Astron. Astrophys. 357, L1-L4 (2000)
4. Results
4.1. Distribution of cut-off radii
Understanding the phenomenon of cut-off radii in galactic disk
requires as an essential step a statistical study of galaxies covering
the Hubble sequence. Fig. 1 shows, already suggested by
Barteldrees & Dettmar (1989) for a smaller sample of 20 galaxies,
that the distance independent ratio of cut-off radius to radial
scalelength is significantly lower than derived from the often
referred sample of van der Kruit & Searle (1982a) with 7 galaxies.
They reported a mean value of
(ranging from 3.4 to 5.3), whereas our sample gives a ratio of
(1.4-4.4) even below their minimal
value. As obvious from Fig. 1 this difference is not caused by
the larger range of Hubble types covered by our sample. The estimated
error for this ratio due to the selection of the best fitting model
described in Paper II is and
has the same order as the quoted standard deviation. As shown in
Paper II for two different dust distributions with values
observed by Xilouris et al. (1999), the influence of the neglected
dust on our fitting process will be an overestimation of the
scalelength h, whereas is
independent. For the worst case, defined by the largest
measured values for ,
, and
, we find that this will chance our
values for by
. Applied to the mean we are in this
case still 0.8 below the value of van der Kruit & Searle (1982a).
We do not find a correlation between
and the Hubble type, although it should be mentioned that in general
for galaxies later than Scd the fitting process is strongly affected
by intrinsic variation, e.g. individual bright HII-regions, which
makes it impossible to fit our simple symmetric model. On the other
side some early type galaxies and particularly lenticulars do not show
any evidence for a cut-off at all. This is already suggested by van der Kruit (1988) observing some early type face-on galaxies and will
be discussed in detail in a forthcoming paper.
![[FIGURE]](img24.gif) |
Fig. 1. Ratio of cut-off radius to radial scalelength versus morphological type T. The 31 galaxies from our sample are marked by a cross, whereas the circles are the values for 7 galaxies from van der Kruit & Searle (1982a). The dashed line represents their and the solid line our mean value.
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Fig. 2 shows a possible correlation between
and the scalelength in absolute
units: Large disks with regard to their
scalelengthshare short in terms of their cut-off
radii. Together with the fact that the cut-off occurs, within the
errors of mag, at nearly the same
surface brightness level, this can be explained with a correlation
between the central surface brightness and the scalelength of the
galaxy, recently proposed by Scorza & van den Bosch (1998) for
galactic disks of different sizes.
![[FIGURE]](img27.gif) |
Fig. 2. Ratio of cut-off radius to radial scalelength versus scalelength in absolute units for the 30 galaxies with measured radial velocities.
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4.2. Comparison with literature
For the 30 galaxies with known radial velocities we find values for
the scalelength of 3.1 up to 19.7 kpc with a median of 6.6 kpc. Van
der Kruit (1987) determines for a diameter limited sample of 51
galaxies scalelengths in the range of
kpc with a maximum of the
distribution at about 3 kpc. De Jong (1996) derives for his sample of
86 face-on galaxies transformed to our
a range of 1.0-14.4 kpc with a
median around 3.0 kpc, whereas Courteau (1996) finds for 290 Sb-Sc
galaxies a range of kpc with a
maximum at 3.9 kpc; reduced to our .
In agreement with de Jong (1996) we do not find a correlation of the
scalelength with the Hubble type.
We find cut-off radii from kpc
with a median at 20.2 kpc, compared to the only available sample of
cut-off radii by van der Kruit & Searle (1982a) with
kpc for their 7 investigated
galaxies. Although we do not find a tight correlation between
catalogued surface brightness radii, e.g.
, and our cut-off radii, they can be
used to compare the sizes of the galaxies within our sample. Rubin et
al. (1980) study 21 Sc galaxies, where they claim radii, characterized
by the radius at the contour reduced
to our , of 81.3 kpc and 35.3 kpc for
the two biggest ones, and Romanishin (1983) finds values of 30-73 kpc
for 107 intrinsically large spiral galaxies.
We find a clear correlation between the determined cut-off radius
and the distance of the galaxy. This implies that we pick
intrinsically large galaxies at higher distances due to our selection
criterion which is based on the angular diameter matching the filed of
view.
