Investigating correlations in time delay interferometry combinations of LISA data

Toher, Jennifer (2009) Investigating correlations in time delay interferometry combinations of LISA data. PhD thesis, University of Glasgow.

Abstract

The detection of Gravitational Waves using the Laser Interferometer Space Antenna (LISA) will open whole new areas of physics and astrophysics for exploration. The lower frequency signals detected by the antenna will allow us to probe gravitational wave sources that are inaccessible with current and future ground based detectors. However, the ability of LISA to detect gravitational wave signals is dependent on the removal of the laser frequency noise realisations from the optical bench measurements, that would otherwise dominate the signal data streams.

Time Delay Interferometry (TDI) provides a method for removing the laser noise contributions by time shifting the individual optical bench measurements. The cancellation of the noise is achieved by identifying the individual optical bench measurements that contain equal numbers of identical realisations of the laser noise but with opposing signs.
Although the TDI combinations produce signal datastreams that are free from the laser frequency noise contributions, the time shifting of the optical bench measurements means that the TDI combination data streams defined at different time stamps will nevertheless contain identical realisations of the remaining detector noise terms.
Independent TDI combinations (denoted A, E and T) can be constructed from the simpler laser-noise cancelling combinations by diagonalising the correlation matrix of the combination data streams at any given timestamp. This ensures that the optimal combinations are independent with respect to each other at this particular timestamp, but this result does not apply when the optimal combinations are compared at different timestamps.
As the time shifting of the optical bench measurements introduces within them identically equal realisations of the remaining detector noise terms, the A, E and T data streams could therefore be correlated in time.

The presence, and potential impact, of these time correlations has been investigated for the first time within this thesis. This work has been carried out by identifying the time stamps and optical bench designations of the individual optical bench terms in the algebraic expression for each TDI combination. The resultant configuration of non-zero off-diagonal terms in the covariance matrix for the TDI combination data streams has been investigated for simplified models of the LISA constellation.

The presence of non-zero correlations between the combination datastreams could pose a serious problem to a number of signal parameter search methods that rely on the datastreams being independent.
The effects on the parameter recovery for a gravitational wave signal containing two sinusoids has been investigated for a simplified LISA model and for the combination datastreams produced using the data from the second Mock LISA Data Challenge. In both cases, the presence of identically equal detector noise realisations in different time stamps of the signal data streams introduces auto and cross correlations between the combinations. When the non-zero covariances were explicitly accounted for within the likelihood function, the confidence intervals, reflecting the uncertainty in our inference of the unknown parameters, were found to be significantly smaller - indicating significantly tighter constraints on the true signal parameters, in comparison to the results obtained with a likelihood function that assumed the data streams to be independent in time.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Keywords: cosmology, data analysis, correlation, gravitational waves, astronomy, covariance, physics, time delay combinations, LISA, time correlations
• Subjects: Q Science > QB Astronomy; Q Science > QC Physics
• Colleges/Schools: College of Science and Engineering > School of Physics and Astronomy
• Supervisor's Name: Hendry, Dr. Martin and Woan, Dr. Graham
• Date of Award: 2009
• Depositing User: Miss Jennifer Toher
• Unique ID: glathesis:2009-748
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 15 May 2009
• Last Modified: 10 Dec 2012 13:25
• URI: https://theses.gla.ac.uk/id/eprint/748