Astron. Astrophys. 358, 57-64 (2000)
6. Results
In Figs. 2 and 3 the results have been presented so as to make
evident the dependence on different parameters. It is obvious that the
star density distribution in real galaxies is not a universal
quantity. It will depend on the nature of the galaxy itself and on its
age, as theoretical evolutive models also show (see e.g. Murphy et al.
1991). Therefore, to compare our results to those derived by Paltani
& Courvoisier 1997 we have reported in Fig. 4 the luminosity and
variability values corresponding to a variety of different pairs of
k and , namely all those
present in Figs. 2 and 3 plus a series of pairs
(k, ) corresponding to density
configurations having a collision rate
. A straight line with the same
slope as that Paltani & Courvoisier 1997 derived as approximative
trend of as a function of
has been also reported in Fig. 4.
This straight line has been arbitrarily shifted since, as described in
the introduction, it is the trend which is important in this
comparison. On the other hand a detailed comparison between our
results and those by Paltani & Courvoisier 1997 would imply the
non-evident task of relating the luminosity and the light curve
observed at a specific wave length with the spectral integrated
luminosity and light curve derived here.
![[FIGURE]](img187.gif) |
Fig. 4. Variability as a function of for , and: a) all the pairs ( ) shown in Figs. 2 and 3 [dots]; b) a series of pairs ( ) corresponding to density configurations with [asterisks]. The straight line has the same slope of that shown in Fig. 1 of Paltani & Courvoisier 1997
|
The straight line with slope -0.08 is compatible with the points
drawn in Fig. 4. It is however important to understand how much this
result depends on the parameter choice. In this figure different pairs
( ) have been reported for a
restricted choice of the collision rate value
( ) and we know from Sect. 5 that the
results are not influenced by other free parameters of the model.
Hence the only possibility is that the allowed range in
, or equivalently that in
, causes the compatibility between
the points of Fig. 4 and the straight line with slope -0.08 derived by
Paltani & Courvoisier 1997.
To test if the compatibility is real, we have added to the pairs
previously computed the results obtained for the case of sixteen
different configurations having the same collision rate
. For these sixteen additional
cases, marked in Fig. 4 by asterisks, the Spearman's correlation
coefficient is equal to -0.63. The probability to get such a high
correlation coefficient for 16 pairs of quantities belonging to two
uncorrelated groups is less than 0.011. We conclude that the
correlation is most probably real. This correlation proves that the
compatibility of all points drawn in Fig. 4 with the line of slope
-0.08 does not depend on the choice of
values, since such a compatibility
still exists for a single value.
© European Southern Observatory (ESO) 2000
Online publication: June 26, 2000
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