Isolated spinning neutron stars, asymmetric with respect to their rotation axis, are expected to be sources of continuous gravitational waves. The most sensitive searches for these sources are based on accurate matched filtering techniques, that assume the continuous wave to be phase-locked with the pulsar beamed emission. While matched filtering maximizes the search sensitivity, a significant signal-to-noise ratio loss will happen in case of a mismatch between the assumed and the true signal phase evolution. Narrow-band algorithms allow for a small mismatch in the frequency and spin-down values of the pulsar while integrating coherently the entire data set. In this paper we describe a narrow-band search using LIGO O2 data for the continuous wave emission of 33 pulsars. No evidence for a continuous wave signal has been found and upper-limits on the gravitational wave amplitude, over the analyzed frequency and spin-down volume, have been computed for each of the targets. In this search we have surpassed the spin-down limit for some of the pulsars already present in the O1 LIGO narrow-band search, such as J1400 - 6325, J1813 - 1246, J1833 - 1034, J1952 + 3252, and for new targets such as J0940 - 5428 and J1747 - 2809. For J1400 - 6325, J1833 - 1034 and J1747 - 2809, this is the first time the spin-down limit is surpassed.
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