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Astronomical Data Analysis Software and Systems VI

ASP Conference Series, Vol. 125, 1997

Editors: Gareth Hunt and H. E. Payne

**Irina B. Vavilova**

Astronomical Observatory of the Kiev University,
Observatornaya str., 3, Kiev 254053 Ukraine,
E-mail: vavilova@rcrm.freenet.kiev.ua

**Piotr Flin**

Pedagogical University, Institute of Physics,
ul.Lesna 16, Kielce 25-509 Poland,
E-mail: sfflin@cyf-kr.edu.pl

The region of the original Jagiellonian Field (JF) sky survey (Rudnicki, Dworak, & Flin 1973) was selected by Zwicky (Zwicky 1962) as a region which is enriched by clusters of galaxies and contains a small number of the brighter galaxies. The JF sky survey (photographic plates in three colors with coordinates of center , (2000.0) taken with the 1.25m Palomar Schmidt telescope) coincides with the CGCG field No. 185. The central part of the JF () was scanned and automatically processed by the COSMOS machine. This procedure allows one to digitize the images on the plate and to receive a set of parameters fitting the inertia ellipse to each image (e.g., Stobie 1980; MacGillivray & Stobie 1984).

Constructing a modern complete galaxy catalogue in the JF region, we decided to carry out an automated procedure of star/galaxy separation on the digitized images. We experimented with the possible combinations of parameters usually applied for such purposes on similar photographic data (e.g., Hewett 1981; Heydon-Dumbleton, Collins, & MacGillivray 1989; Odewahn et al. 1992; Weir, Fayyad, & Djorgovski 1995 with a brief review of discrimination philosophy).

Before applying the procedure, all small objects with
the * COSMOS area* parameter smaller than 60 (in increments)
were removed from our sample and about 35,000 objects remained to
be analyzed.

Among the possible discriminators only three
gave a clear separation of the loci of stars and galaxies. There
were plots presenting the dependence on the * logarithm of
image area* denoted as , the * width of Gaussian
fit* (S) and the * intensity weighted second moment* ()
versus * COSMOS image magnitude* parameter * COSMAG*:
,
where and are the
intensity of **i**-pixel of the image and the intensity of the sky at the
image centroid respectively.

For bright and intermediate magnitudes we used
the * log(area) vs. COSMAG* discriminator. Due
to lower surface brightness for this range of magnitudes,
the galaxies lie above the stellar sequence on this plane.

For the intermediate magnitudes we applied the * intensity
weighted second moment* discriminator giving an
estimate of the filling of
the image by an ellipse fitted to its semiaxes:
, where and are the
intensity weighted semi-major and semi-minor
axes of the inertia ellipse respectively.
The more centrally concentrated images (stars) have the
smallest values of this parameter and occupy a tight locus
under the galaxy sequence.

For the fainter and intermediate objects we used
the * width of a best Gaussian fit* (S) to the
threshold intensity and maximum image intensity:
,
where are the threshold
and maximum image intensity respectively. On this
diagram the Gaussian width for stars is determined by the
point spread function; galaxies lie above this sequence.

We checked all the brightest objects by visual inspection.

The principal point of the automated star/galaxy classification is: the statistical weight of stars exceeds that of galaxies for the whole range of considered magnitudes, and stars occupy the tighter sequence for each discriminator mentioned above. Therefore, for each magnitude in this range, it is possible to construct the histogram of distribution of the number of objects corresponding to the value of chosen discriminator. This histogram gives the main points for a spline to separate the star and galaxy sequences on the plot of discriminator. Notice that, for intermediate magnitudes, the loci of stars and galaxies are more separated, so we did a spline interactively.

So, the Revised Jagiellonian Field Catalogue (RJFC) is based on the digitized scans of the original JF photographic plates. The RJFC contains information on about 20,000 galaxies (Flin & Vavilova 1997, in preparation).

Modern astronomical data such as, e.g., DPS and digitized POSS II surveys, constitute an excellent base for finding large-scale structures. This structure search must be objective, which requires appropriate mathematical methods. The wavelet technique, being well-suited for approximation of data with sharp discontinuities, seems to be one such promising tool. For this reason we decided to verify the applicability of the wavelet analysis, having at our disposal data similar to DPS data, by carrying out the mapping of a small region of the sky.

