109 research outputs found
Self-Similar Force-Free Wind From an Accretion Disk
We consider a self-similar force-free wind flowing out of an infinitely thin
disk located in the equatorial plane. On the disk plane, we assume that the
magnetic stream function scales as , where is the
cylindrical radius. We also assume that the azimuthal velocity in the disk is
constant: , where is a constant. For each choice of the
parameters and , we find an infinite number of solutions that are
physically well-behaved and have fluid velocity throughout the domain
of interest. Among these solutions, we show via physical arguments and
time-dependent numerical simulations that the minimum-torque solution, i.e.,
the solution with the smallest amount of toroidal field, is the one picked by a
real system. For , the Lorentz factor of the outflow increases
along a field line as \gamma \approx M(z/\Rfp)^{(2-\nu)/2} \approx R/R_{\rm
A}, where \Rfp is the radius of the foot-point of the field line on the disk
and R_{\rm A}=\Rfp/M is the cylindrical radius at which the field line
crosses the Alfven surface or the light cylinder. For , the Lorentz
factor follows the same scaling for z/\Rfp < M^{-1/(1-\nu)}, but at larger
distances it grows more slowly: \gamma \approx (z/\Rfp)^{\nu/2}. For either
regime of , the dependence of on shows that the rotation of
the disk plays a strong role in jet acceleration. On the other hand, the
poloidal shape of a field line is given by z/\Rfp \approx
(R/\Rfp)^{2/(2-\nu)} and is independent of . Thus rotation has neither a
collimating nor a decollimating effect on field lines, suggesting that
relativistic astrophysical jets are not collimated by the rotational winding up
of the magnetic field.Comment: 21 pages, 15 figures, accepted to MNRA
Wave Damping by Magnetohydrodynamic Turbulence and Its Effect on Cosmic-Ray Propagation in the Interstellar Medium
Cosmic rays scatter off magnetic irregularities (Alfvén waves) with which they are resonant, that is, waves of wavelength comparable to their gyroradii. These waves may be generated either by the cosmic rays themselves, if they stream faster than the Alfvén speed, or by sources of MHD turbulence. Waves excited by streaming cosmic rays are ideally shaped for scattering, whereas the scattering efficiency of MHD turbulence is severely diminished by its anisotropy. We show that MHD turbulence has an indirect effect on cosmic-ray propagation by acting as a damping mechanism for cosmic-ray-generated waves. The hot ("coronal") phase of the interstellar medium is the best candidate location for cosmic-ray confinement by scattering from self-generated waves. We relate the streaming velocity of cosmic rays to the rate of turbulent dissipation in this medium for the case in which turbulent damping is the dominant damping mechanism. We conclude that cosmic rays with up to 10^2 GeV could not stream much faster than the Alfvén speed but 10^6 GeV cosmic rays would stream unimpeded by self-generated waves, unless the coronal gas were remarkably turbulence-free
Spoke formation under moving plasma clouds
Goertz and Morfill (1983) propose that spokes on Saturn's rings form under
radially moving plasma clouds produced by meteoroid impacts. We demonstrate
that the speed at which a plasma cloud can move relative to the ring material
is bounded from above by the difference between the Keplerian and corotation
velocities. The radial orientation of new spokes requires radial speeds that
are at least an order of magnitude larger than this upper limit, thus the model
advanced by Goertz and Morfill fails to make radial spokes.Comment: 15 pages, 2 figures, Icarus in pres
Optical Identification of Close White Dwarf Binaries in the LISA Era
The Laser Interferometer Space Antenna (LISA) is expected to detect close
white dwarf binaries (CWDBs) through their gravitational radiation. Around 3000
binaries will be spectrally resolved at frequencies > 3 mHz, and their
positions on the sky will be determined to an accuracy ranging from a few tens
of arcminutes to a degree or more. Due to the small binary separation, the
optical light curves of >~ 30% of these CWDBs are expected to show eclipses,
giving a unique signature for identification in follow-up studies of the LISA
error boxes. While the precise optical location improves binary parameter
determination with LISA data, the optical light curve captures additional
physics of the binary, including the individual sizes of the stars in terms of
the orbital separation. To optically identify a substantial fraction of CWDBs
and thus localize them very accurately, a rapid monitoring campaign is
required, capable of imaging a square degree or more in a reasonable time, at
intervals of 10--100 seconds, to magnitudes between 20 and 25. While the
detectable fraction can be up to many tens of percent of the total resolved
LISA CWDBs, the exact fraction is uncertain due to unknowns related to the
white dwarf spatial distribution, and potentially interesting physics, such as
induced tidal heating of the WDs due to their small orbital separation.Comment: 4 pages, 2 figure
Occultation Searches for Kuiper Belt Objects
The occultation of background stellar sources by foreground Kuiper Belt
Objects (KBOs) can be used to survey physical properties of the KBO population.
