Bayesian searches for gravitational waves from pulsars
Methods for searching for periodic gravitational wave signals from triaxial pulsars using interferometric gravitational wave detectors have been developed. Since the gravitational wave signals from pulsars are expected to be weak, long stretches of data must be used for any detection. Over the course of a day, and a year, these periodic signals are Doppler shifted due to the motion of the Earth. The response of the interferometers to each polarisation of gravitational waves will also give rise to an amplitude modulation of the periodic signal. These effects are taken into account and an end-to-end Bayesian scheme for making inferences from the data is presented. Several software tests have been performed to validate the core routines, such as barycentring, using independent software. The GEO 600 and LIGO interferometers had their first scientific data run (S1) for 17 days between 23 August and 9 September 2002. An analysis was carried out to search for gravitational wave signals from pulsar B1937+21. While no signals were detected, a 95% upper limit of h0 < 1.4 x 10-22 was determined using S1 data where h0 is the amplitude of the gravitational waves. Given that pulsar B1937+21 is at a distance of 3.6 kpc, and assuming a moment of inertia of 1038kg m2, the corresponding upper limit on the equatorial ellipticity was determined to be = 2.9 x 10-4. The upper limit on gravitational waves from pulsar B1937+21 using S1 data was over an order of magnitude lower than the previous best limit at the time. Data from LIGO's second science run (S2) in the spring of 2003 was analysed with the sensitivity of each detector in the network being roughly an order of magnitude better than in S1 across a large range of frequencies. Upper limits were placed on a total of 28 isolated pulsars using the S2 data. The analysis procedure for S2 was more robust to interfering spectral lines and took advantage of the longer stationarity of the S2 data. Two hardware injections of hypothetical pulsars were injected in the LIGO interferometers during S2. The successful extraction of these signals from the LIGO S2 data significantly increased our confidence in the the overall data analysis pipeline. For four of the closest pulsars their equatorial ellipticities were constrained to less than = 10-5 with 95% confidence. These limits are beginning to reach interesting ellipticities which some exotic theories suggest could be supported in neutron stars. The third science run (S3) in which GEO 600 and LIGO participated took place from late October 2003 to early January 2004. Again, the improvement in sensitivity compared to the previous run (S2) was significant. Preliminary multi-detector results were determined for the same previous 28 pulsars using S3 data. The equatorial ellipticities for 11 of these pulsars are constrained to less = 10-5 with 95% confidence. With the S3 data, the upper limit on the gravitational wave emission from the Crab pulsar was only approximately a factor of four from the upper limits inferred from the spindown of the pulsar. When this barrier is overcome the prospects of detecting gravitational waves from the Crab pulsar will become more plausible. Future work based on these implementations will examine a larger set of missing known pulsars including binary systems. Studies in Markov Chain Monte Carlo techniques may also allow the expansion this method to a larger parameter space.