Vortex stretching in self-gravitating protoplanetary discs

Horseshoe-shaped brightness asymmetries of several transitional discs are thought to be caused by large-scale vortices. Anticyclonic vortices are efficiently collect dust particles, therefore they can play a major role in planet formation. Former studies suggest that the disc self-gravity weakens vortices formed at the edge of the gap opened by a massive planet in discs whose masses are in the range of 0.01<=M_disc/M_*<=0.1. Here we present an investigation on the long-term evolution of the large-scale vortices formed at the viscosity transition of the discs' dead zone outer edge by means of two-dimensional hydrodynamic simulations taking disc self-gravity into account. We perform a numerical study of low mass, 0.001<=M_disc/M_*<=0.01, discs, for which cases disc self-gravity was previously neglected. The large-scale vortices are found to be stretched due to disc self-gravity even for low-mass discs with M_disc/M_*>=0.005 where initially the Toomre Q-parameter was <=50 at the vortex distance. As a result of stretching, the vortex aspect ratio increases and a weaker azimuthal density contrast develops. The strength of the vortex stretching is proportional to the disc mass. The vortex stretching can be explained by a combined action of a non-vanishing gravitational torque caused by the vortex, and the Keplerian shear of the disc. Self-gravitating vortices are subject to significantly faster decay than non-self-gravitating ones. We found that vortices developed at sharp viscosity transitions of self-gravitating discs can be described by a GNG model as long as the disc viscosity is low, i.e. alpha_dz<=10^-5.Comment: 13 pages, 8 figures, appear in MNRA

Trapping of giant-planet cores - I. Vortex aided trapping at the outer dead zone edge

In this paper the migration of a 10 Earth-mass planetary core is investigated at the outer boundary of the dead zone of a protoplanetary disc by means of 2D hydrodynamic simulations done with the graphics processor unit version of the FARGO code. In the dead zone, the effective viscosity is greatly reduced due to the disc self-shielding against stellar UV radiation, X-rays from the stellar magnetosphere and interstellar cosmic rays. As a consequence, mass accumulation occurs near the outer dead zone edge, which is assumed to trap planetary cores enhancing the efficiency of the core-accretion scenario to form giant planets. Contrary to the perfect trapping of planetary cores in 1D models, our 2D numerical simulations show that the trapping effect is greatly dependent on the width of the region where viscosity reduction is taking place. Planet trapping happens exclusively if the viscosity reduction is sharp enough to allow the development of large-scale vortices due to the Rossby wave instability. The trapping is only temporarily, and its duration is inversely proportional to the width of the viscosity transition. However, if the Rossby wave instability is not excited, a ring-like axisymmetric density jump forms, which cannot trap the 10 Earth-mass planetary cores. We revealed that the stellar torque exerted on the planet plays an important role in the migration history as the barycentre of the system significantly shifts away from the star due to highly non-axisymmetric density distribution of the disc. Our results still support the idea of planet formation at density/pressure maximum, since the migration of cores is considerably slowed down enabling them further growth and runaway gas accretion in the vicinity of an overdense region.Comment: 23 pages, 31 figures, accepted for publication in MNRA

Asymmetric fundamental band CO lines as a sign of an embedded giant planet

We investigate the formation of double-peaked asymmetric line profiles of CO in the fundamental band spectra emitted by young (1-5Myr) protoplanetary disks hosted by a 0.5-2 Solar mass star. Distortions of the line profiles can be caused by the gravitational perturbation of an embedded giant planet with q=4.7 10^-3 stellar-to-planet mass ratio. Locally isothermal, 2D hydrodynamic simulations show that the disk becomes globally eccentric inside the planetary orbit with stationary ~0.2-0.25 average eccentricity after ~2000 orbital periods. For orbital distances 1-10 AU, the disk eccentricity is peaked inside the region where the fundamental band of CO is thermal excitated. Hence, these lines become a sensitive indicators of the embedded planet via their asymmetries (both in flux and wavelength). We find that the line shape distortions (e.g. distance, central dip, asymmetry and positions of peaks) of a given transition depend on the excitation energy (i.e. on the rotational quantum number J). The magnitude of line asymmetry is increasing/decreasing with J if the planet orbits inside/outside the CO excitation zone (R_CO<=3, 5 and 7 AU for a 0.5,1 and 2 Solar mass star, respectively), thus one can constrain the orbital distance of a giant planet by determining the slope of peak asymmetry-J profile. We conclude that the presented spectroscopic phenomenon can be used to test the predictions of planet formation theories by pushing the age limits for detecting the youngest planetary systems.Comment: 7 pages, 5 figures, to appear in ApJ

