How do we study and detect gravitational lensing effects?

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Studying and Detecting Gravitational Lensing Effects

Introduction to Gravitational Lensing

Gravitational lensing occurs when the trajectory of light or gravitational waves is bent due to the gravitational potential of a massive object. This phenomenon can create multiple images with varying amplifications, arrival times, and types, providing a unique method to study the universe's structure and the properties of massive objects.

Microlensing and Strong Lensing of Gravitational Waves

Microlensing Effects

Microlensing occurs when a gravitational wave encounters a smaller mass, such as a star, along its path. This effect can be particularly significant for type-II strongly-lensed images, which are typically demagnified. Studies have shown that microlensing on type-II images induces larger mismatches with un-microlensed waveforms compared to type-I images. Bayesian parameter estimation with an isolated point mass lens template has been used to detect microlensed signals, although more realistic templates are necessary for accurate detection.

Strong Lensing by Massive Objects

Strong gravitational lensing by massive objects, such as galaxies, can significantly amplify, deflect, and delay gravitational wave signals. This effect is crucial for analyzing the physical properties of the lens. For instance, the TianQin space-borne detector is expected to detect dozens of mergers of massive black hole binaries, with a high probability of observing at least one lensed event during its mission lifetime. Different lens models, such as the point mass model, the singular isothermal sphere (SIS) model, and the Navarro-Frenk-White (NFW) model, are used to analyze these effects.

Detection Techniques and Challenges

Advanced Detectors and Parameter Estimation

Advanced gravitational wave detectors like LIGO and the Einstein Telescope have been used to study the lensing effects on gravitational wave signals. Using Markov chain Monte Carlo simulations and matched filtering methods, researchers have found that the lensing effect becomes significant when the lens object's mass exceeds 1000 solar masses. Templates that include lensing effects are essential for accurate signal detection and parameter estimation.

Wave-Optics Effects

Wave-optics effects are crucial when the Schwarzschild radius of the lens is smaller than the wavelength of the radiation. These frequency-dependent effects can help infer lens parameters, potentially with a single detection. Analytical solutions for point-mass and singular isothermal sphere lenses have been used to study these effects, showing that LISA can detect lensed signals with higher impact parameters and lower lens masses than previously estimated.

Plasma Effects on Gravitational Lensing

The presence of plasma around the lens can induce an additional deflection angle, affecting the lensed image positions, especially in low-frequency radio observations. The inhomogeneous plasma distribution generates a more significant effect than a homogeneous one, potentially causing detectable changes in image positions. This effect can be used to estimate the plasma density in the lens, although Earth's ionosphere strongly affects low-frequency radio observations.

Multimessenger Opportunities and Future Prospects

Tidal Disruption Events

Gravitational lensing can also affect the gravitational wave signals from tidal disruption events (TDEs). Future space-based observatories like LISA and DECIGO are expected to detect numerous lensed TDEs, providing exciting multimessenger opportunities. However, adequate data analysis techniques are necessary to reconstruct the astrophysical properties of the source accurately.

Cross-Correlation with Galaxy Surveys

Combining gravitational wave data with galaxy surveys offers a new way to test theories of gravity. The cross-correlation of gravitational wave strain with galaxy surveys can probe the effects of gravitational lensing and the propagation of gravitational waves in space-time. This method is expected to detect weak gravitational lensing of gravitational waves in the low-redshift universe within the next decade.

Conclusion

Gravitational lensing of gravitational waves provides a powerful tool for studying the universe's structure and the properties of massive objects. Advanced detectors, sophisticated models, and multimessenger approaches are essential for accurately detecting and analyzing these effects. Future space-based observatories and cross-correlation with galaxy surveys promise to enhance our understanding of gravitational lensing and its implications for astrophysics and cosmology.