3. The neighborhood of the Polar Ring Galaxies
In the first approach the extension of the search area for each field has been established to be 5 times the diameter of the central object, according to the previous studies on the environment of peculiar galaxies (Theys & Spiegel 1976 , Few & Madore 1986 ). Such a portion of sky should be large enough to include objects able to perturb, or to have recently perturbed, the PR host galaxy. In our sample, the fields have extensions of 20 20 , including much more than five times the maximum galaxy diameter. The research area based on diameters is advantageous because it allows to use the whole objects sample and to refer the separation of the objects from the central galaxy to a distance independent scale.
The normal galaxies fields, used as a control sample, were selected
using the following criteria:
3.1. Data production
The study of the environments of these fields was based on the counts of the objects present and on the statistical analysis of their properties, such as the projected distance r from the PR and the apparent diameter D. The positions and diameters within a fixed isophote were then extracted from the APM Sky Catalogue, available on-line from the Observatory of Edinburgh. A total of 29 fields, mainly in the northern sky, were obtained. The data concerning two fields selected as good examples of polar ring galaxies, ESO603-G21 and ESO503-G17, were not available. All the remaining PR fields were analyzed from our PDS scans using the FOCAS (Faint Object Classification and Analysis System) procedures operating in the IRAF software package.
APM archive (Irwing et al. 1994 ) furnishes data extracted from both R and B plates of Palomar Sky Survey. It lists all the objects present in the plates over the brightness level of 24 mag/arcsec2 for the blue plates and 23 mag/arcsec2 for the red plates. Their corresponding B and R limiting magnitudes have been respectively estimated to be 21.5 and 20.0. The measured parameters are: the and coordinates, at 1950.0 equinox, the B and R apparent magnitudes, the semi-major axis, the ellipticity and P.A. of the ellipse fitting the image. An object is defined as non-stellar or stellar by comparing it with the Point Spread Function of an 'average' stellar image. The objects with very small FWHM are considered as local noise. We note that in the APM catalogue, the very large galaxies are sometimes fragmented into many small 'extended' objects because of the identification software used. In order to avoid this overpopulation of false faint objects, we had to exclude these fields. They are the regions of NGC 660, NGC 3384 and NGC 3718. This reduced our APM sample to 24 fields.
A different approach was needed with scans analyzed using FOCAS. The Point Spread Function (PSF) had to be measured for each field, using several isolated and relatively bright stars. After that, a set of rules was defined to classify the different kinds of object in a similar way as the APM. After many attempts, we established that the objects whose FWHM was between 0.6 and 1.2 times the PSF can be considered stars; those ones between 1.21 and 10 times the PSF were classified galaxies; while detections with smaller and larger FWHM were considered small- and large- scale noise respectively. Here also, three galaxies were too large for being recognized by the software as single objects, and were fragmented into several spurious identifications. They are NGC 2865, NGC 4672 and IC 3370. The corresponding fields were all discarded and the sample reduced to 24 fields. We used the radial moments xx, yy and xy, furnished by FOCAS, to calculate the diameters D in arcsec, through the formula
We also computed the radial distance r of each galaxy from the central galaxy (PR or NG).
The final set of data includes a total of 48 PRFs (24 from APM and 24 from PDS+FOCAS). Including the control sample, the total number of examined fields is 96.
3.2. Magnitude calibration for PR galaxies
In the PRC, a lot of PRs lack B magnitude. In the automatic surveys catalogues, such as APM or similar ones, the peculiar cross-shaped structure of the PR often induces a false classification as "star", generating unbelievably high magnitude values (from 8 to 10, in some cases). On the contrary, the magnitudes extracted using the FOCAS package on many galaxies of our sample were more accurate.
To produce new magnitude data from the scanned images, we first fixed the zero-point level to an arbitrary sky value and then we compared the so obtained magnitudes with those of PR galaxies whose total magnitudes were already known. This comparison indicated a zero-point shift of 0.71 magnitudes. When this correction was applied to the data, the difference with the total magnitudes of the catalogues such as RC3 (de Vaucouleurs et al. 1991 ) or LEDA 2 became lower than half a magnitude (Figure 1). The new determined magnitudes for PRs lacking this value in the literature are listed in Table 1.
3.3. Statistical tests
where (i,j) could assume the values 0, 1, (2,2) and (3,2.4). From the above formula, represents the number of neighboring galaxies, is the number weighted by the relative size, is weighted by proximity and is weighted by size and proximity. The parameter is a dimensionless one proportional to the gravitational force exerted by the surrounding galaxies on the central object, while is proportional to the tidal interaction between the surrounding galaxies and the central one. The last two parameters were introduced by Fuentes-Williams & Stocke (1988). They amplify the effects present in the parameter .
The diameters and the distances from the center of the fields were both converted in units of the central galaxy diameter and the resulting set of parameters is listed in Table 2. As said in the previous sections, only the diffuse objects lying at 5 diameters from the center were selected, discarding those ones outside this limit. To remove the contribution of the background galaxies, all the objects with diameters smaller than 1/5 of the polar ring size were excluded. Considering the real size of the galaxies with known redshift, this cut-off limit only excludes surrounding objects with size 2-4 kpc.
For those polar rings whose distance is known, and for the corresponding control sample, a set of similar parameters has been built on a scale unit of 100 kpc and the maximum limit of the search area has been fixed at 100 kpc from the center of the fields. The unit and the limit assumed are similar to those used for the previous investigations (Heckman et al. 1985) and define a research area which is, in most cases, similar to that of the used fields (20 ). The sample reduces to 31 objects, and the conclusions drawn are useful if compared to those deduced from the analysis based on the diameters. The resulting parameters are not listed here because they bring to similar results as those of the extended sample.
Finally, after defining the parameters for the two samples of PRs and normal galaxies scaled on diameters, a Kolgomorov-Smirnov test has been applied by means of a Fortran program that utilizes the IMSL library routine. The same tests have been performed for the restricted sample of PRs for which the distance is known. The cumulative curves are shown in Fig. 2 where the fields of PR galaxies are compared with the control fields of normal galaxies. The results are summarized in Table 3 that will be discussed in the Sect. 5.
Table 3. Summary of Kolgomorov-Smirnov tests. D is the maximum difference observed between the two distributions, while SL is the percentage significance level at which the two distributions compared are different. The negative values of D indicates a lower value of the parameter in the first sample with respect to the second one.
© European Southern Observatory (ESO) 1997
Online publication: April 8, 1998