The work presented in this thesis focuses on the prospect of detecting continuous gravitational waves (CWs) from pulsars. It first looks at a method of obtaining evidence of CWs without the use of gravitational wave (GW) data. The braking index, n, of a pulsar is a measure of its angular momentum loss and its value corresponds to various spindown mechanisms. For a pulsar spinning down due to GW emission from the principal mass quadrupole mode alone, the braking index would equal exactly 5. Unfortunately, for millisecond pulsars, it can be hard to measure observationally due to the extremely small second time derivative of the rotation frequency, ¨f. This thesis examines whether it could be possible to extract the distribution of n for a whole population of pulsars rather than measuring the values individually. Simulated data is used with an injected n = 5 signal for 47 millisecond pulsars and the distribution is extracted using hierarchical Bayesian inference methods. It is found that while detection is theoretically possible, observation times of over 20 years and RMS noise on the order of 10−5 ms are needed.
Next, a targeted search for CWs from 236 pulsars using combined data from the second and third observing runs of the LIGO and Virgo interferometric GW detectors are presented. Searches for emission from the l = m = 2 mass quadrupole mode with a frequency at only twice the pulsar rotation frequency (single-harmonic) and from the l = 2, m = 1, 2 modes frequencies of both once and twice the rotation frequency (dual-harmonic) are performed using a Bayesian analysis method. No evidence of GWs is found, so for the single-harmonic search 95% credible upper limits on the strain amplitudes h0 are presented along with limits on the pulsars’ mass quadrupole moments Q22 and ellipticities ε. Of the pulsars studied, 23 have strain amplitudes that are lower than the limits calculated from their electromagnetically measured spin-down rates. These pulsars include the millisecond pulsars J0437−4715 and J0711−6830 which have spin-down ratios of 0.87 and 0.57 respectively. For nine pulsars, their spin-down limits have been surpassed for the first time. For the Crab and Vela pulsars the limits are factors of ∼ 100 and ∼ 20 times more constraining than their spin-down limits respectively. In the dual-harmonic search, new limits are placed on the strain amplitudes C21 and C22.
Finally, a targeted search for CWs from 45 pulsars using the first part of the fourth LIGO–Virgo–KAGRA observing run is presented. Similarly to the previous analysis, searches are performed for the singleand dual-harmonic emission models for each pulsar using a Bayesian analysis method. No evidence is found for a CW signal and so 95% credible upper limits are set on the signal amplitudes, as well as ellipticities and mass quadrupoles where applicable. For the singleharmonic search, 29 pulsars have surpassed their spin-down limits. The lowest upper limit on the amplitude is 6.4×10−27 for the young energetic pulsar J0537−6910, while the lowest constraint on the ellipticity is 8.8×10−9 for the nearby millisecond pulsar J0437−4715.