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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 themore »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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We developed convolutional neural networks (CNNs) to rapidly and directly infer the planet mass from radio dust continuum images. Substructures induced by young planets in protoplanetary discs can be used to infer the potential young planets’ properties. Hydrodynamical simulations have been used to study the relationships between the planet’s properties and these disc features. However, these attempts either fine-tuned numerical simulations to fit one protoplanetary disc at a time, which was time consuming, or azimuthally averaged simulation results to derive some linear relationships between the gap width/depth and the planet mass, which lost information on asymmetric features in discs. To cope with these disadvantages, we developed Planet Gap neural Networks (PGNets) to infer the planet mass from two-dimensional images. We first fit the gridded data in Zhang et al. as a classification problem. Then, we quadrupled the data set by running additional simulations with near-randomly sampled parameters, and derived the planet mass and disc viscosity together as a regression problem. The classification approach can reach an accuracy of 92 per cent, whereas the regression approach can reach 1σ as 0.16 dex for planet mass and 0.23 dex for disc viscosity. We can reproduce the degeneracy scaling α ∝ $M_\mathrm{ p}^3$ found in the linearmore »fitting method, which means that the CNN method can even be used to find degeneracy relationship. The gradient-weighted class activation mapping effectively confirms that PGNets use proper disc features to constrain the planet mass. We provide programs for PGNets and the traditional fitting method from Zhang et al., and discuss each method’s advantages and disadvantages.

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Abstract Rings and gaps are ubiquitous in protoplanetary disks. Larger dust grains will concentrate in gaseous rings more compactly due to stronger aerodynamic drag. However, the effects of dust concentration on the ring’s thermal structure have not been explored. Using MCRT simulations, we self-consistently construct ring models by iterating the ring’s thermal structure, hydrostatic equilibrium, and dust concentration. We set up rings with two dust populations having different settling and radial concentration due to their different sizes. We find two mechanisms that can lead to temperature dips around the ring. When the disk is optically thick, the temperature drops outside the ring, which is the shadowing effect found in previous studies adopting a single-dust population in the disk. When the disk is optically thin, a second mechanism due to excess cooling of big grains is found. Big grains cool more efficiently, which leads to a moderate temperature dip within the ring where big dust resides. This dip is close to the center of the ring. Such a temperature dip within the ring can lead to particle pileup outside the ring and feedback to the dust distribution and thermal structure. We couple the MCRT calculations with a 1D dust evolution modelmore »and show that the ring evolves to a different shape and may even separate to several rings. Overall, dust concentration within rings has moderate effects on the disk’s thermal structure, and a self-consistent model is crucial not only for protoplanetary disk observations but also for planetesimal and planet formation studies.« less

ABSTRACT The streaming instability is a fundamental process that can drive dust–gas dynamics and ultimately planetesimal formation in protoplanetary discs. As a linear instability, it has been shown that its growth with a distribution of dust sizes can be classified into two distinct regimes, fast- and slow-growth, depending on the dust-size distribution and the total dust-to-gas density ratio ϵ. Using numerical simulations of an unstratified disc, we bring three cases in different regimes into non-linear saturation. We find that the saturation states of the two fast-growth cases are similar to its single-species counterparts. The one with maximum dimensionless stopping time τs,max = 0.1 and ϵ = 2 drives turbulent vertical dust–gas vortices, while the other with τs,max = 2 and ϵ = 0.2 leads to radial traffic jams and filamentary structures of dust particles. The dust density distribution for the former is flat in low densities, while the one for the latter has a low-end cut-off. By contrast, the one slow-growth case results in a virtually quiescent state. Moreover, we find that in the fast-growth regime, significant dust segregation by size occurs, with large particles moving towards dense regions while small particles remain in the diffuse regions, and the meanmore »radial drift of each dust species is appreciably altered from the (initial) drag-force equilibrium. The former effect may skew the spectral index derived from multiwavelength observations and change the initial size distribution of a pebble cloud for planetesimal formation. The latter along with turbulent diffusion may influence the radial transport and mixing of solid materials in young protoplanetary discs.« less

ABSTRACT The core accretion model of giant planet formation has been challenged by the discovery of recycling flows between the planetary envelope and the disc that can slow or stall envelope accretion. We carry out 3D radiation hydrodynamic simulations with an updated opacity compilation to model the proto-Jupiter’s envelope. To isolate the 3D effects of convection and recycling, we simulate both isolated spherical envelopes and envelopes embedded in discs. The envelopes are heated at given rates to achieve steady states, enabling comparisons with 1D models. We vary envelope properties to obtain both radiative and convective solutions. Using a passive scalar, we observe significant mass recycling on the orbital time-scale. For a radiative envelope, recycling can only penetrate from the disc surface until ∼0.1–0.2 planetary Hill radii, while for a convective envelope, the convective motion can ‘dredge up’ the deeper part of the envelope so that the entire convective envelope is recycled efficiently. This recycling, however, has only limited effects on the envelopes’ thermal structure. The radiative envelope embedded in the disc has identical structure as the isolated envelope. The convective envelope has a slightly higher density when it is embedded in the disc. We introduce a modified 1D approach whichmore »can fully reproduce our 3D simulations. With our updated opacity and 1D model, we recompute Jupiter’s envelope accretion with a 10 M⊕ core, and the time-scale to runaway accretion is shorter than the disc lifetime as in prior studies. Finally, we discuss the implications of the efficient recycling on the observed chemical abundances of the planetary atmosphere (especially for super-Earths and mini-Neptunes).« less

