Gravitational Waves from the Merger of Binary Neutron Stars in a Fully General Relativistic Simulation

We performed 3D numerical simulations of the merger of equal-mass binary neutron stars in full general relativity using a new large scale supercomputer. We take the typical grid size as (505,505,253) for (x,y,z) and the maximum grid size as (633,633,317). These grid numbers enable us to put the outer boundaries of the computational domain near the local wave zone and hence to calculate gravitational waveforms of good accuracy (within $\sim 10$ error) for the first time. To model neutron stars, we adopt a $\Gamma$-law equation of state in the form $P=(\Gamma-1)\rho\epsilon$, where P, $\rho$, \varep and $\Gamma$ are the pressure, rest mass density, specific internal energy, and adiabatic constant. It is found that gravitational waves in the merger stage have characteristic features that reflect the formed objects. In the case that a massive, transient neutron star is formed, its quasi-periodic oscillations are excited for a long duration, and this property is reflected clearly by the quasi-periodic nature of waveforms and the energy luminosity. In the case of black hole formation, the waveform and energy luminosity are likely damped after a short merger stage. However, a quasi-periodic oscillation can still be seen for a certain duration, because an oscillating transient massive object is formed during the merger. This duration depends strongly on the initial compactness of neutron stars and is reflected in the Fourier spectrum of gravitational waves. To confirm our results and to calibrate the accuracy of gravitational waveforms, we carried out a wide variety of test simulations, changing the resolution and size of the computational domain.Comment: 40 pages; pubslihed in Prog. Theor. Phys. 107 (2002), 26

An Improved Search Method for Gravitational Ringing of Black Holes

A black hole has characteristic quasi-normal modes that will be excited when it is formed or when the geometry is perturbed. The state of a black hole when the quasi-normal modes are excited is called the gravitational ringing, and detections of it will be a direct confirmation of the existence of black holes. To detect it, a method based on matched filtering needs to be developed. Generically, matched filtering requires a large number of templates, because one has to ensure a proper match of a real gravitational wave with one of template waveforms to keep the detection efficiency as high as possible. On the other hand, the number of templates must be kept as small as possible under limited computational costs. In our previous paper, assuming that the gravitational ringing is dominated by the least-damped (fundamental) mode with the least imaginary part of frequency, we constructed an efficient method for tiling the template space. However, the dependence of the template space metric on the initial phase of a wave was not taken into account. This dependence arises because of an unavoidable mismatch between the parameters of a signal waveform and those given discretely in the template space. In this paper, we properly take this dependence into account and present an improved, efficient search method for gravitational ringing of black holes.Comment: 19 pages, 9 figure

Continuous phase transition in polydisperse hard-sphere mixture

In a previous paper (J. Zhang {\it et al.}, J. Chem. Phys. {\bf 110}, 5318 (1999)) we introduced a model for polydisperse hard sphere mixtures that is able to adjust its particle-size distribution. Here we give the explanation of the questions that arose in the previous description and present a consistent theory of the phase transition in this system, based on the Percus-Yevick equation of state. The transition is continuous, and like Bose-Einstein condensation a macroscopic aggregate is formed due to the microscopic interactions. A BMCSL-like treatment leads to the same conclusion with slightly more accurate predictions.Comment: 7 pages including 5 figures in revte

Dirac Quasinormal modes of Schwarzschild black hole

The quasinormal modes (QNMs) associated with the decay of Dirac field perturbation around a Schwarzschild black hole is investigated by using continued fraction and Hill-determinant approaches. It is shown that the fundamental quasinormal frequencies become evenly spaced for large angular quantum number and the spacing is given by $\omega_{\lambda+1}- \omega_{\lambda}=0.38490-0.00000i$. The angular quantum number has the surprising effect of increasing real part of the quasinormal frequencies, but it almost does not affect imaginary part, especially for low overtones. In addition, the quasinormal frequencies also become evenly spaced for large overtone number and the spacing for imaginary part is $Im(\omega_{n+1})-Im(\omega_n)\approx -i/4M$ which is same as that of the scalar, electromagnetic, and gravitational perturbations.Comment: 14 pages, 5 figure

Touch screen assays of behavioural flexibility and error characteristics in Eastern grey squirrels (Sciurus carolinensis)

