We present a search for gravitational waves from 116 known millisecond and
young pulsars using data from the fifth science run of the LIGO detectors. For
this search ephemerides overlapping the run period were obtained for all
pulsars using radio and X-ray observations. We demonstrate an updated search
method that allows for small uncertainties in the pulsar phase parameters to be
included in the search. We report no signal detection from any of the targets
and therefore interpret our results as upper limits on the gravitational wave
signal strength. Our best (lowest) upper limit on gravitational wave amplitude
is 2.3x10^-26 for J1603-7202 and our best (lowest) limit on the inferred pulsar
ellipticity is 7.0x10^-8 for J2124-3358. Of the recycled millisecond pulsars
several of the measured upper limits are only about an order of magnitude above
their spin-down limits. For the young pulsars J1913+1011 and J1952+3252 we are
only a factor of a few above the spin-down limit, and for the X-ray pulsar
J0537-6910 we reach the spin-down limit under the assumption that any
gravitational wave signal from it stays phase locked to the X-ray pulses over
timing glitches. We also present updated limits on gravitational radiation from
the Crab pulsar, where the measured limit is now a factor of seven below the
spin-down limit. This limits the power radiated via gravitational waves to be
less than ~2% of the available spin-down power.
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