Binary Systems Of Compact Objects Research Articles

New algorithm of measuring gravitational wave radiation from rotating binary system

In order to investigate the gravitational wave (GW) radiation, without resorting to the traceless transverse gauge approach to the GW formalism of the linearized general relativity, we formulate the so-called modified linearized general relativity (MLGR). As an application of the MLGR, we construct a novel paradigm of measuring the GW radiation from a binary system of compact objects, to theoretically interpret its phenomenology. To accomplish this, we formulate the mass scalar and mass vector potentials for the merging binary compact objects, from which we construct the mass magnetic field in addition to the mass electric one which also includes the mass vector potential effect. Next, defining the mass Poyinting vector in terms of the mass electric and mass magnetic fields in the MLGR, we find the GW radiation intensity profile possessing a prolate ellipsoid geometry due to the merging binary compact objects source. At a given radial distance from the binary compact objects, the GW radiation intensity on the revolution axis of the binary compact objects is shown to be twice that on the equatorial plane. Moreover, we explicitly obtain the total radiation power of the GW, which has the same characteristic as that of the electromagnetic wave in the rotating charge electric dipole moment. We also find that, in no distorting limit of the merging binary compact objects, the compact objects in the MLGR do not yield the total GW radiation power, consistent with the result of the traceless transverse gauge algorithm in the linearized general relativity.

Frequency domain analysis of the gravitational wave energy loss in hyperbolic encounters

The energy radiated (without the 1.5PN tail contribution which requires a different treatment) by a binary system of compact objects moving in a hyperboliclike orbit is computed in the frequency domain through the second post-Newtonian level as an expansion in the large-eccentricity parameter up to next-to-next-to-leading order, completing the time domain corresponding information (fully known in closed form at the second post-Newtonian of accuracy). The spectrum contains quadratic products of the modified Bessel functions of the first kind (Bessel K functions) with frequency-dependent order (and argument) already at Newtonian level, so preventing the direct evaluation of Fourier integrals. However, as the order of the Bessel functions tends to zero for large eccentricities, a large-eccentricity expansion of the spectrum allows for analytical computation beyond the lowest order.

Effective field theory for binary cosmic strings

We extend the effective field theory (EFT) formalism for gravitational radiation from a binary system of compact objects to the case of extended objects. In particular, we study the EFT for a binary system consisting of two infinitely-long cosmic strings with small velocity and small spatial substructure, or "wiggles". The complexity of the system requires the introduction of two perturbative expansion parameters, constructed from the velocity and size of the wiggles, in contrast with the point particle case, for which a single parameter is sufficient. This further requires us to assign new power counting rules in the system. We integrate out the modes corresponding to potential gravitons, yielding an effective action for the radiation gravitons. We show that this action describes a changing quadrupole, sourced by the bending modes of the string, which in turn generates gravitational waves. We study the ultraviolet divergences in this description, and use them to obtain the classical renormalization group flow of the string tension in such a setting.

Next-to-leading order spin-orbit effects in the equations of motion, energy loss, and phase evolution of binaries of compact bodies in the effective field theory approach

We compute spin-orbit effects in the equations of motion, binding energy, and energy loss of binary systems of compact objects at the next-to-leading order in the post-Newtonian approximation in the effective field theory (EFT) framework. We then use these quantities to compute the evolution of the orbital frequency and accumulated orbital phase including spin-orbit effects beyond the dominant order. To obtain the results presented in this paper, we make use of known ingredients in the EFT literature, such as the potential and the multipole moments with spin effects at next-to-leading order, and which are given in the linearized harmonic gauge and with the spins in the locally flat frame. We also obtain the correction to the center-of-mass frame caused by spin-orbit effects at next-to-leading order. We demonstrate the equivalence between our EFT results and those which were obtained elsewhere using different formalisms. The results presented in this paper provide us with the final ingredients for the construction of theoretical templates for gravitational waves including next-to-leading order spin-orbit effects, which will be presented in a future publication.

Estimates for disk and ejecta masses produced in compact binary mergers

There is irresistible observational evidence that binary systems of compact objects with at least one neutron star are progenitors of short gamma-ray bursts, as well as a production site for r-process elements, at least when some matter is ejected by the merger and an accretion disk is formed. The recent observations of gravitational waves in conjunction with electromagnetic counterparts fuel the need for models predicting the outcome of a given merger and the properties of the associated matter outflows as a function of the initial parameters of the binary. In this manuscript, we provide updated fitting formulae that estimate the disk mass for double neutron star binaries and ejecta masses for black hole-neutron star and double neutron star binaries, fitted to the results of numerical simulations. Our proposed fitting formulae improve on existing models by aiming for analytical simplicity, by covering a larger region of parameter space, and by accounting for regions of parameter space not covered by numerical simulations but with physically manifest merger outcomes.

