Testing a Simplified Version of Einstein's Equations for Numerical Relativity

Solving dynamical problems in general relativity requires the full machinery of numerical relativity. Wilson has proposed a simpler but approximate scheme for systems near equilibrium, like binary neutron stars. We test the scheme on isolated, rapidly rotating, relativistic stars. Since these objects are in equilibrium, it is crucial that the approximation work well if we are to believe its predictions for more complicated systems like binaries. Our results are very encouraging.Comment: 9 pages (RevTeX 3.0 with 6 uuencoded figures), CRSR-107

Quasi-circular Orbits for Spinning Binary Black Holes

Using an effective potential method we examine binary black holes where the individual holes carry spin. We trace out sequences of quasi-circular orbits and locate the innermost stable circular orbit as a function of spin. At large separations, the sequences of quasi-circular orbits match well with post-Newtonian expansions, although a clear signature of the simplifying assumption of conformal flatness is seen. The position of the ISCO is found to be strongly dependent on the magnitude of the spin on each black hole. At close separations of the holes, the effective potential method breaks down. In all cases where an ISCO could be determined, we found that an apparent horizon encompassing both holes forms for separations well inside the ISCO. Nevertheless, we argue that the formation of a common horizon is still associated with the breakdown of the effective potential method.Comment: 13 pages, 10 figures, submitted to PR

Spinning down newborn neutron stars: nonlinear development of the r-mode instability

We model the nonlinear saturation of the r-mode instability via three-mode couplings and the effects of the instability on the spin evolution of young neutron stars. We include one mode triplet consisting of the r-mode and two near resonant inertial modes that couple to it. We find that the spectrum of evolutions is more diverse than previously thought. The evolution of the star is dynamic and initially dominated by fast neutrino cooling. Nonlinear effects become important when the r-mode amplitude grows above its first parametric instability threshold. The balance between neutrino cooling and viscous heating plays an important role in the evolution. Depending on the initial r-mode amplitude, and on the strength of the viscosity and of the cooling this balance can occur at different temperatures. If thermal equilibrium occurs on the r-mode stability curve, where gravitational driving equals viscous damping, the evolution may be adequately described by a one-mode model. Otherwise, nonlinear effects are important and lead to various more complicated scenarios. Once thermal balance occurs, the star spins-down oscillating between thermal equilibrium states until the instability is no longer active. For lower viscosity we observe runaway behavior in which the r-mode amplitude passes several parametric instability thresholds. In this case more modes need to be included to model the evolution accurately. In the most optimistic case, we find that gravitational radiation from the r-mode instability in a very young, fast spinning neutron star within about 1 Mpc of Earth may be detectable by advanced LIGO for years, and perhaps decades, after formation. Details regarding the amplitude and duration of the emission depend on the internal dissipation of the modes of the star, which would be probed by such detections.Comment: 23 pages, 13 figures, 1 table. Submitted to Phys. Rev. D. Detectability discussion expanded. Includes referee inpu

A Nonlinear Coupling Network to Simulate the Development of the r-mode Instablility in Neutron Stars II. Dynamics

Two mechanisms for nonlinear mode saturation of the r-mode in neutron stars have been suggested: the parametric instability mechanism involving a small number of modes and the formation of a nearly continuous Kolmogorov-type cascade. Using a network of oscillators constructed from the eigenmodes of a perfect fluid incompressible star, we investigate the transition between the two regimes numerically. Our network includes the 4995 inertial modes up to n<= 30 with 146,998 direct couplings to the r-mode and 1,306,999 couplings with detuning< 0.002 (out of a total of approximately 10^9 possible couplings). The lowest parametric instability thresholds for a range of temperatures are calculated and it is found that the r-mode becomes unstable to modes with 13<n<15. In the undriven, undamped, Hamiltonian version of the network the rate to achieve equipartition is found to be amplitude dependent, reminiscent of the Fermi-Pasta-Ulam problem. More realistic models driven unstable by gravitational radiation and damped by shear viscosity are explored next. A range of damping rates, corresponding to temperatures 10^6K to 10^9K, is considered. Exponential growth of the r-mode is found to cease at small amplitudes, approximately 10^-4. For strongly damped, low temperature models, a few modes dominate the dynamics. The behavior of the r-mode is complicated, but its amplitude is still no larger than about 10^-4 on average. For high temperature, weakly damped models the r-mode feeds energy into a sea of oscillators that achieve approximate equipartition. In this case the r-mode amplitude settles to a value for which the rate to achieve equipartition is approximately the linear instability growth rate.Comment: 18 Pages 14 Figure

