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.Comment: 25 pages, 9 figures, accepted for publication in ApJ, refereed version, updated, for quicktime movie, see http://www.phys.lsu.edu/~ou/movie/fmode/new/fmode.b181.om4.2e5.mo

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

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.Comment: 28 pages, submitted to ApJ, quicktime movies are available at: http://www.phys.lsu.edu/~ou/movie/s_type/index.htm

Millisecond Pulsars: Detectable Sources of Continuous Gravitational Waves?

Laboratory searches for the detection of gravitational waves have focused on the detection of burst signals emitted during a supernova explosion, but have not resulted in any confirmed detections. An alternative approach has been to search for continuous wave (CW) gravitational radiation from the Crab pulsar. In this paper, we examine the possibility of detecting CW gravitational radiation from pulsars and show that nearby millisecond pulsars are generally much better candidates. We show that the minimum strain h_c ~ 10E-26 that can be detected by tuning an antenna to the frequency of the milli- second pulsar PSR 1957+20, with presently available detector technology, is orders of magnitude better than what has been accomplished so far by observing the Crab pulsar, and within an order of magnitude of the maximum strain that may be produced by it. In addition, we point out that there is likely to be a population of rapidly rotating neutron stars (not necessarily radio pulsars) in the solar neighborhood whose spindown evolution is driven by gravitational radiation. We argue that the projected sensitivity of modern resonant detectors is sufficient to detect the subset of this population that lies within 0.1 kpc of the sun.Comment: 17 pages (including 2 Postscript figures), LaTeX file, uses AASTeX macros, accepted for publication in the Astrophysical Journa

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.Comment: 27 pages, 6 figures. Please see http://www.phys.lsu.edu/faculty/tohline/astroph/mftd07/ for animations and full resolution figures. Accepted for publication in the Astrophysical Journa

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.Comment: 4 pages, 4 figures, final, accepted (ApJL) versio

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.Comment: 51 pages, 10 figures, submitted for publication in Astrophysical Journal Supplement Serie