How to understand high-energy gamma-ray bursts?

Gamma-ray bursts (GRBs) are short-duration flashes of gamma rays occurring at cosmological distances and the most violent explosive phenomena since the cosmic big bang. GRBs were accidentally discovered by Vela military satellites of United States in 1967. The BATSE instrument onboard the Compton Space Gamma-Ray Observatory found two types of GRBs, long-duration ($T_{90}>$ 2s) and short-duration ($T_{90} Science as one of the top ten scientific breakthroughs of the year. In 1999, long GRBs were found to be associated with the birth of stellar mass black holes. In 2003, the HETE-II satellite discovered the first direct association of a long GRB with a type Ic supernova, confirming that long GRBs are linked to the core collapse of massive stars. Science ranked these two major advances as one of the worlds top ten scientific breakthroughs of the year in 1999 and 2003, respectively. In 2005, the Swift satellite made the first accurate localization of short GRBs, leading to the discoveries of afterglows, host galaxies and redshifts of short GRBs. These observations provide indirect evidence that short GRBs originate from mergers of binary systems of compact objects (at least including one neutron star) at cosmological distances. In particular, on 2017 August 17, the LIGO/Virgo gravitational wave (GW) detectors, for the first time, discovered a GW event from a binary neutron star (BNS) merger, GW170817. About 1.74 s after the merger, Fermi/GBM detected a short gamma-ray burst (named GRB170817A). Subsequently, many ground-based and space-based telescopes detected X-ray, ultraviolet, optical, nearly infrared, and radio counterparts to GW170817, especially including a multi-wavelength kilonova (named AT2017gfo). These discoveries mark the beginning of a new era of multi-messenger astronomy. To summarize, all the observations have shown that long bursts originate from the core collapse of massive stars and short bursts originate from the mergers of binary compact objects (at least including one neutron star); besides prompt gamma-ray emission, the sources of GRBs produce X-ray, optical and radio afterglows in timescales of weeks, months and years after the burst trigger, respectively. Theoretically, prompt gamma-ray emissions of GRBs are thought to arise from some energy dissipation processes in the interiors of relativistic jets and multi-wavelength afterglows arise from forward shocks due to collisions between the jets and their ambient media. Therefore, GRBs are not only astronomical laboratories of studying extremely physical phenomena (e.g., newborn compact objects including stellar-mass black holes and neutron stars, gravitational waves, ultra-high-energy cosmic rays, and high-energy neutrinos) and of testing the basic physical principles with high accuracy, but also become an important probe of the star formation and evolution in the early universe, high-redshift galaxies, and cosmology. GRBs now are a multidisciplinary field (including astronomy, cosmology, and physics) and thus one of the most competitive fundamental research fields. In this paper, we review recent researches of GRBs and electromagnetic counterparts to gravitational waves, by focusing on the relevant key scientific issues, and discuss how to seize the opportunity to plan the interdisciplinary strategy based on the development trend and the research foundation in China, to maximize domestic scientific equipment achievements, and to enhance Chinese international influence in this field.

Brane-world extra dimensions in light of GW170817

The search for extra dimensions is a challenging endeavor to probe physics beyond the Standard Model. The joint detection of gravitational waves (GW) and electromagnetic (EM) signals from the merging of a binary system of compact objects like neutron stars (NS), can help constrain the geometry of extra dimensions beyond our 3+1 spacetime ones. A theoretically well-motivated possibility is that our observable Universe is a 3+1-dimensional hypersurface, or brane, embedded in a higher 4+1-dimensional Anti-de Sitter (AdS$_5$) spacetime, in which gravity is the only force which propagates through the infinite bulk space, while other forces are confined to the brane. In these types of brane-world models, GW and EM signals between two points on the brane would, in general, travel different paths. This would result in a time-lag between the detection of GW and EM signals emitted simultaneously from the same source. We consider the recent near-simultaneous detection of the GW event GW170817 from the LIGO/Virgo collaboration, and its EM counterpart, the short gamma-ray burst GRB170817A detected by the Fermi Gamma-ray Burst Monitor and the INTEGRAL Anti-Coincidence Shield spectrometer. Assuming the standard $\Lambda$-Cold Dark Matter ($\Lambda$CDM) scenario and performing a likelihood analysis which takes into account astrophysical uncertainties associated to the measured time-lag, we set an upper limit of $\ell \lesssim 0.535\,$Mpc at $68\%$ confidence level on the AdS$_5$ radius of curvature $\ell$. Although the bound is not competitive with current Solar System constraints, it is the first time that data from a multi-messenger GW-EM measurement is used to constrain extra-dimensional models. Thus, our work provides a proof-of-principle for the possibility of using multi-messenger astronomy for probing the geometry of our space-time.

