Binary neutron star mergers: a jet engine for short gamma-ray bursts

We perform magnetohydrodynamic simulations in full general relativity (GRMHD) of quasi-circular, equal-mass, binary neutron stars that undergo merger. The initial stars are irrotational, $n=1$ polytropes and are magnetized. We explore two types of magnetic-field geometries: one where each star is endowed with a dipole magnetic field extending from the interior into the exterior, as in a pulsar, and the other where the dipole field is initially confined to the interior. In both cases the adopted magnetic fields are initially dynamically unimportant. The merger outcome is a hypermassive neutron star that undergoes delayed collapse to a black hole (spin parameter $a/M_{\rm BH} \sim 0.74$) immersed in a magnetized accretion disk. About $4000M \sim 60(M_{\rm NS}/1.625M_\odot)$ ms following merger, the region above the black hole poles becomes strongly magnetized, and a collimated, mildly relativistic outflow --- an incipient jet --- is launched. The lifetime of the accretion disk, which likely equals the lifetime of the jet, is $\Delta t \sim 0.1 (M_{\rm NS}/1.625M_\odot)$ s. In contrast to black hole--neutron star mergers, we find that incipient jets are launched even when the initial magnetic field is confined to the interior of the stars.Comment: 6 pages, 3 figures, 1 table, matches published versio

Localizing coalescing massive black hole binaries with gravitational waves

Massive black hole binary coalescences are prime targets for space-based gravitational wave (GW) observatories such as {\it LISA}. GW measurements can localize the position of a coalescing binary on the sky to an ellipse with a major axis of a few tens of arcminutes to a few degrees, depending on source redshift, and a minor axis which is $2 - 4$ times smaller. Neglecting weak gravitational lensing, the GWs would also determine the source's luminosity distance to better than percent accuracy for close sources, degrading to several percent for more distant sources. Weak lensing cannot, in fact, be neglected and is expected to limit the accuracy with which distances can be fixed to errors no less than a few percent. Assuming a well-measured cosmology, the source's redshift could be inferred with similar accuracy. GWs alone can thus pinpoint a binary to a three-dimensional ``pixel'' which can help guide searches for the hosts of these events. We examine the time evolution of this pixel, studying it at merger and at several intervals before merger. One day before merger, the major axis of the error ellipse is typically larger than its final value by a factor of $\sim 1.5-6$. The minor axis is larger by a factor of $\sim 2-9$, and, neglecting lensing, the error in the luminosity distance is larger by a factor of $\sim 1.5-7$. This large change over a short period of time is due to spin-induced precession, which is strongest in the final days before merger. The evolution is slower as we go back further in time. For $z = 1$, we find that GWs will localize a coalescing binary to within $\sim 10\ \mathrm{deg}^2$ as early as a month prior to merger and determine distance (and hence redshift) to several percent.Comment: 30 pages, 10 figures, 5 tables. Version published in Ap

Sky localization of complete inspiral-merger-ringdown signals for nonspinning massive black hole binaries

We investigate the capability of LISA to measure the sky position of equal-mass, nonspinning black hole binaries, combining for the first time the entire inspiral-merger-ringdown signal, the effect of the LISA orbits, and the complete three-channel LISA response. We consider an ensemble of systems near the peak of LISA's sensitivity band, with total rest mass of 2\times10^6 M\odot, a redshift of z = 1, and randomly chosen orientations and sky positions. We find median sky localization errors of approximately \sim3 arcminutes. This is comparable to the field of view of powerful electromagnetic telescopes, such as the James Webb Space Telescope, that could be used to search for electromagnetic signals associated with merging massive black holes. We investigate the way in which parameter errors decrease with measurement time, focusing specifically on the additional information provided during the merger-ringdown segment of the signal. We find that this information improves all parameter estimates directly, rather than through diminishing correlations with any subset of well- determined parameters. Although we have employed the baseline LISA design for this study, many of our conclusions regarding the information provided by mergers will be applicable to alternative mission designs as well.Comment: 9 pages, 5 figures, submitted to Phys. Rev.

