On the Connection between Spiral Arm Pitch Angle and Galaxy Properties

We measure the pitch angle ( ) of spiral arms in a sample of 79 galaxies to perform a systematic study of the dependence of on galaxy morphology, mass, and kinematics to investigate the physical origin of spiral arms. We find that decreases (arms are more tightly wound), albeit with significant scatter, in galaxies with earlier Hubble type, more prominent bulges, higher concentration, and larger total galaxy stellar mass ( ). For a given concentration, galaxies with larger stellar masses tend to have tighter spiral arms, and vice versa. We also find that obeys a tight inverse correlation with central stellar velocity dispersion for c 100 km s−1, whereas remains approximately constant for c 100 km s−1. We demonstrate that the - c and - relations are projections of a more fundamental three-dimensional relation, such that pitch angle is determined by c for massive galaxies but by for less massive galaxies. Contrary to previous studies, we find that correlates only loosely with the galaxy's shear rate. For a given shear rate, spirals generated from N-body simulations exhibit much higher than observed, suggesting that galactic disks are dynamically cooler (Toomre's Q 1.2). Instead, the measured pitch angles show a much stronger relation with morphology of the rotation curve of the central region, such that galaxies with centrally peaked rotation curves have tight arms, while those with slow-rising rotation curves have looser arms. These behaviors are qualitatively consistent with predictions of density wave theory.