Global Spiral Density Wave Modes in Protoplanetary Disks: Morphology of Spiral Arms
Abstract
We analyze twoarmed global spiral density wave modes generated by gravitational instability in razorthin, nonviscous, selfgravitating protoplanetary disks to understand the dependence of spiral arm morphology (pitch angle α and amplitude) on various disk conditions. The morphologies of the resulting spiral density wave modes closely resemble observations. Their pitch angles and pattern speeds are insensitive to the boundary conditions adopted. Gaussian disks exhibit more tightly wound spirals (smaller pitch angle) than powerlaw disks under the same conditions. We find that at a fixed disktostar mass ratio (M_{d}/M_{*}), the pitch angle increases with average Toomre's stability parameter ( $\overline{Q}$ ) or average disk aspect ratio ( $\overline{h}$ ). For a given $\overline{Q}$ , density wave modes with higher M_{d}/M_{*} have larger pitch angles, while the behavior reverses for a given $\overline{h}$ . The interdependence between pitch angle and disk properties can be roughly approximated by $\alpha \propto {c}_{s}^{2}/{M}_{d}$ , where c_{s} is the sound speed. Our gravitational instabilityexcited spiral density waves can be distinguished from planetlaunched spirals: (1) massive cool disks have spiral pitch angle falling with radius, while lowmass hot disks have spiral pitch angle rising with radius; (2) the profile of spiral amplitude presents several dips and bumps. We propose that gravitational instabilityexcited density waves can serve as an alternative scenario to explain the observed spiral arms in selfgravitating protoplanetary disks.
 Publication:

The Astrophysical Journal
 Pub Date:
 January 2021
 DOI:
 10.3847/15384357/abc7c5
 arXiv:
 arXiv:2011.05324
 Bibcode:
 2021ApJ...906...19C
 Keywords:

 Protoplanetary disks;
 Spiral arms;
 Spiral pitch angle;
 Gravitational instability;
 Density wave model;
 1300;
 1559;
 1561;
 668;
 373;
 Astrophysics  Earth and Planetary Astrophysics;
 Astrophysics  Astrophysics of Galaxies
 EPrint:
 17 pages, 11 figures, accepted for publication in ApJ