Models

Models that have been proposed through the years for some of the X-ray pulsars of the new class differ with respect to the energy production mechanism as well as binary versus single nature of the magnetic degenerate star. Among models based on rotational energy dissipation, simple radio pulsar models can be ruled out based on the fact that measured spin-down rates correspond to a rotational energy loss by a magnetic neutron star which is more than two orders of magnitude lower than the inferred X-ray luminosities. Carlini & Treves (1989) suggest a modified radio pulsar scenario in which the emission beam of a freely precessing neutron star sweeps the Earth from different angles, depending on the precession phase. In their model, the observed X-ray periodicity reflects the precession period of a weakly magnetised (B  G) neutron star with mass 0.3 and with a spin period of only a few milliseconds. Morini et al. (1988) and Paczynski (1990) propose instead a white dwarf equivalent of the standard radio pulsar model. Due to the factor of larger moment of inertia, the white dwarf rotational energy loss implied by the measured is considerably larger than the measured X-ray luminosity. Within this framework, the spin-down rate changes of 1E 2259+586 observed by Iwasawa, Koyama & Halpern (1992) have been interpreted by Usov (1994) in terms of white dwarf glitches. In a different vein, Thompson & Duncan (1993) suggest that 1E 2559+586 spins down like a standard radio pulsar, while the emitted radiation results from the gradual dissipation of the intense magnetic field (  G) of the neutron star.

All the models outlined above are virtually ruled out by two recent studies. Baykal & Swank (1996) show that the spin period history of 1E 2259+586 consists of short term spin-up episodes superposed on a secular spin-down and that its fluctuation level is similar to that of a number of accreting X-ray pulsars in HMXBs. More crucially Mereghetti (1996) revealed an increased spin-down episode from 1E1048.1-5937, which is clearly incompatible with the spin-down rate expected in the unconventional applications of the radio pulsar model described above.

Models based on matter accretion onto a magnetic rotating neutron star are clearly favoured. These models, in turn, envisage both possibilities that the neutron star is isolated or in a binary system. Israel, Mereghetti & Stella (1994) and Corbet et al. (1995b) suggest that the neutron stars in 4U 0142+614 and 1E 2259+586, respectively, might be accreting matter from a dense region of a molecular cloud. The problem with this scenario is that the highest expected mass capture rates are in the g s range, therefore giving rise to an accretion luminosity of  erg s . This is well below the inferred X-ray luminosities.

Based on the Galactic distribution of four of the X-ray pulsars in the sample (4U1626-67 is excluded because of its binary nature), van Paradijs, Taam & van den Heuvel (1995) propose that they are the result of the evolution of a neutron star spiraling in a massive star, after the so-called Thorne-Zytkov stage. Therefore, these sources should consist of isolated neutron stars accreting matter from a residual disc.

Mass accretion from a companion star is the simplest explanation to account for the observed X-ray emission. In this framework, the peculiar period distribution of these sources can be explained by assuming that these neutron stars are rotating close to their equilibrium period (see Mereghetti & Stella 1995 for details). Due to the high angular momentum content, mass transfer in LMXBs is mediated by an accretion disc, resulting in a secular spin-up, unless the corotation radius is close to the size of the neutron star magnetosphere. In this ``equilibrium rotator" regime (cf. Ghosh & Lamb 1979) a spin-down may result from the torques exerted by the magnetic field lines threading the accretion disc. The equilibrium rotator condition is given by :

