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 Blandfords 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.
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