Space-borne Gravitational Wave Detectors Research Articles

THE LISA PATHFINDER MISSION

Laser Interferometer Space Antenna (LISA) Pathfinder (formerly known as SMART-2) is a European Space Agency mission designed to pave the way for the joint ESA/NASA LISA mission by testing in flight the critical technologies required for space borne gravitational wave detection; it will put two test masses in a near-perfect gravitational free-fall and control and measure their motion with unprecedented accuracy. This is achieved through technology comprising inertial sensors, high precision laser metrology, drag-free control and an ultra precise micro-Newton propulsion system. LISA Pathfinder (LPF) essentially mimics one arm of space-borne gravitational wave detectors by shrinking the million kilometer scale armlengths down to a few tens of centimeters, giving up the sensitivity to gravitational waves, but keeping the measurement technology. The scientific objective of the LPF mission consists then of the first in-flight test of low frequency gravitational wave detection metrology.

Gravitational wave observations of galactic intermediate-mass black hole binaries with DECIGO path finder

DECIGO path finder is a space-borne gravitational wave (GW) detector with sensitivity in the frequency band 0.1–100 Hz. As a first step mission to DECIGO, it is aiming for launching in 2016–2017. Although its main objective is to demonstrate technology for GW observation in space, DPF still has a chance of detecting GW signals and performing astrophysical observations. With an observable range up to 50 kpc, its main targets are GW signals from galactic intermediate-mass black hole (IMBH) binaries. By using inspiral–merger–ringdown phenomenological waveforms, we perform both pattern-averaged analysis and Monte Carlo simulations including the effect of detector motion to find that the masses and (effective) spins of the IMBHs could be determined with errors of a few percent, should the signals be detected. Since GW signals from IMBH binaries with masses above 104M⊙ cannot be detected by ground-based detectors, these objects can be unique sources for DPF. If the inspiral signal of a 103M⊙ IMBH binary is detected with DPF, it can give alert to the ringdown signal for the ground-based detectors 102–103 s before coalescence. We also estimate the possible bound on the graviton Compton wavelength from a possible IMBH binary in ω Centauri. We obtain a slightly weaker constraint than that from the solar system experiment and an about two orders of magnitude stronger constraint than that from binary pulsar tests. Unfortunately, the detection rate of IMBH binaries is rather small.

Stochastic gravitational wave background from the single-degenerate channel of type Ia supernovae

We demonstrate that the integrated gravitational wave signal of type Ia supernovae (SNe Ia) in the single-degenerate channel out to cosmological distances gives rise to a continuous background to spaceborne gravitational wave detectors, including the Big Bang Observer and Deci-Hertz Interferometer Gravitational wave Observatory planned missions. This gravitational wave background from SNe Ia acts as a noise background in the frequency range 0.1--10 Hz, which heretofore was thought to be relatively free from astrophysical sources apart from neutron-star and white-dwarf binaries, and therefore a key window in which to study primordial gravitational waves generated by inflation. While inflationary energy scales of $\ensuremath{\gtrsim}{10}^{16}\text{ }\text{ }\mathrm{GeV}$ yield inflationary gravitational wave backgrounds in excess of our range of predicted backgrounds, for lower energy scales of $\ensuremath{\sim}{10}^{15}\text{ }\text{ }\mathrm{GeV}$, the inflationary gravitational wave background becomes comparable to the noise background from SNe Ia.

