Abstract Recent observations have revealed a gallery of substructures in the dust component of nearby protoplanetary discs, including rings, gaps, spiral arms, and lopsided concentrations. One interpretation of these substructures is the existence of embedded planets. Not until recently, however, most of the modelling effort to interpret these observations ignored the dust back reaction to the gas. In this work, we conduct local-shearing-sheet simulations for an isothermal, inviscid, non-self-gravitating, razor-thin dusty disc with a planet on a fixed circular orbit. We systematically examine the parameter space spanned by planet mass (0.1Mth ≤ Mp ≤ 1Mth, where Mth is the thermal mass), dimensionless stopping time (10−3 ≤ τs ≤ 1), and solid abundance (0 < Z ≤ 1). We find that when the dust particles are tightly coupled to the gas (τs < 0.1), the spiral arms are less open and the gap driven by the planet becomes deeper with increasing Z, consistent with a reduced speed of sound in the approximation of a single dust-gas mixture. By contrast, when the dust particles are marginally coupled (0.1 ≲ τs ≲ 1), the spiral structure is insensitive to Z and the gap structure in the gas can become significantly skewed and unidentifiable. When the latter occurs, the pressure maximum radially outside of the planet is weakened or even extinguished, and hence dust filtration by a low-mass (Mp < Mth) planet could be reduced or eliminated. Finally, we find that the gap edges where the dust particles are accumulated as well as the lopsided large-scale vortices driven by a massive planet, if any, are unstable, and they are broken into numerous small-scale dust-gas vortices.
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A simple time-dependent method for calculating spirals: applications to eccentric planets in protoplanetary discs
Spirals in protoplanetary discs have been used to locate the potential planet in discs. Since only the spiral shape from a circularly orbiting perturber is known, most previous works assume that the planet is in a circular orbit. We develop a simple semi-analytical method to calculate the shape of the spirals launched by an eccentric planet. We assume that the planet emits wavelets during its orbit, and the wave fronts of these propagating wavelets form the spirals. The resulting spiral shape from this simple method agrees with numerical simulations exceptionally well. The spirals excited by an eccentric planet can detach from the planet, bifurcate, or even cross each other, which are all reproduced by this simple method. The spiral’s bifurcation point corresponds to the wavelet that is emitted when the planet’s radial speed reaches the disc’s sound speed. Multiple spirals can be excited by an eccentric planet (more than five spirals when e ≳ 0.2). The pitch angle and pattern speed are different between different spirals and can vary significantly across one spiral. The spiral wakes launched by high-mass eccentric planets steepen to spiral shocks and the crossing of spiral shocks leads to distorted or broken spirals. With the same mass, a more eccentric planet launches weaker spirals and induces a shallower gap over a long period of time. The observed unusually large/small pitch angles of some spirals, the irregular multiple spirals, and the different pattern speeds between different spirals may suggest the existence of eccentric perturbers in protoplanetary discs.
more » « less- Award ID(s):
- 1753168
- NSF-PAR ID:
- 10361436
- Publisher / Repository:
- Oxford University Press
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Volume:
- 510
- Issue:
- 3
- ISSN:
- 0035-8711
- Page Range / eLocation ID:
- p. 3986-3999
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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