# A Tight Relation between Spiral Arm Pitch Angle and Protoplanetary Disk Mass

## TL;DR

This study finds a strong correlation between spiral arm pitch angle and disk mass in protoplanetary disks, indicating that more massive disks tend to have tighter spiral arms, which can serve as an independent measure of disk mass.

## Contribution

It establishes a novel empirical relation between spiral arm pitch angle and disk mass in protoplanetary disks, using Fourier analysis of observational data.

## Key findings

- Smaller pitch angles are associated with higher disk masses.
- The relation holds across disks with and without known companions.
- Pitch angle can serve as an independent indicator of disk mass.

## Abstract

We use two-dimensional Fourier transformation to measure the pitch angle ($\varphi$) of the dominant spiral Fourier mode of well-defined spiral arms in 13 protoplanetary disks, making use of near-infrared scattered-light images of AB Aur, SAO 206462, MWC 758, V1247 Ori, HD 142527, DZ Cha, LkH$\alpha$ 330, and HD 100453, and ALMA millimeter continuum images of Elias 2-27, IM Lup, AS 205, and HT Lup. We find that the measured pitch angle correlates strongly with disk mass ($M_{D}$), such that more massive protoplanetary disks have smaller pitch angles, following $|\varphi| = -(7.8\pm1.7)\log(M_{D}/M_{\odot})+(2.7\pm2.6)$. Interestingly, four disks with a known companion (HD 142527, HD 100453, AS 205, and HT Lup) share the same trend. Such a strong dependence of spiral arm pitch angle on disk mass suggests that the disk mass, independent of the formation mechanism, plays a fundamental role in determining the arm tightness of the observed spiral structure. The physical origin of the $\varphi-M_D$ relation is still not clear. The pitch angle of spiral arms in protoplanetary disks provides an independent constraint on the disk mass.