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 $P$ scales as $P\propto R^\nu$, where $R$ is the cylindrical radius. We also assume that the azimuthal velocity in the disk is constant: $v_\phi = Mc$, where $M<1$ is a constant. For each choice of the parameters $\nu$ and $M$, we find an infinite number of solutions that are physically well-behaved and have fluid velocity $\leq c$ 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 $\nu \geq 1$, 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 $\nu < 1$, 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 $\nu$, the dependence of $\gamma$ on $M$ 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 $M$. 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