Approximate waveforms for extreme-mass-ratio inspirals in modified gravity spacetimes

Extreme mass-ratio inspirals, in which a stellar-mass compact object spirals into a supermassive black hole, are prime candidates for detection with space-borne milliHertz gravitational wave detectors, similar to the Laser Interferometer Space Antenna. The gravitational waves generated during such inspirals encode information about the background in which the small object is moving, providing a tracer of the spacetime geometry and a probe of strong-field physics. In this paper, we construct approximate, ``analytic-kludge'' waveforms for such inspirals with parametrized post-Einsteinian corrections that allow for generic, model-independent deformations of the supermassive black hole background away from the Kerr metric. These approximate waveforms include all of the qualitative features of true waveforms for generic inspirals, including orbital eccentricity and relativistic precession. The deformations of the Kerr metric are modeled using a recently proposed, modified gravity bumpy metric, which parametrically deforms the Kerr spacetime while ensuring that three approximate constants of the motion remain for geodesic orbits: a conserved energy, azimuthal angular momentum and Carter constant. The deformations represent modified gravity effects and have been analytically mapped to several modified gravity black hole solutions in four dimensions. In the analytic kludge waveforms, the conservative motion is modeled by a post-Newtonian expansion of the geodesic equations in the deformed spacetimes, which in turn induce modifications to the radiation-reaction force. These analytic-kludge waveforms serve as a first step toward complete and model-independent tests of general relativity with extreme mass-ratio inspirals.

Domain walls and gravitational waves after thermal inflation

Thermal inflation is an attractive solution to the cosmological moduli problem. However, domain walls may be formed after thermal inflation and some mechanisms are needed to eliminate the domain wall before it dominates the Universe. We point out that gravitational waves produced by the dynamics of domain walls may be observed by the pulsar timing experiments and future space-borne gravitational wave detectors, which provides a probe into the period of thermal inflation. We also show that the QCD instanton effect can effectively eliminate the domain walls with producing observable amount of gravitational waves.

Bumpy black holes in alternative theories of gravity

We generalize the bumpy black hole framework to allow for alternative theory deformations. We construct two model-independent parametric deviations from the Kerr metric: one built from a generalization of the quasi-Kerr and bumpy metrics and one built directly from perturbations of the Kerr spacetime in Lewis-Papapetrou form. We find the conditions that these "bumps" must satisfy for there to exist an approximate second-order Killing tensor so that the perturbed spacetime still possesses three constants of the motion (a deformed energy, angular momentum and Carter constant) and the geodesic equations can be written in first-order form. We map these parameterized metrics to each other via a diffeomorphism and to known analytical black hole solutions in alternative theories of gravity. The parameterized metrics presented here serve as frameworks for the systematic calculation of extreme-mass ratio inspiral waveforms in parameterized non-GR theories and the investigation of the accuracy to which space-borne gravitational wave detectors can constrain such deviations.

Coupling characterization and noise studies of the optical metrology system onboard the LISA Pathfinder mission

We describe the first investigations of the complete engineering model of the optical metrology system (OMS), a key subsystem of the LISA Pathfinder science mission to space. The latter itself is a technological precursor mission to LISA, a spaceborne gravitational wave detector. At its core, the OMS consists of four heterodyne Mach-Zehnder interferometers, a highly stable laser with an external modulator, and a phase meter. It is designed to monitor and track the longitudinal motion and attitude of two floating test masses in the optical reference frame with (relative) precision in the picometer and nanorad range, respectively. We analyze sensor signal correlations and determine a physical sensor noise limit. The coupling parameters between motional degrees of freedom and interferometer signals are analytically derived and compared to measurements. We also measure adverse cross-coupling effects originating from system imperfections and limitations and describe algorithmic mitigation techniques to overcome some of them. Their impact on system performance is analyzed within the context of the Pathfinder mission.

Constraining the evolutionary history of Newton’s constant with gravitational wave observations

Space-borne gravitational wave detectors, such as the proposed Laser Interferometer Space Antenna, are expected to observe black hole coalescences to high redshift and with large signal-to-noise ratios, rendering their gravitational waves ideal probes of fundamental physics. The promotion of Newton's constant to a time-function introduces modifications to the binary's binding energy and the gravitational wave luminosity, leading to corrections in the chirping frequency. Such corrections propagate into the response function and, given a gravitational wave observation, they allow for constraints on the first time-derivative of Newton's constant at the time of merger. We find that space-borne detectors could indeed place interesting constraints on this quantity as a function of sky position and redshift, providing a {\emph{constraint map}} over the entire range of redshifts where binary black hole mergers are expected to occur. A LISA observation of an equal-mass inspiral event with total redshifted mass of 10^5 solar masses for three years should be able to measure $\dot{G}/G$ at the time of merger to better than 10^(-11)/yr.

