## 3. A brief description of the survey and the dataThe LCRS consists of 6 alternating slices each subtending in right-ascension and in declination, 3 each in the Northern and Southern Galactic Caps centered at and respectively. The survey extends to a redshift of corresponding to in the radial direction. The survey contains about 24000 galaxies distributed with a mean redshift of corresponding to . We next elaborate a little on the shape of the individual slices. Consider two cones both with the same axis and with their vertices at the same point. Let the angle between the first cone and the axis be and the second cone and the axis be so that the angle between the two cones is . Next truncate both the cones at a radial distance of from the vertex. Finally, a slice centered at a declination corresponds to a wedge of the region between these two cones. The effect of the extrinsic curvature of the cones is small for the three northern slices and we have restricted our analysis to only these three slices for which we have neglected the effect of the curvature. Each slice in the LCRS is made up of x fields some of which were observed with a 50 object fibre system and others with a 112 object fibre system. Of the three northern slices the one at is exclusively made up of 112 fibre fields while the slice at is mostly 50 fibre, and the slice at has got both 50 and 112 fibre fields. For each field, redshifts were determined for those galaxies which
satisfy the magnitude limits and the central brightness limits of the
survey. These limits are different for the 50 fibre and the 112 fibre
fields. In addition, for those fields where the number of galaxies
satisfying the criteria for inclusion in the survey exceeded the
number of fibres, the redshifts were determined for only a fraction of
the galaxies in the field. This effect is quantified by the "galaxy
sampling function" when analyzing the survey. The factor discussed above takes into account the effects of the field-to-field sampling fraction and the incompleteness as a function of the apparent magnitude and central surface brightness. In addition, the selection function has also to be taken into account, and this depends on both the differential luminosity function and the magnitude limits of the survey. The luminosity function of LCRS has been studied by Lin et al. (1996) who have determined the luminosity function for different sub-samples of LCRS. They find that the Schechter form with the parameters , and provides a good fit for the luminosity function in the absolute magnitude range . They have obtained these parameters from the analysis of the combined Northern and Southern 112 fibre fields and we shall refer to the Schechter luminosity function with these set of parameters as the NS112 luminosity function. The analysis of Lin et al. (1996) shows that this luminosity function can be used for the Northern 50 fibre fields in addition to the Northern and Southern 112 fibre fields, and we have used the NS112 luminosity function for most of our analysis. Lin et al. (1996) have also separately provided the luminosity function determined using just the Northern 112 fibre fields. This has the Schechter form with the parameters , and and we refer to this as the N112 luminosity function. We have used this in some of our analysis of the slice which contains only 112 fibre fields. The selection function quantifies
the fact that the fraction of the galaxies which are expected to be
included in the survey varies with the distance from the observer. For
a magnitude limited survey the apparent magnitude limits
and
can be converted to absolute
magnitude limits and
at some redshift The apparent magnitude limits are different for the 50 and 112 fibre fields and we have used the appropriate magnitude limits and the N50/ N112 luminosity functions to calculate the selection function at the redshift of each of the galaxies. This is then used to calculate a weight factor for each of the galaxies, and the contribution of the galaxy in the survey has to be weighed by Another effect that we have to correct for arises because of the fact that we would like to treat the distribution of galaxies in each slice as a two dimensional distribution. Each slice consists of galaxies that are contained within a thin conical shell of thickness and we construct a two dimensional distribution by collapsing the thickness of the slice. The thickness of each slice increases with the distance from the observer and in order to compensate for this effect we weigh each galaxy by the inverse of the thickness of the slice at its red-shift. Taking this effect into account the weight factor gets modified to which we use to weigh the contribution from the galaxy in the LCRS. We should also point out that through the process of flattening the conical slices and collapsing its thickness, the three dimensional galaxy distribution has been converted to a 2-dimensional distribution and the whole of our multi-fractal analysis is for a planar 2-dimensional point distribution. In our analysis we have considered various subsamples of LCRS all chosen from the 3 Northern slices. In addition to the apparent magnitude limits of the survey we have imposed further absolute magnitude and redshift cutoffs to construct both volume and apparent magnitude limited subsamples whose details are presented in Table 1.
© European Southern Observatory (ESO) 1999 Online publication: November 3, 1999 |