Unlike Fourier analysis, the wavelet algorithms process
data at different scales (resolutions). In the case of
applying the wavelets for detachment of the structure of
galaxy cluster, the task is to convolve the two dimensional
galaxy distribution (* signal function*, ) on a grid of
N**×**N pixels by the * analyzing wavelet* , where
** a ** denotes the scale of the wavelet. This parameter determines
an effective radius of wavelet or, in other words, the extent of
spreading of the density distribution of galaxies in space of * wavelet
coefficients* (WC). So, such convolution leads to the ``spread''
galaxy distribution in terms of a wavelet, and
the further analysis of this distribution
can be performed using just the corresponding WC.
Adapting the best * analyzing function*
to data or cutting the WCs
below a threshold we sparsely represent our data.

From the whole RJFC we chose small regions containing Abell
clusters: A1226, A1228, and A1257, two of them never studied
before. For the galaxy distribution in these three regions the
* analyzing wavelet* known as the ``Mexican Hat'' was
adopted. Avoiding the edge effects where discontinuities
occur, we analyzed a region greater than the cluster
itself. The ``Mexican Hat'' function has a radial shape
permitting however the detection of non-circular structure:
,
where ** r ** is the distance between center
and point in which the ``Mexican Hat'' is calculated.
This approach has already been described and performed for
identification of structure of clusters of galaxies (e.g.,
Slezak, Bijaoui, & Mars 1990; Escalera et al. 1994).

Our procedure had several principal steps:

- (
**i**) - normalizing the galaxy distribution data in the working zone
of the wavelets through a linear transformation into the range
[
**-**1, 1], so the radius of the analyzed zone is ; - (
**ii**) - applying the ``Mexican Hat'' formula to the
normalized data;
- (
**iii**) - using a full set of scale wavelet
parameters: the analysis starts at the largest scale
, where the structure of the whole cluster is
detected, and ends at the smallest one, where only one galaxy
is located inside the region;
- (
**iv**) - performing a Monte-Carlo simulation using the same
number of galaxies, distributed in the same zone,
to verify the reality of detected structures and substructures;
- (
**v**) - picking up the galaxies inside the detected structure
of the cluster to study the properties of galaxy cluster.

The first results of mapping of the RJFC gave additional support for the correctness and efficiency of the wavelet analysis both for detachment of the structure of galaxy clusters itself and for the further investigation of their morphological properties (Flin & Vavilova 1995, 1996).

Notice that, in our case,
the existence of the structures had been known * a
priori* and the task here was to adapt the analyzing function.
The problem of finding the structure of the
galaxy cluster and the galaxy group (e.g., with low richness,
having different geometrical scales, and lying close to
each other in two- or three-dimensional space)
in a general distribution is not easy. For mapping the
general galaxy distribution in the whole RJFC, some other
families of wavelet systems and approaches should be applied.
It looks as if, in this case, it would be correct to use a hierarchical
algorithm, sometimes called a * pyramidal algorithm*
(e.g., Bijaoui 1996, private, communication), providing the multiscale vision of
a sky survey like the RJFC.

IBV thanks the ADASS VI Organizing Committee for the financial support enabling her to participate in so exciting and fruitful conference, as well as Pedagogical University in Kielce for hospitality during her stay there.

Escalera, E., Biviano, A., Girardi, M., Giuricin, G., Mardirossian, F., Mazure, A., & Mezzetti, M. 1994, ApJ, 423, 539

Flin, P., & Vavilova, I. B. 1995, SISSA Ref. 65/95/A, ed. G. Giuricin, F. Mardirossian, M. Mezzetti

Flin, P., & Vavilova, I. B. 1996, Astrophys. Letters & Communications, to be published

Hewett, P. 1981, report for internal distribution ROE

Heydon-Dumbleton, N. H., Collins, C. A., & MacGillivray, H. T. 1989, MNRAS, 238, 379

MacGillivray, H. T., Stobie, R. S. 1984, Vistas in Astron., 27, 4, 433

Odewahn, S. C., Stockwell, R. L., Pennington, R. M., Humphreys, R. M., & Zumach, W. A. 1992, AJ, 103, 318

Rudnicki, K., Dworak, T. Z., & Flin, P. 1973, Acta Cosmologica, 1, 7

Slezak, E., Bijaoui, A., & Mars, G. 1990, A&A, 227, 301

Stobie, R. S. 1980, JBIS, 33, 323

Weir, N., Fayyad, U., & Djorgovski, S. 1995, AJ, 109, 2401

Zwicky, F. 1962, in Problems of Extra-galactic Research, ed. G. C. McVittie (New York: Macmillan), 347

© Copyright 1997 Astronomical Society of the Pacific, 390 Ashton Avenue, San Francisco, California 94112, USA

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