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Astron. Astrophys. 352, 129-137 (1999)

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1. Introduction

It has been known for many decades that the distribution of the stellar velocities in the solar neighbourhood is far from isotropic. A longstanding problem in stellar dynamics (or in recent times more appropriately called galactic dynamics) has been the question of the shape and orientation of the velocity ellipsoid (i.e. the three-dimensional distribution of velocities) of stars in disks of spiral galaxies. The local ellipsoid has generated debate and research for at least a century. There still is no consensus on the question of the orientation of the longest axis of the velocity ellipsoid (the "tilt" away from parallel to the plane) at small and moderate distances from the symmetry plane of the Galaxy (but see Cuddeford & Amendt 1991a,b), which is of vital importance for attempts to estimate the local surface density of the Galactic plane from vertical dynamics of stars. The radial versus tangential dispersion ratio is reasonably well understood as a result of the local sheer, which through the Oort constants governs the shape of the epicyclic stellar orbits (but see Cuddeford & Binney 1994 and Kuijken & Tremaine 1994 for higher order effects as a result of deviations from circular symmetry).

There are two general classes of models for the origin of the velocity dispersions of stars in galactic disks. The first, going back to Spitzer & Schwarzschild (1951), is scattering by irregularities in the gravitational field, later identified with the effects of Giant Molecular Clouds (GMCs). The second class of models can be traced back to the work of Barbanis & Woltjer (1967), who suggested transient spiral waves as the scattering agent; this model has been extended by Carlberg & Sellwood (1985). Recently, the possiblity of infall of satellite galaxies has been recognized as a third option (e.g. Velázquez & White, 1999).

In the solar neighbourhood the ratio of the radial and vertical velocity dispersion of the stars [FORMULA] is usually taken as roughly 0.5 to 0.6 (Wielen 1977; see also Gomez et al. 1990), although values on the order of 0.7 are also found in the literature (Woolley et al. 1977; Meusinger et al. 1991). The value of this ratio can be used to test predictions for the secular evolution in disks and perhaps distinguish between the general classes of models. Lacey (1984) and Villumsen (1985) have concluded that the Spitzer-Schwarzschild mechanism is not in agreement with observations: the predicted time dependence of the velocity dispersion of a group of stars as a function of age disagrees with the observed age - velocity dispersion relation (see also Wielen 1977), while it would not be possible for the axis ratio of the velocity ellipsoid [FORMULA] to be less than about 0.7 (but see Ida et al. 1993)

Jenkins & Binney (1990) argued that it is likely that the dynamical evolution in the directions in the plane and that perpendicular to it could have proceeded with both mechanisms contributing, but in different manners. Scattering by GMCs would then be responsible for the vertical velocity dispersion, while scattering from spiral irregularities would produce the velocity dispersions in the plane. The latter would be the prime source of the secular evolution with the scattering by molecular clouds being a mechanism by which some of the energy in random motions in the plane is converted into vertical random motions, hence determining the thickness of galactic disks. The effects of a possible slow, but significant accretion of gas onto the disks over their lifetime has been studied by Jenkins (1992), who pointed out strong effects on the time dependence of the vertical velocity dispersions, in particular giving rise to enhanced velocities for the old stars.

The only other galaxy in which a direct measurement of the velocity ellipsoid has been reported, is NGC488 (Gerssen et al. 1997). NGC488 is a moderately inclined galaxy, which enables these authors to solve for the dispersions from a comparison of measurements along the major and minor axes. NGC488 is a giant Sb galaxy with a photometric scale length of about 6 kpc (in the B -band) and an amplitude of the rotation curve of about 330 km s-1. The axis ratio [FORMULA] is 0.70 [FORMULA] 0.19; this value, which is probably larger than that for the Galaxy, suggests that the spiral irregularities mechanism should be relatively less important, in agreement with the optical morphology.

The light distribution in galactic disks has in the radial direction an exponential behaviour (Freeman 1970), characterised by a scale length h. In the vertical direction -at least away from the central layer of young stars and dust that is obvious in edge-on galaxies- it turns out that the light distribution can also be characterised by an exponential scale height [FORMULA], which is independent of galactocentric distance (van der Kruit & Searle 1981, but see de Grijs & Peletier 1997). It then is usually assumed that the three-dimensional light distribution traces the distribution of mass; this seems justifiable since the light measured is that of the old disk population, which contains most of the stellar disk mass and dominates the light away from the plane. On general grounds, these two typical length scales are expected to be independent, the radial one resulting from the distribution of angular momentum in the protogalaxy (e.g. van der Kruit 1987; Dalcanton et al. 1997) or that resulting from the merging of pre-galactic units in the galaxy's early stages, while the length scale in the z-direction would result from the subsequent, and much slower, disk heating and the consequent thickening of the disk. It is not a priori clear, therefore, that the two scale lengths should correlate. Yet, they do bear a relation to the ratio of the velocity dispersions of the stars in the old disk population. The vertical one follows directly from hydrostatic equilibrium. In the radial direction it is somewhat indirect; a relation between the radial scale length and the corresponding velocity dispersion comes about through conditions of local stability (e.g. Bottema 1993).

In a recent study, de Grijs (1997, 1998; see also de Grijs & van der Kruit 1996) has determined the two scale parameters in a statistically complete sample of edge-on galaxies and found the ratio of the two (h/[FORMULA]) to increase with later morphological type. In this paper we will examine this dataset in detail in order to investigate whether it can be used to derive information on the axis ratios of the velocity ellipsoid and help make progress in resolving the general issues described above.

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© European Southern Observatory (ESO) 1999

Online publication: November 23, 1999
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