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Astron. Astrophys. 337, 815-818 (1998)

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4. Discussion

The transient X-ray pulsars in which QPOs have been detected, are the high mass X-ray binaries (HMXB) EXO 2030+375 (Angelini et al. 1989), A 0535+262 (Finger et al. 1996), 4U 0115+63 (Soong & Swank 1989) and V 0332+53 (Takeshima et al. 1994) and the LMXB GRO J1744-28 (Zhang et al. 1996; See Finger 1998 for a review of the QPO in transient X-ray pulsars). QPOs have also been observed in some of the persistent HMXB sources: Cen X-3 (Takeshima et al. 1991), SMC X-1 (Angelini et al. 1991), X Persei (Takeshima 1997) and 4U 1907+09 (in'tZand et al. 1998) and the LMXB 4U 1626-67 (Shinoda et al. 1990; Kommers et al. 1998). Both the Keplerian frequency model (in which the QPOs are produced because some inhomogeneous structure in the Keplerian disk attenuates the pulsar beam regularly) and the beat frequency model (in which the material influx to the pulsar from the disk is modulated at the Keplerian frequency) are in very good aggrement with the observations in EXO 2030+375 and A 0535+262. In 4U 0115+63, V 0332+52, Cen X-3, 4U 1626-67 and SMC X-1 however, the QPO frequency is found to be lower than the pulsation frequency hence the Keplerian frequency model is not applicable in these sources because if the Keplerian frequency at the magnetospheric boundary is less than the spin frequency, centrifugal inhibition of mass accretion will take place. For V 0332+52 the beat frequency model may also be inapplicable because the magnetospheric boundary calculated from the QPO properties and from observed luminosity are in disagreement in this source. In the LMXB transient pulsar GRO J1744-28, large change in X-ray flux was found to be associated with a very little change in the QPO frequency which ruled out both the Keplerian and the beat frequency models for QPOs in this source (Zhang et al. 1996). The beat frequency model is applicable in many sources though there is no convincing evidence of positive correlation between the QPO frequency and the X-ray luminosity in some of them.

According to the beat frequency model, the QPOs are a result of beat phenomena between the rotation of the innermost part of the disk and the spin of the neutron star. The Keplerian rotation frequency [FORMULA] of the disk at the magnetosphere boundary, the rotation frequency of the neutron star [FORMULA] and the QPO frequency [FORMULA] are related as [FORMULA] = [FORMULA] - [FORMULA]. Assuming that the QPOs are produced as a result of this phenomena, the Keplerian rotational frequency of the innermost part of the disk is just sum of the QPO frequency and the rotation frequency of the pulsar. For an assumed mass of 1.4 [FORMULA], this can be related to the magnetospheric radius rM of the X-ray pulsar.

In XTE J1858+034, we find that [FORMULA] = 0.11 [FORMULA] 0.01 Hz, [FORMULA] = 0.0045 Hz and the radius of the magnetospheric boundary is calculated to be


where M is the mass of the neutron star.

The pulse averaged X-ray flux in the 1.3-100 keV band is 6.5 10-10 erg cm-2 s-1 which, for a distance of rkpc, amounts to an X-ray luminosity LX of 7.9 1034 r[FORMULA] erg s-1. For a standard accretion disk with disk axis parallel to the magnetic field axis and dipole magnetic field structure of the neutron star, the radius of the inner transition zone can also be expressed as (Frank et al. 1992)


where, R6 is the radius of the neutron star in unit of 106 cm, L37 is X-ray luminosity in unit of 1037 erg and [FORMULA] is magnetic moment in unit of 1030 cm3 Gauss.

Combining the above two equations, and using M = 1.4 [FORMULA], R6 = 1, the magnetic moment [FORMULA] of the pulsar is calculated to be [FORMULA] 0.4 [FORMULA] 1030 rkpc, which for a neutron star radius of 106 cm, is equivalent to a magnetic field of 0.8 [FORMULA] 1012 rkpc Gauss.

If origin of the QPOs in this source is the magnetospheric boundary, the QPOs cannot arise from the modulation of X-rays emitted from the accretion disk because for a magnetospheric radius of 3 [FORMULA] 108 cm the disk temperature is rather low to emit in X-rays. The X-ray modulation at the QPO frequency can arise either because some inhomogeneous structure in the Keplerian disk attenuates the pulsar beam regularly at its rotation frequency, or the material influx to the pulsar from the disk is modulated at the Keplerian frequency. The fact that the strength of the QPO is greater at higher energies indicates that the latter is likely to be the case for XTE J1858+034. A detailed analysis (which is currently in progress) of the QPO feature as a function of pulse phase and energy will help in firmly deciding one of the two alternatives for the QPO phenomenon.

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© European Southern Observatory (ESO) 1998

Online publication: August 27, 1998