Observable signatures of general relativistic dynamics in compact binaries

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2009.This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from student submitted PDF version of thesis.Includes bibliographical references (p. 217-237).The effects of general relativity (GR) in astrophysical systems are often difficult to calculate, but they can have important consequences for observables. This thesis considers the impact of previously-ignored GR effects in two different types of compact binary systems. The first is the coalescence of massive black holes in high-redshift galaxies. The gravitational waves (GWs) from these systems can be detected by the proposed low-frequency gravitational wave detector LISA and used to determine the various parameters which characterize the binary. Most studies of LISA's parameter estimation capability have ignored a significant piece of physics: the relativistic precession of the binary's angular momentum vectors. In the first two-thirds of this thesis, we show how including precession effects in the waveform model helps to break various degeneracies and improve the expected parameter errors. We give special attention to the localization parameters, sky position and distance. When distance is converted to an approximate redshift, these parameters define a "pixel" on the sky in which astronomers can search for an electromagnetic counterpart to the GW event. The final third of this thesis focuses on stellar -mass compact binaries in which at least one member is a neutron star. The measurement of tidal effects in these systems may shed some light on the poorly understood high-density equation of state. We first calculate the point at which a neutron star tidally disrupts in the field of a black hole. Previous calculations of this effect have used Newtonian self-gravity, which is inappropriate for a neutron star; we correct this by using relativistic perturbation theory.(cont.) We then turn to small tidal distortions of neutron stars, which can be characterized by a quantity known as the Love number. We calculate relativistic Love numbers for a wide variety of equations of state and investigate their impact on the GWs from neutron star-neutron star binaries.by Ryan Nathan Lang.Ph.D

Design of a high index contrast arrayed waveguide grating

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science; and, (S.B.)--Massachusetts Institute of Technology, Dept. of Physics, 2003.S.B. and S.M. theses issued separately.Includes bibliographical references (p. 115-119).Arrayed waveguide gratings (AWGs) are useful structures for the implementation of wavelength division multiplexing. The AWG consists of an input splitter, a dispersive waveguide array which creates the wavelength demultiplexing and multiplexing effects, and an output coupler. Because the dispersive waveguide array consists of bent waveguides, the size of an AWG is limited by the light loss in the bends. In their current form, silica-based gratings are too large to be made cheaply or to use as an integrated component. The proposed solution is to redesign the AWG using high index contrast materials for tight confinement of the waveguide modes and, consequently, low bend loss. A rough design is presented for a high index contrast AWG using multimode interference couplers as the coupling stages. The major components were simulated using finite difference time domain (FDTD) techniques to find low loss but rather high crosstalk. A second possible design is also presented, making use of a coupled waveguide array as the input element. The coupling coefficients of as many as 41 coupled waveguides were adjusted to create a Gaussian profile as an input to the dispersive section of the AWG. The output coupler, however, will make use of more standard free space diffraction techniques, making the overall concept a unique mixture of waveguide and free space optical elements.by Ryan N. Lang.S.B.M.Eng

Measuring parameters of massive black hole binaries with partially aligned spins

The future space-based gravitational wave detector LISA will be able to measure parameters of coalescing massive black hole binaries, often to extremely high accuracy. Previous work has demonstrated that the black hole spins can have a strong impact on the accuracy of parameter measurement. Relativistic spin-induced precession modulates the waveform in a manner which can break degeneracies between parameters, in principle significantly improving how well they are measured. Recent studies have indicated, however, that spin precession may be weak for an important subset of astrophysical binary black holes: those in which the spins are aligned due to interactions with gas. In this paper, we examine how well a binary's parameters can be measured when its spins are partially aligned and compare results using waveforms that include higher post-Newtonian harmonics to those that are truncated at leading quadrupole order. We find that the weakened precession can substantially degrade parameter estimation. This degradation is particularly devastating for the extrinsic parameters sky position and distance. Absent higher harmonics, LISA typically localizes the sky position of a nearly aligned binary a factor of $\sim 6$ less accurately than for one in which the spin orientations are random. Our knowledge of a source's sky position will thus be worst for the gas-rich systems which are most likely to produce electromagnetic counterparts. Fortunately, higher harmonics of the waveform can make up for this degradation. By including harmonics beyond the quadrupole in our waveform model, we find that the accuracy with which most of the binary's parameters are measured can be substantially improved. In some cases, parameters can be measured as well in partially aligned binaries as they can be when the binary spins are random.Comment: 18 pages, 16 figures, version accepted by PRD (with improved distributions of partially aligned spins

Tidal deformability of neutron stars with realistic equations of state and their gravitational wave signatures in binary inspiral

The early part of the gravitational wave signal of binary neutron star inspirals can potentially yield robust information on the nuclear equation of state. The influence of a star's internal structure on the waveform is characterized by a single parameter: the tidal deformability lambda, which measures the star's quadrupole deformation in response to the companion's perturbing tidal field. We calculate lambda for a wide range of equations of state and find that the value of lambda spans an order of magnitude for the range of equation of state models considered. An analysis of the feasibility of discriminating between neutron star equations of state with gravitational wave observations of the early part of the inspiral reveals that the measurement error in lambda increases steeply with the total mass of the binary. Comparing the errors with the expected range of lambda, we find that Advanced LIGO observations of binaries at a distance of 100 Mpc will probe only unusually stiff equations of state, while the proposed Einstein Telescope is likely to see a clean tidal signature.Comment: 12 pages, submitted to PR