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

Abstract

We use two-dimensional Fourier transformation to measure the pitch angle ($\phi$) 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 $|\phi |=-(7.8\pm 1.7)\log (M_D/M_{\odot })+(2.7\pm 2.6)$. 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 $\phi -M_D$ relation is still not clear. The pitch angle of spiral arms in protoplanetary disks provides an independent constraint on the disk mass.

arXiv comment11 pages, 5 figures. ApJ in press

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