An Exact, Three-Dimensional, Time-Dependent Wave Solution in Local Keplerian Flow

We present an exact three-dimensional wave solution to the shearing sheet equations of motion. The existence of this solution argues against transient amplification as a route to turbulence in unmagnetized disks. Moreover, because the solution covers an extensive dynamical range in wavenumber space, it is an excellent test of the dissipative properties of numerical codes.Comment: 22 pages, 4 figures. To appear Apj Dec 1 200

Using secret sharing for searching in encrypted data

When outsourcing data to an untrusted database server, the data should be encrypted. When using thin clients or low-bandwidth networks it is best to perform most of the work at the server. We present a method, inspired by secure multi-party computation, to search efficiently in encrypted data. XML elements are translated to polynomials. A polynomial is split into two parts: a random polynomial for the client and the difference between the original polynomial and the client polynomial for the server. Since the client polynomials are generated by a random sequence generator only the seed has to be stored on the client. In a combined effort of both the server and the client a query can be evaluated without traversing the whole tree and without the server learning anything about the data or the query

Neutron starquakes and the nature of gamma-ray bursts

The possibility that gamma-ray bursts originate from quakes deep in the solid crust of a neutron star is investigated. Seismic waves are radiated if shear stress is relieved by brittle fracture. However they cannot propagate directly to the surface but are temporarily trapped below a reflecting layer. The shaking of the stellar surface couples the seismic waves to Alfven waves which propagate out into the magnetosphere. The crust-magnetosphere transmission coefficient strongly increases with wave frequency and magnetic field strength. Alfven wave luminosities sufficient to power galactic gamma-ray bursts are possible if magnetic fields greater than 100 billion G cover at least part of the stellar surface. As the Alfven waves propagate out into the low density magnetosphere, they become increasingly charge starved, thereby accelerating particles to relativistic energies

Migration and the formation of systems of hot super-Earths and Neptunes

The existence of extrasolar planets with short orbital periods suggests that planetary migration induced by tidal interaction with the protoplanetary disk is important. Cores and terrestrial planets may undergo migration as they form. In this paper we investigate the evolution of a population of cores with initial masses in the range 0.1-1 earth mass embedded in a disk. Mutual interactions lead to orbit crossing and mergers, so that the cores grow during their evolution. Interaction with the disk leads to orbital migration, which results in the cores capturing each other in mean motion resonances. As the cores migrate inside the disk inner edge, scatterings and mergers of planets on unstable orbits together with orbital circularization causes strict commensurability to be lost. Near commensurability however is usually maintained. All the simulations end with a population of typically between two and five planets, with masses depending on the initial mass. These results indicate that if hot super-Earths or Neptunes form by mergers of inwardly migrating cores, then such planets are most likely not isolated. We would expect to always find at least one, more likely a few, companions on close and often near-commensurable orbits. To test this hypothesis, it would be of interest to look for planets of a few to about 10 earth masses in systems where hot super-Earths or Neptunes have already been found.Comment: 29 pages, to be published in Ap

Eccentricity Evolution for Planets in Gaseous Disks

We investigate the hypothesis that interactions between a giant planet and the disk from which it forms promote eccentricity growth. These interactions are concentrated at discrete Lindblad and corotation resonances. Interactions at principal Lindblad resonances cause the planet's orbit to migrate and open a gap in the disk if the planet is sufficiently massive. Those at first order Lindblad and corotation resonances change the planet's orbital eccentricity. Eccentricity is excited by interactions at external Lindblad resonances which are located on the opposite side of corotation from the planet, and damped by co-orbital Lindblad resonances which overlap the planet's orbit. If the planet clears a gap in the disk, the rate of eccentricity damping by co-orbital Lindblad resonances is reduced. Density gradients associated with the gap activate eccentricity damping by corotation resonances at a rate which initially marginally exceeds that of eccentricity excitation by external Lindblad resonances. But the corotation torque drives a mass flux which reduces the density gradient near the resonance. Sufficient partial saturation of corotation resonances can tip the balance in favor of eccentricity excitation. A minimal initial eccentricity of a few percent is required to overcome viscous diffusion which acts to unsaturate corotation resonances by reestablishing the large scale density gradient. Thus eccentricity growth is a finite amplitude instability. Formally, interactions at the apsidal resonance, which is a special kind of co-orbital Lindblad resonance, appears to damp eccentricity faster than external Lindblad resonances can excite it. However, apsidal waves have such long wavelengths that they do not propagate in protoplanetary disks. This reduces eccentricity damping by the apsidal resonance to a modest level.Comment: Submitted to Ap