Method to measure a relative transverse velocity of a source-lens-observer system using gravitational lensing of gravitational waves

Gravitational waves propagate along null geodesics like light rays in the geometrical optics approximation, and they may have a chance to suffer from gravitational lensing by intervening objects, as is the case for electromagnetic waves. Long wavelength of gravitational waves and compactness of possible sources may enable us to extract information in the interference among the lensed images. We point out that the interference term contains information of relative transverse velocity of the source-lens-observer system, which may be obtained by possible future space-borne gravitational wave detectors such as BBO/DECIGO.

Relativistic Effects in Extreme Mass Ratio Gravitational Wave Bursts

Extreme mass ratio bursts (EMRBs) have been proposed as a possible source for future space-borne gravitational wave detectors, such as the Laser Interferometer Space Antenna (LISA). These events are characterized by long-period, nearly-radial orbits of compact objects around a central massive black hole. The gravitational radiation emitted during such events consists of a short burst, corresponding to periapse passage, followed by a longer, silent interval. In this paper we investigate the impact of including relativistic corrections to the description of the compact object's trajectory via a geodesic treatment, as well as including higher-order multipole corrections in the waveform calculation. The degree to which the relativistic corrections are important depends on the EMRB's orbital parameters. We find that relativistic EMRBs (v_{max}}/c > 0.25) are not rare and actually account for approximately half of the events in our astrophysical model. The relativistic corrections tend to significantly change the waveform amplitude and phase relative to a Newtonian description, although some of this dephasing could be mimicked by parameter errors. The dephasing over several bursts could be of particular importance not only to gravitational wave detection, but also to parameter estimation, since it is highly correlated to the spin of the massive black hole. Consequently, we postulate that if a relativistic EMRB is detected, such dephasing might be used to probe the relativistic character of the massive black hole and obtain information about its spin.

SLIDING MODE TECHNIQUE APPLIED TO TEST MASS SUSPENSION CONTROL

A Sliding Mode control design is presented for a Test Mass suspension control problem applied to the LISA Pathfinder mission. LISA Pathfinder is an ESA enabling technology project for LISA, a spaceborne gravitational wave detector. The LISA Technology Package on board LISA Pathfinder features two high precision Gravitational Reference Sensors, each of them encompassing a free floating cubic Test Mass surrounded by a capacitive housing. This paper covers equipment modeling, actuation strategy description, controller law definition and design rules, stability and robustness analysis, performance results, and comparison with standard control design.

Demonstration of the zero-crossing phasemeter with a LISA test-bed interferometer

The laser interferometer space antenna (LISA) is being designed to detect and study in detail gravitational waves from sources throughout the Universe such as massive black hole binaries. The conceptual formulation of the LISA space-borne gravitational wave detector is now well developed. The interferometric measurements between the sciencecraft remain one of the most important technological and scientific design areas for the mission. Our work has concentrated on developing the interferometric technologies to create a LISA-like optical signal and to measure the phase of that signal using commercially available instruments. One of the most important goals of this research is to demonstrate the LISA phase timing and phase reconstruction for a LISA-like fringe signal, in the case of a high fringe rate and a low signal level. We present current results of a test-bed interferometer designed to produce an optical LISA-like fringe signal previously discussed in Jennrich O, Stebbins R T, Bender P L and Pollack S (2001 Class. Quantum Grav. 18 4159–64) and Pollack S E, Jennrich O, Stebbins R T and Bender P (2003 Class. Quantum Grav. 20 S291–00).

