Joel E. Tohline

Shifted Fresnel diffraction for computational holography

Fourier-based approaches to calculate the Fresnel diffraction of light provide one of the most efficient algorithms for holographic computations because this permits the use of the fast Fourier transform (FFT). This research overcomes the limitations on sampling imposed by Fourier-based algorithms by the development of a fast shifted Fresnel transform. This fast shifted Fresnel transform is used to develop a tiling approach to hologram construction and reconstruction, which computes the Fresnel propagation of light between parallel planes having different resolutions.

Dynamic fission instabilities in rapidly rotating n = 3/2 polytropes - A comparison of results from finite-difference and smoothed particle hydrodynamics codes

The effectiveness of three different hydrodynamics models is evaluated for the analysis of the effects of fission instabilities in rapidly rotating, equilibrium flows. The instabilities arise in nonaxisymmetric Kelvin modes as rotational energy in the flow increases, which may occur in the formation of close binary stars and planets when the fluid proto-object contracts quasi-isostatically. Two finite-difference, donor-cell methods and a smoothed particle hydrodynamics (SPH) code are examined, using a polytropic index of 3/2 and ratios of total rotational kinetic energy to gravitational energy of 0.33 and 0.38. The models show that dynamic bar instabilities with the 3/2 polytropic index do not yield detached binaries and multiple systems. Ejected mass and angular momentum form two trailing spiral arms that become a disk or ring around the central remnant. The SPH code yields the same data as the finite difference codes but with less computational effort and without acceptable fluid constraints in low density regions. Methods for improving both types of codes are discussed. 68 references.

Numerical Simulations of the Onset and Stability of Dynamical Mass Transfer in Binaries

Hydrodynamical simulations of semidetached, polytropic binary stars are presented in an effort to study the onset and stability of dynamical mass transfer events. Initial, synchronously rotating equilibrium models are constructed using a self-consistent field technique and then evolved with an Eulerian hydrodynamics code in a fully self-consistent manner. We describe code improvements introduced over the past few years that permit us to follow dynamical mass transfer events through more than 30 orbits. Mass transfer evolutions are presented for two different initial configurations: a dynamically unstable binary with initial mass ratio (donor/accretor) q0 = 1.3 that leads to a complete merger in ~10 orbits, and a double-degenerate binary with initial mass ratio q0 = 0.5 that, after some initial unstable growth of mass transfer, tends to separate as the mass transfer rate levels off.

Magnetized Neutron-Star Mergers and Gravitational-Wave Signals

We investigate the influence of magnetic fields upon the dynamics of, and resulting gravitational waves from, a binary neutron-star merger in full general relativity coupled to ideal magnetohydrodynamics. We consider two merger scenarios: one where the stars have aligned poloidal magnetic fields and one without. Both mergers result in a strongly differentially rotating object. In comparison to the nonmagnetized scenario, the aligned magnetic fields delay the full merger of the stars. During and after merger we observe phenomena driven by the magnetic field, including Kelvin-Helmholtz instabilities in shear layers, winding of the field lines, and transition from poloidal to toroidal magnetic fields. These effects not only mediate the production of electromagnetic radiation, but also can have a strong influence on the gravitational waves. Thus, there are promising prospects for studying such systems with both types of waves.

Nonlinear Evolution of the r-Modes in Neutron Stars

The evolution of a neutron-star r-mode driven unstable by gravitational radiation is studied here using numerical solutions of the full nonlinear fluid equations. The dimensionless amplitude of the mode grows to order unity before strong shocks develop which quickly damp the mode. In this simulation the star loses about 40% of its initial angular momentum and 50% of its rotational kinetic energy before the mode is damped. The nonlinear evolution causes the fluid to develop strong differential rotation which is concentrated near the surface and poles of the star.

Simulating binary neutron stars: Dynamics and gravitational waves

We model two mergers of orbiting binary neutron stars, the first forming a black hole and the second a differentially rotating neutron star. We extract gravitational waveforms in the wave zone. Comparisons to a post-Newtonian analysis allow us to compute the orbital kinematics, including trajectories and orbital eccentricities. We verify our code by evolving single stars and extracting radial perturbative modes, which compare very well to results from perturbation theory. The Einstein equations are solved in a first-order reduction of the generalized harmonic formulation, and the fluid equations are solved using a modified convex essentially non-oscillatory method. All calculations are done in three spatial dimensions without symmetry assumptions. We use the had computational infrastructure for distributed adaptive mesh refinement.

