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Register a new userThe lensing time delay between gravitational and electromagnetic waves
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The recent detection of gravitational waves (GWs) and electromagnetic (EM) waves originating from the same source marks the start of a new multi-messenger era in astronomy. The arrival time difference between the GW and EM signal can be used to constrain differences in their propagation speed, and thus gravitational theories. We study to what extent a non-zero time delay can be explained by gravitational lensing when the line of sight to the source passes near a massive object. For galaxy scale lenses, this delay becomes relevant for GWs with frequencies between $10^{-6}$ and $10^{-9}$ Hz, sourced by super massive binary black-holes. In addition to GWs detectable by Pulsar Timing Arrays (PTAs), we expect to find also a unique and recognizable EM signal. We show that the delay between the GW and EM signal can be of the order of days to months; within reach of future observations. The effect may become important in future multi-messenger astronomy probing of gravitational propagation and interactions.
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LISA will open the mHz band of gravitational waves (GWs) to the astronomy community. The strong gravity which powers the variety of GW sources in this band is also crucial in a number of important astrophysical processes at the current frontiers of astronomy. These range from the beginning of structure formation in the early universe, through the origin and cosmic evolution of massive black holes in concert with their galactic environments, to the evolution of stellar remnant binaries in the Milky Way and in nearby galaxies. These processes and their associated populations also drive current and future observations across the electromagnetic (EM) spectrum. We review opportunities for science breakthroughs, involving either direct coincident EM+GW observations, or indirect multimessenger studies. We argue that for the US community to fully capitalize on the opportunities from the LISA mission, the US efforts should be accompanied by a coordinated and sustained program of multi-disciplinary science investment, following the GW data through to its impact on broad areas of astrophysics. Support for LISA-related multimessenger observers and theorists should be sized appropriately for a flagship observatory and may be coordinated through a dedicated mHz GW research center.
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.
Gravitational waves from the distant sources are gravitationally lensed during their propagation through the intervening matter inhomogeneities before arriving at detectors. It has been proposed in the literature that the variance of the lensed waveform can be used to extract information of the matter power spectrum at very small scales and of low-mass dark halos. In this paper, we show that the variance of the amplitude fluctuation and that of the phase fluctuation of the lensed waveform obey a simple relation irrespective of the shape of the matter power spectrum. We study conditions under which this relation can be violated and discuss some potential applications of the relation. This relation may be used to confirm the robustness of claimed observations of gravitational lensing of gravitational waves and the subsequent reconstruction of the matter power spectrum.
As of today, we have directly detected exactly one source in both gravitational waves (GWs) and electromagnetic (EM) radiation, the binary neutron star merger GW170817, its associated gamma-ray burst GRB170817A, and the subsequent kilonova SSS17a/AT 2017gfo. Within ten years, we will detect hundreds of events, including new classes of events such as neutron-star-black-hole mergers, core-collapse supernovae, and almost certainly something completely unexpected. As we build this sample, we will explore exotic astrophysical topics ranging from nucleosynthesis, stellar evolution, general relativity, high-energy astrophysics, nuclear matter, to cosmology. The discovery potential is extraordinary, and investments in this area will yield major scientific breakthroughs. Here we outline some of the most exciting scientific questions that can be answered by combining GW and EM observations.
The weak gravitational lensing formalism can be extended to the strong lensing regime by integrating a nonlinear version of the geodesic deviation equation. The resulting roulette expansion generalises the notion of convergence, shear and flexion to arbitrary order. The independent coefficients of this expansion are screen space gradients of the optical tidal tensor which approximates to the usual lensing potential in the weak field limit. From lensed images, knowledge of the roulette coefficients can in principle be inverted to reconstruct the mass distribution of a lens. In this paper, we simplify the roulette expansion and derive a family of recursion relations between the various coefficients, generalising the Kaiser-Squires relations beyond the weak-lensing regime.
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