A Technique for Separating the Gravitational Torques of Bars and Spirals in Disk Galaxies

Abstract

We describe a Fourier-based method of separating bars from spirals in near-infrared images. The method takes advantage of the fact that a bar is typically a feature with a relatively fixed position angle, and uses the simple assumption that the relative Fourier amplitudes due to the bar decline with radius past a maximum in the same or a similar manner as they rose to that maximum. With such an assumption, the bar can be extrapolated into the spiral region and removed from an image, leaving just the spiral and the axisymmetric background disk light. The procedure allows us to estimate the maximum gravitational torque per unit mass per unit square of the circular speed for the bar and spiral forcing separately, parameters which quantitatively define the bar strength Q_b and the spiral strength Q_s following the recent study of Buta & Block. We outline the complete procedure here using a 2.1 micron image of NGC 6951, a prototypical SAB(rs)bc spiral. We justify our assumption on how to make the bar extrapolation using an analysis of NGC 4394, a barred spiral with only weak near-infrared spiral structure, and we justify the number of needed Fourier terms using NGC 1530, one of the most strongly-barred galaxies (bar class 7) known. We also evaluate the main uncertainties in the technique. Allowing for uncertainties in vertical scaleheight, bar extrapolation, sky subtraction, orientation parameters, and the asymmetry in the spiral arms themselves, we estimate Q_b=0.28\pm0.04 and Q_s=0.21\pm0.06 for NGC 6951. (abridged)