Active laser frequency stabilization and resolution enhancement of interferometers for the measurement of gravitational waves in space

Laser frequency stabilization is notably one of the major challenges on the way to a space-borne gravitational wave observatory. The proposed Laser Interferometer Space Antenna (LISA) is presently under development in an ESA, NASA collaboration. We present a novel method for active laser stabilization and phase noise suppression in such a gravitational wave detector. The proposed approach is a further evolution of the "arm locking" method, which in essence consists of using an interferometer arm as an optical cavity, exploiting the extreme long-run stability of the cavity size in the frequency band of interest. We extend this method by using the natural interferometer arm length differences and existing interferometer signals as additional information sources for the reconstruction and active suppression of the quasi-periodic laser frequency noise, enhancing the resolution power of space-borne gravitational wave detectors.

LISA propulsion module separation study

The Laser Interferometer Space Antenna (LISA) mission is a space-borne gravitational wave detector consisting of three sciencecraft in heliocentric orbit. Each sciencecraft is delivered to its operational orbit by a propulsion module. Because of the strict thermal and mass balancing requirements of LISA, the baseline mission concept requires that the propulsion module separate from the sciencecraft after delivery. The only propulsion system currently included in the sciencecraft design are micronewton level thrusters, such as field emission electric propulsion (FEEP) or colloid thrusters, that are used to balance the 30–40 µN of solar radiation pressure and provide the drag-free and attitude control of the sciencecraft. Due to these thrusters' limited authority, the separation of the propulsion module from the sciencecraft must be well controlled to not induce a large tip-off rotation of the sciencecraft. We present here the results of a study of the propulsion module separation system requirements that are necessary to safely deliver the three LISA sciencecraft to their final operational orbits.

Successful testing of the LISA Technology Package (LTP) interferometer engineering model

The LISA Technology Package (LTP), to be launched by ESA in 2008, is a technology demonstration mission in preparation for the LISA space-borne gravitational wave detector. A central part of the LTP is the optical metrology package (heterodyne interferometer with phasemeter) that measures the distance between two test masses with a noise level of 10 pm Hz−1/2 between 3 mHz and 30 mHz and also the test mass alignment with a noise level of <10 nrad Hz−1/2. An engineering model of the interferometer has been built and environmentally tested. Extensive functionality and performance tests were conducted. This paper reports on the successful test results.

Forward modeling of space-borne gravitational wave detectors

Planning is underway for several space-borne gravitational wave observatories to be built in the next ten to twenty years. Realistic and efficient forward modeling will play a key role in the design and operation of these observatories. Space-borne interferometric gravitational wave detectors operate very differently from their ground based counterparts. Complex orbital motion, virtual interferometry, and finite size effects complicate the description of space-based systems, while nonlinear control systems complicate the description of ground based systems. Here we explore the forward modeling of space-based gravitational wave detectors and introduce an adiabatic approximation to the detector response that significantly extends the range of the standard low frequency approximation. The adiabatic approximation will aid in the development of data analysis techniques, and improve the modeling of astrophysical parameter extraction.

The LTP interferometer and phasemeter

The LISA Technology Package (LTP), to be launched by ESA in 2006/2007, is a technology demonstration mission in preparation for the LISA space-borne gravitational wave detector. A central part of the LTP is the optical metrology package (heterodyne interferometer with phasemeter) which monitors the distance between two test masses with a noise level of 10 pm Hz−1/2 between 3 mHz and 30 mHz. It has a dynamic range of >100 µm without any actuators for the pathlength. In addition to the longitudinal measurements, it provides alignment measurements with an expected noise level of <10 nrad Hz−1/2. While the basic design has been described previously by Heinzel et al (2003 Class. Quantum Grav. 20 S153–61), this paper gives new details on the laser stabilization, the phasemeter and recent prototype results.

