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Astron. Astrophys. 357, 164-168 (2000)

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3. Discussion and conclusions

We tried to evaluate the region of parameters which are excluded for models of the exponential magnetic field decay in NSs using the possibility that several ROSAT soft X-ray sources are indeed old accreting isolated NSs in X-rays. Of course we are not absolutely sure that all of the observed candidates are accreting NSs. Some of them can be cooling NSs or magnetars (this appears plausible, for example, for the source RX J0720-3125 as it has a spin period similar to soft gamma-ray repeaters). Future observations (especially the proper motion and [FORMULA] measurements) are required.

The intermediate values of [FORMULA] ([FORMULA]) in combination with the intermediate values of [FORMULA] ([FORMULA]) for [FORMULA] can be excluded for progenitors of isolated accreting NSs because NSs with such parameters would always remain on the ejector stage and never pass to the accretion stage. Even if all modern candidates are not accreting objects, the possibility of limitations of magnetic field decay models based on future observations of isolated accreting NSs should be addressed.

As seen in Fig. 2, for higher [FORMULA] NSs should reach [FORMULA] even for [FORMULA] yrs, for weaker fields the "forbidden" region becomes wider. The results are dependent on the initial magnetic field [FORMULA], the ISM density n, and NS velocity v. So here different ideas can be investigated. For example, this implies that the observed accreting isolated NSs can come from objects with a high initial magnetic field, and the others never appear as accreting objects because their parameters lie in the forbidden region. To explore this idea in details, the population synthesis of NSs for realistic distributions of v, [FORMULA] and n is needed. It is clear, however, that accreting old isolated NSs can hardly be formed from the initially high-field objects because the fraction of the high-field NSs cannot be large (as follows from radio pulsars observations). Since the fraction of the low velocity NSs is not more than several percent (Popov et al. 2000) and the volume fraction filled with relatively high density ISM is also small, accreting old isolated NSs should come from the "typical" population, i.e. from NSs with [FORMULA] about [FORMULA].

In fact the limits obtained are even stronger than they could be in nature, because we did not take into account that NSs can spend some significant time (in the case with field decay) at the propeller stage (the spin-down rate at this stage is very uncertain, see the list of formulae, for example, in Lipunov & Popov 1995 or Lipunov 1992). The calculations of this effect for different models of non-exponential field decay will be studied separately.

We cannot derive parameters of the field decay in accreting NSs in close binaries, because there the situation is completely different due to high accretion rates that can significantly affect the process of magnetic field decay. So our results cannot be applied to millisecond radio pulsars or other objects which were formed in close binary systems.

Note that there is another reason for which a very fast decay down to small values of [FORMULA] can also be excluded, because this would lead to a huge amount of accreting isolated NSs in drastic contrast with observations. This situation is similar to the "turn-off" of the magnetic field of an INS (i.e., quenching any magnetospheric effect on the accreting matter). So for any velocity and density distributions we should expect significantly more accreting isolated NSs than we know from ROSAT observations (of course, for high velocities X-ray sources will be very dim, but close NSs can be observed even for velocities [FORMULA] km s-1).

We conclude that the existence of several old isolated accreting NSs observed by ROSAT (if it is the correct interpretation of observations), can put important bounds on the models of the magnetic field decay for isolated NSs (without influence of accretion, which can stimulate field decay). These models should explain observations of [FORMULA] accreting isolated NSs in the solar vicinity. Here we cannot fully discuss the relations between decay parameters and X-ray observations of isolated NSs without detailed calculations. What we showed is that this connection should be taken into account and made some illustrations of it, and future investigations in that field RE desirable.

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© European Southern Observatory (ESO) 2000

Online publication: May 3, 2000