814 research outputs found

### Numerical simulations of imbalanced strong magnetohydrodynamic turbulence

Magnetohydrodynamics (MHD) is invoked to address turbulent fluctuations in a
variety of astrophysical systems. MHD turbulence in nature is often anisotropic
and imbalanced, in that Alfvenic fluctuations moving in opposite directions
along the background magnetic field carry unequal energies. This work
formulates specific requirements for effective numerical simulations of strong
imbalanced MHD turbulence with a guide field B0 High-resolution simulations are
then performed and they suggest that the spectra of the counter-propagating
Alfven modes do not differ from the balanced case, while their amplitudes and
the corresponding rates of energy cascades are significantly affected by the
imbalance. It is further proposed that the stronger the imbalance the larger
the magnetic Reynolds number that is required in numerical simulations in order
to correctly reproduce the turbulence spectrum. This may explain current
discrepancies among numerical simulations and observations of imbalanced MHD
turbulence.Comment: Submitted to ApJ

### Theory of Secular Chaos and Mercury's Orbit

We study the chaotic orbital evolution of planetary systems, focusing on
secular (i.e., orbit-averaged) interactions, because these often dominate on
long timescales. We first focus on the evolution of a test particle that is
forced by multiple massive planets. To linear order in eccentricity and
inclination, its orbit precesses with constant frequencies. But nonlinearities
can shift the frequencies into and out of secular resonance with the planets'
eigenfrequencies, or with linear combinations of those frequencies. The overlap
of these nonlinear secular resonances drive secular chaos in planetary systems.
We quantify the resulting dynamics for the first time by calculating the
locations and widths of nonlinear secular resonances. When results from both
analytical calculations and numerical integrations are displayed together in a
newly developed "map of the mean momenta" (MMM), the agreement is excellent.
This map is particularly revealing for non-coplanar planetary systems and
demonstrates graphically that chaos emerges from overlapping secular
resonances. We then apply this newfound understanding to Mercury. Previous
numerical simulations have established that Mercury's orbit is chaotic, and
that Mercury might even collide with Venus or the Sun. We show that Mercury's
chaos is primarily caused by the overlap between resonances that are
combinations of four modes, the Jupiter-dominated eccentricity mode, the
Venus-dominated inclination mode and Mercury's free eccentricity and
inclination. Numerical integration of the Solar system confirms that a slew of
these resonant angles alternately librate and circulate. We are able to
calculate the threshold for Mercury to become chaotic: Jupiter and Venus must
have eccentricity and inclination of a few percent. Mercury appears to be
perched on the threshold for chaos.Comment: 18 pages, submitted to Ap

### Lower Limits on Lorentz Factors in Gamma Ray Bursts

As is well-known, the requirement that gamma ray bursts (GRB's) be optically
thin to high energy photons yields a lower limit on the Lorentz factor (\gamma)
of the expansion. In this paper, we provide a simple derivation of the lower
limit on \gamma due to the annihilation of photon pairs, and correct the errors
in some of the previous calculations of this limit. We also derive a second
limit on \gamma due to scattering of photons by pair-created electrons and
positrons. For some bursts, this limit is the more stringent. In addition, we
show that a third limit on \gamma, which is obtained by considering the
scattering of photons by electrons which accompany baryons, is nearly always
less important than the second limit. Finally, we evaluate these limits for a
number of bursts.Comment: ApJ accepted, 5 page

### 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

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