The work presented here looks at several aspects of searching for continuous gravitational waves from pulsars, often referred to simply as continuous waves or CWs.This begins with an examination of noise in the current generation of laser interferometer gravitational wave detectors in the region below ~100 Hz.This frequency region is of particular interest with regards to CW detection as two prime sources for a first CW detection, the Crab and Vela pulsars, are expected to emit CWs in this frequency range.The Crab pulsar's frequency lies very close to a strong noise line due to the 60 Hz mains electricity in the LIGO detectors.The types of noise generally present in this region are discussed.Also presented are investigations into the noise features present in the LIGO S6 data and the Virgo VSR2 data using a program called Fscan.A particular noise feature present during VSR2 was discovered with the use of Fscan, which I report on and show how it degrades the sensitivity of searches for CWs from the Vela pulsar using this data.I next present search results for CWs from the Vela pulsar using VSR2 and VSR4 data.Whilst these searches did not find any evidence for gravitational waves being present in the data, they were able to place upper limits on the strength of gravitational wave emission from Vela lower than the upper limit set by the pulsars spin-down, making it only the second pulsar for which this milestone has been achieved.The lowest upper limit derived from these searches confines the spin-down energy lost from Vela due to gravitational waves as just 9% of Vela's total spin-down energy.The data from VSR2 and VSR4 are also examined, analysis of hardware injections in these datasets verify the calibration of the data and the search method.Similar results are also presented for a search for CWs from the Crab pulsar, where data from VSR2, VSR3, VSR4, S5 and S6 are combined to produce an upper limit on the gravitational wave (GW) amplitude lower than has been previously possible, representing 0.5% of the energy lost by the pulsar as seen through its spin-down.The same search method is also applied to analyse data for another 110 known pulsars, with five of these being gamma-ray pulsars that have been timed by the Fermi satellite.GWs from the pulsars timed by Fermi are expected at frequencies below 40 Hz, the LIGO detectors are not calibrated below these frequencies but the Virgo detector is.Hence the data used to search for GWs from these pulsars is the Virgo VSR4 data.The other 105 pulsars were analysed using out of date ephemerides obtained for the LIGO S5 run and the data analysed was from the LIGO S6 run, hence the results obtained for these pulsars are presented as an indication of what results can be expected with updated ephemerides only.For these 110 pulsars the spin-down limits were not able to be beaten, although there are a few pulsars for which this may be able to be achieved with an analysis combining all the possible datasets, in particular J1913+1011.The final part of this thesis reports extensions to the search method used for the analyses previously described.The first way in which this search method is extended is the use of a nested sampling algorithm to perform the parameter estimation stage of the analysis which was previously preformed using a MCMC.The nested sampling code also allows for model selection through the computation of the Bayesian evidence, I present results from characterisation tests of this nested sampling search code that demonstrate the equivalence of its results to those from the MCMC and grid based codes.The other extension to the search method looks at a new CW emission mechanism from a neutron star with a pinned superfluid core that is misaligned from the star's principle axes.This emission model predicts CWs at both the stars spin frequency f and twice its spin frequency 2f, providing an extra data channel with which to perform a search when compared to the triaxial rotator model which only emits at 2f.I present the development of a search for the emission from this new model, tests of the algorithm developed using simulated data, and results from a search using actual data from the VSR4 run for CWs from the Crab pulsar.The testing of the search algorithm shows that the posterior for the model is sufficiently complex to inhibit useful parameter estimation, but that the computation of the Bayesian evidence allows one to distinguish between this model and the triaxial rotator given a low SNR signal in the f data channel.
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