Gamma-ray bursts at high and very high energies

Gamma-Ray Bursts (GRBs) are extra-galactic and extremely energetic transient emissions of gamma rays, which are thought to be associated with the death of massive stars or the merger of compact objects in binary systems. Their huge luminosities involve the presence a newborn stellar-mass black hole emitting a relativistic collimated outflow, which accelerates particles and produces non-thermal emissions from the radio domain to the highest energies. In this article, I review recent progresses in the understanding of GRB jet physics above 100 MeV, based on Fermi observations of bright GRBs. I discuss the physical implications of these observations and their impact on GRB modeling, and I present some prospects for GRB observation at very high energies in the near future.

Gravitational waves from direct collapse black holes formation

The possible formation of Direct Collapse Black Holes (DCBHs) in the first metal-free atomic cooling halos at high redshifts ($z > 10$) is nowadays object of intense study and several methods to prove their existence are currently under development. The abrupt collapse of a massive ($\sim 10^4 - 10^5 \, \mathrm{M_{\odot}}$) and rotating object is a powerful source of gravitational waves emission. In this work, we employ modern waveforms and the improved knowledge on the DCBHs formation rate to estimate the gravitational signal emitted by these sources at cosmological distances. Their formation rate is very high ($\sim 10^4 \, \mathrm{yr^{-1}}$ up to $z\sim20$), but due to a short duration of the collapse event ($\sim 2-30\, \mathrm{s}$, depending on the DCBH mass) the integrated signal from these sources is characterized by a very low duty-cycle (${\cal D}\sim 10^{-3}$), i.e. a shot-noise signal. Our results show that the estimated signal lies above the foreseen sensitivity of the Ultimate-DECIGO observatory in the frequency range $(0.8-300) \, \mathrm{mHz}$, with a peak amplitude $\Omega_{gw} = 1.1 \times 10^{-54}$ at $\nu_{max} = 0.9 \, \mathrm{mHz}$ and a peak Signal-to-Noise Ratio $\mathrm{SNR}\sim 22$ at $\nu = 20 \, \mathrm{mHz}$. This amplitude is lower than the Galactic confusion noise, generated by binary systems of compact objects in the same frequency band. For this reason, advanced techniques will be required to separate this signal from background and foreground noise components. As a proof-of-concept, we conclude by proposing a simple method, based on the auto-correlation function, to recognize the presence of a ${\cal D} \ll 1$ signal buried into the continuous noise. The aim of this work is to test the existence of a large population of high-z DCBHs, by observing the gravitational waves emitted during their infancy.

Where do the progenitors of millisecond pulsars come from?

AbstractObservations of a large population of millisecond pulsars (MSPs) show a wide divergence in the orbital periods (from approximately hours to a few months). In the standard view, low‐mass X‐ray binaries (LMXBs) are considered as progenitors for some MSPs during the recycling process. We present a systematic study that combines different types of compact objects in binaries such as cataclysmic variables (CVs), LMXBs, and MSPs. We plot them together in the so called Corbet diagram. Larger and different samples are needed to better constrain the result as a function of the environment and formations. A scale diagram showing the distribution of MSPs for different orbital periods and the aspects for their progenitors relying on accretion induced collapse (AIC) of white dwarfs in binaries. Thus massive CVs (M ≥ 1.1 M⊙) can play a vital role on binary evolution, as well as of the physical processes involved in the formation and evolution of neutron stars and their magnetic fields, and could turn into binary MSPs with different scales of orbital periods; this effect can be explained by the AIC process. This scenario also suggests that some fraction of isolated MSPs in the Galactic disk could be formed through the same channel, forming the contribution of some CVs to the single‐degenerate progenitors of Type Ia supernova. Furthermore, we have refined the statistical distribution and evolution by using updated data. This implies that the significant studies of compact objects in binary systems can benefit from the Corbet diagram.Observations of a large population of millisecond pulsars (MSPs) show a wide divergence in the orbital periods (from approximately hours to a few months). In the standard view, low‐mass X‐ray binaries (LMXBs) are considered as progenitors for some MSPs during the recycling process. We present a systematic study that combines different types of compact objects in binaries such as cataclysmic variables (CVs), LMXBs, and MSPs. We plot them together in the so called Corbet diagram. Larger and different samples are needed to better constrain the result as a function of the environment and formations. A scale diagram showing the distribution of MSPs for different orbital periods and the aspects for their progenitors re

