Low-frequency Gravitational Radiation Research Articles

Multimessenger Gravitational-wave Searches with Pulsar Timing Arrays: Application to 3C 66B Using the NANOGrav 11-year Data Set

Abstract When galaxies merge, the supermassive black holes in their centers may form binaries and emit low-frequency gravitational radiation in the process. In this paper, we consider the galaxy 3C 66B, which was used as the target of the first multimessenger search for gravitational waves. Due to the observed periodicities present in the photometric and astrometric data of the source, it has been theorized to contain a supermassive black hole binary. Its apparent 1.05-year orbital period would place the gravitational-wave emission directly in the pulsar timing band. Since the first pulsar timing array study of 3C 66B, revised models of the source have been published, and timing array sensitivities and techniques have improved dramatically. With these advances, we further constrain the chirp mass of the potential supermassive black hole binary in 3C 66B to less than (1.65 ± 0.02) × 109 M ⊙ using data from the NANOGrav 11-year data set. This upper limit provides a factor of 1.6 improvement over previous limits and a factor of 4.3 over the first search done. Nevertheless, the most recent orbital model for the source is still consistent with our limit from pulsar timing array data. In addition, we are able to quantify the improvement made by the inclusion of source properties gleaned from electromagnetic data over “blind” pulsar timing array searches. With these methods, it is apparent that it is not necessary to obtain exact a priori knowledge of the period of a binary to gain meaningful astrophysical inferences.

Classical proof of the classical soft graviton theorem in D>4

Classical soft graviton theorem gives an expression for the spectrum of low frequency gravitational radiation, emitted during a classical scattering process, in terms of the trajectories and spin angular momenta of ingoing and outgoing objects, including hard radiation. This has been proved to subleading order in the expansion in powers of frequency by taking the classical limit of the quantum soft graviton theorem. In this paper we give a direct proof of this result by analyzing the classical equations of motion of a generic theory of gravity coupled to interacting matter in space-time dimensions larger than four.

Gravitational-wave detector as a direction finder for low-frequency gravitational radiation sources from binary relativistic astrophysical objects

The design of a gravitational-wave direction finder for sources of low-frequency gravitational radiation from binary relativistic astrophysical objects is described.

Energy of gravitational radiation in plane-symmetric space-times

Gravitational radiation in plane-symmetric space-times can be encoded in a complex potential, satisfying a nonlinear wave equation. An effective energy tensor for the radiation is given, taking a scalar-field form in terms of the potential, entering the field equations in the same way as the matter energy tensor. It reduces to the Isaacson energy tensor in the linearized, high-frequency approximation. An energy conservation equation is derived for a quasilocal energy, essentially the Hawking energy. A transverse pressure exerted by interacting low-frequency gravitational radiation is predicted.

Modulator noise suppression in the LISA time-delay interferometric combinations

Laser Interferometer Space Antenna (LISA) is a mission to detect and study low-frequency cosmic gravitational radiation through its influence on the phases of six modulated laser beams exchanged between three remote spacecraft. We previously showed how the measurements of some 18 time series of relative frequency or phase shifts could be combined (1) to cancel the phase noise of the lasers, (2) to cancel the Doppler fluctuations due to non-inertial motions of the six optical benches and (3) to remove the phase noise of the onboard reference oscillators required to track the photodetector fringes, all the while preserving signals from passing gravitational waves. Here we analyze the effect of the additional noise due to the optical modulators used for removing the phase fluctuations of the onboard reference oscillators. We use the recently measured noise spectrum of an individual modulator (Klipstein et al 2006 Proc. 6th Int. LISA Symp. (Greenbelt, MA) (AIP Conf. Proc. vol 873) ed S M Merkowitz and J C Livas pp 19–23) to quantify the contribution of modulator noise to the first and second-generation time-delay interferometric (TDI) combinations as a function of the modulation frequency. We show that modulator noise can be made smaller than the expected proof-mass acceleration and optical-path noises if the modulation frequencies are larger than ≈682 MHz in the case of the unequal-arm Michelson TDI combination X1, ≈ 1.08 GHz for the Sagnac TDI combination α1, and ≈706 MHz for the symmetrical Sagnac TDI combination ζ1. These modulation frequencies are substantially smaller than previously estimated and may lead to less stringent requirements on the LISA's oscillator noise calibration subsystem. The measurements in Klipstein et al were performed in a laboratory experiment for a range of modulation frequencies, but we emphasize that, for the reference oscillator noise calibration algorithm to work, the modulation frequencies must be equal to the frequencies of the reference oscillators.

