arXiv subjects

Joel E. Tohline

Publications and source records attributed to Joel E. Tohline.

At least 19 recordsLinked to original sources

arXiv2014

A Numerical Method for Studying Super-Eddington Mass Transfer in Double White Dwarf Binaries

We present a numerical method for the study of double white dwarf (DWD) binary systems at the onset of super-Eddington mass transfer. We incorporate the physics of ideal inviscid hydrodynamical flow, Newtonian self-gravity, and radiation transport on a three-dimensional uniformly rotating cylindrical Eulerian grid. Care has been taken to conserve the key physical quantities such as angular momentum and energy. Our new method conserves total energy to a higher degree of accuracy than other codes that are presently being used to model mass-transfer in DWD systems. We present the results of verification tests and we simulate the first 20+ orbits of a binary system of mass ratio q = 0.7 at the onset of dynamically unstable direct impact mass transfer. The mass transfer rate quickly exceeds the critical Eddington limit by many orders of magnitude, and thus we are unable to model a trans-Eddington phase. It appears that radiation pressure does not significantly effect the accretion flow in the highly super-Eddington regime. An optically thick common envelope forms around the binary within a few orbits. Although this envelope quickly exceeds the spatial domain of the computational grid, the fraction of the common envelope that exceeds zero gravitational binding energy is extremely small, suggesting that radiation-driven mass loss is insignificant in this regime. It remains to be seen whether simulations that capture the trans-Eddington phase of such flows will lead to the same conclusion or show that substantial material gets expelled.

astro-ph.SR↗

arXiv2014

A Hybrid Advection Scheme for Conserving Angular Momentum on a Refined Cartesian Mesh

We test a new "hybrid" scheme for simulating dynamical fluid flows in which cylindrical components of the momentum are advected across a rotating Cartesian coordinate mesh. This hybrid scheme allows us to conserve angular momentum to machine precision while capitalizing on the advantages offered by a Cartesian mesh, such as a straightforward implementation of mesh refinement. Our test focuses on measuring the real and imaginary parts of the eigenfrequency of unstable axisymmetric modes that naturally arise in massless polytropic tori having a range of different aspect ratios, and quantifying the uncertainty in these measurements. Our measured eigenfrequencies show good agreement with the results obtained from the linear stability analysis of Kojima (1986) and from nonlinear hydrodynamic simulations performed on a cylindrical coordinate mesh by Woodward et al. (1994). When compared against results conducted with a traditional Cartesian advection scheme, the hybrid scheme achieves qualitative convergence at the same or, in some cases, much lower grid resolutions and conserves angular momentum to a much higher degree of precision. As a result, this hybrid scheme is much better suited for simulating astrophysical fluid flows, such as accretion disks and mass-transferring binary systems.

astro-ph.SR↗

arXiv2012

Do R Coronae Borealis Stars Form from Double White Dwarf Mergers?

A leading formation scenario for R Coronae Borealis (RCB) stars invokes the merger of degenerate He and CO white dwarfs (WD) in a binary. The observed ratio of 16O/18O for RCB stars is in the range of 0.3-20 much smaller than the solar value of ~500. In this paper, we investigate whether such a low ratio can be obtained in simulations of the merger of a CO and a He white dwarf. We present the results of five 3-dimensional hydrodynamic simulations of the merger of a double white dwarf system where the total mass is 0.9 Mdot and the initial mass ratio (q) varies between 0.5 and 0.99. We identify in simulations with $q\lesssim0.7$ a feature around the merged stars where the temperatures and densities are suitable for forming 18O. However, more 16O is being dredged-up from the C- and O-rich accretor during the merger than the amount of 18O that is produced. Therefore, on a dynamical time scale over which our hydrodynamics simulation runs, a 16O/18O ratio of ~2000 in the "best" case is found. If the conditions found in the hydrodynamic simulations persist for 10^6 seconds the oxygen ratio drops to 16 in one case studied, while in a hundred years it drops to ~4 in another case studied, consistent with the observed values in RCB stars. Therefore, the merger of two white dwarfs remains a strong candidate for the formation of these enigmatic stars.

astro-ph.SR↗

arXiv2009

Constructing Synchronously Rotating Double White Dwarf Binaries

We have developed a self-consistent-field technique similar to the one described by Hachisu, Eriguchi, & Nomoto (1986b) that can be used to construct detailed force-balanced models of synchronously rotating, double white dwarf (DWD) binaries that have a wide range of total masses, mass ratios, and separations. In addition to providing a computational tool that can be used to provide quiet initial starts for dynamical studies of the onset of mass transfer in DWD systems, we show that this SCF technique can be used to construct model sequences that mimic the last portion of the detached inspiral phase of DWD binary evolutions, and semi-detached model sequences that mimic a phase of conservative mass transfer.