A Modified DIviding RECTangles Algorithm for a Problem in Astrophysics

We present a modification of the DIRECT (DIviding RECTangles) algorithm, called DIRECT-G, to solve a box-constrained global optimization problem arising in the detection of gravitational waves emitted by coalescing binary systems of compact objects. This is a hard problem, since the objective function is highly nonlinear and expensive to evaluate, has a huge number of local extrema and unavailable derivatives. DIRECT performs a sampling of the feasible domain over a set of points that becomes dense in the limit, thus ensuring the everywhere dense convergence; however, it becomes ineffective on significant instances of the problem under consideration, because it tends to produce a uniform coverage of the feasible domain, by oversampling regions that are far from the optimal solution. DIRECT has been modified by embodying information provided by a suitable discretization of the feasible domain, based on the signal theory, which takes into account the variability of the objective function. Numerical experiments show that DIRECT-G largely outperforms DIRECT and the grid search, the latter being the reference algorithm in the astrophysics community. Furthermore, DIRECT-G is comparable with a genetic algorithm specifically developed for the problem. However, DIRECT-G inherits the convergence properties of DIRECT, whereas the genetic algorithm has no guarantee of convergence.

Thermodynamics of magnetized binary compact objects

Binary systems of compact objects with electromagnetic field are modeled by helically symmetric Einstein-Maxwell spacetimes with charged and magnetized perfect fluids. Previously derived thermodynamic laws for helically symmetric perfect-fluid spacetimes are extended to include the electromagnetic fields, and electric currents and charges; the first law is written as a relation between the change in the asymptotic Noether charge $\ensuremath{\delta}Q$ and the changes in the area and electric charge of black holes, and in the vorticity, baryon rest mass, entropy, charge and magnetic flux of the magnetized fluid. Using the conservation laws of the circulation of magnetized flow found by Bekenstein and Oron for the ideal magnetohydrodynamic fluid, and also for the flow with zero conducting current, we show that, for nearby equilibria that conserve the quantities mentioned above, the relation $\ensuremath{\delta}Q=0$ is satisfied. We also discuss a formulation for computing numerical solutions of magnetized binary compact objects in equilibrium with emphasis on a first integral of the ideal magnetohydrodynamic-Euler equation.

Prospects for joint radio telescope and gravitational-wave searches for astrophysical transients

The radio skies remain mostly unobserved when it comes to transient phenomena. The direct detection of gravitational waves (GWs) will mark a major milestone of modern astronomy, as an entirely new window will open on the universe. Two apparently independent phenomena can be brought together in a coincident effort that has the potential to boost both searches. In this paper we will outline the scientific case that stands behind these future joint observations and will describe the methods that might be used to conduct the searches and analyse the data. The targeted sources are binary systems of compact objects, known to be strong candidate sources for GWs. Detection of transients coincident in these two channels would be a significant ‘smoking gun’ for first direct detection of GWs and would open up a new field for characterization of astrophysical transients involving massive compact objects.

A genetic algorithm for a global optimization problem arising in the detection of gravitational waves

The detection of gravitational waves is a long-awaited event in modern physics and, to achieve this challenging goal, detectors with high sensitivity are being used or are under development. In order to extract gravitational signals emitted by coalescing binary systems of compact objects (neutron stars and/or black holes), from noisy data obtained by interferometric detectors, the matched filter technique is generally used. Its computational kernel is a box-constrained global optimization problem with many local solutions and a highly nonlinear and expensive objective function, whose derivatives are not available. To tackle this problem, we designed a real-coded genetic algorithm that exploits characteristic features of the problem itself; special attention was devoted to the choice of the initial population and of the recombination operator. Computational experiments showed that our algorithm is able to compute a reasonably accurate solution of the optimization problem, requiring a much smaller number of function evaluations than the grid search, which is generally used to solve this problem. Furthermore, the genetic algorithm largely outperforms other global optimization algorithms on significant instances of the problem.

