Searcharxiv⌕ Search

arXiv subjects

Zhoujian Cao

Publications and source records attributed to Zhoujian Cao.

At least 127 records · Page 7Linked to original sources
arXiv2018

Binary black hole simulation with an adaptive finite element method II: Application of local discontinuous Galerkin method to Einstein equations

Finite difference method and pseudo-spectral method have been widely used in the numerical relativity to solve the Einstein equations. As the third major category method to solve partial differential equations, finite element method is much less used in numerical relativity. In this paper we design a finite element algorithm to solve the evolution part of the Einstein equations. This paper is the second one of a systematic investigation of applying adaptive finite element method to the Einstein equations, especially aim for binary compact objects simulations. The first paper of this series has been contributed to the constrained part of the Einstein equations for initial data. Since applying finite element method to the Einstein equations is a big project, we mainly propose the theoretical framework of a finite element algorithm together with local discontinuous Galerkin method for the Einstein equations in the current work. In addition, we have tested our algorithm based on the spherical symmetric spacetime evolution. In order to simplify our numerical tests, we have reduced the problem to a one-dimensional space problem by taking the advantage of the spherical symmetry. Our reduced equation system is a new formalism for spherical symmetric spacetime simulation. Based on our test results, we find that our finite element method can capture the shock formation which is introduced by numerical error. In contrast, such shock is smoothed out by numerical dissipation within the finite difference method. We suspect this is the part reason for that the accuracy of finite element method is higher than finite difference method. At the same time kinds of formulation parameters setting are also discussed.

gr-qc↗
arXiv2018

Relationship between Bondi-Sachs quantities and source of gravitational radiation in asymptotically de Sitter spacetime

Gravitational radiation plays an important role in astrophysics. Based on the fact that our universe is expanding, the gravitational radiation when a positive cosmological constant is presented has been studied along with two different ways recently, one is the Bondi-Sachs (BS) framework in which the result is shown by BS quantities in the asymptotic null structure, the other is the perturbation approach in which the result is presented by the quadrupoles of source. Therefore, it is worth to interpret the quantities in asymptotic null structure in terms of the information of the source. In this paper, we investigate this problem and find the explicit expressions of BS quantities in terms of the quadrupoles of source in asymptotically de Sitter spacetime. We also estimate how far away the source is, the cosmological constant may affect the detection of the gravitational wave.

gr-qc↗
arXiv2018

A more stringent constraint on the mass ratio of binary neutron star merger GW170817

Recently, the LIGO-Virgo collaboration reported their first detection of gravitational wave (GW) signals from a low mass compact binary merger GW170817, which is most likely due to a double neutron star (NS) merger. With the GW signals only, the chirp mass of the binary is precisely constrained to $1.188^{+0.004}_{-0.002}~\rm{M_{\odot}}$, but the mass ratio is loosely constrained in the range $0.4-1$, so that a very rough estimation of the individual NS masses ($0.86~{\rm M_{\odot}}<M_1<1.36~\rm{M_{\odot}}$ and $1.36~{\rm M_{\odot}}<M_2<2.26~\rm{M_{\odot}}$) was obtained. Here we propose that if one can constrain the dynamical ejecta mass through performing kilonova modeling of the optical/IR data, by utilizing an empirical relation between the dynamical ejecta mass and the mass ratio of NS binaries, one may place a more stringent constraint on the mass ratio of the system. For instance, considering that the red "kilonova" component is powered by the dynamical ejecta, we reach a tight constraint on the mass ratio in the range of $0.46-0.59$. Alternatively, if the blue "kilonova" component is powered by the dynamical ejecta, the mass ratio would be constrained in the range of $0.53-0.67$. Overall, such a multi-messenger approach could narrow down the mass ratio of GW170817 system to the range of $0.46-0.67$, which gives a more precise estimation of the individual NS mass than pure GW signal analysis, i.e. $0.90~{\rm M_{\odot}}<M_1<1.16~{\rm M_{\odot}}$ and $1.61~{\rm M_{\odot}}<M_2<2.11~{\rm M_{\odot}}$.

