The general theory of porcupines, perfect and imperfect

TL;DR

This paper develops a comprehensive theoretical framework for networks of gravitational wave detectors called porcupines, focusing on optimal estimation, sensitivity, and configurations that are direction- and polarization-independent.

Contribution

It introduces the theory of porcupines, including optimal estimators and properties of perfect configurations, and applies these to simple porcupine networks.

Findings

Derived formulas for spin-averaged and rotationally-averaged SNR^2.

Identified conditions for perfect porcupines with uniform sensitivity.

Provided a simple derivation of perfect porcupine properties.

Abstract

Porcupines are networks of gravitational wave detectors in which the detectors and the distances between them are short relative to the gravitational wavelengths of interest. Perfect porcupines are special configurations whose sensitivity to a gravitational plane wave is independent of the propagation direction or polarization of the wave. I develop the theory of porcupines, including the optimal estimator \hat{h}^{ij} for the gravitational wave field; useful formulae for the spin-averaged and rotationally-averaged SNR^{2}; and a simple derivation of the properties of perfect porcupines. I apply these results to the interesting class of ``simple'' porcupines, and mention some open problems.