Reduced order modelling in searches for continuous gravitational waves - I. Barycentering time delays

TL;DR

This paper introduces a reduced order model for calculating barycentric time delays in gravitational wave searches, significantly speeding up computations while maintaining high accuracy, thus enabling more efficient long-duration source tracking.

Contribution

The study demonstrates that barycentric time delays can be efficiently approximated using only four basis vectors, achieving up to 30-fold speed-ups in gravitational wave data analysis.

Findings

Delay reconstruction accuracy within sub-nanosecond range.

Speed-up factors of up to 30 times for time delay calculations.

Effective modeling of binary system delays with eccentricities < 0.25.

Abstract

The frequencies and phases of emission from extra-solar sources measured by Earth-bound observers are modulated by the motions of the observer with respect to the source, and through relativistic effects. These modulations depend critically on the source's sky-location. Precise knowledge of the modulations are required to coherently track the source's phase over long observations, for example, in pulsar timing, or searches for continuous gravitational waves. The modulations can be modelled as sky-location and time-dependent time delays that convert arrival times at the observer to the inertial frame of the source, which can often be the Solar system barycentre. We study the use of reduced order modelling for speeding up the calculation of this time delay for any sky-location. We find that the time delay model can be decomposed into just four basis vectors, and with these the delay for any sky-location can be reconstructed to sub-nanosecond accuracy. When compared to standard routines for time delay calculation in gravitational wave searches, using the reduced basis can lead to speed-ups of 30 times. We have also studied components of time delays for sources in binary systems. Assuming eccentricities $< 0.25$ we can reconstruct the delays to within 100s of nanoseconds, with best case speed-ups of a factor of 10, or factors of two when interpolating the basis for different orbital periods or time stamps. In long-duration phase-coherent searches for sources with sky-position uncertainties, or binary parameter uncertainties, these speed-ups could allow enhancements in their scopes without large additional computational burdens.