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Astronomical Data Analysis Software and Systems IV
ASP Conference Series, Vol. 77, 1995
R. A. Shaw, H. E. Payne, and J. J. E. Hayes, eds.
Spatial Structure of NGC 6822: An Example for
Statistical Modeling of Astronomical Data
L. P'asztor
MTA TAKI, H­1022 Budapest, Herman Ott'o ' ut 15, Hungary
C. Gallart, A. Aparicio, J. M. V'ilchez
IAC, V'ia L'actea a/n 38200 La Laguna, Tenerife, Spain
Abstract. The spatial distribution of stars in the Local Group dwarf
irregular galaxy NGC 6822 has been studied, using recent positions and
deep photometry for about 15,000 stars in the galaxy. Based on photo­
metrical data, OB stars and red stars could be studied separately. Spatial
statistical tools have been applied to the analysis of the spatial structure.
The primary aim of the analysis was to find associations among OB stars
of the sample in statistical way; that is to quantify the grouping tendency
visible in the images of the dwarf galaxy with the aid of merely statistical
models. In the present paper the technical aspects of the analysis are
discussed.
1. Introduction
The Local Group dwarf irregular galaxy NGC 6822 is characterized by small
dimensions and structural simplicity; its distance is about 500 kpc. The surface
distribution of stars in the direction of NGC 6822 (total: 22,958 objects) came
from recent position and deep photometric observations (Gallart et al. 1994 and
references therein). After removing the foreground contamination (estimated by
the aid of a representative comparison field located near to the galaxy) 15,343
objects retained in the sample.
Blue stars [(B \Gamma V ) ! 0:5 and (V \Gamma R) ! 0:35; a total of 1,631 objects] and
red stars [(V \Gamma R) ? 0:65; a total of 8,998 objects] in the filtered sample were
separated in (B \Gamma V ) \Gamma (V \Gamma R) parameter space which was accompanied by a
separation also in 2D geometrical space (a similar effect was published for NGC
3109 by Bresolin et al. 1993).
Our approach to group identification has been based on merely statistical
tools, as opposed to recent works on similar efforts finding associations in nearby
galaxies, like Bresolin et al. (1993 or Wilson (1991, 1992). The main character­
istic of the present method is the subsequent refinement of point process models
fitted to the sample.
1

2
Figure 1. Identification of significant scales by NNS.
2. Model Fitting, Step 1
Rejection of CSR, (complete spatial randomness; for details on the following
spatial statistical models see P'asztor and T'oth 1995) was based on the results
of the NNS (nearest­neighbors statistic). Principles of NNS can be summa­
rized as follows. Consider every pair of objects whose separation is less than a
predefined limit: The number of pairs whose distance is between h \Gamma dh=2 and
h + dh=2 versus their separation is a well defined function, and widely used in
point pattern analysis. This function is the derivative of another important point
process function, the K function which is related to second­order properties of
point processes (for details see Cressie 1991). For HPP (homogeneous Poisson
point process), the function is linear: upward deviation indicates aggregation,
while a deviation downward is due to some regularity in the point pattern. The
significance of deviation from CSR results from comparisons to 100 Monte Carlo
simulations of HPP , so the significance of deviation from CSR is p ! 0:01 for
every scale.
3. Model Fitting, Step 2
Refinement of the model was carried out by taking into consideration the ap­
parent large­scale structure present in the sample. The newer 100 Monte Carlo
simulations were generated as realizations of IPP (inhomogeneous Poisson point
process) with fixed (and identical with that of the real sample) marginal distri­
butions (P'asztor et al. 1993). Result of NNS (Figure.1) shows significant
(p ! 0:01) clustering at around the scales of 25, 40, 65, and 90 pc, and addi­
tionally vacancies at scales smaller than 5 pc. This latter is a resukt of an SIP
(simple inhibition point process), and is probably due to the limit in resolution
of the observations.

3
Figure 2. Model selection by the aid of CAIC.
4. Model Fitting, Step 3
All of the objects which dominant the significant clustering at a given scale are
thought to be members of groups with a characteristic size comparable with the
scale value. However the number, shape, and location of these groups is a priori
unknown. A sequence of non­hierarchical clustering models was carried out,
providing partitions of the sample as well as results of PCP (Poisson cluster
process) models. In choosing an optimum and minimal model over the set of
these competing models, an information theoretic criterion, the CAIC (a more
strictly inforced version of Akaike's Information Criterion) (Eisenbl¨atter and
Bozdogan 1988), was used (Figure 2).
5. Results
A final partition of the blue stars into groups (associations) on the level charac­
terized by characteristics scale of 25, 40, 65, and 90 pc can be seen on Figure 3.
Circles with radii of the scale values should not be interpreted as anything but
models of fuzzy sets with radii varying around these values. Th centers scattered
around the centers of the resultant circles, and shapes are approximate.
Acknowledgments. L. P'asztor was partially supported by the Hungarian
State Research Found (Grant No. OTKA­F 4239). L. P'asztor is grateful to the
Organizers of the conference and the Hungarian State Research Found for the
travel grants.

4
Figure 3. Clustering of OB stars on scales of 25, 40, 65 and 90 pc.
References
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Cressie, N. A. C. 1991, Statistics for Spatial Data (New York, Wiley)
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of Data Analysis, ed. H. H. Bock (Amsterdam, North­Holland), p. 91
Gallart, C., Aparacio, A., Chiosi, C., Bertelli, G., & V'ilchez, J. M. 1994, ApJ,
425, L9
P'asztor, L., T'oth, L. V., & Bal'azs, L. G. 1993, A&A, 268, 108
P'asztor, L., T'oth, L. V. 1995, this volume, p. ??
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