# On the Connection Between Spiral Arm Pitch Angle and Galaxy Properties

## TL;DR

This study systematically analyzes how spiral arm pitch angles relate to galaxy properties, revealing correlations with galaxy morphology, mass, and kinematics, and providing insights into the physical mechanisms behind spiral structure formation.

## Contribution

It introduces a comprehensive analysis of the dependence of spiral arm pitch angle on multiple galaxy properties, highlighting a fundamental three-dimensional relation and challenging previous assumptions about shear rate influence.

## Key findings

- Pitch angle decreases with earlier Hubble type and larger stellar mass.
- Strong inverse correlation between pitch angle and central stellar velocity dispersion.
- Galaxies with peaked rotation curves have tighter spiral arms.

## Abstract

We measure the pitch angle ($\varphi$) of spiral arms in a sample of 79 galaxies to perform a systematic study of the dependence of $\varphi$ on galaxy morphology, mass, and kinematics to investigate the physical origin of spiral arms. We find that $\varphi$ 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 ($M_*^{\rm gal}$). For a given concentration, galaxies with larger stellar masses tend to have tighter spiral arms, and vice versa. We also find that $\varphi$ obeys a tight inverse correlation with central stellar velocity dispersion for $\sigma_c$$\gtrsim$$100$ km s$^{-1}$, whereas $\varphi$ remains approximately constant for $\sigma_c\lesssim100$ km s$^{-1}$. We demonstrate that the $\varphi$-$\sigma_c$ and $\varphi$-$M_*^{\rm gal}$ relations are projections of a more fundamental three-dimensional $\varphi-\sigma_c-M_*^{\rm gal}$ relation, such that pitch angle is determined by $\sigma_c$ for massive galaxies but by $M_*^{\rm gal}$ for less massive galaxies. Contrary to previous studies, we find that $\varphi$ correlates only loosely with the galaxy's shear rate. For a given shear rate, spirals generated from $N$-body simulations exhibit much higher $\varphi$ than observed, suggesting that galactic disks are dynamically cooler (Toomre's $Q \approx 1.2$). 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.