Problems

It is now becoming clear that the predictions of the "standard" model are too optimistic (e.g. Motch et al. 1996; Belloni et al. 1996), suggesting that the range of parameters of needs to be more constrained.
There are several sources of uncertainties which may influence theoretical predictions, such as the velocity distribution and density of ONSs, the strength of the relic magnetic field, the neutron star birth rate and the total number of ONSs. Scattering by molecular clouds and spiral arms (dynamical heating) may boost a fraction of low velocity stars to higher speeds, reducing the number counts up to an order of magnitude (Madau & Blaes 1994). Also, evidence has been found (Lyne & Lorimer 1994) for a neutron star mean birth velocity much higher than the one used here (even if the recent results by Hansen & Phinney point towards a pulsar distribution not depleted of slow objects). Moreover, Blaes, Warren & Madau (1995) argued that preheating of the ambient gas to temperatures higher than 10⁴ K may significantly reduce the accretion rate, hence decreasing the number of detectable objects.

From a more radical point of view, the candidates that have been put forward up to now, should belong to a different class of objects. They should be isolated YOUNG neutron stars which emit radiation due to the cooling of their hot surfaces. Objects like Geminga or other young neutron star which are radio silent. Otherwise a kind of extreme BL Lac could also match the observation properties of the candidates.