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.
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.
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