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Register a new userThe theory of kinks -- I. A semi-analytic model of velocity perturbations due to planet-disc interaction
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A new technique to detect protoplanets is by observing the kinematics of the surrounding gas. Gravitational perturbations from a planet produce peculiar `kinks in channel maps of different gas species. In this paper, we show that such kinks can be reproduced using semi-analytic models for the velocity perturbation induced by a planet. In doing so we i) confirm that the observed kinks are consistent with the planet-induced wake; ii) show how to quantify the planet mass from the kink amplitude; in particular, we show that the kink amplitude scales with the square root of the planet mass for channels far from the planet velocity, steepening to linear as the channels approach the planet; iii) show how to extend the theory to include the effect of damping, which may be needed in order to have localized kinks.
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During the process of planet formation, the planet-discs interactions might excite (or damp) the orbital eccentricity of the planet. In this paper, we present two long ($tsim 3times 10^5$ orbits) numerical simulations: (a) one (with a relatively light disc, $M_{rm d}/M_{rm p}=0.2$) where the eccentricity initially stalls before growing at later times and (b) one (with a more massive disc, $M_{rm d}/M_{rm p}=0.65$) with fast growth and a late decrease of the eccentricity. We recover the well-known result that a more massive disc promotes a faster initial growth of the planet eccentricity. However, at late times the planet eccentricity decreases in the massive disc case, but increases in the light disc case. Both simulations show periodic eccentricity oscillations superimposed on a growing/decreasing trend and a rapid transition between fast and slow pericentre precession. The peculiar and contrasting evolution of the eccentricity of both planet and disc in the two simulations can be understood by invoking a simple toy model where the disc is treated as a second point-like gravitating body, subject to secular planet-planet interaction and eccentricity pumping/damping provided by the disc. We show how the counterintuitive result that the more massive simulation produces a lower planet eccentricity at late times can be understood in terms of the different ratios of the disc-to-planet angular momentum in the two simulations. In our interpretation, at late times the planet eccentricity can increase more in low-mass discs rather than in high-mass discs, contrary to previous claims in the literature.
We study the probability distribution function (PDF) of relative velocity between two different dark matter halos (i.e. pairwise velocity) with a set of high-resolution cosmological $N$-body simulations. We investigate the pairwise velocity PDFs over a wide range of halo masses of $10^{12.5-15}, h^{-1}M_{odot}$ and redshifts of $0<z<1$. At a given set of masses, redshift and the separation length between two halos, our model requires three parameters to set the pairwise velocity PDF, whereas previous non-Gaussian models in the literature assume four or more free parameters. At the length scales of $r=5-40, [h^{-1}, mathrm{Mpc}]$, our model predicts the mean and dispersion of the pairwise velocity for dark matter halos with their masses of $10^{12.5-13.5} , [h^{-1}M_{odot}]$ at $0.3 < z < 1$ with a 5%-level precision, while the model precision reaches a 20% level (mostly a 10% level) for other masses and redshifts explored in the simulations. We demonstrate that our model of the pairwise velocity PDF provides an accurate mapping of the two-point clustering of massive-galaxy-sized halos at the scales of $O(10), h^{-1}mathrm{Mpc}$ between redshift and real space for a given real-space correlation function. For a mass-limited halo sample with their masses greater than $10^{13.5}, h^{-1}M_{odot}$ at $z=0.55$, our model can explain the monopole and quadropole moments of the redshift-space two-point correlations with a precision better than 5% at the scales of $5-40$ and $10-30, h^{-1}mathrm{Mpc}$, respectively. Our model of the pairwise velocity PDF will give a detailed explanation of statistics of massive galaxies at the intermediate scales in redshift surveys, including the non-linear redshift-space distortion effect in two-point correlation functions and the measurements of the kinematic Sunyaev-Zeldovich effect.
Protoplanets may be born into dust-rich environments if planetesimals formed through streaming or gravitational instabilities, or if the protoplanetary disc is undergoing mass loss due to disc winds or photoevaporation. Motivated by this possibility, we explore the interaction between low mass planets and dusty protoplanetary discs with focus on disc-planet torques. We implement Lin & Youdins newly developed, purely hydrodynamic model of dusty gas into the PLUTO code to simulate dusty protoplanetary discs with an embedded planet. We find that for imperfectly coupled dust and high metallicity, e.g. Stokes number $10^{-3}$ and dust-to-gas ratio $Sigma_mathrm{d}/Sigma_mathrm{g}=0.5$ , a `bubble develops inside the planets co-orbital region, which introduces unsteadiness in the flow. The resulting disc-planet torques sustain large amplitude oscillations that persists well beyond that in simulations with perfectly coupled dust or low dust-loading, where co-rotation torques are always damped. We show that the desaturation of the co-rotation torques by finite-sized particles is related to potential vorticity generation from the misalignment of dust and gas densities. We briefly discuss possible implications for the orbital evolution of protoplanets in dust-rich discs. We also demonstrate Lin & Youdins dust-free framework reproduces previous results pertaining to dusty protoplanetary discs, including dust-trapping by pressure bumps, dust settling, and the streaming instability.
We present a global MHD simulation of a turbulent accretion disc interacting with a protoplanet of 5 Jupiter masses. The disc model had H/r=0.1,and a value of the Shakura & Sunyaev alpha ~ 0.005. The protoplanet opened a gap in the disc, with the interaction leading to inward migration on the expected time scale. Spiral waves were launched by the protoplanet and although they were diffused and dissipated through interaction with the turbulence, they produced an outward angular momentum flow which compensated for a reduced flux associated with the turbulence, so maintaining the gap. When compared with laminar disc models with the same estimated alpha, the gap was found to be deeper and wider indicating that the turbulent disc behaved as if it possessed a smaller alpha. This may arise for two reasons. First, the turbulence does not provide a source of constantly acting friction in the near vicinity of the planet that leads to steady mass flow into the gap region. Instead the turbulence is characterised by large fluctuations in the radial velocity, and time averaging over significant time scales is required to recover the underlying mass flow through the disc. Near the planet the disc material experiences high amplitude perturbations on time scales that are short relative to the time scale required for averaging. The disc response is thus likely to be altered relative to a Navier--Stokes model. Second, the simulation indicates that an ordered magnetic connection between the inner and outer disc can occur enabling angular momentum to flow out across the gap, helping to maintain it independently of the protoplanets tide. This type of effect may assist gap formation for smaller mass protoplanets which otherwise would not be able to maintain them.
We perform numerical simulations of a disc-planet system using various grid-based and smoothed particle hydrodynamics (SPH) codes. The tests are run for a simple setup where Jupiter and Neptune mass planets on a circular orbit open a gap in a protoplanetary disc during a few hundred orbital periods. We compare the surface density contours, potential vorticity and smoothed radial profiles at several times. The disc mass and gravitational torque time evolution are analyzed with high temporal resolution. There is overall consistency between the codes. The density profiles agree within about 5% for the Eulerian simulations while the SPH results predict the correct shape of the gap although have less resolution in the low density regions and weaker planetary wakes. The disc masses after 200 orbital periods agree within 10%. The spread is larger in the tidal torques acting on the planet which agree within a factor 2 at the end of the simulation. In the Neptune case the dispersion in the torques is greater than for Jupiter, possibly owing to the contribution from the not completely cleared region close to the planet.
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