A Gravitational Wave Detector Based on a Two-Cavity Laser Measurement System

Results are presented on detecting low-frequency periodic gravitational radiation from binary relativistic astrophysical objects.

White-dwarf–white-dwarf galactic background in the LISA data

LISA (Laser Interferometer Space Antenna) is a proposed space mission, which will use coherent laser beams exchanged between three remote spacecraft to detect and study low-frequency cosmic gravitational radiation. In the low-part of its frequency band, the LISA strain sensitivity will be dominated by the incoherent superposition of hundreds of millions of gravitational wave signals radiated by inspiraling white-dwarf binaries present in our own galaxy. In order to estimate the magnitude of the LISA response to this background, we have simulated a synthesized population that recently appeared in the literature. We find the amplitude of the galactic white-dwarf binary background in the LISA data to be modulated in time, reaching a minimum equal to about twice that of the LISA noise for a period of about two months around the time when the Sun-LISA direction is roughly oriented towards the Autumn equinox. Since the galactic white-dwarfs background will be observed by LISA not as a stationary but rather as a cyclostationary random process with a period of one year, we summarize the theory of cyclostationary random processes, present the corresponding generalized spectral method needed to characterize such process, and make a comparison between our analytic results and those obtained by applying our method to the simulated data. We find that, by measuring the generalized spectral components of the white-dwarf background, LISA will be able to infer properties of the distribution of the white-dwarfs binary systems present in our Galaxy.

Low-frequency gravitational radiation from coalescing massive black holes

We compute the expected low-frequency gravitational wave signal from coalescing massive black-hole (MBH) binaries at the centres of galaxies. We follow the merging history of halos and associated holes via cosmological Monte Carlo realizations of the merger hierarchy from early times to the present in a ΛCDM cosmology. MBHs get incorporated through a series of mergers into larger and larger halos, sink to the centre owing to dynamical friction, accrete a fraction of the gas in the merger remnant to become more massive, and form a binary system. Stellar dynamical processes dominate the orbital evolution of the binary at large separations, while gravitational wave emission takes over at small radii, causing the final coalescence of the system. We discuss the observability of inspiralling MBH binaries by a low-frequency gravitational wave experiment such as the planned Laser Interferometer Space Antenna (LISA), discriminating between resolvable sources and unresolved confusion noise. Over a three-year observing period LISA should resolve this GWB into discrete sources, detecting ≈90 individual events above a S/N = 5 confidence level, while expected confusion noise is well below planned LISA capabilities.

Low‐Frequency Gravitational Waves from Massive Black Hole Binaries: Predictions forLISAand Pulsar Timing Arrays

The coalescence of massive black hole (BH) binaries due to galaxy mergers provides a primary source of low-frequency gravitational radiation detectable by pulsar timing measurements and by the proposed the Laser Interferometry Space Antenna (LISA) observatory. We compute the expected gravitational radiation signal from sources at all redshifts by combining the predicted merger rate of galactic halos with recent measurements of the relation between BH mass, MBH, and the velocity dispersion of its host galaxy, ?. Our main findings are as follows: (1) the nHz frequency background is dominated by BH binaries at redshifts z 2, and existing limits from pulsar timing data place tight constraints on the allowed normalization and power-law slope of the MBH-? relation or on the fraction of BH binaries that proceed to coalescence; (2) more than half of all discrete mHz massive BH sources detectable by LISA are likely to originate at redshifts z 7; (3) the number of LISA sources per unit redshift per year should drop substantially after reionization as long as BH formation is triggered by gas cooling in galaxies. Studies of the highest redshift sources among the few hundred detectable events per year will provide unique information about the physics and history of black hole growth in galaxies.

