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Register a new userIdentification of Lensed Gravitational Waves with Deep Learning
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Similar to light, gravitational waves (GWs) can be lensed. Such lensing phenomena can magnify the waves, create multiple images observable as repeated events, and superpose several waveforms together, inducing potentially discernible patterns on the waves. In particular, when the lens is small, $lesssim 10^5 M_odot$, it can produce lensed images with time delays shorter than the typical gravitational-wave signal length that conspire together to form ``beating patterns. We present a proof-of-principle study utilizing deep learning for identification of such a lensing signature. We bring the excellence of state-of-the-art deep learning models at recognizing foreground objects from background noises to identifying lensed GWs from noise present spectrograms. We assume the lens mass is around $10^3 M_odot$ -- $10^5 M_odot$, which can produce the order of millisecond time delays between two images of lensed GWs. We discuss the feasibility of distinguishing lensed GWs from unlensed ones and estimating physical and lensing parameters. Suggested method may be of interest to the study of more complicated lensing configurations for which we do not have accurate waveform templates.
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In general relativity (GR), gravitational waves (GWs) propagate the well-known plus and cross polarization modes which are the signature of a massless spin-2 field. However, diffraction of GWs caused by intervening objects along the line of sight can cause the apparent rise of additional polarizations due to GW-curvature interactions. In this paper, we continue the analysis by two of the authors of the present article, on lensing of gravitational waves beyond geometric optics. In particular, we calculate the lensing effect caused by a point-like lens, in the regime where its Schwarzschild radius $R_s$ is much smaller than the wavelength $lambda$ of the signal, itself smaller than the impact parameter $b$. In this case, the curvature of spacetime induces distortions in the polarization of the wave such that effective scalar and vector polarizations may appear. We find that the amplitude of these apparent non-GR polarizations is suppressed by a factor $R_slambda/b^2$ with respect to the amplitude of the GR-like tensor modes. We estimate the probability to develop these extra polarization modes for a nearly monochromatic GW in the Pulsar Timing Arrays band traveling through a distribution of galaxies.
Gravitational wave detectors are already operating at interesting sensitivity levels, and they have an upgrade path that should result in secure detections by 2014. We review the physics of gravitational waves, how they interact with detectors (bars and interferometers), and how these detectors operate. We study the most likely sources of gravitational waves and review the data analysis methods that are used to extract their signals from detector noise. Then we consider the consequences of gravitational wave detections and observations for physics, astrophysics, and cosmology.
Assessing the probability that two or more gravitational waves (GWs) are lensed images of the same source requires an understanding of the image properties, including their relative phase shifts in strong lensing (SL). For non-precessing, circular binaries dominated by quadrupole radiation these phase shifts are degenerate with either a shift in the coalescence phase or a detector and inclination dependent shift in the orientation angle. This degeneracy is broken by the presence of higher harmonic modes with $|m| e 2$ in the former and $|m| e l$ in the latter. Precession or eccentricity will also break this degeneracy. This implies that lensed GWs will not necessarily be consistent with (unlensed) predictions from general relativity (GR). Therefore, unlike EM lensing, GW SL can lead to images with an observable modified phase evolution. However, for a wide parameter space, the lensed waveform is similar enough to an unlensed waveform that detection pipelines will still find it. For present detectors, templates with a shifted detector-dependent orientation angle have SNR differences of less than $1%$ for mass ratios up to 0.1, and less than $5%$ for precession parameters up to 0.5 and eccentricities up to 0.4 at 20Hz. The mismatch is lower than $10%$ with the alternative detector-independent coalescence phase shift. Nonetheless, for a loud enough source, even with one image it may be possible to directly identify it as a SL image from its non-GR waveform. In more extreme cases, lensing may lead to considerable distortions, and the lensed GWs may be undetected with current searches. Nevertheless, an exact template with a phase shift in Fourier space can always be constructed to fit any lensed GW. We conclude that an optimal search strategy would incorporate phase information in all stages, with an exact treatment in the final assessment of the probability of multiple lensed events.
We present a first proof-of-principle study for using deep neural networks (DNNs) as a novel search method for continuous gravitational waves (CWs) from unknown spinning neutron stars. The sensitivity of current wide-parameter-space CW searches is limited by the available computing power, which makes neural networks an interesting alternative to investigate, as they are extremely fast once trained and have recently been shown to rival the sensitivity of matched filtering for black-hole merger signals. We train a convolutional neural network with residual (short-cut) connections and compare its detection power to that of a fully-coherent matched-filtering search using the WEAVE pipeline. As test benchmarks we consider two types of all-sky searches over the frequency range from $20,mathrm{Hz}$ to $1000,mathrm{Hz}$: an `easy search using $T=10^5,mathrm{s}$ of data, and a `harder search using $T=10^6,mathrm{s}$. Detection probability $p_mathrm{det}$ is measured on a signal population for which matched filtering achieves $p_mathrm{det}=90%$ in Gaussian noise. In the easiest test case ($T=10^5,mathrm{s}$ at $20,mathrm{Hz}$) the DNN achieves $p_mathrm{det}sim88%$, corresponding to a loss in sensitivity depth of $sim5%$ versus coherent matched filtering. However, at higher-frequencies and longer observation time the DNN detection power decreases, until $p_mathrm{det}sim13%$ and a loss of $sim 66%$ in sensitivity depth in the hardest case ($T=10^6,mathrm{s}$ at $1000,mathrm{Hz}$). We study the DNN generalization ability by testing on signals of different frequencies, spindowns and signal strengths than they were trained on. We observe excellent generalization: only five networks, each trained at a different frequency, would be able to cover the whole frequency range of the search.
The recent direct observation of gravitational waves (GW) from merging black holes opens up the possibility of exploring the theory of gravity in the strong regime at an unprecedented level. It is therefore interesting to explore which extensions to General Relativity (GR) could be detected. We construct an Effective Field Theory (EFT) satisfying the following requirements. It is testable with GW observations; it is consistent with other experiments, including short distance tests of GR; it agrees with widely accepted principles of physics, such as locality, causality and unitarity; and it does not involve new light degrees of freedom. The most general theory satisfying these requirements corresponds to adding to the GR Lagrangian operators constructed out of powers of the Riemann tensor, suppressed by a scale comparable to the curvature of the observed merging binaries. The presence of these operators modifies the gravitational potential between the compact objects, as well as their effective mass and current quadrupoles, ultimately correcting the waveform of the emitted GW.
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