We perform population synthesis studies of different types of neutron stars (thermally emitting isolated neutron stars, normal radio pulsars, magnetars) taking into account the magnetic field decay and using results from the most recent advances in n
eutron star cooling theory. For the first time, we confront our results with observations using {it simultaneously} the Log N -- Log S distribution for nearby isolated neutron stars, the Log N -- Log L distribution for magnetars, and the distribution of radio pulsars in the $P$ -- $dot P$ diagram. For this purpose, we fix a baseline neutron star model (all microphysics input), and other relevant parameters to standard values (velocity distribution, mass spectrum, birth rates ...), allowing to vary the initial magnetic field strength. We find that our theoretical model is consistent with all sets of data if the initial magnetic field distribution function follows a log-normal law with $<log (B_0/[G])>sim 13.25$ and $sigma_{log B_0}sim 0.6$. The typical scenario includes about 10% of neutron stars born as magnetars, significant magnetic field decay during the first million years of a NS life (only about a factor of 2 for low field neutron stars but more than an order of magnitude for magnetars), and a mass distribution function dominated by low mass objects. This model explains satisfactorily all known populations. Evolutionary links between different subclasses may exist, although robust conclusions are not yet possible.
We propose that the strong millisecond extragalactic radio burst (mERB) discovered by Lorimer et al. (2007) may be related to a hyperflare from an extragalactic soft gamma-ray repeater. The expected rate of such hyperflares, $sim$ 20 - 100 d$^{-1}$ G
pc$^{-3}$, is in good correspondence with the value estimated by Lorimer et al. The possible mechanism of radio emission can be related to the tearing mode instability in the magnetar magnetosphere as discussed by Lyutikov (2002), and can produce the radio flux corresponding to the observed $sim$ 30 Jy from the mERB using a simple scaling of the burst energy.
We present our new advanced model for population synthesis of close-by cooling NSs. Detailed treatment of the initial spatial distribution of NS progenitors and a detailed ISM structure up to 3 kpc give us an opportunity to discuss the strategy to lo
ok for new isolated cooling NSs. Our main results in this respect are the following: new candidates are expected to be identified behind the Gould Belt, in directions to rich OB associations, in particular in the Cygnus-Cepheus region; new candidates, on average, are expected to be hotter than the known population of cooling NS. Besides the usual approach (looking for soft X-ray sources), the search in empty $gamma$-ray error boxes or among run-away OB stars may yield new X-ray thermally emitting NS candidates.
