Nonlinear Evolution of Hydrodynamical Shear Flows in Two Dimensions

We examine how perturbed shear flows evolve in two-dimensional, incompressible, inviscid hydrodynamical fluids, with the ultimate goal of understanding the dynamics of accretion disks. To linear order, vorticity waves are swung around by the background shear, and their velocities are amplified transiently before decaying. It has been speculated that sufficiently amplified modes might couple nonlinearly, leading to turbulence. Here we show how nonlinear coupling occurs in two dimensions. This coupling is remarkably simple because it only lasts for a short time interval, when one of the coupled modes is in mid-swing. We focus on the interaction between a swinging and an axisymmetric mode. There is instability provided that k_{y,swing}/k_{x,axi} < omega/q, i.e., that the ratio of wavenumbers is less than the ratio of the axisymmetric mode's vorticity to the background vorticity. If this is the case, then when the swinging mode is in mid-swing it couples with the axisymmetric mode to produce a new leading swinging mode that has larger vorticity than itself; this new mode in turn produces an even larger leading mode, etc. Therefore all axisymmetric modes, regardless of how small in amplitude, are unstable to perturbations with sufficiently large azimuthal wavelength. We show that this shear instability occurs whenever the momentum transported by a perturbation has the sign required for it to diminish the background shear; only when this occurs can energy be extracted from the mean flow and hence added to the perturbation. For an accretion disk, this means that the instability transports angular momentum outwards while it operates.Comment: published versio

Dynamical constraints on the origin of hot and warm Jupiters with close friends

Gas giants orbiting their host star within the ice line are thought to have migrated to their current locations from farther out. Here we consider the origin and dynamical evolution of observed Jupiters, focusing on hot and warm Jupiters with outer friends. We show that the majority of the observed Jupiter pairs (twenty out of twenty-four) will be dynamically unstable if the inner planet was placed at >~1AU distance from the stellar host. This finding is at odds with formation theories that invoke the migration of such planets from semi-major axes >~1AU due to secular dynamical processes (e.g., secular chaos, Lidov-Kozai oscillations) coupled with tidal dissipation. In fact, the results of N-body integrations show that the evolution of dynamically unstable systems does not lead to tidal migration but rather to planet ejections and collisions with the host star. This and other arguments lead us to suggest that most of the observed planets with a companion could not have been transported from further out through secular migration processes. More generally, by using a combination of numerical and analytic techniques we show that the high-e Lidov-Kozai migration scenario can only account for less than 10% of all gas giants observed between 0.1-1 AU. Simulations of multi-planet systems support this result. Our study indicates that rather than starting on highly eccentric orbits with orbital periods above one year, these "warm" Jupiters are more likely to have reached the region where they are observed today without having experienced significant tidal dissipation.Comment: Accepted to AAS journals (AJ). 15 pages, 9 figure

Imbalanced Strong MHD Turbulence

We present a phenomenological model of imbalanced MHD turbulence in an incompressible magnetofluid. The steady-state cascades, of waves traveling in opposite directions along the mean magnetic field, carry unequal energy fluxes to small length scales, where they decay due to viscous and resistive dissipation. The inertial-range scalings are well-understood when both cascades are weak. We study the case when both cascades are, in a sense, strong. The inertial-range of this imbalanced cascade has the following properties: (i) the ratio of the r.m.s. Elsasser amplitudes is independent of scale, and is equal to the ratio of the corresponding energy fluxes; (ii) in common with the balanced strong cascade, the energy spectra of both Elsasser waves are of the anisotropic Kolmogorov form, with their parallel correlation lengths equal to each other on all scales, and proportional to the two-thirds power of the transverse correlation length; (iii) the equality of cascade time and waveperiod (critical balance) that characterizes the strong balanced cascade does not apply to the Elsasser field with the larger amplitude. Instead, the more general criterion that always applies to both Elsasser fields is that the cascade time is equal to the correlation time of the straining imposed by oppositely-directed waves. Our results are particularly relevant for turbulence in the solar wind. Spacecraft measurements have established that, in the inertial range of solar wind turbulence, waves travelling away from the sun have higher amplitudes than those travelling towards it. Result (i) allows us to infer the turbulent flux ratios from the amplitude ratios, thus providing insight into the origin of the turbulence

REBOUND: An open-source multi-purpose N-body code for collisional dynamics

REBOUND is a new multi-purpose N-body code which is freely available under an open-source license. It was designed for collisional dynamics such as planetary rings but can also solve the classical N-body problem. It is highly modular and can be customized easily to work on a wide variety of different problems in astrophysics and beyond. REBOUND comes with three symplectic integrators: leap-frog, the symplectic epicycle integrator (SEI) and a Wisdom-Holman mapping (WH). It supports open, periodic and shearing-sheet boundary conditions. REBOUND can use a Barnes-Hut tree to calculate both self-gravity and collisions. These modules are fully parallelized with MPI as well as OpenMP. The former makes use of a static domain decomposition and a distributed essential tree. Two new collision detection modules based on a plane-sweep algorithm are also implemented. The performance of the plane-sweep algorithm is superior to a tree code for simulations in which one dimension is much longer than the other two and in simulations which are quasi-two dimensional with less than one million particles. In this work, we discuss the different algorithms implemented in REBOUND, the philosophy behind the code's structure as well as implementation specific details of the different modules. We present results of accuracy and scaling tests which show that the code can run efficiently on both desktop machines and large computing clusters.Comment: 10 pages, 9 figures, accepted by A&A, source code available at https://github.com/hannorein/reboun

