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

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1. Introduction

Many astrophysical manifestations of neutron stars (NSs) are determined by their periods and magnetic fields. Four main evolutionary stages of isolated NSs can be singled out (see e.g. Lipunov 1992 for more detail): the ejector , when the star is observed as an active radio pulsar or a dead pulsar, which spins down according to magneto-dipole formula; the propeller , when the gravitationally captured matter is stopped near the NS magnetosphere and cannot get through the centrifugal barrier; the accretor , when the matter can reach the surface and the NS appears as an X-ray source; and the georotator , when the gravitational attraction becomes insignificant in comparison with the magnetic pressure and the NS magnetosphere interaction with the interstellar medium (ISM) is similar to the Earth magnetosphere interacting with the solar wind.

Magnetic field decay in NSs is a matter of controversy. Many models of the magnetric field decay have been proposed starting from the first simple models (Gunn & Ostriker 1970) up to the recent calculations (Sang & Chanmugam 1990; Urpin & Muslimov 1992, see also Ding et al. 1993; Jahan Miri & Bhattacharya 1994). The strongest direct observational evidence seems to come from non-observing decay effects in radio pulsars (Lyne et al. 1998) for the exponential (or nearly exponential) decay characteristic time scales [FORMULA] shorter than [FORMULA]. Additional constraints for longer time scales can be obtained from comparing the properties of NS calculated by the population synthesis method with those observed in radio pulsars (see e.g. Verbunt 1994; Bhattacharya et al. 1992; Hartman et al. 1996).

The magnetic field decay was used by Konenkov & Popov (1997) and Wang (1997) to explain properties of the source RX J0720-3125, which is considered to be a candidate for old isolated accreting NSs. If this source really represents an old accreting NS and, assuming that it was born as a normal radio pulsar (with a small period of [FORMULA] s and a standard magnetic field of [FORMULA] G), its properties can be explained only by field decay.

Bhattacharya et al. (1992) performed population synthesis calculations to study the field decay in single radio pulsars and came to some important conclusions about NS properties on the time scales [FORMULA] Myr. Recently the effect of the field decay in isolated NSs was studied by Colpi et al. (1998) and Livio et al. (1998).

Here we try to put some limits on the parameters of the exponential field decay assuming that some accreting X-ray sources observed by ROSAT are indeed old isolated NSs (Walter et al. 1996; Haberl et al. 1996, 1998; Neühauser & Trümper 1999; Schwope et al. 1999). There are two main possibilities for the explanation of the nature of these sources: accretion and cooling. We do not consider the possibility that all of them are normal cooling NSs or highly magnetized NSs, "magnetars" (see Neühauser & Trümper (1999) and we gave a brief discussion on this subject in Popov et al. (2000)). Cooling NSs have short lifetimes ([FORMULA] yrs) in comparison with the age of a Galaxy ([FORMULA] yrs) and thus might be relatively rare objects. Our calculations (Popov et al. 2000) show, that only for lifetimes of about [FORMULA] yrs, cooling NSs and accreting NSs can be observed in the solar vicinity with comparable probability. Proper motion measurements are necessary to estimate spatial velocities of these candidates. High velocities ([FORMULA]-50 km/s) can exclude the accretion interpretation. However at the present time the question of interpretation is open, and one cannot exclude any variant, but we discuss here only the accretion interpretation.

On average, NSs should have high velocities due to an additional kick obtained during the supernova explosion (Lyne & Lorimer 1994; Lorimer et al. 1997). The ISM accretion rate for high velocity objects should be rather low. However, recent population synthesis calculations (Popov et al. 2000) indicate that several old accreting NSs can be observed in the solar vicinity even for the space velocity distribution similar to one that has been derived from radio pulsar observations. And since there is the theoretical possibility of accreting isolated NSs, we wish to discuss how they can be used (possibly in the future) to put some limits on the models of field decay.

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© European Southern Observatory (ESO) 2000

Online publication: May 3, 2000
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