The distribution of maximum relative gravitational torques in disk galaxies

The maximum value of the ratio of the tangential force to the mean background radial force is a useful quantitative measure of the strength of nonaxisymmetric perturbations in disk galaxies. Here we consider the distribution of this ratio, called Q(g), for a statistically well-defined sample of 180 spiral galaxies from the Ohio State University Bright Galaxy Survey and the Two Micron All Sky Survey. The ratio Q(g) can be interpreted as the maximum gravitational torque per unit mass per unit square of the circular speed and is derived from gravitational potentials inferred from near-infrared images under the assumptions of a constant mass-to-light ratio and an exponential vertical density law. In order to derive the most reliable maximum relative torques, orientation parameters based on blue-light isophotes are used to deproject the galaxies, and the more spherical shapes of bulges are taken into account using two-dimensional decompositions that allow for analytical fits to bulges, disks, and bars. Also, vertical scale heights h(z) are derived by scaling the radial scale lengths h(R) from the two-dimensional decompositions, allowing for the type dependence of h(R)/h(z) indicated by optical and near-infrared studies of edge-on spiral galaxies. The impact of dark matter is assessed using a universal rotation curve'' parameterization and is found to be relatively insignificant for our sample. In agreement with a previous study by Block et al., the distribution of maximum relative gravitational torques is asymmetric toward large values and shows a deficiency of low-Q(g) galaxies. However, because of the above refinements, our distribution shows more low-Q(g) galaxies than that of Block et al. We also find a significant type dependence in maximum relative gravitational torques, in the sense that Q(g) is lower on average in early-type spirals than in late-type spirals. The effect persists even when the sample is separated into bar-dominated and spiral-dominated subsamples and also when near-infrared types are used, as opposed to optical types.