Bondi accretion and the problem of the missing isolated neutron stars

A large number of neutron stars (NSs), ∼109, populate the Galaxy, but only a tiny fraction of them is observable during the short radio pulsar lifetime. The majority of these isolated NSs, too cold to be detectable by their own thermal emission, should be visible in X-rays as a result of accretion from the interstellar medium. The ROSAT All-Sky Survey has, however, shown that such accreting isolated NSs are very elusive: only a few tentative candidates have been identified, contrary to theoretical predictions that up to several thousand should be seen. We suggest that the fundamental reason for this discrepancy lies in the use of the standard Bondi formula to estimate the accretion rates. We compute the expected source counts using updated estimates of the pulsar velocity distribution, realistic hydrogen atmosphere spectra, and a modified expression for the Bondi accretion rate, as suggested by recent MHD simulations and supported by direct observations in the case of accretion around supermassive black holes in nearby galaxies and in our own. We find that, whereas the inclusion of atmospheric spectra partly compensates for the reduction in the counts due to the higher mean velocities of the new distribution, the modified Bondi formula dramatically suppresses the source counts. The new predictions are consistent with a null detection at the ROSAT sensitivity.