The effects of orbital motion on LISA time delay interferometry

In an effort to eliminate laser phase noise in laser interferometer spaceborne gravitational wave detectors, several combinations of signals have been found that allow the laser noise to be cancelled out while gravitational wave signals remain. This process is called time delay interferometry (TDI). In the papers that defined the TDI variables, their performance was evaluated in the limit that the gravitational wave detector is fixed in space. However, the performance depends on certain symmetries in the armlengths that are available if the detector is fixed in space, but that will be broken in the actual rotating and flexing configuration produced by the LISA orbits. In this paper we investigate the performance of these TDI variables for the real LISA orbits. First, addressing the effects of rotation, we verify Daniel Shaddock's result that the Sagnac variables α(t), β(t) and γ(t) will not cancel out the laser phase noise, and we also find the same result for the symmetric Sagnac variable ζ(t). The loss of the latter variable would be particularly unfortunate since this variable also cancels out gravitational wave signal, allowing instrument noise in the detector to be isolated and measured. Fortunately, we have found a set of more complicated TDI variables, which we call Δ-Sagnac variables, one of which accomplishes the same goal as ζ(t) to good accuracy. Finally, however, as we investigate the effects of the flexing of the detector arms due to non-circular orbital motion, we show that all variables, including the interferometer variables, X(t), Y(t) and Z(t), which survive the rotation-induced loss of direction symmetry, will not completely cancel laser phase noise when the armlengths are changing with time. This unavoidable problem will place a stringent requirement on laser stability of ∼5 Hz Hz−1/2.

SyZyGy: A straight interferometric spacecraft system for gravity wave observations

We apply TDI, unfolding the general triangular configuration, to the special case of a linear array of three spacecraft. We show that such an array ("SyZyGy") has, compared with an equilateral triangle GW detector of the same scale, degraded (but non-zero) sensitivity at low-frequencies (f<<c/(arrany size)) but similar peak and high-frequency sensitivities to GWs. Sensitivity curves are presented for SyZyGys having various arm-lengths. A number of technical simplifications result from the linear configuration. These include only one faceted (e.g., cubical) proof mass per spacecraft, intra-spacecraft laser metrology needed only at the central spacecraft, placement in a single appropriate orbit can reduce Doppler drifts so that no laser beam modulation is required for ultra-stable oscillator noise calibration, and little or no time-dependent articulation of the telescopes to maintain pointing. Because SyZyGy's sensitivity falls off more sharply at low frequency than that of an equilateral triangular array, it may be more useful for GW observations in the band between those of ground-based interferometers (10-2000 Hz) and LISA (.1 mHz-.1 Hz). A SyZyGy with ~1 light- second scale could, for the same instrumental assumptions as LISA, make obseervations in this intermediate frequency GW band with 5 sigma sensitivity to sinusoidal waves of ~2.5 x 10^-23 in a year's integration.

The information content of gravitational wave harmonics in compact binary inspiral

The nonlinear aspect of gravitational wave generation that produces power at harmonics of the orbital frequency, above the fundamental quadrupole frequency, is examined to see what information about the source is contained in these higher harmonics. We use an order (4/2) post-Newtonian expansion of the gravitational wave waveform of a binary system to model the signal seen in a spaceborne gravitational wave detector such as the proposed LISA detector. Covariance studies are then performed to determine the ultimate accuracy to be expected when the parameters of the source are fit to the received signal. We find three areas where the higher harmonics contribute crucial information that breaks degeneracies in the model and allows otherwise badly correlated parameters to be separated and determined. First, we find that the position of a coalescing massive black-hole binary in an ecliptic-plane detector, such as OMEGA, is well determined with the help of these harmonics. Second, we find that the individual masses of the stars in a chirping neutron star binary can be separated because of the mass dependence of the harmonic contributions to the wave. Finally, we note that supermassive black-hole binaries, whose frequencies are too low to be seen in the detector sensitivity window for long, may still have their masses, distances and positions determined since the information content of the higher harmonics compensates for the information lost when the orbit-induced modulation of the signal does not last long enough to be apparent in the data.