Data collected by the GEO600 and LIGO interferometric gravitational wave detectors during their first observational science run were searched for continuous gravitational waves from the pulsar J1939+2134 at twice its rotation frequency. Two independent analysis methods were used and are demonstrated in this paper: a frequency domain method and a time domain method. Both achieve consistent null results, placing new upper limits on the strength of the pulsars gravitational wave emission. A model emission mechanism is used to interpret the limits as a constraint on the pulsars equatorial ellipticity.
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