4.3. Comparison with the Milky Way
It is of particular interest to compare our statistical result with
the structural parameters derived for the Milky Way. Robin et al.
(1992) as well as Ruphy et al. (1996) determine the radial structure
of the galactic disk with a synthetic stellar population model using
optical and NIR star-counts, respectively. They confirm a sharp
truncation of the old stellar disk at
kpc and
kpc, respectively. Freudenreich
(1998) fits a model for the old galactic disk to the NIR data obtained
from the survey of the DIRBE experiment also confirms an outer
truncation of the disk around kpc.
The result of both methods depend directly on the distance to the
galactic center ( kpc). These values
are in agreement with the findings of Heyer et al. (1998), who measure
a sharp decline in the CO mass surface density and conclude that the
molecular disk is effectively truncated at
kpc.
In contrast to former investigations (van der Kruit 1986, Lewis
& Freeman 1989, Nikolaev & Weinberg 1997) placing the Milky
Way scalelength around 4-5.5 kpc, Robin et al. (1992), Ruphy et al.
(1996), and Freudenreich (1998) quote significantly lower scalelengths
of kpc,
kpc, and
kpc, respectively. This leads to
values of ,
, and
for
. Whereas the first two values are
significantly higher than any value found in our sample (even the
highest value of van der Kruit & Searle is only 5.3) the latter
determination by Freudenreich is consistent with our highest value of
4.4 within the errors.
If the Milky Way is a `typical' galaxy with
the scalelength should be expected
to be kpc for
kpc.
4.4. Comparison with models
Only few theoretical models can be found in the literature
addressing a physical description for the origin of cut-off radii.
Taking into account a basic picture of galaxy formation, starting
with a rotating protocloud, Seiden et al. (1984) explain in their
framework of a stochastic, self-propagating star-formation theory
(SSPSF) several properties of galactic disks. The crucial point is,
that they assume a dependence
instead of an exponential law for the total surface density. In this
case they show that a feature similar to a cut-off radius
automatically appears in the radial profile, which is directly linked
with the scalelength. This is in contrast to Fig. 2, where
and h vary independently.
Van der Kruit & Searle (1981a) proposed that within a scenario
of slow disk formation (Larson 1976) this radius might be that radius
where disk formation time equals the present age of the galaxy. This
isolated slow evolution is in contradiction to recent models
preferring interaction and merging as a driver for galaxy evolution
(Barnes 1999).
Later van der Kruit (1987) proposed a working hypotheses which
already includes some of the currently accepted ingredients for galaxy
formation to explain the truncation as a result of the formation
process. Galactic disks develop from collapsing, rotating
proto-clouds. After the dark matter has settled into an isothermal
sphere first star-formation in the center builds up a bulge component
and the remaining material settles in gaseous form with dissipation in
a flat disk under conservation of specific angular momentum. This
leads to a constant value for of 4.5,
which is in contrast to our observations.
In a recent paper about galaxy formation and viscous evolution
Zhang & Wyse (2000) additionally consider a self-consistent
description of the disk-halo system by dropping the assumption of a
static halo and find that the disk cut-off radii indeed constrain the
specific angular momentum.
Kennicutt (1989) shows that for a sample of 15 face-on spiral
galaxies, analysing HI, CO and data,
star-formation stops below a critical threshold value, which is
associated with large scale gravitational instabilities. Taking into
account the dynamical critical gas density
for a thin, rotating, isothermal gas
disk proposed by Toomre (1964) he observes the abrupt decrease in
star-formation at a radius where the measured gas density drops below
. In the case of NGC 628 this radius
coincides with determined by Shostak
& van der Kruit (1984).
Although it is still unknown if the cut-off radius is an
evolutionary phenomenon or has its origin in the galaxy formation
process a star-formation threshold at the `optical edge' seems to be a
promising approach to address this problem (Elmegreen & Parravano
1994, and references therein; Ferguson et al. 1998). This will be done
in the future by enlarging the sample with a better defined selection
criterion which also includes the environment.
© European Southern Observatory (ESO) 2000
Online publication: May 3, 2000
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