High frequency longitudinal and transverse dynamics in water

High-resolution, inelastic x-ray scattering measurements of the dynamic structure factor S(Q,\omega) of liquid water have been performed for wave vectors Q between 4 and 30 nm^-1 in distinctly different thermodynamic conditions (T= 263 - 420 K ; at, or close to, ambient pressure and at P = 2 kbar). In agreement with previous inelastic x-ray and neutron studies, the presence of two inelastic contributions (one dispersing with Q and the other almost non-dispersive) is confirmed. The study of their temperature- and Q-dependence provides strong support for a dynamics of liquid water controlled by the structural relaxation process. A viscoelastic analysis of the Q-dispersing mode, associated with the longitudinal dynamics, reveals that the sound velocity undergoes the complete transition from the adiabatic sound velocity (c_0) (viscous limit) to the infinite frequency sound velocity (c_\infinity) (elastic limit). On decreasing Q, as the transition regime is approached from the elastic side, we observe a decrease of the intensity of the second, weakly dispersing feature, which completely disappears when the viscous regime is reached. These findings unambiguously identify the second excitation to be a signature of the transverse dynamics with a longitudinal symmetry component, which becomes visible in the S(Q,\omega) as soon as the purely viscous regime is left.Comment: 28 pages, 12 figure

SubmilliJansky Transients in Archival Radio Observations

[ABRIDGED] We report the results of a 944-epoch survey for transient sources with archival data from the Very Large Array spanning 22 years with a typical epoch separation of 7 days. Observations were obtained at 5 or 8.4 GHz for a single field of view with a full-width at half-maximum of 8.6' and 5.1', respectively, and achieved a typical point-source detection threshold at the beam center of ~300 microJy per epoch. Ten transient sources were detected with a significance threshold such that only one false positive would be expected. Of these transients, eight were detected in only a single epoch. Two transients were too faint to be detected in individual epochs but were detected in two-month averages. None of the ten transients was detected in longer-term averages or associated with persistent emission in the deep image produced from the combination of all epochs. The cumulative rate for the short timescale radio transients above 370 microJy at 5 and 8.4 GHz is 0.07 < R < 40 deg^-2 yr^-1, where the uncertainty is due to the unknown duration of the transients, 20 min < t_char < 7 days. A two-epoch survey for transients will detect 1.5 +/- 0.4 transient per square degrees above a flux density of 370 microJy. Two transients are associated with galaxies at z=0.040 and z=0.249. These may be similar to the peculiar Type Ib/c radio supernova SN 1998bw associated with GRB 980428. Six transients have no counterparts in the optical or infrared (R=27, Ks=18). The hosts and progenitors of these transients are unknown.Comment: Accepted for ApJ; full quality figures available at http://astro.berkeley.edu/~gbower/ps/rt.pd

The Space Motion of the Globular Cluster NGC 6397

As a by-product of high-precision, ultra-deep stellar photometry in the Galactic globular cluster NGC 6397 with the Hubble Space Telescope, we are able to measure a large population of background galaxies whose images are nearly point-like. These provide an extragalactic reference frame of unprecedented accuracy, relative to which we measure the most accurate absolute proper motion ever determined for a globular cluster. We find mu_alpha = 3.56 +/- 0.04 mas/yr and mu_delta = -17.34 +/- 0.04 mas/yr. We note that the formal statistical errors quoted for the proper motion of NGC 6397 do not include possible unavoidable sources of systematic errors, such as cluster rotation. These are very unlikely to exceed a few percent. We use this new proper motion to calculate NGC 6397's UVW space velocity and its orbit around the Milky Way, and find that the cluster has made frequent passages through the Galactic disk.Comment: 5 pages including 3 figures, accepted for publication in the Astrophysical Journal Letters. Very minor changes in V2. typos fixe

