Continuous gravitational waves signals, emitted by asymmetric spinning
neutron stars, are among the main targets of current detectors like Advanced
LIGO and Virgo. In the case of sources, like pulsars, which rotational
parameters are measured through electromagnetic observations, typical searches
assume that the gravitational wave frequency is at a given known fixed ratio
with respect to the star rotational frequency. For instance, for a neutron star
rotating around one of its principal axis of inertia the gravitational signal
frequency would be exactly two times the rotational frequency of the star. It
is possible, however, that this assumption is wrong. This is why search
algorithms able to take into account a possible small mismatch between the
gravitational waves frequency and the frequency inferred from electromagnetic
observations have been developed. In this paper we present an improved pipeline
to perform such narrow-band searches for continuous gravitational waves from
neutron stars, about three orders of magnitude faster than previous
implementations. The algorithm that we have developed is based on the {\it
5-vectors} framework and is able to perform a fully coherent search over a
frequency band of width O(Hertz) and for hundreds of spin-down
values running a few hours on a standard workstation. This new algorithm opens
the possibility of long coherence time searches for objects which rotational
parameters are highly uncertain.Comment: 19 pages, 8 figures, 6 tables, submitted to CQ
