Constraining the Equation of State with Moment of Inertia Measurements

We estimate that the moment of inertia of star A in the recently discovered double pulsar system PSR J0737-3039 may be determined after a few years of observation to something like 10% accuracy. This would enable accurate estimates of the radius of the star and the presure of matter in the vicinity of 1 to 2 times the nuclear saturation density, which would in turn provide strong constraints on the equation of state of neutron stars and the physics of their interiors.Comment: Submitted to ApJ, 4 figure

Post-Newtonian accurate parametric solution to the dynamics of spinning compact binaries in eccentric orbits: The leading order spin-orbit interaction

We derive Keplerian-type parametrization for the solution of post-Newtonian (PN) accurate conservative dynamics of spinning compact binaries moving in eccentric orbits. The PN accurate dynamics that we consider consists of the third post-Newtonian accurate conservative orbital dynamics influenced by the leading order spin effects, namely the leading order spin-orbit interactions. The orbital elements of the representation are explicitly given in terms of the conserved orbital energy, angular momentum and a quantity that characterizes the leading order spin-orbit interactions in Arnowitt, Deser, and Misner-type coordinates. Our parametric solution is applicable in the following two distinct cases: (i) the binary consists of equal mass compact objects, having two arbitrary spins, and (ii) the binary consists of compact objects of arbitrary mass, where only one of them is spinning with an arbitrary spin. As an application of our parametrization, we present gravitational wave polarizations, whose amplitudes are restricted to the leading quadrupolar order, suitable to describe gravitational radiation from spinning compact binaries moving in eccentric orbits. The present parametrization will be required to construct `ready to use' reference templates for gravitational waves from spinning compact binaries in inspiralling eccentric orbits. Our parametric solution for the post-Newtonian accurate conservative dynamics of spinning compact binaries clearly indicates, for the cases considered, the absence of chaos in these systems. Finally, we note that our parametrization provides the first step in deriving a fully second post-Newtonian accurate `timing formula', that may be useful for the radio observations of relativistic binary pulsars like J0737-3039.Comment: 18 pages, accepted by Phys. Rev.

A new numerical method to construct binary neutron star initial data

We present a new numerical method for the generation of binary neutron star initial data using a method along the lines of the the Wilson-Mathews or the closely related conformal thin sandwich approach. Our method uses six different computational domains, which include spatial infinity. Each domain has its own coordinates which are chosen such that the star surfaces always coincide with domain boundaries. These properties facilitate the imposition of boundary conditions. Since all our fields are smooth inside each domain, we are able to use an efficient pseudospectral method to solve the elliptic equations associated with the conformal thin sandwich approach. Currently we have implemented corotating configurations with arbitrary mass ratios, but an extension to arbitrary spins is possible. The main purpose of this paper is to introduce our new method and to test our code for several different configurations.Comment: 18 pages, 8 figures, 1 tabl

Angular Resolution of the LISA Gravitational Wave Detector

We calculate the angular resolution of the planned LISA detector, a space-based laser interferometer for measuring low-frequency gravitational waves from galactic and extragalactic sources. LISA is not a pointed instrument; it is an all-sky monitor with a quadrupolar beam pattern. LISA will measure simultaneously both polarization components of incoming gravitational waves, so the data will consist of two time series. All physical properties of the source, including its position, must be extracted from these time series. LISA's angular resolution is therefore not a fixed quantity, but rather depends on the type of signal and on how much other information must be extracted. Information about the source position will be encoded in the measured signal in three ways: 1) through the relative amplitudes and phases of the two polarization components, 2) through the periodic Doppler shift imposed on the signal by the detector's motion around the Sun, and 3) through the further modulation of the signal caused by the detector's time-varying orientation. We derive the basic formulae required to calculate the LISA's angular resolution $\Delta \Omega_S$ for a given source. We then evaluate $\Delta \Omega_S$ for two sources of particular interest: monchromatic sources and mergers of supermassive black holes. For these two types of sources, we calculate (in the high signal-to-noise approximation) the full variance-covariance matrix, which gives the accuracy to which all source parameters can be measured. Since our results on LISA's angular resolution depend mainly on gross features of the detector geometry, orbit, and noise curve, we expect these results to be fairly insensitive to modest changes in detector design that may occur between now and launch. We also expect that our calculations could be easily modified to apply to a modified design.Comment: 15 pages, 5 figures, RevTex 3.0 fil