Implementing an apparent-horizon finder in three dimensions

Locating apparent horizons is not only important for a complete understanding of numerically generated spacetimes, but it may also be a crucial component of the technique for evolving black-hole spacetimes accurately. A scheme proposed by Libson et al., based on expanding the location of the apparent horizon in terms of symmetric trace-free tensors, seems very promising for use with three-dimensional numerical data sets. In this paper, we generalize this scheme and perform a number of code tests to fully calibrate its behavior in black-hole spacetimes similar to those we expect to encounter in solving the binary black-hole coalescence problem. An important aspect of the generalization is that we can compute the symmetric trace-free tensor expansion to any order. This enables us to determine how far we must carry the expansion to achieve results of a desired accuracy. To accomplish this generalization, we describe a new and very convenient set of recurrence relations which apply to symmetric trace-free tensors.Comment: 14 pages (RevTeX 3.0 with 3 figures

Anatomy and origin of authochthonous late Pleistocene forced regression deposits, east Coromandel inner shelf, New Zealand: implications for the development and definition of the regressive systems tract

High-resolution seismic reflection data from the east Coromandel coast, New Zealand, provide details of the sequence stratigraphy beneath an autochthonous, wave dominated inner shelf margin during the late Quaternary (0-140 ka). Since c. 1 Ma, the shelf has experienced limited subsidence and fluvial sediment input, producing a depositional regime characterised by extensive reworking of coastal and shelf sediments during glacio-eustatic sea-level fluctuations. It appears that only one complete fifth-order (c. 100 000 yr) depositional sequence is preserved beneath the inner shelf, the late Pleistocene Waihi Sequence, suggesting any earlier Quaternary sequences were mainly cannibalised into successively younger sequences. The predominantly Holocene-age Whangamata Sequence is also evident in seismic data and modern coastal deposits, and represents an incomplete depositional sequence in its early stages of formation. A prominent aspect of the sequence stratigraphy off parts of the east Coromandel coast is the presence of forced regressive deposits (FRDs) within the regressive systems tract (RST) of the late Pleistocene Waihi Sequence. The FRDs are interpreted to represent regressive barrier-shoreface sands that were sourced from erosion and onshore reworking of underlying Pleistocene sediments during the period of slow falling sea level from isotope stages 5 to 2 (c. 112-18 ka). The RST is volumetrically the most significant depositional component of the Waihi Sequence; the regressive deposits form a 15-20 m thick, sharp-based, tabular seismic unit that downsteps and progrades continuously across the inner shelf. The sequence boundary for the Waihi Sequence is placed at the most prominent, regionally correlative, and chronostratigraphically significant surface, namely an erosional unconformity characterised in many areas by large incised valleys that was generated above the RST. This unconformity is interpreted as a surface of maximum subaerial erosion generated during the last glacial lowstand (c. 18 ka). Although the base of the RST is associated with a prominent regressive surface of erosion, this is not used as the sequence boundary as it is highly diachronous and difficult to identify and correlate where FRDs are not developed. The previous highstand deposits are limited to subaerial barrier deposits preserved behind several modern Holocene barriers along the coast, while the transgressive systems tract is preserved locally as incised-valley fill deposits beneath the regressive surface of erosion at the base of the RST. Many documented late Pleistocene RSTs have been actively sourced from fluvial systems feeding the shelf and building basinward-thickening, often stacked wedges of FRDs, for which the name allochthonous FRDs is suggested. The Waihi Sequence RST is unusual in that it appears to have been sourced predominantly from reworking of underlying shelf sediments, and thus represents an autochthonous FRD. Autochthonous FRDs are also present on the Forster-Tuncurry shelf in southeast Australia, and may be a common feature in other shelf settings with low subsidence and low sediment supply rates, provided shelf gradients are not too steep, and an underlying source of unconsolidated shelf sediments is available to source FRDs. The preservation potential of such autochthonous FRDs in ancient deposits is probably low given that they are likely to be cannibalised during subsequent sea-level falls