astro-ph.HE↗
arXiv2017

Gravitational wave source localization for eccentric binary coalesce with a ground-based detector network

Gravitational wave source localization problem is important in gravitational wave astronomy. Regarding ground-based detector, almost all of the previous investigations only considered the difference of arrival time among the detector network for source localization. Within the matched filtering framework, the information beside the arrival time difference can possibly also do some help on source localization. Especially when an eccentric binary is considered, the character involved in the gravitational waveform may improve the source localization. We investigate this effect systematically in the current paper. During the investigation, the enhanced post-circular (EPC) waveform model is used to describe the eccentric binary coalesce. We find that the source localization accuracy does increase along with the eccentricity increases. But such improvement depends on the total mass of the binary. For total mass 100M${}_\odot$ binary, the source localization accuracy may be improved about 2 times in general when the eccentricity increases from 0 to 0.4. For total mass 65M${}_\odot$ binary (GW150914-like binary), the improvement factor is about 1.3 when the eccentricity increases from 0 to 0.4. For total mass 22M${}_\odot$ binary (GW151226-like binary), such improvement is ignorable.

gr-qc↗
arXiv2017

Note on the gravitational and electromagnetic radiation for the Einstein-Maxwell equations with cosmological constant

In the middle of last century, Bondi and his coworkers proposed an out going boundary condition for the Einstein equations. Based on such boundary condition the authors theoretically solved the puzzle of the existence problem of gravitational wave. Currently many works on gravitational wave source modeling use Bondi's result to do the analysis including the gravitational wave calculation in numerical relativity. Recently more and more observations imply that the Einstein equations should be modified with an nonzero cosmological constant. In this work we use Bondi's original method to treat the Einstein equations with cosmological constant for theoretical curiosity. We find that the gravitational wave does not essentially exist if Bondi's original out going boundary condition is imposed. We find this unphysical result is due to the non-consistency between Bondi's original out going boundary condition and the Einstein equations with cosmological constant. Based on theoretical analysis, we propose an new Bondi-type out going boundary condition for the Einstein equations with cosmological constant. With this new boundary condition, the gravitational wave behavior for the Einstein equations with cosmological constant is similar to the Einstein equations without cosmological constant. In particular, when the cosmological constant goes to zero, the behavior of the Einstein equations without cosmological constant is recovered. Together with gravitational wave, electromagnetic wave is also analyzed. The boundary conditions for electromagnetic wave does not depend on the cosmological constant.

gr-qc↗
arXiv2017

Long-Term Postmerger Simulations of Binary Neutron Star Coalescence: Formation of Toroidal Remnants and Gravitational Wave Afterglow

It has been estimated that a significant proportion of binary neutron star merger events produce long-lived massive remnants supported by differential rotation and subject to rotational instabilities. To examine formation and oscillation of rapidly rotating neutron stars (NS) after merger, we present an exploratory study of fully general-relativistic hydrodynamic simulations using the public code Einstein Toolkit. The attention is focused on qualitative aspects of long-term postmerger evolution. As simplified test models, we use a moderately stiff Gamma=2 ideal-fluid equation of state and unmagnetized irrotational equal-mass binaries with three masses well below the threshold for prompt collapse. Our high resolution simulations generate postmerger "ringdown" gravitational wave (GW) signals of 170 ms, sustained by rotating massive NS remnants without collapsing to black holes. We observe that the high-density double-core structure inside the remnants gradually turns into a quasi-axisymmetric toroidal shape. It oscillates in a quasi-periodic manner and shrinks in size due to gravitational radiation. In the GW spectrograms, dominant double peaks persist throughout the postmerger simulations and slowly drift to higher frequencies. A new low-frequency peak emerges at about 100 ms after merger, owing to the growth of GW-driven unstable oscillation modes. The long-term effect of grid resolution is also investigated using the same initial model. Moreover, we comment on physical conditions that are favorable for the transient toroidal configuration to form, and discuss implication of our findings on future GW observation targeting rapidly rotating NSs.

gr-qc↗
arXiv2017

Excitation of high frequency voices from intermediate-mass-ratio inspirals with large eccentricity

