5, 10.0, 12.5 and 15.0 arcsec from the centroid of the candidate, at each of 8 positions for each separation. A total of 160 simulated images were used.
Table 3 presents the results of the simulations. While merging of the artificial faint galaxy with the candidate is a major problem for separations smaller than 10 arcsec, it does not significantly affect separations greater than 10 arcsec. The results of Table 2 for the interval 10 to 60 arcsec are therefore unaffected by image blending and our null result remains. Table 3 does show that merging of the blue galaxy with a third image does occur. It has been assumed that the distribution of this general background of galaxies with which some of the faint blue galaxy images merge is uniform across the frame, and therefore affects clustering statistics equally on all scales.
Table 3. Statistics for the detection of faint galaxy images in the vicinity of four candidate galaxies
Table 4. Selection criteria for samples of galaxies. The selection criteria for the samples of galaxies are summarised in the table. An additional constraint was imposed that the image lay within the expected selection limits of the 1995 February 15 data. In practice this affected the most extreme faint blue galaxies only
Table 5. Star contamination of the galaxy samples
© European Southern Observatory (ESO) 1997
Online publication: July 3, 1998