Time-delay interferometry for LISA

LISA (Laser Interferometer Space Antenna) is a mission to detect and study low-frequency cosmic gravitational radiation through its influence on the phases or frequencies of laser beams exchanged between three remote spacecraft. We previously showed how, with lasers of identical frequencies on stationary spacecraft, the measurement of twelve time series of Doppler shifts could be combined to cancel exactly the phase noise of the lasers and the Doppler fluctuations due to noninertial motions of the six optical benches, while preserving gravitational wave signals. Here we generalize those results on gravitational wave detection with time-delay interferometry to the expected LISA instrument. The six lasers have different center frequencies (in the nominal LISA configuration these center frequencies may well differ by several hundred megahertz) and the distances between spacecraft pairs will change with time (these slowly varying orbital Doppler shifts are expected to be up to tens of megahertz). We develop time-delay data combinations which, as previously, preserve gravitational waves and exactly cancel the leading noise source (phase fluctuations of the six lasers); these data combinations then imply transfer functions for the remaining system noises. Using these, we plot frequency and phase power spectra for modeled system noises in the unequal Michelson combination X and the symmetric Sagnac combination $\ensuremath{\zeta}.$ Although optical bench noise can no longer be cancelled exactly, with the current LISA specifications it is suppressed to negligible levels. It is known that the presently anticipated laser center frequency differences and the orbital Doppler drifts introduce another source of phase noise, arising from the onboard oscillators required to track the photodetector fringes. For the presently planned mission, our analysis indeed demonstrates that noise from current-generation ultrastable oscillators would, if uncorrected, dominate the LISA noise budget. To meet the LISA sensitivity goals either achievable improvements in oscillator stability must be combined with much stricter requirements on the allowed laser center frequency differences and on the allowed Doppler shifts from orbital drifts or, as has been previously suggested, additional calibrating interspacecraft data must be taken, by modulating the laser beams and considerably increasing system complexity. We generalize prior schemes for obtaining the required oscillator instability calibration data to the case of six proof masses, six lasers, and three onboard oscillators. For this realistic configuration we derive appropriate time-delayed combinations of the calibrating data to correct each of the laser-noise-free data combinations.

Time-delay analysis of LISA gravitational wave data: Elimination of spacecraft motion effects

LISA (Laser Interferometer Space Antenna) is a proposed mission which will use coherent laser beams exchanged between three remote spacecraft to detect and study low-frequency cosmic gravitational radiation.

Parametric method for selecting an infralow-frequency signal in the Dulkyn gravitational-wave detector

A parametric method for selecting a response signal in the Dulkyn laser gravitational-wave detector is considered that allows the observation time required for detecting low-frequency periodic gravitational radiation from double relativistic astrophysical sources to be reduced to several periods of detectable signal.

Gravitational Radiation from Globular Clusters

Space-based gravitational wave detectors will have the ability to observe continuous low frequency gravitational radiation from binary star systems. They can determine the direction to continuous sources with an angular resolution approaching tens of arcminutes. This resolution should be sufficient to identify binary sources as members of some nearby globular clusters. Thus, gravitational radiation can be used to determine the population of hard binaries in globular clusters. For particularly hard binaries, the orbital period may change as a result of gravitational wave emission. If one of these binaries can be identified with a globular cluster, then the distance to that cluster can be determined. Thus, gravitational radiation may provide reddening-independent distance measurements to globular clusters.

