Binary compact object inspiral: Detection expectations

We review the current estimates of binary compact object inspiral rates in particular in view of the recently discovered highly relativistic binary pulsar J0737-3039. One of the robust results is that, because of this discovery, the rate estimates for binary neutron stars have increased by a factor of 6–7 independent of any uncertainties related to the pulsar population properties. This rate increase has dramatic implications for gravitational wave detectors. For initial LIGO, the most probable detection rates for double neutron star (DNS) inspirals is 1 event/(5-250) yr; at 95% confidence we obtain rates up to 1/1.5 yr. For advanced LIGO, the most probable rates are 20–1000 events/yr. These predictions, for the first time, bring the expectations for DNS detections by initial LIGO to the astrophysically relevant regime. We also use our models to predict that the largescale Parkes multibeam pulsar survey with acceleration searches could detect an average of three to four binary pulsars similar to those known at present. In comparison, rate estimates for binaries with black holes are derived based on binary evolution calculation, and based on the optimistic ends of the ranges, remain an important candidate for inspiral detection in the next few years. We also consider another aspect of the detectability of binary inspiral: the effect of precession on the detection efficiency of astrophysically relevant binaries. Based on our current astrophysical expectations, large tilt angles are not favored. As a result the decrease in detection rate varies rather slowly with black hole spin magnitude and is within 20–30% of the maximum possible values.     

Estimation of parameters of gravitational waves from coalescing binaries

In this paper we deal with the measurement of parameters of the gravitational wave signal emitted by a coalescing binary system of compact stars. We present the results of Monte Carlo simulations carried out for initial LIGO, incorporating the first post-Newtonian corrections to the waveform. Using the parameters so determined, we estimate the direction to the source. We stress the use of the time-of-coalescence rather than the time-of-arrival of the signal to determine the direction of the source. We show that this can considerably reduce the errors in the determination of the direction of the source.     

旋转致密双星的引力波特征

研究了轨道和旋转效果到2.5阶后牛顿旋转致密双星拉格朗日动力学与引力波的关系, 分析了有序和混沌轨道的引力波特征.发现当加速度不考虑辐射项时, 有序双星系统辐射的引力波具有周期或拟周期的特征, 而混沌双星系统辐射的引力波却具有明显的混沌特征.当加速度含有辐射项贡献时, 双星必会出现并合现象.此时, 原保守有序双星系统需较长时间才能完成并合过程, 引力波形在双星并合前仍保留拟周期的基本特点;然而, 原保守混沌双星系统仅在较短时间内就会并合, 但因并合时间太短, 无法获取足够的动力学信息导致引力波形的特征不易分辨.     

Analytic modeling of tidal effects in the relativistic inspiral of binary neutron stars

To detect the gravitational-wave (GW) signal from binary neutron stars and extract information about the equation of state of matter at nuclear density, it is necessary to match the signal with a bank of accurate templates. We present the two longest (to date) general-relativistic simulations of equal-mass binary neutron stars with different compactnesses, C=0.12 and C=0.14, and compare them with a tidal extension of the effective-one-body (EOB) model. The typical numerical phasing errors over the ?22 GW cycles are Δ??±0.24 rad. By calibrating only one parameter (representing a higher-order amplification of tidal effects), the EOB model can reproduce, within the numerical error, the two numerical waveforms essentially up to the merger. By contrast, the third post-Newtonian Taylor-T4 approximant with leading-order tidal corrections dephases with respect to the numerical waveforms by several radians.     

Equations of motion of compact binaries at the third post-Newtonian order

The equations of motion of two point masses in harmonic coordinates are derived through the third post-Newtonian (3PN) approximation. The problem of selffield regularization (necessary for removing the divergent self-field of point particles) is dealt with in two separate steps. In the first step the extended Hadamard regularization is applied, resulting in equations of motion which are complete at the 3PN order, except for the occurrence of one and only one unknown parameter. In the second step the dimensional regularization (ind dimensions) is used as a powerful argument for fixing the value of this parameter, thereby completing the 3-dimensional Hadamard-regularization result. The complete equations of motion and associated energy at the 3PN order are given in the case of circular orbits.     

Gravity waves, chaos, and spinning compact binaries

Spinning compact binaries are shown to be chaotic in the post-Newtonian expansion of the two-body system. Chaos by definition is the extreme sensitivity to initial conditions and a consequent inability to predict the outcome of the evolution. As a result, the spinning pair will have unpredictable gravitational waveforms during coalescence. This poses a challenge to future gravity wave observatories which rely on a match between the data and a theoretical template.