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Abstract Protoplanetary disks can exhibit asymmetric temperature variations due to phenomena such as shadows cast by the inner disk or localized heating by young planets. We investigate the disk features induced by these asymmetric temperature variations. We find that spirals are initially excited, and then break into two and reconnect to form rings. By carrying out linear analyses, we first study the spiral launching mechanism and find that the effects of azimuthal temperature variations share similarities with effects of external potentials. Specifically, rotating temperature variations launch steady spiral structures at Lindblad resonances, which corotate with the temperature patterns. When the cooling time exceeds the orbital period, these spiral structures are significantly weakened, and a checkerboard pattern may appear. A temperature variation of about 10% can induce spirals with order unity density perturbations, comparable to those generated by a thermal mass planet. We then study ring formation and find it is related to the coupling between azimuthal temperature variations and spirals outside the resonances. Such coupling leads to a radially varying angular momentum flux, which produces anomalous wave-driven accretion and forms dense rings separated by the wavelength of the waves. Finally, we speculate that spirals induced by temperature variations may contribute to disk accretion through nonlinear wave steepening and dissipation. Overall, considering that irradiation determines the temperature structure of protoplanetary disks, the change of irradiation both spatially or/and temporarily may produce observable effects in protoplanetary disks, especially spirals and rings in outer disks beyond tens of au.
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A simple time-dependent method for calculating spirals: applications to eccentric planets in protoplanetary discs
ABSTRACT 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.
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- Award ID(s):
- 1753168
- 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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