Classical back reaction of low-frequency cosmic gravitational radiation

We study in a Brill-Hartle type of approximation the back reaction of a superposition of linear gravitational waves on its own mean gravitational field up to second order in the wave amplitudes. The background field is taken as a spatially flat Einstein--de Sitter geometry. In order to follow inflationary scenarios, the wavelengths are allowed to exceed the temporary Hubble distance. As in optical coherence theory, the wave amplitudes are considered as random variables, which form a homogeneous and isotropic stochastic process, sharing the symmetries of the background metric. A segregation of the field equations into equations for the wave amplitudes and equations for the background field is performed by averaging the field equations and interpreting the averaging process as a stochastic (ensemble) average. The spectral densities satisfy a system of ordinary differential equations. The effective stress-energy tensor for the random gravity waves is calculated in terms of correlation functions and covers subhorizon as well as superhorizon modes, where superhorizon modes give in many cases negative contributions to energy density and pressure. We discuss solutions of the second-order equations including pure gravitational radiation universes.

Intraperiodic and interperiodic signal accumulation in the Dulkyn gravitational-wave detector

The intraperiodic and interperiodic signal, accumulation in the Dulkyn laser pentagonal gravitational-wave detector is considered. Such signal accumulation allows the time required to observe low-frequency periodic gravitational radiation from double relativistic astrophysical sources of type PSR J1537+1155 to be reduced by 1–2 orders of magnitude.

Ultra--Low-Frequency Gravitational Radiation from Massive Black Hole Binaries

For massive black hole binaries produced in galactic mergers, we examine the possibility of inspiral induced by interaction with field stars. We model the evolution of such binaries for a range of galaxy core and binary parameters, using numerical results from the literature to compute the binary's energy and angular momentum loss rates due to stellar encounters and including the effect of back-action on the field stars. We find that only a small fraction of binary systems can merge within a Hubble time via unassisted stellar dynamics. External perturbations may, however, cause efficient inspiral. Averaging over a population of central black holes and galaxy mergers, we compute the expected background of gravitational radiation with periods Pw ~ 1-10 yr. Comparison with sensitivities from millisecond pulsar timing suggests that the strongest sources may be detectable with modest improvements to present experiments.

Composite antennas for low-frequency gravitational radiation

Four types of composite torsion antennas for low-frequency gravitational radiation have been developed and tested at low temperature. They exhibited high quality factors comparable with that of a single-piece antenna. These experiments suggest a large-scale composite antenna may be built and retain a high quality factor.

Mechanically modulated microwave cavity for detection of low-frequency gravitational radiation.

Consideration of the estimated strengths and rates of occurrence of various classes of gravitational-radiation sources points to the desirability of developing detectors with sensitivity that is sufficient for seeing predicted events at frequencies below 1 kHz. This paper discusses the sensitivity limitations of a laboratory-scale detector consisting of a microwave cavity with ends that are free to move in response to a gravitational wave. Fundamental sensitivity limits due to readout amplifier noise as well as limitations due to thermal, seismic, and oscillator noise sources are considered. Between roughly 10 and 200 Hz it appears feasible to operate a detector at the linear amplifier sensitivity limit with a dimensionless strain noise spectral density of 10/sup -21//Hz/sup 1/2/ at 100 Hz. This sensitivity is sufficient for detecting 100 M/sub c//sub i//sub r//sub d//sub o//sub t/ black-hole coalescence events to a distance of 50 Mpc with an amplitude signal-to-noise ratio greater than 10.

An upper limit on the stochastic background of ultralow-frequency gravitational waves

Using pulse arrival time data for PSR 1237+25, a pulsar with unusually regular timing behavior, we place a firm upper limit on the magnitude of any stochastic background of low-frequency gravitational radiation in the universe. At frequencies between 0.3 x 10/sup -8/ Hz, the equivalent energy density limits are well below those needed to close the universe on account of gravitational waves alone.

Development and Use of High Stability Clocks in Space

The most stringent requirements for high-stability oscillators will be in space appleations involving the generation and propagation of microwave signals for distance and angle measurement and for time and frequency comparison. This paper describes systems for cancelling the effects of the ionosphere and troposphere on signal propagation so as to make full use of the stability currently available from atomic clocks.An advanced form of Doppler tracking system for gravitational and relativistic tests is described and its use in the search for low-frequency (10-3 Hz) gravitational pulsed radiation is discussed. The current status and future trends of clocks for space use are also reviewed.