TY - JOUR

T1 - Reduced order modelling in searches for continuous gravitational waves - I. Barycentring time delays

AU - Pitkin, M.

AU - Doolan, S.

AU - McMenamin, L.

AU - Wette, K.

N1 - This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Monthly Notices of the Royal Astronomical Society following peer review. The definitive publisher-authenticated version M Pitkin, S Doolan, L McMenamin, K Wette, Reduced order modelling in searches for continuous gravitational waves – I. Barycentring time delays, Monthly Notices of the Royal Astronomical Society, Volume 476, Issue 4, June 2018, Pages 4510–4519 is available online at: https://academic.oup.com/mnras/article/476/4/4510/4913653

PY - 2018/2/28

Y1 - 2018/2/28

N2 - 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 100 s 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.

AB - 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 100 s 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.

U2 - 10.1093/mnras/sty548

DO - 10.1093/mnras/sty548

M3 - Journal article

VL - 476

SP - 4510

EP - 4519

JO - Monthly Notices of the Royal Astronomical Society

JF - Monthly Notices of the Royal Astronomical Society

SN - 0035-8711

IS - 4

ER -