Third-and-a-half order post-Newtonian equations of motion for relativistic compact binaries using the strong field point particle limit

We report our rederivation of the equations of motion for relativistic compact binaries through the third-and-a-half post-Newtonian (3.5 PN) order approximation to general relativity using the strong field point particle limit to describe self-gravitating stars instead of the Dirac delta functional. The computation is done in harmonic coordinates. Our equations of motion describe the orbital motion of the binary consisting of spherically symmetric non-rotating stars. The resulting equations of motion fully agree with the 3.5 PN equations of motion derived in the previous works. We also show that the locally defined energy of the star has a simple relation with its mass up to the 3.5 PN order.Comment: 38 pages, no figures. Accepted for publication in Phys. Rev.

Comparing single-frequency bioelectrical impedance analysis against deuterium dilution to assess total body water.

Background/Objectives: In this study, we aimed to validate the accuracy of single-frequency bioelectrical impedance analysis (SF-BIA) at 50 kHz to assess total body water (TBW) against the reference technique deuterium dilution (D(2)O) and to explore if the simple clinical parameters extracellular fluid (ECF) composition and body shape explain individual differences between D(2)O and SF-BIA (Diff(BIA-D(2)O)). Subjects/Methods: We assessed TBW with D(2)O and SF-BIA in 26 women and 26 men without known disease or anomalous body shapes. In addition, we measured body shape with anthropometry and ECF composition (osmolality, albumin, glucose, urea, creatinine, sodium and potassium). Results: On group average, SF-BIA to predict TBW agreed well with D(2)O (SF-BIA, 39.8±10.1 l; D(2)O, 40.4±10.2 l; and Diff(BIA-D(2)O) -0.7 l). In four individuals ('outliers'; 15% of the study population), Diff(BIA-D(2)O) was high (-6.8 to +3.8 l). Diff(BIA-D(2)O) was associated with individual variations in body shape rather than ECF composition. Using gender-specific analysis, we found that individual variability of waist circumference in men and arm length in women significantly contributed to Diff(BIA-D(2)O). When removing the four 'outliers', these associations were lost. Conclusions: In the majority of our sample, BIA agreed well with D(2)O. Adjusting for individual variability in body shape by anthropometrical assessment could possibly improve the accuracy of SF-BIA for individuals who deviate from mean values with respect to body shape. However, further studies with higher subject numbers are needed to confirm our findings

Detecting gravitational waves from test-mass bodies orbiting a Kerr black hole with P-approximant templates

In this study we apply post-Newtonian (T-approximants) and resummed post-Newtonian (P-approximants) to the case of a test-particle in equatorial orbit around a Kerr black hole. We compare the two approximants by measuring their effectualness (i.e. larger overlaps with the exact signal), and faithfulness (i.e. smaller biases while measuring the parameters of the signal) with the exact (numerical) waveforms. We find that in the case of prograde orbits, T-approximant templates obtain an effectualness of ~0.99 for spins q < 0.75. For 0.75 < q < 0.95, the effectualness drops to about 0.82. The P-approximants achieve effectualness of > 0.99 for all spins up to q = 0.95. The bias in the estimation of parameters is much lower in the case of P-approximants than T-approximants. We find that P-approximants are both effectual and faithful and should be more effective than T-approximants as a detection template family when q > 0. For q < 0 both T- and P-approximants perform equally well so that either of them could be used as a detection template family. However, for parameter estimation, the P-approximant templates still outperforms the T-approximants.Comment: 11 Pages - 9 figures. Accepted for publication. Proceedings of GWDAW 9. Special edition of Classical and Quantum Gravit

Equation of state for nuclear matter based on density dependent effective interaction

An interesting method of obtaining equation of state for nuclear matter, from a density dependent M3Y interaction, by minimizing the energy per nucleon is described. The density dependence parameters of the interaction are obtained by reproducing the saturation energy per nucleon and the saturation density of spin and isospin symmetric cold infinite nuclear matter. The nuclear matter equation of state thus obtained is then used to calculate the pressure, the energy density, the nuclear incompressibility and the velocity of sound in nuclear medium. The results obtained are in good agreement with experimental data and provide a unified description of radioactivity, scattering and nuclear matter.Comment: 10 pages including 2 figure