On the Connection between Spiral Arm Pitch Angle and Galaxy Properties

We measure the pitch angle (φ) of spiral arms in a sample of 79 galaxies to perform a systematic study of the dependence of φ on galaxy morphology, mass, and kinematics to investigate the physical origin of spiral arms. We find that φ 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 ({M}_* ^gal}). For a given concentration, galaxies with larger stellar masses tend to have tighter spiral arms, and vice versa. We also find that φ obeys a tight inverse correlation with central stellar velocity dispersion for σ _c ≳ 100 km s^-1, whereas φ remains approximately constant for σ _c ≲ 100 km s^-1. We demonstrate that the φ-σ _c and φ-{M}_* ^gal} relations are projections of a more fundamental three-dimensional \varphi {--}{σ }_c{--}{M}_* ^gal} relation, such that pitch angle is determined by σ _c for massive galaxies but by {M}_* ^gal} for less massive galaxies. Contrary to previous studies, we find that φ correlates only loosely with the galaxy’s shear rate. For a given shear rate, spirals generated from N-body simulations exhibit much higher φ 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.