Non-linear evolution of the tidal elliptical instability in gaseous planets and stars

Tidally distorted rotating stars and gaseous planets are subject to a well-known linear fluid instability – the elliptical instability. It has been proposed that this instability might drive enough energy dissipation to solve the long-standing problem of the origin of tidal dissipation in stars and planets. But the non-linear outcome of the elliptical instability has yet to be investigated in the parameter regime of interest, and the resulting turbulent energy dissipation has not yet been quantified. We do so by performing three-dimensional hydrodynamical simulations of a small patch of a tidally deformed fluid planet or star subject to the elliptical instability. We show that when the tidal deformation is weak, the non-linear outcome of the instability leads to the formation of long-lived columnar vortices aligned with the axis of rotation. These vortices shut off the elliptical instability, and the net result is insufficient energy dissipation to account for tidal dissipation. However, further work is required to account for effects neglected here, including magnetic fields, turbulent convection and realistic boundary conditions

Theory and Simulations of Rotating Convection

We study thermal convection in a rotating fluid in order to better understand the properties of convection zones in rotating stars and planets. We first derive a mixing-length theory for rapidly rotating convection, arriving at the results of Stevenson via simple physical arguments. The theory predicts the properties of convection as a function of the imposed heat flux and rotation rate, independent of microscopic diffusivities. In particular, it predicts the mean temperature gradient, the rms velocity and temperature fluctuations, and the size of the eddies that dominate heat transport. We test all of these predictions with high resolution three-dimensional hydrodynamical simulations of Boussinesq convection in a Cartesian box. The results agree remarkably well with the theory across more than two orders of magnitude in rotation rate. For example, the temperature gradient is predicted to scale as the rotation rate to the four-fifths power at fixed flux, and the simulations yield 0.75 ± 0.06. We conclude that the mixing-length theory is a solid foundation for understanding the properties of convection zones in rotating stars and planets

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

A Brief History of Trans-Neptunian Space

The Edgeworth-Kuiper belt encodes the dynamical history of the outer solar system. Kuiper belt objects (KBOs) bear witness to coagulation physics, the evolution of planetary orbits, and external perturbations from the solar neighborhood. We critically review the present-day belt's observed properties and the theories designed to explain them. Theories are organized according to a possible time-line of events. In chronological order, epochs described include (1) coagulation of KBOs in a dynamically cold disk, (2) formation of binary KBOs by fragmentary collisions and gravitational captures, (3) stirring of KBOs by Neptune-mass planets (``oligarchs''), (4) eviction of excess oligarchs, (5) continued stirring of KBOs by remaining planets whose orbits circularize by dynamical friction, (6) planetary migration and capture of Resonant KBOs, (7) creation of the inner Oort cloud by passing stars in an open stellar cluster, and (8) collisional comminution of the smallest KBOs. Recent work underscores how small, collisional, primordial planetesimals having low velocity dispersion permit the rapid assembly of ~5 Neptune-mass oligarchs at distances of 15-25 AU. We explore the consequences of such a picture. We propose that Neptune-mass planets whose orbits cross into the Kuiper belt for up to ~20 Myr help generate the high-perihelion members of the hot Classical disk and Scattered belt. By contrast, raising perihelia by sweeping secular resonances during Neptune's migration might fill these reservoirs too inefficiently when account is made of how little primordial mass might reside in bodies having sizes of order 100 km. These and other frontier issues in trans-Neptunian space are discussed quantitatively.Comment: Final proofed version for Protostars and Planets V; some numbers adjusted by factors of 2; references update

