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Register a new userGravitational lensing of gravitational waves: wave nature and prospects for detection
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Added by
Jasjeet Singh Bagla
Publication date
2019
fields
Physics
and research's language is
English
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We discuss the gravitational lensing of gravitational wave signals from coalescing binaries. We delineate the regime where wave effects are significant from the regime where geometric limit can be used. Further, we focus on the effect of micro-lensing and the combined effect of strong lensing and micro-lensing. We find that micro-lensing combined with strong lensing can introduce time varying phase shift in the signal and hence can lead to detectable differences in the signal observed for different images produced by strong lensing. This, coupled with the coarse localization of signal source in the sky for gravitational wave detections, can make it difficult to identify the common origin of signal corresponding to different images and use observables like time delay. In case we can reliably identify corresponding images, micro-lensing of individual images can be used as a tool to constrain properties of micro-lenses. Sources of gravitational waves can undergo microlensing due to lenses in the disk/halo of the Galaxy, or due to lenses in an intervening galaxy even in absence of strong lensing. In general the probability for this is small with one exception: Extragalactic sources of gravitational waves that lie in the galactic plane are highly likely to be micro-lensed. Wave effects are extremely important for such cases. In case of detections of such sources with low SNR, the uncertainty of occurrence of microlensing or otherwise introduces an additional uncertainty in the parameters of the source.
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With increasing sensitivities of the current ground-based gravitational-wave (GW) detectors, the prospects of detecting a strongly lensed GW signal are going to be high in the coming years. When such a signal passes through an intervening lensing galaxy or galaxy cluster, the embedded stellar-mass microlenses lead to interference patterns in the signal that may leave observable signatures. In this work, we present an extensive study of these wave effects in the LIGO/Virgo frequency band ($10$-$10^4$ Hz) due to the presence of the microlens population in galaxy-scale lenses for the first time. We consider a wide range of strong lensing (macro) magnifications and the corresponding surface microlens densities found in lensing galaxies and use them to generate realisations of the amplification factor. The methodologies for simulating amplification curves for both types of images (minima and saddle points) are also discussed. We then study how microlensing is broadly affected by the parameters like macro-magnifications, stellar densities, the initial mass function (IMF), types of images, and microlens distribution around the source. In general, with increasing macro-magnification values, the effects of microlensing become increasingly significant regardless of other parameters. Mismatch analysis between the lensed and the unlensed GW waveforms from chirping binaries suggests that, while inferring the source parameters, microlensing can not be neglected for macro-magnification $gtrsim 15$. Furthermore, for extremely high macro-magnifications $gtrsim 100$, the mismatch can even exceed $5%$, which can result in both a missed detection and, consequently, a missed lensed signal.
Analysis of high-precision timing observations of an array of approx. 20 millisecond pulsars (a so-called timing array) may ultimately result in the detection of a stochastic gravitational-wave background. The feasibility of such a detection and the required duration of this type of experiment are determined by the achievable rms of the timing residuals and the timing stability of the pulsars involved. We present results of the first long-term, high-precision timing campaign on a large sample of millisecond pulsars used in gravitational-wave detection projects. We show that the timing residuals of most pulsars in our sample do not contain significant low-frequency noise that could limit the use of these pulsars for decade-long gravitational-wave detection efforts. For our most precisely timed pulsars, intrinsic instabilities of the pulsars or the observing system are shown to contribute to timing irregularities on a five-year timescale below the 100 ns level. Based on those results, realistic sensitivity curves for planned and ongoing timing array efforts are determined. We conclude that prospects for detection of a gravitational-wave background through pulsar timing array efforts within five years to a decade are good.
Advanced LIGO and Advanced Virgo could observe the first lensed gravitational waves in the coming years, while the future Einstein Telescope could observe hundreds of lensed events. Ground-based gravitational-wave detectors can resolve arrival time differences of the order of the inverse of the observed frequencies. As LIGO/Virgo frequency band spans from a few $rm Hz$ to a few $ rm kHz$, the typical time resolution of current interferometers is of the order of milliseconds. When microlenses are embedded in galaxies or galaxy clusters, lensing can become more prominent and result in observable time delays at LIGO/Virgo frequencies. Therefore, gravitational waves could offer an exciting alternative probe of microlensing. However, currently, only a few lensing configurations have been worked out in the context of gravitational-wave lensing. In this paper, we present lensingGW, a Python package designed to handle both strong and microlensing of compact binaries and the related gravitational-wave signals. This synergy paves the way for systematic parameter space investigations and the detection of arbitrary lens configurations and compact sources. We demonstrate the working mechanism of lensingGW and its use to study microlenses embedded in galaxies.
We present the first numerical simulations of gravitational waves (GWs) passing through a potential well generated by a compact object in 3-D space, with a realistic source waveform derived from numerical relativity for the merger of two black holes. Unlike the previous work, our analyses focus on the time-domain, in which the propagation of GWs is a well-posed initial-value problem for the hyperbolic equations with rigorous rooting in mathematics and physics. Based on these simulations, we investigate for the first time in realistic 3-D space how the wave nature of GWs affects the speed and waveform of GWs in a potential well. We find that GWs travel faster than the prediction of the Shapiro time-delay in the geometric limit due to the effects of diffraction and wavefront geometry. As the wave speed of GWs is closely related to the locality and wavefront geometry of GWs, which are inherently difficult to be addressed in the frequency-domain, our analyses in the time-domain, therefore, provide the first robust analyses to date on this issue based on solid physics. Moreover, we also investigate, for the first time, the interference between the incident and the scattered waves (the echoes of the incident waves). We find that such interference makes the total lensed waveforms dramatically different from those of the original incident ones not only in the amplitude but also in the phase and pattern, especially for signals near the merger of the two back holes.
Gravitational wave memory is theorized to arise from the integrated history of gravitational wave emission, and manifests as a spacetime deformation in the wake of a propagating gravitational wave. We explore the detectability of the memory signals from a population of coalescencing supermassive black hole binaries with pulsar timing arrays and the Laser Interferometer Space Antenna (LISA). We find that current pulsar timing arrays have poor prospects, but it is likely that between 1 and 10 memory events with signal-to-noise ratio in excess of 5 will occur within LISAs planned 4-year mission.
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