  We study, via a Monte Carlo simulation, a population of isolated asymmetric
neutron stars where the magnitude of the magnetic field is low enough so that
the dynamical evolution is dominated by the emission of gravitational waves. A
starting population, with age uniformly distributed back to 100 Myr (or 500
Myr) and endowed with a birth kick velocity, is evolved in the Galactic
gravitational potential to the present time. In describing the initial spatial
distribution, the Gould Belt, with an enhanced neutron star formation rate, is
taken into account. Different models for the initial period distribution are
considered. The star ellipticity, measuring the amount of deformation, is drawn
from an exponential distribution. We estimate the detectability of the emitted
gravitational signals by the first and planned second generation of
interferometric detectors. Results are parametrized by the fraction of the
whole galactic neutron star population made of this kind of sources. Some
possible mechanisms, which would make possible the existence of such a
population, are discussed. A comparison of the gravitational spin-down with the
braking due to a possible interaction of the neutron star with the interstellar
medium is also presented.
