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

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. We refer to such a bar-subtracted image as the ‘‘ spiral plus disk ’’ image. The axisymmetric background (Fourier index m = 0 image) can then be added back to the bar image to give the ‘‘ bar plus disk ’’ image. 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 that quantitatively define the bar strength Qb and the spiral strength Qs following the recent study of Buta & Block. For the first time, we are able to measure the torques generated by spiral arms alone, and we can now define spiral torque classes, in the same manner as bar torque classes are delineated. We outline the complete procedure here using a 2.1 lm image of NGC 6951, a prototypical SAB(rs)bc spiral having an absolute blue magnitude of 21 and a maximum rotation velocity of 230 km s 1. Comparison between a rotation curve predicted from the m = 0 near-infrared light distribution and an observed rotation curve suggests that NGC 6951 is maximum disk in its bar and main spiral region, implying that our assumption of a constant mass-to-light ratio in our analysis is probably reliable. 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 scale height, bar extrapolation, sky subtraction, orientation parameters, and the asymmetry in the spiral arms themselves, we estimateQb = 0.28 0.04 andQs = 0.21 0.06 for NGC 6951.