astro-ph.SR↗

arXiv2008

NuGrid: Toward High Precision Double-Degenerate Merger Simulations with SPH in 3D

We present preliminary results from recent high-resolution double-degenerate merger simulations with the Smooth Particle Hydrodynamics (SPH) technique. We put particular emphasis on verification and validation in our effort and show the importance of details in the initial condition setup for the final outcome of the simulation. We also stress the dynamical importance of including shocks in the simulations. These results represent a first step toward a suite of simulations that will shed light on the question whether double-degenerate mergers are a viable path toward type 1a supernovae. In future simulations, we will make use of the capabilities of the NuGrid collaboration in post-processing SPH particle trajectories with a complete nuclear network to follow the detailed nuclear reactions during the dynamic merger phase.

astro-ph↗

arXiv2008

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 (MHD). We consider two merger scenarios, one where the stars begin with initially aligned poloidal magnetic fields and one with no magnetic field. Both mergers result in a strongly differentially rotating object. In comparison to the non-magnetized scenario, the aligned magnetic fields delay the final merger of the two 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 fields. These effects not only produce 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.

gr-qc↗

arXiv2008

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.

gr-qc↗

arXiv2007

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, semi-detached equilibrium binary is evolved hydrodynamically with the gravitational potential being computed through the solution of Poisson's equation. Upon initiating deep contact in our baseline simulation, the mass transfer rate grows by more than an order of magnitude over approximately ten 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 accretor's spin saturates and 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 q_crit has evolved to approximately 2/3. Despite the absence of a fully developed disk, tidal interactions appear effective in returning excess spin angular momentum to the orbit.

astro-ph↗

arXiv2007

Further Evidence for an Elliptical Instability in Rotating Fluid Bars and Ellipsoidal Stars

Using a three-dimensional nonlinear hydrodynamic code, we examine the dynamical stability of more than twenty self-gravitating, compressible, ellipsoidal fluid configurations that initially have the same velocity structure as Riemann S-type ellipsoids. Our focus is on ``adjoint'' configurations, in which internal fluid motions dominate over the collective spin of the ellipsoidal figure; Dedekind-like configurations are among this group. We find that, although some models are stable and some are moderately unstable, the majority are violently unstable toward the development of $m=1$, $m=3$, and higher-order azimuthal distortions that destroy the coherent, $m=2$ bar-like structure of the initial ellipsoidal configuration on a dynamical time scale. The parameter regime over which our models are found to be unstable generally corresponds with the regime over which incompressible Riemann S-type ellipsoids have been found to be susceptible to an elliptical strain instability \citep{LL96}. We therefore suspect that an elliptical instability is responsible for the destruction of our compressible analogs of Riemann ellipsoids. The existence of the elliptical instability raises concerns regarding the final fate of neutron stars that encounter the secular bar-mode instability and regarding the spectrum of gravitational waves that will be radiated from such systems.

astro-ph↗

arXiv2006

Population Boundaries for Galactic White Dwarf Binaries in LISA's Amplitude-Frequency Domain

Detached, inspiraling and semi-detached, mass-transferring double white dwarf (DWD) binary systems are both expected to be important sources for the proposed space-based gravitational-wave detector, LISA. The mass-radius relationship of individual white dwarf stars in combination with the constraints imposed by Roche geometries permit us to identify population boundaries for DWD systems in LISA's ``absolute'' amplitude-frequency diagram. With five key population boundaries in place, we are able to identify four principal population sub-domains, including one sub-domain that identifies where progenitors of Type Ia supernovae will reside. Given one full year of uninterrupted operation, LISA should be able to measure the rate at which the gravitational-wave frequency $f$ and, hence, the orbital period is changing in the highest frequency subpopulation of our Galaxy's DWD systems. We provide a formula by which the distance to each DWD system in this subpopulation can be determined; in addition, we show how the masses of the individual white dwarf stars in mass-transferring systems may be calculated.

