On the diversity of magnetic interactions in close-in star-planet systems

PublishedJournal Article© 2014. The American Astronomical Society. All rights reserved..Magnetic interactions between close-in planets and their host star can play an important role in the secular orbital evolution of the planets, as well as the rotational evolution of their host. As long as the planet orbits inside the Alfvén surface of the stellar wind, the magnetic interaction between the star and the planet can modify the wind properties and also lead to direct angular momentum transfers between the two. We model these star-planet interactions using compressible magnetohydrodynamic (MHD) simulations, and quantify the angular momentum transfers between the star, the planet, and the stellar wind. We study the cases of magnetized and non-magnetized planets and vary the orbital radius inside the Alfvén surface of the stellar wind. Based on a grid of numerical simulations, we propose general scaling laws for the modification of the stellar wind torque, for the torque between the star and the planet, and for the planet migration associated with the star-planet magnetic interactions. We show that when the coronal magnetic field is large enough and the star is rotating sufficiently slowly, the effect of the magnetic star-planet interaction is comparable to tidal effects and can lead to a rapid orbital decay.This work was supported by the ANR 2011 Blanc Toupies and the ERC project STARS2. A.S. acknowledges support from the Canada's Natural Sciences and Engineering Research Council. We acknowledge access to supercomputers through GENCI (project 1623), Prace, and ComputeCanada infrastructures

Numerical Aspects of 3D Stellar Winds

This paper explores and compares the pitfalls of modelling the three-dimensional wind of a spherical star with a cartesian grid. Several numerical methods are compared, using either uniform and stretched grid or adaptative mesh refinement (AMR). An additional numerical complication is added, when an orbiting planet is considered. In this case a rotating frame is added to the model such that the orbiting planet is at rest in the frame of work. The three-dimensional simulations are systematically compared to an equivalent two-dimensional, axisymmetric simulation. The comparative study presented here suggests to limit the rotation rate of the rotating frame below the rotating frame of the star and provides guidelines for further three-dimensional modelling of stellar winds in the context of close-in star-planet interactions.AS thanks T. Matsakos for discussions about the modelling of star-planet systems in 3D. This work was supported by the ANR 2011 Blanc Toupies and the ERC project STARS2 (207430). The authors acknowledge CNRS INSU/PNST and CNES/Solar Orbiter fundings. AS acknowledges support from the Canada’s Natural Sciences and Engineering Research Council and from the Canadian Institute of Theoretical Astrophysics (National fellow). We acknowledge access to supercomputers through GENCI (project 1623), Prace, and ComputeCanada infrastructures

The influence of the magnetic topology on the wind braking of sun-like stars.

Stellar winds are thought to be the main process responsible for the spin down of main-sequence stars. The extraction of angular momentum by a magnetized wind has been studied for decades, leading to several formulations for the resulting torque. However, previous studies generally consider simple dipole or split monopole stellar magnetic topologies. Here we consider in addition to a dipolar stellar magnetic field, both quadrupolar and octupolar configurations, while also varying the rotation rate and the magnetic field strength. 60 simulations made with a 2.5D, cylindrical and axisymmetric set-up and computed with the PLUTO code were used to find torque formulations for each topology. We further succeed to give a unique law that fits the data for every topology by formulating the torque in terms of the amount of open magnetic flux in the wind. We also show that our formulation can be applied to even more realistic magnetic topologies, with examples of the Sun in its minimum and maximum phase as observed at the Wilcox Solar Observatory, and of a young K-star (TYC-0486-4943-1) whose topology has been obtained by Zeeman-Doppler Imaging (ZDI).We would like to thank Colin Folsom, Pascal Petit for the magnetic field decomposition coefficients of TYC- 0486-4943-1, J´erome Bouvier and the ANR TOUPIES project which aim to understand the evolution of star?s spin rates, the ERC STARS2 (www.stars2.eu) and CNES support via our Solar Orbiter funding

Modelling the Corona of HD 189733 in 3D

The braking of main sequence stars originates mainly from their stellar wind. The efficiency of this angular momentum extraction depends on the rotation rate of the star, the acceleration profile of the wind and the coronal magnetic field. The derivation of scaling laws parametrizing the stellar wind torque is important for our understanding of gyro-chronology and the evolution of the rotation rates of stars. In order to understand the impact of complex magnetic topologies on the stellar wind torque, we present three-dimensional, dynamical simulations of the corona of HD 189733. Using the observed complex topology of the magnetic field, we estimate how the torque associated with the wind scales with model parameters and compare those trends to previously published scaling laws.AS thank A. Vidotto for discussions about the modelling of the corona of HD 189733. This work was supported by the ANR 2011 Blanc Toupies and the ERC project STARS2 (207430). The authors acknowledge CNRS INSU/PNST and CNES/Solar Orbiter fundings. AS acknowledges support from the Canada’s Natural Sciences and Engineering Research Council and from the Canadian Institute of Theoretical Astrophysics (National fellow). We acknowledge access to supercomputers through GENCI (project 1623), Prace, and ComputeCanada infrastructures

Hierarchical auxetic and isotropic porous medium with extremely negative Poisson's ratio

