It is well-known from optical observations that many disk galaxies show a universal, exponential behaviour of the vertical luminosity away from the galaxy planes. This observation, and the assumption that the mass-to-light ratio in the disk is constant, leads us to believe that galaxies have a universal, exponential vertical mass density profile (e.g., Tsikoudi 1979; van der Kruit & Searle 1981a).
This nearly universal vertical structure is likely the result of secular, internal evolution (van der Kruit & Searle 1981a; Carlberg 1987). As Carlberg (1987) states, the continuous variation of stellar kinematics from the youngest to the oldest disk stars strongly suggests that an ongoing dynamical evolution is indeed present.
We know from observations of our Galaxy that galaxy disks probably consist of multiple components of increasing age, velocity dispersion and scale height; the density is the sum of all these components. An exponentially decreasing density distribution with distance from the galaxy plane therefore puts interesting constraints on the star formation rate (SFR) and the dynamical evolution of the disk. Burkert & Yoshii (1996) have shown, that these exponential vertical density profiles are a natural result of disk evolution if gaseous protodisks settle into isothermal equilibrium prior to star formation. If the star formation and cooling rates are comparable, stellar exponential z -profiles arise due to the gravitational contraction of the gas towards the galaxy plane.
1.2. Observational status
Several models have been proposed and tested to account for the vertical distributions observed close to the galaxy planes.
Van der Kruit & Searle (1981a,b, 1982a,b) studied the surface brightness distributions of edge-on disk galaxies in optical passbands, which were significantly affected by dust contamination. From these studies, they proposed the self-gravitating isothermal sheet (Spitzer 1942) as a model for the description of the vertical light distribution:
where is the surface luminosity in the plane of the galaxy, is the vertical scale parameter and z is the distance from the galaxy plane, respectively. At large z heights, the vertical scale heights are equal for both the isothermal model and the exponential approximation, where equals twice the exponential scale height. At intermediate z, most galaxies are dominated by the thin disk luminosity, which is thought to be locally isothermal (van der Kruit & Searle 1981a).
The relations among the values for the density in the plane, , the vertical scale parameter, , and the vertical velocity dispersion for the solar neighbourhood show that the disk of our Galaxy is self-gravitating (van der Kruit & Searle 1981a). Based on the quite similar values for found by Van der Kruit & Searle (1981a) they argued that it may be reasonable to assume that the disks of other galaxies are also self-gravitating.
Near-infrared observations of edge-on disk galaxies have shown an excess of light over the isothermal model at small distances from the galaxy planes, where the optical photometry is strongly affected by dust absorption (e.g., Wainscoat et al. 1989; Aoki et al. 1991; van Dokkum et al.1994). Wainscoat et al. (1989) show that the z -dependence of the light in the large southern edge-on IC 2531 demonstrates a more strongly peaked profile than expected from the isothermal sheet model, which appears to be better fitted by an exponential:
(where is the exponential vertical scale height), although their limited resolution does not unambiguously differentiate between the models. For the vertical K -band light distribution in NGC 891, Aoki et al. (1991) find that the exponential model fits the data remarkably well up to those z -distances where the seeing convolution becomes significant.
1.3. An intermediate solution
Although the exponential model is mathematically attractive because of its simplicity, there is no firm physical basis for such a model. An exponential vertical mass density distribution can be constructed by adding up multiple stellar disk components. This can only be done if the contributions from stars with larger velocity dispersions are increasingly dominating with increasing distance from the galaxy plane. However, a mechanism to account for such a process is as yet unknown (Burkert & Yoshii 1996).
As van der Kruit (1988) argues, a pure exponential distribution also has some undesired properties, the most important one being a sharp minimum of the velocity dispersion in the plane. Fuchs & Wielen's (1987) results show moderate gradients, much smaller than required for the exponential distribution (Bahcall 1984a,b). Therefore, van der Kruit (1988) proposed that an intermediate distribution, such as the "sech(z)" distribution, could be a more appropriate one to use:
to account for the deviations from an isothermal sheet in the galaxy planes.
1.4. The Galaxy
Studies of the Galaxy provide valuable information on the vertical structure of galaxy disks. These studies, based on star counts, have the advantage over the studies of external galaxies that they are less affected by dust absorption (in the solar neighbourhood) and effects of the presence of a young stellar population. Moreover, studies of the vertical luminosity structure in our Galaxy benefit greatly from the higher spatial resolution compared to that in external galaxies. Gilmore & Reid (1983) and Pritchet (1983) conclude that the stellar z -distribution in our Galaxy is better approximated by an exponential rather than an isothermal profile.
On the other hand, Hill et al. (1979) derived density laws for A and F dwarfs towards the North Galactic Pole, which cannot be fit well by an exponential distribution, although they may be approximated as such in short distance bins. Although they find that the F stars are roughly consistent with a single exponential, the A stars can only be approximated by a single exponential closer to the Galactic Plane and with a significantly smaller scale height than the F dwarfs.
Based on observations in the near-infrared, Kent et al. (1991) concluded that the vertical light distribution (and hence probably also the mass distribution) follows an exponential law more closely than an isothermal sheet approximation. However, they did not compare the observed light distribution to other, intermediate models.
1.5. Near-Infrared Observations
The study of edge-on galaxies in the near-infrared is valuable to reveal the true stellar distributions, as the near-infrared wavelengths permit to study these even at small z.
In this paper we study the vertical luminosity profiles of a statistically complete sample of edge-on disk galaxies in the band. This sample is the largest of its kind available at the moment. For that reason we are able to study the structure of edge-on galaxies in a statistically consistent way, even down to very small distances from the galaxy planes.
The -band light (which is comparable to the standard Johnson K band) is likely to be dominated by the old disk, and the young disk contribution is relatively unimportant. Moreover, the mass-to-light ratio is almost independent of metallicity and age in this band. Rix & Rieke (1993) find, from monitoring the gravity-sensitive CO(2.3 m) index in the large disk galaxy M51, that young red supergiants do not distort the K -band image significantly. They find that at most small portions of the spiral arms at K have large contributions from young stars.
The K -band wavelength is too short for a substantial amount of direct emission from the dust. The high dust temperatures required to emit in K (800 - 1000 K) are associated only with young stellar objects and compact HII regions (see, e.g., Wainscoat et al. 1989).
The light in K is dominated by giants, which constitute only a small fraction of the stellar mass. However, old population giant stars have the same spatial distribution as the main-sequence stars (Rix & Rieke 1993).
Therefore, since neither dust nor young, luminous red stars strongly affect the K -band image, K -band imaging with infrared arrays is a reliable and efficient method to map surface mass variations through surface brightness variations (Rix & Rieke 1993)
In Sect. 2we present the sample properties and describe the data reduction method used. The results of our detailed analysis of the vertical profiles are presented in Sect. 3, in which we also compare the results obtained in the optical I band to those from the band observations. In Sect. 4we discuss the main observational results in the context of star formation and global galaxy structure parameters. Finally, we summarize and conclude the paper in Sect. 5.
© European Southern Observatory (ESO) 1997
Online publication: April 6, 1998