Using Synthetic Spacecraft Data to Interpret Compressible Fluctuations in Solar Wind Turbulence

Kinetic plasma theory is used to generate synthetic spacecraft data to analyze and interpret the compressible fluctuations in the inertial range of solar wind turbulence. The kinetic counterparts of the three familiar linear MHD wave modes---the fast, Alfven, and slow waves---are identified and the properties of the density-parallel magnetic field correlation for these kinetic wave modes is presented. The construction of synthetic spacecraft data, based on the quasi-linear premise---that some characteristics of magnetized plasma turbulence can be usefully modeled as a collection of randomly phased, linear wave modes---is described in detail. Theoretical predictions of the density-parallel magnetic field correlation based on MHD and Vlasov-Maxwell linear eigenfunctions are presented and compared to the observational determination of this correlation based on 10 years of Wind spacecraft data. It is demonstrated that MHD theory is inadequate to describe the compressible turbulent fluctuations and that the observed density-parallel magnetic field correlation is consistent with a statistically negligible kinetic fast wave energy contribution for the large sample used in this study. A model of the solar wind inertial range fluctuations is proposed comprised of a mixture of a critically balanced distribution of incompressible Alfvenic fluctuations and a critically balanced or more anisotropic than critical balance distribution of compressible slow wave fluctuations. These results imply that there is little or no transfer of large scale turbulent energy through the inertial range down to whistler waves at small scales.Comment: Accepted to Astrophysical Journal. 28 pages, 7 figure

Impact of observational uncertainties on universal scaling of MHD turbulence

Scaling exponents are the central quantitative prediction of theories of turbulence and in-situ satellite observations of the high Reynolds number solar wind flow have provided an extensive testbed of these. We propose a general, instrument independent method to estimate the uncertainty of velocity field fluctuations. We obtain the systematic shift that this uncertainty introduces into the observed spectral exponent. This shift is essential for the correct interpretation of observed scaling exponents. It is sufficient to explain the contradiction between spectral features of the Elsasser fields observed in the solar wind with both theoretical models and numerical simulations of Magnetohydrodynamic turbulence

Interesting dynamics at high mutual inclination in the framework of the Kozai problem with an eccentric perturber

We study the dynamics of the 3-D three-body problem of a small body moving under the attractions of a star and a giant planet which orbits the star on a much wider and elliptic orbit. In particular, we focus on the influence of an eccentric orbit of the outer perturber on the dynamics of a small highly inclined inner body. Our analytical study of the secular perturbations relies on the classical octupole hamiltonian expansion (third-order theory in the ratio of the semi-major axes), as third-order terms are needed to consider the secular variations of the outer perturber and potential secular resonances between the arguments of the pericenter and/or longitudes of the node of both bodies. Short-period averaging and node reduction (Laplace plane) reduce the problem to two degrees of freedom. The four-dimensional dynamics is analyzed through representative planes which identify the main equilibria of the problem. As in the circular problem (i.e. perturber on a circular orbit), the "Kozai-bifurcated" equilibria play a major role in the dynamics of an inner body on quasi-circular orbit: its eccentricity variations are very limited for mutual inclination between the orbital planes smaller than ~40^{\deg}, while they become large and chaotic for higher mutual inclination. Particular attention is also given to a region around 35^{\deg} of mutual inclination, detected numerically by Funk et al. (2011) and consisting of long-time stable and particularly low eccentric orbits of the small body. Using a 12th-order Hamiltonian expansion in eccentricities and inclinations, in particular its action-angle formulation obtained by Lie transforms in Libert & Henrard (2008), we show that this region presents an equality of two fundamental frequencies and can be regarded as a secular resonance. Our results also apply to binary star systems where a planet is revolving around one of the two stars.Comment: 12 pages, 9 figures, accepted for publication in MNRA

Evolution of plasma turbulence excited with particle beams

Particles ejected from the Sun that stream through the surrounding plasma of the solar wind are causing instabilities. These generate wavemodes in a certain frequency range especially within shock regions, where particles are accelerated. The aim of this paper is to investigate of amplified Alfvenic wavemodes in driven incompressible magnetohydrodynamic turbulence. Results of different heliospheric scenarios from isotropic and anisotropic plasmas, as well as turbulence near the critical balance are shown. The energy transport of the amplified wavemode is governed by the mechanisms of diffusion, convection and dissipation of energy in wavenumber space. The strength of these effects varies with energy and wavenumber of the mode in question. Two-dimensional energy spectra of spherical k-space integration that permit detailed insight into the parallel and perpendicular development are presented. The evolution of energy injected through driving shows a strong energy transfer to perpendicular wavemodes. The main process at parallel wavemodes is the dissipation of energy in wavenumber space. The generation of higher harmonics along the parallel wavenumber axis is observed. We find evidence for a critical balance in our simulations.Comment: Accepted for publication in A&

Magnetic Lensing near Ultramagnetized Neutron Stars

Extremely strong magnetic fields change the vacuum index of refraction. This induces a lensing effect that is not unlike the lensing phenomenon in strong gravitational fields. The main difference between the two is the polarization dependency of the magnetic lensing, a behaviour that induces a handful of interesting effects. The main prediction is that the thermal emission of neutron stars with extremely strong magnetic fields is polarized - up to a few percent for the largest fields known. This potentially allows a direct method for measuring their magnetic fields.Comment: To appear in MNRAS, 12 pages, 9 figure