  For a uniform population of neutron stars whose spin-down is dominated by the
emission of gravitational radiation, an old argument of Blandford states that
the expected gravitational-wave amplitude of the nearest source is independent
of the deformation and rotation frequency of the objects. Recent work has
improved and extended this argument to set upper limits on the expected
amplitude from neutron stars that also emit electromagnetic radiation. We
restate these arguments in a more general framework, and simulate the evolution
of such a population of stars in the gravitational potential of our galaxy. The
simulations allow us to test the assumptions of Blandford's argument on a
realistic model of our galaxy. We show that the two key assumptions of the
argument (two dimensionality of the spatial distribution and a steady-state
frequency distribution) are in general not fulfilled. The effective scaling
dimension D of the spatial distribution of neutron stars is significantly
larger than two, and for frequencies detectable by terrestrial instruments the
frequency distribution is not in a steady state unless the ellipticity is
unrealistically large. Thus, in the cases of most interest, the maximum
expected gravitational-wave amplitude does have a strong dependence on the
deformation and rotation frequency of the population. The results strengthen
the previous upper limits on the expected gravitational-wave amplitude from
neutron stars by a factor of 6 for realistic values of ellipticity.
