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A large number of neutron stars (NSs), ~10^9, populate the Galaxy, but only atiny fraction of them is observable during the short radio pulsar lifetime. Themajority of these isolated NSs, too cold to be detectable by their own thermalemission, should be visible in X-rays as a result of accretion from theinterstellar medium. The ROSAT all sky survey has however shown that suchaccreting isolated NSs are very elusive: only a few tentative candidates havebeen identified, contrary to theoretical predictions that up to severalthousands should be seen. We suggest that the fundamental reason for thisdiscrepancy lies in the use of the standard Bondi formula to estimate theaccretion rates. We compute the expected source counts using updated estimatesof the pulsar velocity distribution, realistic hydrogen atmosphere spectra, anda modified expression for the Bondi accretion rate as suggested by recent MHDsimulations, and supported by direct observations in the case of accretionaround supermassive black holes in nearby galaxies and in our own. We findthat, whereas the inclusion of atmospheric spectra partly compensates for thereduction in the counts due to the higher mean velocities of the newdistribution, the modified Bondi formula dramatically suppresses the sourcecounts. The new predictions are consistent with a null detection at the ROSATsensitivity.Comment: accepted to ApJ; 19 pages, 4 figure

Bondi Accretion and the Problem of the Missing Isolated Neutron Stars