  We present limits to the log N - log S curve for isolated neutron stars, both
cooling and accreting neutron stars, which are not active as radio pulsars, as
observed with the ROSAT All-Sky Survey and compare it with theoretical
expectations. So far, only one isolated neutron star is identified optically
among ROSAT sources, namely RXJ185635-3754 (Walter & Matthews 1997). Three more
promising candidates have been suggested. In addition, several upper limit
estimates are available on the space density of such neutron stars from
different optical follow-up studies. We show that the log N - log S curve
according to the current observations, including the identified neutron star,
the three additional candidates, and the upper limits, lies between the
theoretical expectations for middle-aged cooling neutron stars and old
accreting neutron stars. At least one of the neutron star candidates found so
far with ROSAT may be cooling instead of accreting. We suggest that the fact
that more accreting isolated old neutron stars were expected (e.g., Madau &
Blaes 1994) than observed is mostly due to the velocity distribution used in
those calculations. More recent radio observations indicate that there are
fewer slow neutron stars, ie., fewer accreting X-ray bright old neutron stars.
At the X-ray bright end of the log N - log S curve, however, the ROSAT
observations agree well with the theoretical expectations.