The coalescence of a stellar-mass compact object together with an intermediate-mass black hole, also known as intermediate-mass-ratio inspiral, is usually not expected to be a viable gravitational wave source for the current ground-based gravitational wave detectors, due to the generally lower frequency of such source. In this paper, we adopt the effective-one-body formalism as the equation of motion, and obtain the accurately calculated gravitational waveforms by solving the Teukolsky equation in frequency-domain. We point out that high frequency modes of gravitational waves can be excited by large eccentricities of intermediate-mass-ratio inspirals. These high frequency modes can extend to more than 10 Hz, and enter the designed sensitive band of Advanced LIGO and Advanced Virgo. We propose that such kind of highly eccentric intermediate-mass-ratio inspirals could be feasible sources and potentially observable by the ground-based gravitational wave detectors, like the Advanced LIGO and Advanced Virgo.

gr-qc↗
arXiv2017

A waveform model for eccentric binary black hole based on effective-one-body-numerical-relativity (EOBNR) formalism

Binary black hole systems are among the most important sources for gravitational wave detection. And also they are good objects for theoretical research for general relativity. Gravitational waveform template is important to data analysis. Effective-one-body-numerical-relativity (EOBNR) model has played an essential role in the LIGO data analysis. For future space-based gravitational wave detection, many binary systems will admit somewhat orbit eccentricity. At the same time the eccentric binary is also an interesting topic for theoretical study in general relativity. In this paper we construct the first eccentric binary waveform model based on effective-one-body-numerical-relativity framework. Our basic assumption in the model construction is that the involved eccentricity is small. We have compared our eccentric EOBNR model to the circular one used in LIGO data analysis. We have also tested our eccentric EOBNR model against to another recently proposed eccentric binary waveform model; against to numerical relativity simulation results; and against to perturbation approximation results for extreme mass ratio binary systems. Compared to numerical relativity simulations with eccentricity as large as about 0.2, the overlap factor for our eccentric EOBNR model is better than 0.98 for all tested cases including spinless binary and spinning binary; equal mass binary and unequal mass binary. Hopefully our eccentric model can be the start point to develop a faithful template for future space-based gravitational wave detectors.

gr-qc↗
arXiv2017

Magnetic-distortion-induced ellipticity and gravitational wave radiation of neutron stars: millisecond magnetars in short GRBs, Galactic pulsars, and magnetars

Neutron stars may sustain a non-axisymmetric deformation due to magnetic distortion and are potential sources of continuous gravitational waves (GWs) for ground-based interferometric detectors. With decades of searches using available GW detectors, no evidence of a GW signal from any pulsar has been observed. Progressively stringent upper limits of ellipticity have been placed on Galactic pulsars. In this work, we use the ellipticity inferred from the putative millisecond magnetars in short gamma-ray bursts (SGRBs) to estimate their detectability by current and future GW detectors. For $\sim 1$ ms magnetars inferred from the SGRB data, the detection horizon is $\sim 30$ Mpc and $\sim 600$ Mpc for advanced LIGO (aLIGO) and Einstein Telescope (ET), respectively. Using the ellipticity of SGRB millisecond magnetars as calibration, we estimate the ellipticity and gravitational wave strain of Galactic pulsars and magnetars assuming that the ellipticity is magnetic-distortion-induced. We find that the results are consistent with the null detection results of Galactic pulsars and magnetars with the aLIGO O1. We further predict that the GW signals from these pulsars/magnetars may not be detectable by the currently designed aLIGO detector. The ET detector may be able to detect some relatively low frequency signals ($<50$ Hz) from some of these pulsars. Limited by its design sensitivity, the eLISA detector seems not suitable for detecting the signals from Galactic pulsars and magnetars.