astro-ph↗

arXiv2006

Unexpected Dynamical Instabilities In Differentially Rotating Neutron Stars

A one-armed spiral instability has been found to develop in differentially rotating stellar models that have a relatively stiff, $n=1$ polytropic equation of state and a wide range of rotational energies. This suggests that such instabilities can arise in neutron stars that are differentially, although not necessarily rapidly, rotating. The instability seems to be directly triggered by the presence of a corotation resonance inside the star. Our analysis also suggests that a resonant cavity resulting from a local minimum in the radial vortensity profile of the star plays an important role in amplifying the unstable mode. Hence, it appears as through this instability is closely related to the so-called ``Rossby wave instability'' \citep{LLCN99} that has been found to arise in accretion disks. In addition to the one-armed ($m=1$) spiral mode, we have found that higher-order ($m = 2$ and $m=3$) nonaxisymmetric modes also can become unstable if corotation points that resonate with the eigenfrequencies of these higher-order modes also appear inside the star. The growth rate of each mode seems to depend on the location of its corotation radius with respect to the vortensity profile (or on the depth of its corotation radius inside the vortensity well). The existence of such instabilities makes the stability criterion for differentially rotating neutron stars non-unique. Also, the gravitational-waves emitted from such unstable systems generally will not have a monochromatic frequency spectrum.

astro-ph↗

arXiv2005

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

Hydrodynamical simulations of semi-detached, 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) $q_0 = 1.3$ that leads to a complete merger in $\sim 10$ orbits; and a double-degenerate binary with initial mass ratio $q_0 = 0.5$ that, after some initial unstable growth of mass transfer, tends to separate as the mass-transfer rate levels off.

astro-ph↗

arXiv2005

One-armed Spiral Instability in a Low T/|W| Postbounce 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 solar mass 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 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.

astro-ph↗

arXiv2004

Nonlinear Development of the Secular Bar-mode Instability in Rotating Neutron Stars

We have modelled the nonlinear development of the secular bar-mode instability that is driven by gravitational radiation-reaction (GRR) forces in rotating neutron stars. In the absence of any competing viscous effects, an initially uniformly rotating, axisymmetric $n=1/2$ polytropic star with a ratio of rotational to gravitational potential energy $T/|W| = 0.181$ is driven by GRR forces to a bar-like structure, as predicted by linear theory. The pattern frequency of the bar slows to nearly zero, that is, the bar becomes almost stationary as viewed from an inertial frame of reference as GRR removes energy and angular momentum from the star. In this ``Dedekind-like'' state, rotational energy is stored as motion of the fluid in highly noncircular orbits inside the bar. However, in less than 10 dynamical times after its formation, the bar loses its initially coherent structure as the ordered flow inside the bar is disrupted by what appears to be a purely hydrodynamical, short-wavelength, ``shearing'' type instability. The gravitational waveforms generated by such an event are determined, and an estimate of the detectability of these waves is presented.

astro-ph↗

arXiv2002

Numerical evolutions of nonlinear r-modes in neutron stars

Nonlinear evolution of the gravitational radiation (GR) driven instability in the r-modes of neutron stars is studied by full numerical 3D hydrodynamical simulations. The growth of the r-mode instability is found to be limited by the formation of shocks and breaking waves when the dimensionless amplitude of the mode grows to about three in value. This maximum mode amplitude is shown by numerical tests to be rather insensitive to the strength of the GR driving force. Upper limits on the strengths of possible nonlinear mode--mode coupling are inferred. Previously unpublished details of the numerical techniques used are presented, and the results of numerous calibration runs are discussed.

astro-ph↗

arXiv2001

Alternative Fourier Expansions for Inverse Square Law Forces

Few-body problems involving Coulomb or gravitational interactions between pairs of particles, whether in classical or quantum physics, are generally handled through a standard multipole expansion of the two-body potentials. We discuss an alternative based on a compact, cylindrical Green's function expansion that should have wide applicability throughout physics. Two-electron "direct" and "exchange" integrals in many-electron quantum systems are evaluated to illustrate the procedure which is more compact than the standard one using Wigner coefficients and Slater integrals.

physics.atom-ph↗

arXiv2001

Non-Linear Evolution of the r-Modes in Neutron Stars

The evolution of a neutron-star r-mode driven unstable by gravitational radiation (GR) is studied here using numerical solutions of the full non-linear fluid equations. The 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 non-linear evolution causes the fluid to develop strong differential rotation which is concentrated near the surface and especially near the poles of the star.

astro-ph↗

arXiv2001

Populating Stellar Orbits Inside a Rotating, Gaseous Bar

In an effort to better understand the formation and evolution of barred galaxies, we have examined the properties of equatorial orbits in the effective potential of one model of a rapidly rotating, steady-state gas-dynamical bar that has been constructed via a self-consistent hydrodynamical simulation. Using a ``Restriction Hypothesis'' to determine initial conditions, we find that a significant fraction of orbits in this potential are quasi-ergodic and that regular orbits have a ``bowtie'' shape in contrast to the more typical x1 orbits. This bowtie orbit should give a boxy-peanut shape to such systems.

astro-ph↗