The Stability of Double White Dwarf Binaries Undergoing Direct-Impact Accretion

We present numerical simulations of dynamically unstable mass transfer in a double white dwarf binary with initial mass ratio q = 0.4. The binary components are approximated as polytropes of index n = 3/2, and the initially synchronously rotating, semidetached equilibrium binary is evolved hydrodynamically, with the gravitational potential being computed through the solution of Poissons equation. Upon initiating deep contact in our baseline simulation, the mass transfer rate grows by more than an order of magnitude over approximately 10 orbits, as would be expected for dynamically unstable mass transfer. However, the mass transfer rate then reaches a peak value, the binary expands, and the mass transfer event subsides. The binary must therefore have crossed the critical mass ratio for stability against dynamical mass transfer. Despite the initial loss of orbital angular momentum into the spin of the accreting star, we find that the accretors spin saturates and that angular momentum is returned to the orbit more efficiently than has been previously suspected for binaries in the direct-impact accretion mode. To explore this surprising result, we directly measure the critical mass ratio for stability by imposing artificial angular momentum loss at various rates to drive the binary to an equilibrium mass transfer rate. For one of these driven evolutions, we attain equilibrium mass transfer and deduce that, effectively, qcrit has evolved to approximately 2/3. Despite the absence of a fully developed disk, tidal interactions appear to be effective in returning excess spin angular momentum to the orbit.

A Provenance-Based Infrastructure to Support the Life Cycle of Executable Papers

As publishers establish a greater online presence as well as infrastructure to support the distribution of more varied information, the idea of an executable paper that enables greater interaction has developed. An executable paper provides more information for computational experiments and results than the text, tables, and figures of standard papers. Executable papers can bundle computational content that allow readers and reviewers to interact, validate, and explore experiments. By including such content, authors facilitate future discoveries by lowering the barrier to reproducing and extending results. We present an infrastructure for creating, disseminating, and maintaining executable papers. Our approach is rooted in provenance, the documentation of exactly how data, experiments, and results were generated. We seek to improve the experience for everyone involved in the life cycle of an executable paper. The automated capture of provenance information allows authors to easily integrate and update results into papers as they write, and also helps reviewers better evaluate approaches by enabling them to explore experimental results by varying parameters or data. With a provenance-based system, readers are able to examine exactly how a result was developed to better understand and extend published findings.

One-Armed Spiral Instability in a Slowly Rotating, Post-Bounce Supernova Core

A three-dimensional, Newtonian hydrodynamic technique is used to follow the postbounce phase of a stellar core collapse event. For realistic initial data, we have employed post-core-bounce snapshots of the iron core of a 20 M☉ star. The models exhibit strong differential rotation but have centrally condensed density stratifications. We demonstrate for the first time that such postbounce cores are subject to a so-called low-T/|W| nonaxisymmetric instability and, in particular, can become dynamically unstable to an (m = 1)-dominated spiral mode at T/|W| ~ 0.08. We calculate the gravitational wave (GW) emission by the instability and find that the emitted waves may be detectable by current and future GW observatories from anywhere in the Milky Way.

The stability of thick, self-gravitating disks in protostellar systems

Using numerical hydrodynamics techniques, we perform a nonlinear stability analysis of accretion disk systems that contain thick, self-gravitating disks. The systems are initially represented by a point mass M(sub c) at the center and a geometrically thick, axisymmetric disk of mass M(sub d) that supports uniform specific angular momentum and obeys an n = 3/2, polytropic equation of state. The equilibrium disk structure is uniquely defined upon the specification of two key dimensionless system parameters: M(sub d)/M(sub c) and T/absolute value of W (the ratio of rotational kinetic energy if the disk to the gravitational potential energy of the system). The focus of this work is on the identification of systems within this two-dimensional parameter space that are marginally unstable toward the development of nonaxisymmetric distortions. The geometric form and relative pattern speed of the disks distortion as well as the likelihood of disk fragmentation as a result of such instabilities is examined, particularly in the context of protostellar systems. The value of T/absolute value of W at which thick disks first become dynamically unstable to nonaxisymmetric distortions is found to vary significantly with the mass ratio of the accertion disk system. Nonaxisymmetric eigenmodes with four distinctly different characters are identified in systems with mass ratios in the range 0.2 less than or equal to (M(sub d)/M(sub c)) less than or equal to 5.