astro-ph.HE↗
arXiv2017

The Gravitational-Wave Physics

The direct detection of gravitational wave by Laser Interferometer Gravitational-Wave Observatory indicates the coming of the era of gravitational-wave astronomy and gravitational-wave cosmology. It is expected that more and more gravitational-wave events will be detected by currently existing and planned gravitational-wave detectors. The gravitational waves open a new window to explore the Universe and various mysteries will be disclosed through the gravitational-wave detection, combined with other cosmological probes. The gravitational-wave physics is not only related to gravitation theory, but also is closely tied to fundamental physics, cosmology and astrophysics. In this review article, three kinds of sources of gravitational waves and relevant physics will be discussed, namely gravitational waves produced during the inflation and preheating phases of the Universe, the gravitational waves produced during the first-order phase transition as the Universe cools down and the gravitational waves from the three phases: inspiral, merger and ringdown of a compact binary system, respectively. We will also discuss the gravitational waves as a standard siren to explore the evolution of the Universe.

gr-qc↗
arXiv2016

Binary Black Hole merger in f(R) theory

In the near future, gravitational wave detection is set to become an important observational tool for astrophysics. It will provide us with an excellent means to distinguish different gravitational theories. In effective form, many gravitational theories can be cast into an f(R) theory. In this article, we study the dynamics and gravitational waveform of an equal-mass binary black hole system in f(R) theory. We reduce the equations of motion in f(R) theory to the Einstein-Klein-Gordon coupled equations. In this form, it is straightforward to modify our existing numerical relativistic codes to simulate binary black hole mergers in f(R) theory. We considered binary black holes surrounded by a shell of scalar field. We solve the initial data numerically using the Olliptic code. The evolution part is calculated using the extended AMSSNCKU code. Both codes were updated and tested to solve the problem of binary black holes in f(R) theory. Our results show that the binary black hole dynamics in f(R) theory is more complex than in general relativity. In particular, the trajectory and merger time are strongly affected. Via the gravitational wave, it is possible to constrain the quadratic part parameter of f(R) theory in the range |a_2|<10^{11} m^2 . In principle, a gravitational wave detector can distinguish between a merger of binary black hole in f(R) theory and the respective merger in general relativity. Moreover, it is possible to use gravitational wave detection to distinguish between f(R) theory and a non self-interacting scalar field model in general relativity.

gr-qc↗
arXiv2016

Multi-horizon and Critical Behavior in Gravitational Collapse of Massless Scalar

This paper studies the whole process of gravitational collapse and accretion of a massless scalar field in asymptotically flat spacetime. Two kinds of initial configurations are considered. One is the initial data without black hole, the other contains a black hole. Under suitable initial conditions, we find that multi-horizon will appear, which means that the initial black hole formed by gravitational collapse or existing at the beginning will instantly expand and suddenly grow, rather than grows gradually in the accretion process. A new type of critical behavior is found around the instant expansion. The numerical computation shows that the critical exponents are universal.

gr-qc↗
arXiv2016

Gravitational wave astronomy: the current status

In the centenary year of Einstein's General Theory of Relativity, this paper reviews the current status of gravitational wave astronomy across a spectrum which stretches from attohertz to kilohertz frequencies. Sect. 1 of this paper reviews the historical development of gravitational wave astronomy from Einstein's first prediction to our current understanding the spectrum. It is shown that detection of signals in the audio frequency spectrum can be expected very soon, and that a north-south pair of next generation detectors would provide large scientific benefits. Sect. 2 reviews the theory of gravitational waves and the principles of detection using laser interferometry. The state of the art Advanced LIGO detectors are then described. These detectors have a high chance of detecting the first events in the near future. Sect. 3 reviews the KAGRA detector currently under development in Japan, which will be the first laser interferometer detector to use cryogenic test masses. Sect. 4 of this paper reviews gravitational wave detection in the nanohertz frequency band using the technique of pulsar timing. Sect. 5 reviews the status of gravitational wave detection in the attohertz frequency band, detectable in the polarisation of the cosmic microwave background, and discusses the prospects for detection of primordial waves from the big bang. The techniques described in sects. 1-5 have already placed significant limits on the strength of gravitational wave sources. Sects. 6 and 7 review ambitious plans for future space based gravitational wave detectors in the millihertz frequency band. Sect. 6 presents a roadmap for development of space based gravitational wave detectors by China while sect. 7 discusses a key enabling technology for space interferometry known as time delay interferometry.

