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Astron. Astrophys. 320, L9-L12 (1997)

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4. Discussion

The frequent and large variations in the X-ray luminosity of GX 1+4 observed with BATSE are quite similar to those found in the other accretion-powered X-ray pulsars. Power spectrum analysis of the luminosity fluctuations shows a power-law component (index= -2.1) indicative of a red noise in the system and has been seen before (Baykal & Ogelman 1993). Power spectrum analysis of the period fluctuations also shows a red-noise component. Period fluctuations have also been seen in other accreting pulsars with time scales down to a few days, but the red noise component seen here suggests that these fluctuations might represent torques that are internal to the neutron star rather than due to inhomogeneities in the accretion flow (White et al. 1995). The luminosity fluctuations are found to be correlated with the instantaneous [FORMULA], which always stays positive throughout the observation. The direct positive correlation of [FORMULA] with the X-ray luminosity is difficult to explain in terms of accretion disk models (Ghosh & Lamb 1991) as in such models an increase in luminosity is related to increased mass accretion rate that decreases the inner radius of the disk and leads to a spin-up of the neutron star i.e., negative [FORMULA]. On the other hand, if GX 1+4 accretes matter directly through stellar wind with negligible specific angular momentum, then the reversal of spin change sign could mean a reversal in the direction of the small disk that can form. A positive correlation between [FORMULA] and [FORMULA] can then be expected, as a sudden decrease in the net angular momentum can lead to an increase in accretion (King 1995).

The delay between [FORMULA] and [FORMULA] is difficult to explain in any accretion theory. The region of hard X-ray emission is very close to the neutron star surface and one cannot expect any delay between the X-ray emission and the resultant angular momentum transfer to the neutron star. Hence we look for some phenomena internal to the neutron star as a possible explanation to the delay. In this regard it is very instructive to compare these results to a similar phenomena observed in GRO J1744-28 (Stark et al. 1996). Stark et al. have found a phase lag in the bursting X-ray pulsar GRO J1744-28. During an X-ray burst when the X-ray luminosity increased by more than a factor of 15 in about 10 s, the phase lag increased to about 28 ms and subsequently the phase lag relaxes back with an exponential decay time of about 720 s. Interpreting this phenomenon in terms of models for pulsar glitches developed for radio pulsars, the phase lag during the burst corresponds to an initial spin-down with [FORMULA] - 10-3. The exponential decay time scale is equated to the crust-core coupling time scale, which is (4 [FORMULA] 102 - 104) P, where P is the rotation period of the neutron star (Alpar & Sauls 1988). If the phenomena observed in GRO J1744-28 is treated as an impulse response to luminosity change and if this phenomena is common to GX 1+4 too, continuous changes in luminosity (as seen in GX 1+4) will reflect as a delay in the [FORMULA] variation. The magnitude of period variation in GX 1+4 (dP/P = - [FORMULA] [FORMULA] 10-3) is comparable to that seen in GRO J1744-28. Further, the observed time scale (6 days) agrees with the relation between [FORMULA] and P given by Alpar & Sauls (1988).

The observed lag of [FORMULA] with respect to [FORMULA] is, therefore, consistent with the impulse response of X-ray luminosity variation seen in GRO J1744-28, with the time scales scaled up according to the relation given for core-crust relaxation. As pointed out by Stark et al., for the core-crust relaxation to occur, first the crust has to decouple and the angular momentum has to be transferred to the crust and the crust couples back to the core in a time scale given by Alpar & Sauls.

In conclusion, our analysis of the period and X-ray luminosity history of GX 1+4 observed with the BATSE shows: (i) a positive correlation between pulsed hard X-ray luminosity and spin-down rate, and (ii) the spin-down rate lags by 5.6 [FORMULA] 1.2 days with respect to the pulsed luminosity. These results suggest that the internal torque of the neutron star can play a dominant role in the period-luminosity history of GX 1+4. in

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© European Southern Observatory (ESO) 1997

Online publication: June 30, 1998
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