Neptune Trojans as a Testbed for Planet Formation

The problem of accretion in the Trojan 1:1 resonance is akin to the standard problem of planet formation, transplanted from a star-centered disk to a disk centered on the Lagrange point. The newly discovered class of Neptune Trojans promises to test theories of planet formation by coagulation. Neptune Trojans resembling the prototype 2001 QR322 (``QR'')--whose radius of ~100 km is comparable to that of the largest Jupiter Trojan--may outnumber their Jovian counterparts by a factor of ~10. We discover that seeding the 1:1 resonance with debris from planetesimal collisions and having the seed particles accrete in situ naturally reproduces the inferred number of QR-sized Trojans. We analyze accretion in the Trojan sub-disk by applying the two-groups method, accounting for kinematics specific to the resonance. We find that a Trojan sub-disk comprising decimeter-sized seed particles and having a surface density 1e-3 that of the local minimum-mass disk produces ~10 QR-sized objects in ~1 Gyr, in accord with observation. Further growth is halted by collisional diffusion of seed particles out of resonance. In our picture, the number and sizes of the largest Neptune Trojans represent the unadulterated outcome of dispersion-dominated, oligarchic accretion. Large Neptune Trojans, perhaps the most newly accreted objects in our Solar System, may today have a dispersion in orbital inclination of less than ~10 degrees, despite the existence of niches of stability at higher inclinations. Such a vertically thin disk, born of a dynamically cold environment necessary for accretion, and raised in minimal contact with external perturbations, contrasts with the thick disks of other minor body belts.Comment: Accepted to ApJ April 6, 200

Transformation of the Poynting flux into the kinetic energy in relativistic jets

The acceleration of relativistic jets from the Poynting to the matter dominated stage is considered. The are generally two collimation regimes, which we call equilibrium and non-equilibrium, correspondingly. In the first regime, the jet is efficiently accelerated till the equipartition between the kinetic and electro-magnetic energy. We show that after the equilibrium jet ceases to be Poynting dominated, the ratio of the electro-magnetic to the kinetic energy decreases only logarithmically so that such jets become truly matter dominated only at extremely large distances. Non-equilibrium jets remain generally Poynting dominated till the logarithmically large distances. In the only case when a non-equilibrium jet is accelerated till the equipartition level, we found that the flow is not continued to the infinity but is focused towards the axis at a finite distance from the origin.Comment: Submitted to MNRAS Minor changes in the Conclusion

Nonlinear energy transfers in accretion discs MRI turbulence. I-Net vertical field case

The magnetorotational instability (MRI) is believed to be responsible for most of the angular momentum transport in accretion discs. However, molecular dissipation processes may drastically change the efficiency of MRI turbulence in realistic astrophysical situations. The physical origin of this dependency is still poorly understood as linear and quasi linear theories fail to explain it. In this paper, we look for the link between molecular dissipation processes and MRI transport of angular momentum in non stratified shearing box simulations including a mean vertical field. We show that magnetic helicity is unimportant in the model we consider. We perform a spectral analysis on the simulations tracking energy exchanges in spectral space when turbulence is fully developed. We find that the energy exchanges are essentially direct (from large to small scale) whereas some non linear interactions appear to be non local in spectral space. We speculate that these non local interactions are responsible for the correlation between turbulent transport and molecular dissipation. We argue that this correlation should then disappear when a significant scale separation is achieved and we discuss several methods by which one can test this hypothesis.Comment: 10 pages, 9 figures, accepted for publication in Astronomy & Astrophysic

Secular dynamics of multiplanet systems: implications for the formation of hot and warm Jupiters via high-eccentricity migration

Stars and planetary system

UV/Optical Emission Accompanying Gamma-ray Burst

We discuss the possible simultaneously UV/optical emission accompanying Gamma-ray bursts (GRBs). We show that as long as the intrinsic spectrum of GRB can extend to $\sim$10 GeV or higher, there is a large amount of relativistic $e^\pm$ pairs generated due to the annihilation of the soft $\gamma-$rays with the very energetic photons, which dominates over the electrons/positrons associated with the fireball, no matter the fireball is highly magnetized or not (For the highly magnetized fireball, the magnetic field is ordered, the high linear polarization of the multi-wavelength emission is expected). We find that these $e^\pm$ pairs can power an UV flash with $m\simeq 12-13{\rm th}$ magnitude, and the corresponding optical emission can be up to $m_{\rm R}\simeq15-16{\rm th}$ magnitude. Such bright UV emission can be detected by the upcoming satellite Swift, planned for launch in early 2004. The behavior of the optical-UV spectrum ($F_{\nu}\propto \nu^{5/2}$) differs significantly from that of the reverse shock emission ($F_{\nu}\propto \nu^{-\beta/2}$, $\beta \simeq 2.2$), which is a signature of the emission accompanying with GRB. The mild optical emission can be detected with the ROTSE-IIIa telescope system, if the response to the GRB alert is fast enough.Comment: 5 pages, no figures. MNRAS in pres