physics.ins-det↗
arXiv2015

Pseudotensor applied to Numerical Relativity in Calculating Global Quantities

In this work we apply the Landau-Lifshitz pseudotensor flux formalism to the calculation of the total mass and the total angular momentum during the evolution of a binary black hole system. We also compare its performance with the traditional integrations for the global quantities. It shows that the advantage of the pseudotensor flux formalism is the smoothness of the numerical value of the global quantities, especially of the total angular momentum. Although the convergence behavior of the global quantities with the pseudotensor flux method is only comparable with the ones with the traditional method, the smoothness of its numerical value allows using a larger radius for surface integration to obtain more accurate result.

gr-qc↗
arXiv2015

Improved fast-rotating black hole evolution simulations with modified Baumgarte-Shapiro-Shibata-Nakamura formulation

Different formulations of Einstein's equations used in numerical relativity can affect not only the stability but also the accuracy of numerical simulations. In the original Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation, the loss of the angular momentum, $J$, is non-negligible in highly spinning single black hole evolutions. This loss also appears, usually right after the merger, in highly spinning binary black hole simulations, The loss of $J$ may be attributed to some unclear numerical dissipation. Reducing unphysical dissipation is expected to result in more stable and accurate evolutions. In the previous work \cite{yhlc12} we proposed several modifications which are able to prevent black hole evolutions from the unphysical dissipation, and the resulting simulations are more stable than in the traditional BSSN formulation. Specifically, these three modifications (M1, M2, and M3) enhance the effects of stability, hyperbolicity, and dissipation of the formulation. We experiment further in this work with these modifications, and demonstrate that these modifications improve the accuracy and also effectively suppress the loss of $J$, particularly in the black hole simulations with the initially large ratio of $J$ and the square of the ADM mass.

gr-qc↗
arXiv2014

Descope of the ALIA mission

The present work reports on a feasibility study commissioned by the Chinese Academy of Sciences of China to explore various possible mission options to detect gravitational waves in space alternative to that of the eLISA/LISA mission concept. Based on the relative merits assigned to science and technological viability, a few representative mission options descoped from the ALIA mission are considered. A semi-analytic Monte Carlo simulation is carried out to understand the cosmic black hole merger histories starting from intermediate mass black holes at high redshift as well as the possible scientific merits of the mission options considered in probing the light seed black holes and their coevolution with galaxies in early Universe. The study indicates that, by choosing the armlength of the interferometer to be three million kilometers and shifting the sensitivity floor to around one-hundredth Hz, together with a very moderate improvement on the position noise budget, there are certain mission options capable of exploring light seed, intermediate mass black hole binaries at high redshift that are not readily accessible to eLISA/LISA, and yet the technological requirements seem to within reach in the next few decades for China.

gr-qc↗
arXiv2012

Compact binary evolutions with the Z4c formulation

Numerical relativity simulations of compact binaries with the Z4c and BSSNOK formulations are compared. The Z4c formulation is advantageous in every case considered. In simulations of non-vacuum spacetimes the constraint violations due to truncation errors are between one and three orders of magnitude lower in the Z4c evolutions. Improvements are also found in the accuracy of the computed gravitational radiation. For equal-mass irrotational binary neutron star evolutions we find that the absolute errors in phase and amplitude of the waveforms can be up to a factor of four smaller. The quality of the Z4c numerical data is also demonstrated by a remarkably accurate computation of the ADM mass from surface integrals. For equal-mass non-spinning binary puncture black hole evolutions we find that the absolute errors in phase and amplitude of the waveforms can be up to a factor of two smaller. In the same evolutions we find that away from the punctures the Hamiltonian constraint violation is reduced by between one and two orders of magnitude. Furthermore, the utility of gravitational radiation controlling, constraint preserving boundary conditions for the Z4c formulation is demonstrated. The evolution of spacetimes containing a single compact object confirm earlier results in spherical symmetry. The boundary conditions avoid spurious and non-convergent effects present in high resolution runs with either formulation with a more naive boundary treatment. We conclude that Z4c is preferable to BSSNOK for the numerical solution of the 3+1 Einstein equations with the puncture gauge.

gr-qc↗