Third post-Newtonian angular momentum flux and the secular evolution of orbital elements for inspiralling compact binaries in quasi-elliptical orbits

The angular momentum flux from an inspiralling binary system of compact objects moving in quasi-elliptical orbits is computed at the third post-Newtonian (3PN) order using the multipolar post-Minkowskian wave generation formalism. The 3PN angular momentum flux involves the instantaneous, tail, and tail-of-tails contributions as for the 3PN energy flux, and in addition a contribution due to non-linear memory. We average the angular momentum flux over the binary's orbit using the 3PN quasi-Keplerian representation of elliptical orbits. The averaged angular momentum flux provides the final input needed for gravitational wave phasing of binaries moving in quasi-elliptical orbits. We obtain the evolution of orbital elements under 3PN gravitational radiation reaction in the quasi-elliptic case. For small eccentricities, we give simpler limiting expressions relevant for phasing up to order $e^2$. This work is important for the construction of templates for quasi-eccentric binaries, and for the comparison of post-Newtonian results with the numerical relativity simulations of the plunge and merger of eccentric binaries.

Exploring accretion theory with X-ray binaries in the Small Magellanic Cloud

The understanding of the accretion process on to compact objects in binary systems is an important part of modern astrophysics. Theoretical work, primarily that of Ghosh & Lamb (1979), has made clear predictions for the behaviour of such systems which have been generally supported by observational results of considerably varying quality from galactic accreting pulsar systems. In this work a much larger homogeneous population of such objects in the Small Magellanic Cloud (SMC) is used to provide more demanding tests of the accretion theory. The results are extremely supportive of the theoretical models and provide useful statistical insights into the manner in which accreting pulsars behave and evolve.

Status of NINJA: the Numerical INJection Analysis project

The 2008 NRDA conference introduced the Numerical INJection Analysis project (NINJA), a new collaborative effort between the numerical relativity community and the data analysis community. NINJA focuses on modeling and searching for gravitational wave signatures from the coalescence of binary system of compact objects. We review the scope of this collaboration and the components of the first NINJA project, where numerical relativity groups, shared waveforms and data analysis teams applied various techniques to detect them when embedded in colored Gaussian noise.

Assigning confidence to inspiral gravitational wave candidates with Bayesian model selection

Bayesian model selection provides a powerful and mathematically transparent framework to tackle hypothesis testing, such as detection tests of gravitational waves emitted during the coalescence of binary systems using ground-based laser interferometers. Although its implementation is computationally intensive, we have developed an efficient probabilistic algorithm based on a technique known as nested sampling that makes Bayesian model selection applicable to follow-up studies of candidate signals produced by on-going searches of inspiralling compact binaries. We discuss the performance of this approach, in terms of ‘false alarm rate’ and ‘detection probability’ of restricted second post-Newtonian inspiral waveforms from non-spinning compact objects in binary systems. The results confirm that this approach is a viable tool for detection tests in current searches for gravitational wave signals.

Inspiralling compact binaries in quasi-elliptical orbits: The complete third post-Newtonian energy flux

The instantaneous contributions to the third post-Newtonian (3PN) gravitational wave luminosity from the inspiral phase of a binary system of compact objects moving in a quasi-elliptical orbit is computed using the multipolar post-Minkowskian wave generation formalism. The necessary inputs for this calculation include the 3PN accurate mass quadrupole moment for general orbits and the mass octupole and current quadrupole moments at 2PN. Using the recently obtained 3PN quasi-Keplerian representation of elliptical orbits, the flux is averaged over the binary's orbit. Supplementing this by the important hereditary contributions arising from tails, tails of tails, and tails-squared terms calculated in a previous paper, the complete 3PN energy flux is obtained. The final result presented in this paper would be needed for the construction of ready-to-use templates for binaries moving on noncircular orbits, a plausible class of sources not only for the space-based detectors like LISA but also for the ground-based ones.

Tail effects in the third post-Newtonian gravitational wave energy flux of compact binaries in quasi-elliptical orbits

The far-zone flux of energy contains hereditary (tail) contr ibutions that depend on the entire past history of the source. Using the multipolar post-Minkowskian wave generation formalism, we propose and implement a semi-analytical method in the frequency domain to compute these contributions from the inspiral phase of a binary system of compact objects moving in quasi-elliptical orbits up to third post-Newtonian (3PN) order. The method explicitly uses the quasi-Keplerian representation of elliptical orbits at 1PN order and exploits the doubly periodic nature of the motion to average the 3PN flu xes over the binary’s orbit. Together with the instantaneous (non-tail) contributions evaluated in a companion paper, it provides crucial inputs for the construction of ready-to-use templates for compact binaries moving on quasi-elliptic orbits, an interesting class of sources for the ground based gravitational wave detectors such as LIGO and Virgo as well as space based detectors like LISA.