skip to main content

Title: 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 more » 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.

« less
Award ID(s):
Publication Date:
Journal Name:
Monthly Notices of the Royal Astronomical Society
Page Range or eLocation-ID:
p. 3986-3999
Oxford University Press
Sponsoring Org:
National Science Foundation
More Like this
  1. 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.more »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.« less

    Despite many methods developed to find young massive planets in protoplanetary discs, it is challenging to directly detect low-mass planets that are embedded in discs. On the other hand, the core-accretion theory suggests that there could be a large population of embedded low-mass young planets at the Kelvin-Helmholtz (KH) contraction phase. We adopt both 1D models and 3D simulations to calculate the envelopes around low-mass cores (several to tens of M⊕) with different luminosities, and derive their thermal fluxes at radio wavelengths. We find that, when the background disc is optically thin at radio wavelengths, radio observations can see through the disc and probe the denser envelope within the planet’s Hill sphere. When the optically thin disc is observed with the resolution reaching one disc scale height, the radio thermal flux from the planetary envelope around a 10 M⊕ core is more than 10 per cent higher than the flux from the background disc. The emitting region can be extended and elongated. Finally, our model suggests that the au-scale clump at 52 au in the TW Hydrae disc revealed by ALMA is consistent with the envelope of an embedded 10–20 M⊕ planet, which can explain the detected flux, the spectral index dip,more »and the tentative spirals. The observation is also consistent with the planet undergoing pebble accretion. Future ALMA and ngVLA observations may directly reveal more such low-mass planets, enabling us to study core growth and even reconstruct the planet formation history using the embedded ‘protoplanet’ population.

    « less

    In recent years, a number of eccentric debris belts have been observed in extrasolar systems. The most common explanation for their shape is the presence of a nearby eccentric planetary companion. The gravitational perturbation from such a companion would induce periodic eccentricity variations on the planetesimals in the belt, with a range of precession frequencies. The overall expected shape is an eccentric belt with a finite minimum width. However, several observed eccentric debris discs have been found to exhibit a narrower width than the theoretical expectation. In this paper, we study two mechanisms that can produce this small width: (i) the protoplanetary disc can interact with the planet and/or the planetesimals, slowly driving the eccentricity of the former and damping the eccentricities of the latter; and (ii) the companion planet could have gained its eccentricity stochastically, through planet–planet scatterings. We show that under appropriate conditions, both of these scenarios offer a plausible way to reduce the minimum width of an eccentric belt exterior to a perturbing planet. However, the effects of protoplanetary discs are diminished at large separations (a > 10 au) due to the scarcity of gas and the limited disc lifetime. These findings suggest that one canmore »use the shape and width of debris discs to shed light on the evolution of extrasolar systems, constraining the protoplanetary disc properties and the prevalence of planet–planet scatterings. Further observations of debris-harbouring systems could confirm whether thin debris belts are a common occurrence, or the results of rare initial conditions or evolutionary processes.

    « less

    A test particle orbit around an eccentric binary has two stationary states in which there is no nodal precession: coplanar and polar. Nodal precession of a misaligned test particle orbit centres on one of these stationary states. A low-mass circumbinary disc undergoes the same precession and moves towards one of these states through dissipation within the disc. For a massive particle orbit, the stationary polar alignment occurs at an inclination less than 90°, which is the prograde-polar stationary inclination. A sufficiently high angular momentum particle has an additional higher inclination stationary state, the retrograde-polar stationary inclination. Misaligned particle orbits close to the retrograde-polar stationary inclination are not nested like the orbits close to the other stationary points. We investigate the evolution of a gas disc that begins close to the retrograde-polar stationary inclination. With hydrodynamical disc simulations, we find that the disc moves through the unnested crescent shape precession orbits and eventually moves towards the prograde-polar stationary inclination, thus increasing the parameter space over which circumbinary discs move towards polar alignment. If protoplanetary discs form with an isotropic orientation relative to the binary orbit, then polar discs may be more common than coplanar discs around eccentric binaries, even formore »massive discs. This has implications for the alignment of circumbinary planets.

    « less

    Many observations of protoplanetary discs studied with ALMA have revealed the complex substructure present in the discs. Rings and gaps in the dust continuum are now a common sight in many discs; however, their origins still remain unknown. We look at all protoplanetary disc images taken with ALMA from cycles 0 to 5 and find that 56 discs show clear substructure. We further study the 56 discs and classify the morphology seen according to four categories: Rim, Ring, Horseshoe, and Spiral. We calculate the ages of the host stars using stellar isochrones and investigate the relation between the morphology of the substructure seen in the protoplanetary discs and the age of the host stars. We find that there is no clear evolutionary sequence in the protoplanetary discs as the stars increase in age, although there is a slight tendency for spirals to appear in younger systems and horseshoes to be seen in more evolved systems. We also show that majority of the images of protoplanetary discs made by ALMA may not have had a sufficiently high resolution or sensitivity to resolve substructure in the disc. We show that angular resolution is important in detecting substructure within protoplanetary discs, withmore »sensitivity distinguishing between the different types of substructure. We compare the substructure seen in protoplanetary discs at sub-mm to those seen in scattered light. We find that cavities are a common substructure seen in discs at both sub-mm wavelengths and in scattered light.

    « less