ABSTRACT Recent ALMA molecular line observations have revealed 3D gas velocity structure in protoplanetary discs, shedding light on mechanisms of disc accretion and structure formation. (1) By carrying out viscous simulations, we confirm that the disc’s velocity structure differs dramatically using vertical stress profiles from different accretion mechanisms. Thus, kinematic observations tracing flows at different disc heights can potentially distinguish different accretion mechanisms. On the other hand, the disc surface density evolution is mostly determined by the vertically integrated stress. The sharp disc outer edge constrained by recent kinematic observations can be caused by a radially varying α in the disc. (2) We also study kinematic signatures of a young planet by carrying out 3D planet–disc simulations. The relationship between the planet mass and the ‘kink’ velocity is derived, showing a linear relationship with little dependence on disc viscosity, but some dependence on disc height when the planet is massive (e.g. 10MJ). We predict the ‘kink’ velocities for the potential planets in DSHARP discs. At the gap edge, the azimuthally averaged velocities at different disc heights deviate from the Keplerian velocity at similar amplitudes, and its relationship with the planet mass is consistent with that in 2D simulations. After removingmore »the planet, the azimuthally averaged velocity barely changes within the viscous time-scale, and thus the azimuthally averaged velocity structure at the gap edge is due to the gap itself and not directly caused to the planet. Combining both axisymmetric kinematic observations and the residual ‘kink’ velocity is needed to probe young planets in protoplanetary discs.« less

ABSTRACT A recent study suggests that the streaming instability, one of the leading mechanisms for driving the formation of planetesimals, may not be as efficient as previously thought. Under some disc conditions, the growth time-scale of the instability can be longer than the disc lifetime when multiple dust species are considered. To further explore this finding, we use both linear analysis and direct numerical simulations with gas fluid and dust particles to mutually validate and study the unstable modes of the instability in more detail. We extend the previously studied parameter space by one order of magnitude in both the range of the dust-size distribution [Ts, min, Ts, max] and the total solid-to-gas mass ratio ε and introduce a third dimension with the slope q of the size distribution. We find that the fast-growth regime and the slow-growth regime are distinctly separated in the ε–Ts, max space, while this boundary is not appreciably sensitive to q or Ts, min. With a wide range of dust sizes present in the disc (e.g. Ts, min ≲ 10−3), the growth rate in the slow-growth regime decreases as more dust species are considered. With a narrow range of dust sizes (e.g. Ts, max/Ts, minmore »= 5), on the other hand, the growth rate in most of the ε–Ts, max space is converged with increasing dust species, but the fast and the slow growth regimes remain clearly separated. Moreover, it is not necessary that the largest dust species dominate the growth of the unstable modes, and the smaller dust species can affect the growth rate in a complicated way. In any case, we find that the fast-growth regime is bounded by ε ≳ 1 or Ts, max ≳ 1, which may represent the favourable conditions for planetesimal formation.« less

ABSTRACT We have carried out 2D hydrodynamical simulations to study the effects of disc self-gravity and radiative cooling on the formation of gaps and spirals. (1) With disc self-gravity included, we find stronger, more tightly wound spirals and deeper gaps in more massive discs. The deeper gaps are due to the larger Angular Momentum Flux (AMF) of the waves excited in more massive discs, as expected from the linear theory. The position of the secondary gap does not change, provided that the disc is not extremely massive (Q ≳ 2). (2) With radiative cooling included, the excited spirals become monotonically more open (less tightly wound) as the disc’s cooling time-scale increases. On the other hand, the amplitude and strength of the spirals decrease when the cooling time increases from a small value to ∼1/Ω, but then the amplitude starts to increase again when the cooling time continues to increase. This indicates that radiative dissipation becomes important for waves with Tcool ∼ 1. Consequently, the induced primary gap is narrower and the secondary gap becomes significantly shallower when the cooling time becomes ∼1/Ω. When the secondary gap is present, the position of it moves to the inner disc from the fastmore »cooling cases to the slow cooling cases. The dependence of gap properties on the cooling time-scale (e.g. in AS 209) provides a new way to constrain the disc optical depth and thus disc surface density.« less