This is the final version of the article. Available from the publisher via the DOI in this record.Behavioural flexibility allows animals to adjust their behaviours according to changing environmental demands. Such flexibility is frequently assessed by the discrimination–reversal learning task. We examined grey squirrels’ behavioural flexibility, using a simultaneous colour discrimination–reversal learning task on a touch screen. Squirrels were trained to select their non-preferred colour in the discrimination phase, and their preferred colour was rewarded in a subsequent reversal phase. We used error rates to divide learning in each phase into three stages (perseveration, chance level and ‘learned’) and examined response inhibition and head-switching during each stage. We found consistent behavioural patterns were associated with each learning stage: in the perseveration stage, at the beginning of each training phase, squirrels showed comparable response latencies to correct and incorrect stimuli, along with a low level of head-switching. They quickly overcame perseveration, typically in one to three training blocks. In the chance-level stage, response latencies to both stimuli were low, but during initial discrimination squirrels showed more head-switches than in the previous stage. This suggests that squirrels were learning the current reward contingency by responding rapidly to a stimulus, but with increased attention to both stimuli. In the learned stage, response latencies to the correct stimulus and the number of head-switches were at their highest, whereas incorrect response latencies were at their lowest, and differed significantly from correct response latencies. These results suggest increased response inhibition and attention allowed the squirrels to minimise errors. They also suggest that errors in the ‘learned’ stage were related to impulsive emission of the pre-potent or previously learned responses

Serial reversal learning in Gray Squirrels: learning efficiency as a function of learning and change of tactics

This is the author accepted manuscript. The final version is available from American Psychological Association via the DOI in this record.Learning allows individuals to adapt their behaviors flexibly to a changing environment. When the same change recurs repeatedly, acquiring relevant tactics may increase learning efficiency. We examined this relationship, along with the effects of proactive interference and other interference information, in a serial spatial reversal task with 5 gray squirrels (Sciurus carolinensis). Squirrels completed an acquisition and 11 reversal phases with a poke box in which 2 of 4 possible reward locations were baited diagonally in a square array. In this situation, an efficient tactic is to locate the diagonally related locations consecutively (integrative search tactic) instead of searching rewards in a clockwise or counterclockwise direction (sequential search tactic). All squirrels formed a learning set, acquiring successive reversals in fewer trials. Although 4 squirrels gradually employed more integrative tactics in locating the rewards both within and between phases, sequential tactics were used in the first trial of each phase. This suggests the integrative tactic did not depend on an association between the rewarded locations but was learned as a spatial pattern and/or by use of extra-apparatus cues to locate individual rewards. Generalized estimating equation models showed that learning efficiency increased with experience and tactic change. Although tactic change partially mediated the effect of learning on learning efficiency, learning was an independent contribution to improved efficiency. Squirrels that used more integrative tactics made fewer total errors than squirrels that used less integrative tactics, suggesting that learning a task-relevant tactic using spatial cues can provide direct benefits in maximizing rewards and minimizing time costs

On the Maximum Mass of Differentially Rotating Neutron Stars

We construct relativistic equilibrium models of differentially rotating neutron stars and show that they can support significantly more mass than their nonrotating or uniformly rotating counterparts. We dynamically evolve such ``hypermassive'' models in full general relativity and show that there do exist configurations which are dynamically stable against radial collapse and bar formation. Our results suggest that the remnant of binary neutron star coalescence may be temporarily stabilized by differential rotation, leading to delayed collapse and a delayed gravitational wave burst.Comment: 4 pages, 2 figures, uses emulateapj.sty; to appear in ApJ Letter

An Effective Search Method for Gravitational Ringing of Black Holes

We develop a search method for gravitational ringing of black holes. The gravitational ringing is due to complex frequency modes called the quasi-normal modes that are excited when a black hole geometry is perturbed. The detection of it will be a direct confirmation of the existence of a black hole. Assuming that the ringdown waves are dominated by the fundamental mode with least imaginary part, we consider matched filtering and develop an optimal method to search for the ringdown waves that have damped sinusoidal wave forms. When we use the matched filtering method, the data analysis with a lot of templates required. Here we have to ensure a proper match between the filter as a template and the real wave. It is necessary to keep the detection efficiency as high as possible under limited computational costs. First, we consider the white noise case for which the matched filtering can be studied analytically. We construct an efficient method for tiling the template space. Then, using a fitting curve of the TAMA300 DT6 noise spectrum, we numerically consider the case of colored noise. We find our tiling method developed for the white noise case is still valid even if the noise is colored.Comment: 17 pages, 9 figures. Accepted to Phys. Rev. D, Note correction to Eq. (3-25), A few comments added and minor typos correcte