We discuss statistics related to a KBO occultation survey, such as the event
duration distribution, and suggest that occultation searches can be effectively
used to probe the KBO size distribution below 10 km. In particular, we suggest
that occultation surveys may be best suited to search for a turnover radius in
the KBO size distribution due to collisions between small-size objects. For
occultation surveys that monitor stellar sources near the ecliptic over a few
square degrees, with time sampling intervals of order 0.1 sec and sensitivity
to flux variations of a few percent or more, a turnover radius between 0.1 and
1.0 km can be probed. While occultation surveys will probe the low-radius limit
and imaging surveys will detect KBOs of size 100 km or more, statistics of
objects with sizes in the intermediate range of around 1 km to 100 km will
likely remain unattainable.Comment: 4 pages, 3 figures; ApJL submitte
Finding White Dwarfs with Transit Searches
We make predictions for the rate of discovery of eclipsing white dwarf-main
sequence (WD-MS) binaries in terrestrial-planet transit searches, taking the
planned Kepler and Eddington missions as examples. We use a population
synthesis model to characterize the Galactic WD-MS population, and we find
that, despite increased noise due to stellar variability compared with the
typical planetary case, discovery of >100 non-accreting, eclipsing WD-MS
systems is likely using Kepler and Eddington, with periods of 2-20 days and
transit amplitudes of |delta m|~0.0003-0.00003 magnitudes. Follow-up
observations of these systems could accurately test the theoretical white dwarf
mass-radius relation or theories of binary star evolution.Comment: 5 pages, 3 figures, one table, accepted for publication in ApJ. Minor
changes to Galactic model and to discusion section; conclusions unchange
Understanding the behavior of Prometheus and Pandora
We revisit the dynamics of Prometheus and Pandora, two small moons flanking
Saturn's F ring. Departures of their orbits from freely precessing ellipses
result from mutual interactions via their 121:118 mean motion resonance.
Motions are chaotic because the resonance is split into four overlapping
components. Orbital longitudes were observed to drift away from Voyager
predictions, and a sudden jump in mean motions took place close to the time at
which the orbits' apses were antialigned in 2000. Numerical integrations
reproduce both the longitude drifts and the jumps. The latter have been
attributed to the greater strength of interactions near apse antialignment
(every 6.2 years), and it has been assumed that this drift-jump behavior will
continue indefinitely. We re-examine the dynamics by analogy with that of a
nearly adiabatic, parametric pendulum. In terms of this analogy, the current
value of the action of the satellite system is close to its maximum in the
chaotic zone. Consequently, at present, the two separatrix crossings per
precessional cycle occur close to apse antialignment. In this state libration
only occurs when the potential's amplitude is nearly maximal, and the 'jumps'
in mean motion arise during the short intervals of libration that separate long
stretches of circulation. Because chaotic systems explore the entire region of
phase space available to them, we expect that at other times the system would
be found in states of medium or low action. In a low action state it would
spend most of the time in libration, and separatrix crossings would occur near
apse alignment. We predict that transitions between these different states can
happen in as little as a decade. Therefore, it is incorrect to assume that
sudden changes in the orbits only happen near apse antialignment.Comment: 22 pages, 13 figs, Icarus accepte
Saturn in hot water: viscous evolution of the Enceladus torus
The detection of outgassing water vapor from Enceladus is one of the great
breakthroughs of the Cassini mission. The fate of this water once ionized has
been widely studied; here we investigate the effects of purely neutral-neutral
interactions within the Enceladus torus. We find that, thanks in part to the
polar nature of the water molecule, a cold (~180 K) neutral torus would undergo
rapid viscous heating and spread to the extent of the observed hydroxyl cloud,
before plasma effects become important. We investigate the physics behind the
spreading of the torus, paying particular attention to the competition between
heating and rotational line cooling. A steady-state torus model is constructed,
and it is demonstrated that the torus will be observable in the millimeter band
with the upcoming Herschel satellite. The relative strength of rotational lines
could be used to distinguish between physical models for the neutral cloud.Comment: submitted to Icarus updated: references fixe
Automating Change of Representation for Proofs in Discrete Mathematics (Extended Version)
Representation determines how we can reason about a specific problem.
Sometimes one representation helps us find a proof more easily than others.
Most current automated reasoning tools focus on reasoning within one
representation. There is, therefore, a need for the development of better tools
to mechanise and automate formal and logically sound changes of representation.
In this paper we look at examples of representational transformations in
discrete mathematics, and show how we have used Isabelle's Transfer tool to
automate the use of these transformations in proofs. We give a brief overview
of a general theory of transformations that we consider appropriate for
thinking about the matter, and we explain how it relates to the Transfer
package. We show our progress towards developing a general tactic that
incorporates the automatic search for representation within the proving
process
Spontaneous axisymmetry breaking of Saturn's external magnetic field
Saturn's magnetic field is remarkably axisymmetric. Its dipole axis is
inclined by less than 0.2 deg with respect to its rotation axis. Rotationally
driven convection of magnetospheric plasma breaks the axisymmetry of its
external magnetic field. Field aligned currents transfer angular momentum from
the planet to a tongue of outflowing plasma. This transfer slows the rate of
rotation of the ionosphere relative to that of the underlying atmosphere. The
currents are the source for the non-axisymmetric components of the field. The
common rotation rates of these components and Saturn's kilometric radio (SKR)
bursts is that of the plasma near the orbit of Enceladus, and by extension the
rotation rate in the ionosphere to which this plasma is coupled. That rate
tells us nothing about the rotation rate of Saturn's deep interior. Of that we
remain ignorant. Magnetic perturbations with magnitudes similar to those
observed by Cassini are produced for Mdot ~ 10^4 g/s, a value similar to
estimates for the rate of production of plasma from Saturn's E-ring.
Enhancement of the SKR occurs in a narrow range of longitudes where the tip of
the outgoing plasma stream connects to the auroral ionosphere via field lines
that are bowed outwards by currents that supply the plasma's centripetal
acceleration. (abridged)Comment: 24 pages, 2 figures, submitted to JGR
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