We propose a novel two-dimensional hierarchical auxetic structure consisting of a porous medium in which a homogeneous matrix includes a rank-two set of cuts characterised by different scales. The six-fold symmetry of the perforations makes the medium isotropic in the plane. Remarkably, the mesoscale interaction between the first- and second-level cuts enables the attainment of a value of the Poisson’s ratio close to the minimum reachable limit of -1. The effective properties of the hierarchical auxetic structure are determined numerically, considering both a unit cell with periodic boundary conditions and a finite structure containing a large number of repeating cells. Further, results of the numerical study are validated experimentally on a polymeric specimen with appropriately arranged rank-two cuts, tested under uniaxial tension. We envisage that the proposed hierarchical design can be useful in numerous engineering applications exploiting an extreme auxetic effect

Analysis of the Reaction Rate Coefficients for Slow Bimolecular Chemical Reactions

Simple bimolecular reactions $A_1+A_2\rightleftharpoons A_3+A_4$ are analyzed within the framework of the Boltzmann equation in the initial stage of a chemical reaction with the system far from chemical equilibrium. The Chapman-Enskog methodology is applied to determine the coefficients of the expansion of the distribution functions in terms of Sonine polynomials for peculiar molecular velocities. The results are applied to the reaction $H_2+Cl\rightleftharpoons HCl+H$, and the influence of the non-Maxwellian distribution and of the activation-energy dependent reactive cross sections upon the forward and reverse reaction rate coefficients are discussed.Comment: 11 pages, 5 figures, to appear in vol.42 of the Brazilian Journal of Physic

On differential rotation and overshooting in solar-like stars

This is the author accepted manuscript. The final version is available from American Astronomical Society via the DOI in this record.We seek to characterize how the change of global rotation rate influences the overall dynamics and large scale flows arising in the convective envelopes of stars covering stellar spectral types from early G to late K. We do so through numerical simulations with the ASH code, where we consider stellar convective envelopes coupled to a radiative interior with various global properties. As solar-like stars spin down over the course of their main sequence evolution, such change must have a direct impact on their dynamics and rotation state. We indeed find that three main states of rotation may exist for a given star: anti-solar-like (fast poles, slow equator), solar-like (fast equator, slow poles), or a cylindrical rotation profile. Under increasingly strict rotational constraints, the latter profile can further evolve into a Jupiter-like profile, with alternating prograde and retrograde zonal jets. We have further assessed how far the convection and meridional flows overshoot into the radiative zone and investigated the morphology of the established tachocline. Using simple mixing length arguments, we are able to construct a scaling of the fluid Rossby number $R_{of} = \tilde{\omega}/2\Omega_* \sim \tilde{v}/2\Omega_* R_*$, which we calibrate based on our 3-D ASH simulations. We can use this scaling to map the behavior of differential rotation versus the global parameters of stellar mass and rotation rate. Finally, we isolate a region on this map ($R_{of} \gtrsim 1.5-2$) where we posit that stars with an anti-solar differential rotation may exist in order to encourage observers to hunt for such targets.We acknowledge funding by ERC STARS2 207430 grant, ANR Blanc Toupies SIMI5-6 020 01, INSU/PNST, CNES SolarOrbiter, PLATO and GOLF grants, FP7 SpaceInn 312844 grant, and NASA grants NNX11AJ36G, NNX13AG18G and NNX16AC92G. K. C. Augustson is funded through the ERC SPIRE 647383 grant. A. Strugarek acknowledges support from the Canadian Institute of Theoretical Astrophysics (National Fellow), from Canadas Natural Sciences and Engineering Research Council and from CNES postdoctoral fellowship

Simulations of Solar and Stellar Dynamos and Their Theoretical Interpretation

This is the final version. Available on open access from Springer via the DOI in this recordWe review the state of the art of three dimensional numerical simulations of solar and stellar dynamos. We summarize fundamental constraints of numerical modelling and the techniques to alleviate these restrictions. Brief summary of the relevant observations that the simulations seek to capture is given. We survey the current progress of simulations of solar convection and the resulting large-scale dynamo. We continue to studies that model the Sun at different ages and to studies of stars of different masses and evolutionary stages. Both simulations and observations indicate that rotation, measured by the Rossby number which is the ratio of rotation period and convective turnover time, is a key ingredient in setting the overall level and characteristics of magnetic activity. Finally, efforts to understand global 3D simulations in terms of mean-field dynamo theory are discussed.Deutsche Forschungsgemeinschaft (DFG)European Union Horizon 2020European Research Council (ERC)CNRS/INSUCNESObservatory OSUPSUniversité Paris-SaclayUniversité Paris CitéScience and Technology Facilities Council (STFC)NAS

Models of Star-Planet Magnetic Interaction

Magnetic interactions between a planet and its environment are known to lead to phenomena such as aurorae and shocks in the solar system. The large number of close-in exoplanets that were discovered triggered a renewed interest in magnetic interactions in star-planet systems. Multiple other magnetic effects were then unveiled, such as planet inflation or heating, planet migration, planetary material escape, and even modification of the host star properties. We review here the recent efforts in modelling and understanding magnetic interactions between stars and planets in the context of compact systems. We first provide simple estimates of the effects of magnetic interactions and then detail analytical and numerical models for different representative scenarii. We finally lay out a series of future developments that are needed today to better understand and constrain these fascinating interactions.Comment: 23 pages, 10 figures, accepted as a chapter in the Handbook of Exoplanet