Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Tight Relation between Spiral Arm Pitch Angle and Protoplanetary Disk
  Mass   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.

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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: chao-dyn
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The categories of this paper are: math
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The categories of this paper are: hep-ex
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The categories of this paper are: q-fin