Motivation
Gravitational wave detectors like LIGO are not truly omni-directional. Due to their L-shaped geometry, they possess inherent blindspots regions in the sky where they are deaf to incoming signals.
This project mathematically models these sensitivity patterns to demonstrate why a single detector is insufficient for continuous all-sky coverage and how the addition of Virgo and KAGRA mitigates this issue.
Theoretical Framework
Antenna Pattern Functions
Note: Defined in the detector's frame, where $\theta$ is the angle from the zenith and $\phi$ is the azimuth relative to the X-arm.
Network Sensitivity
The combined sensitivity is the quadrature sum of individual detector responses.
Methodology
- Tensor Projection: Mapped Sky coordinates (RA/Dec) to Detector Frame (Zenith/Azimuth) using coordinate rotation matrices.
- Real Geometry: Incorporated exact coordinates and arm orientation angles for Hanford, Livingston, Virgo, and KAGRA.
- Visualization: Projected results using the Mollweide Projection to accurately represent the celestial sphere.
Sky Sensitivity Map (Mollweide)
Projected view of the entire celestial sphere (Earth-fixed snapshot).
Simulation Analysis
Initializing simulation...
Multi-messenger Astronomy
Detecting electromagnetic counterparts (e.g., Kilonovae) requires precise source localization. Blindspots are catastrophic for this. A 3+ detector network provides the triangulation needed for telescopes.
Next-Gen Detectors
The Einstein Telescope (ET) will use a triangular topology (60° arms). This geometry intrinsically cancels out the zero-sensitivity nodes of the 90° design, ensuring continuous all-sky coverage.