where is the accretion luminosity at equilibrium and B the surface magnetic field of the neutron star (see, e.g., Henrichs 1983; we use a neutron star mass of and radius of 10 cm). The measured spin-down rate of three of these sources testifies that the neutron star is close to equilibrium. We assume that also RX J1838.4-0301 and 4U 1626-67 are (nearly) equilibrium rotators. In the case of the latter source this is supported by the recent reversal from spin-up to spin-down. A measurement of the magnetic field strength based on cyclotron features is available only for 1E 2259+586, giving G (Iwasawa, Koyama & Halpern 1992, see, however, Corbet et al. 1995b for a different interpretation). The magnetic field of the other systems can be constrained by using the properties of their X-ray continuum. The spectrum of most X-ray pulsars is characterised by a relatively flat power law (photon index 0.5-1.8), with a cut-off around 10-30 keV above which the spectrum is much steeper (White, Swank & Holt 1983). This high energy cutoff is interpreted in terms of resonant cyclotron absorption in the vicinity of the polar caps. In those X-ray pulsars in which cyclotron line features are observed, the cutoff energy, , was empirically determined to be related to the cyclotron line energy through (Makishima et al. 1990b, 1992). Therefore, can be used to approximately estimate the magnetic field strength (see however the case of EXO 2030+375; Reynolds, Parmar & White 1993). With the exception of 4U 1626-67, the photon indexes of the spectra in our sample (measured shortwards of 10 keV) are higher than the range measured in other X-ray pulsars. It is therefore likely that the part of the spectrum above is predominantly observed in the X-ray pulsars in our sample. Due to the combined effects of poor statistics and photoelectric absorption, a cutoff below 2-3 keV would remain undetected in the available spectra of 4U 0142+614, 1E 1048.1-5937 and 1E 2259+586. We conclude that for the pulsars in our sample ;SPMlt; 2-3 keV and therefore B ;SPMlt; 8 10  G.

FIG A.10: Schematic representation of the position occupied by different classes of X-ray binaries in the B, M diagram. Lines of different equilibrium spin periods are also plotted (adapted from Stella, Mereghetti & Israel 1996). These values are substantially lower than those measured (or inferred) from most other X-ray pulsars (10 G). Assuming B = 5 G (based on the analogy with 1E 2259+586), eq. (A.1) yields for the sources in our sample luminosities of 1-4 10 erg s . The corresponding distances, , are reported in Table A.1. These distance and luminosity values are generally in good agreement with the X-ray and optical observational data. The only exception is 4U 1626-67, for which kpc is outside the range of 3-6 kpc derived by Levine et al. (1988) based on the spin-up observed before 1990. This indicates that 4U 1626-67 has a somewhat higher magnetic field ( scales linearly with B), as also suggested by its hard spectrum. A similar conclusion is reached if, in addition to eq.( A.1), the equation for the accretion torque (cf. eq. 28 in Henrichs 1983) is used together with the period derivative observed during the spin-up phase (P/P -2 10 yr ) and a luminosity decrease of a factor 4 observed in correspondence to the P reversal (Bildsten et al. 1994). This provides an independent rough estimate of 1.1 10 G and 10 erg s .

Note --Very recent results were obtained by investigating the properties of 4U0142+ 614 using data obtained with the ASCA observatory and archival data from the Einstein and ROSAT observatories (White et al. 1996). New measurements of the pulse period from 1979 and 1994 confirm that 4U0142+614 is spinning down on a timescale of 127000 yr. The ASCA spectrum is featureless and requires two components consisting of a  0.4 keV blackbody plus a power law with a photon index of 3.7. The blackbody X-ray flux is 40% the total and for a distance greater than 0.5 kpc covers more than 12% of the neutron star surface. This covering fraction is 2 orders of magnitude larger than expected for thin disc accretion onto a magnetised neutron star. These results suggest 4U0142+614 is probably not a low-mass X-ray binary system, but rather is an isolated pulsar undergoing a combination of spherical and disc accretion. The observed properties seem consistent with the suggestion by van Paradijs, Taam, & van den Heuvel (1995) that this pulsar is powered by accretion from the remnant of a Thorne-Zytkow object (TZO). The ROSAT PSPC image shows a dust-scattering halo that is a factor of 2 less than predicted by the measured equivalent hydrogen column density of , suggesting half of the absorbing material is located in the vicinity of the pulsar and possibly the remains of the TZO envelope. Alternatively the halo might be interpreted as a result of a common-envelope and spiral-in phase in a binary system.