Tides in rotating fluids

We consider the tidal disturbance forced in a differentially rotating fluid by a rigidly rotating external potential. The fluid is assumed to be inviscid, insulated, and self-gravitating, and to have laminar unperturbed and perturbed velocity fields. The external potential may exert a steady torque on the fluid which is of second order in Its strength. However, to this order, we prove that there are no secular changes in the angular momenta of fluid particles, except possibly at corotation where the angular velocity, Ω(r,θ), is equal to the pattern speed of the potential, Ω_p. A corollary of our theorem is that, except at corotation, all of the angular momentum transferred to the fluid by the external potential must be transported away by internal stresses. In the applications of which we are aware, these stresses are associated with waves

Tidal friction in early-type stars

The tidal torque on an early-type star is concentrated near the boundary between the convective core and radiative envelope and a train of gravity waves is excited there. The angular momentum which the torque removes from the fluid is transported outward by the gravity waves, which carry negative angular momentum. Before the surface layers are despun to synchronous rotation, the gravity waves propagate to just below the photosphere where they suffer radiative damping and are partially reflected. It is here that the negative angular momentum is deposited and the primary tidal despinning takes place. The surface layers cannot be spun down below synchronous rotation because as a train of gravity waves approaches a corotation resonance its group velocity and wavelength tend to zero, its amplitude diverges, and it is completely absorbed. Thus, tidal despinning to synchronous rotation proceeds from the outside toward the inside of the star. Our picture provides a neat explanation for the otherwise puzzling discovery by Giuricin, Mardirossian, and Mezzetti that Zahn's theory for tidal evolution in early-type close binaries seems to be compatible with the observed rates of orbit circularization while significantly underestimating the observed rates of spin synchronization

On mapping the magnetic field direction in molecular clouds by polarization measurements

We predict that interstellar radio-frequency lines possess a few percent linear polarization, provided that (1) the radiative transition rate is at least comparable to the collision rate, (2) the optical depth is moderate. and anisotropic, and (3) the number of extrema of the velocity component along the line of sight through the source is small. If the Zeeman splitting exceeds both the collisional frequency and the radiative transition rate, then the polarization is aligned either perpendicular to or parallel to the projection of the magnetic field on the plane of the sky

Linear polarization of radio frequency lines in molecular clouds and circumstellar envelopes

We predict that interstellar lines possess a few percent linear polarization provided that the optical depth in the source region is both anisotropic and of order unity and the radiative rates are at least comparable to the collision rates. These conditions are expected to be met in many sources which emit radio and far-infrared line radiation. Under circumstances in which the Zeeman splitting exceeds both the radiative and collisional rates the linear polarization is aligned either parallel or perpendicular to the projection of the magnetic field on the plane of the sky. This "strong magnetic field" limit is expected to apply to all radio frequency lines and to many of those far infrared lines which form between levels whose magnetic moments are comparable to the Bohr magneton. The "weak magnetic field" limit is relevant to most far-infrared lines formed between levels with magnetic moments of order the nuclear magneton. In this limit the polarization direction is determined by the orientation of the propagation direction with respect to the anisotropic optical depth

Linear Analysis of the Hall Effect in Protostellar Disks

The effects of Hall electromotive forces (HEMFs) on the linear stability of protostellar disks are examined. Earlier work on this topic focused on axial field and perturbation wavenumbers. Here we treat the problem more generally. Both axisymmetric and nonaxisymmetric cases are investigated. Though seldom explicitly included in calculations, HEMFs appear to be important whenever Ohmic dissipation is. They allow for the appearance of electron whistler waves, and since these have right-handed polarization, a helicity factor is also introduced into the stability problem. This factor is the product of the components of the angular velocity and magnetic field along the perturbation wavenumber, and it is destabilizing when negative. Unless the field and angular velocity are exactly aligned, it is always possible to find destabilizing wavenumbers. HEMFs can destabilize any differential rotation law, even those with angular velocity increasing outward. Regardless of the sign of the angular velocity gradient, the maximum growth rate is always given in magnitude by the local Oort A value of the disk, as in the standard magnetorotational instability. The role of Hall EMFs may prove crucial to understanding how turbulence is maintained in the ``low state'' of eruptive disk systems.Comment: 34 pages, 10 figures, AAS LaTEx, v.4.0. Submitted to Ap