Mitigating potentially hazardous asteroid impacts revisited

Context: Potentially hazardous asteroids (PHA) in Earth-crossing orbits pose a constant threat to life on Earth. Several mitigation methods have been proposed, and the most feasible technique appears to be the disintegration of the impactor and the generation of a fragment cloud by explosive penetrators at interception. Mitigation analyses, however neglect the effect of orbital dynamics on fragments trajectory. Aims: We aim at studying the effect of orbital dynamics of the impactor's cloud on the number of fragments that hit the Earth assuming different interception dates. The effect of self-gravitational cohesion and the axial rotation of the impactor are also investigated. Methods: The orbits of 10^5 fragments are computed with a high-precision direct N-body integrator of the 8th order, running on GPUs. We consider orbital perturbations from all large bodies in the Solar System and the self-gravity of the cloud fragments. Results: Using a series of numerical experiments, we show that orbital shear causes the fragment cloud to adopt the shape of a triaxial ellipsoid. The shape and alignment of the triaxial ellipsoid are strongly modulated by the cloud's orbital trajectory, and hence the impact cross-section of the cloud with respect to the Earth. Therefore, the number of fragments hitting the Earth is strongly influenced by the orbit of the impactor and the time of interception. A minimum number of impacts occurs for a well-defined orientation of the impactor rotational axis, depending on the date of interception. Conclusions: To minimise the lethal consequences of an PHA's impact, a well-constrained interception timing is necessary. Too early interception may not be ideal for PHAs in the Apollo or Aten groups. The best time to intercept PHA is when it is at the pericentre of its orbit.Comment: Accepted for publication in A&A Letter

Planetary nurseries: vortices formed at smooth viscosity transition

Excitation of Rossby wave instability and development of a large-scale vortex at the outer dead zone edge of protoplanetary discs is one of the leading theories that explains horseshoe-like brightness distribution in transition discs. Formation of such vortices requires a relatively sharp viscosity transition. Detailed modelling, however, indicates that viscosity transitions at the outer edge of the dead zone is relatively smooth. In this study, we present 2D global, non-isothermal, gas-dust coupled hydrodynamic simulations to investigate the possibility of vortex excitation at smooth viscosity transitions. Our models are based on a recently postulated scenario, wherein the recombination of charged particles on the surface of dust grains results in reduced ionisation fraction and in turn the turbulence due to magnetorotational instability. Thus, the alpha-parameter for the disc viscosity depends on the local dust-to-gas mass ratio. We found that the smooth viscosity transitions at the outer edge of the dead zone can become Rossby unstable and form vortices. A single large-scale vortex develops if the dust content of the disc is well coupled to the gas, however, multiple small-scale vortices ensue for the case of less coupled dust. As both type of vortices are trapped at the dead zone outer edge, they provide sufficient time for dust growth. The solid content collected by the vortices can exceed several hundred Earth masses, while the dust-to-gas density ratio within often exceeds unity. Thus, such vortices function as planetary nurseries within the disc, providing ideal sites for formation of planetesimals and eventually planetary systems.Comment: accepted for publication in MNRA

Planet-vortex interaction:How a vortex can shepherd a planetary embryo

Context: Anticyclonic vortices are considered as a favourable places for trapping dust and forming planetary embryos. On the other hand, they are massive blobs that can interact gravitationally with the planets in the disc. Aims: We aim to study how a vortex interacts gravitationally with a planet which migrates toward it or a planet which is created inside the vortex. Methods: We performed hydrodynamical simulations of a viscous locally isothermal disc using GFARGO and FARGO-ADSG. We set a stationary Gaussian pressure bump in the disc in a way that RWI is triggered. After a large vortex is established, we implanted a low mass planet in the outer disc or inside the vortex and allowed it to migrate. We also examined the effect of vortex strength on the planet migration and checked the validity of the final result in the presence of self-gravity. Results: We noticed regardless of the planet's initial position, the planet is finally locked to the vortex or its migration is stopped in a farther orbital distance in case of a stronger vortex. For the model with the weaker vortex, we studied the effect of different parameters such as background viscosity, background surface density, mass of the planet and different planet positions. In these models, while the trapping time and locking angle of the planet vary for different parameters, the main result, which is the planet-vortex locking, remains valid. We discovered that even a planet with a mass less than 5 * 10^{-7} M_{\star} comes out from the vortex and is locked to it at the same orbital distance. For a stronger vortex, both in non-self-gravitated and self-gravitating models, the planet migration is stopped far away from the radial position of the vortex. This effect can make the vortices a suitable place for continual planet formation under the condition that they save their shape during the planetary growth.Comment: 13 pages, 21 figures,Accepted to be published in A&