3. Analysis and results
3.1. Timing analysis
In each of the two detectors the 20-100 keV photons were detected with 128 channel energy information with a time resolution of 1.28 ms. The count rate was binned with 5 sec and 10 sec bin widths and a period search was done in the 50-200 sec range with an FFT algorithm based on the Lomb-Scargle method. For both the detectors very clear periodograms with single sharp peaks around 121.9 seconds were obtained. The reduced data length and energy range in one of the detectors gave a periodogram peak of smaller height compared to that in the other detector. A period search in two different broad energy bands also gave clear periodograms with smaller peaks at the same value of the period. Finally to improve accuracy in determination of the period, data from both the detectors were added and a periodogram was obtained. The pulse period of GX 1+4 as seen on 22nd March 1995 is determined to be s. The false alarm probability of the 121.88 s peak in the periodogram for an average background rate and the number of data points used, was calculated to be negligible . Pulsations in the same source were also detected in a previous balloon observation with the same telescope. The pulse period as seen on 11 December 1993 was s (Rao et al., 1994). Over this period of 15 months, the overall spin down rate of s yr-1 is somewhat smaller than the average spin down rate of 1.4 s yr-1 since 1987. BATSE observations in the intervening period have reported a reversal of the spin change rate (Chakrabarty et al., 1994), from spin-down to spin-up thereby supporting the smaller rate of change derived from the present observation. Pulse profiles in different energy bands were obtained by folding the photon counting rates with the measured period of 121.88 s. A plot of the pulse profile in the 20-100 keV energy range is shown in fig 1. for two cycles. The pulse profiles were obtained by adding data from the two detectors. The pulse fraction in the 20-50 keV range is estimated to be and that in the 50-100 keV range it is . The anti correlation between the pulse fraction and the luminosity found in the 1993 observation is still found to exist. The 20-50 keV pulse profile, which is the most clear one, shows a wide pulse with a valley at the center or two pulses with unequal separation. A double peaked pulse profile similar in structure but narrower in width was seen earlier by Makishima et al. (1988) in the 2-20 keV range. In our earlier observation in December 1993 there was no indication of a double pulse and the detected pulse was also narrower. It is possible that during the recent source brightening, there might have been a gradual change in the emission, from a pencil beam to a fan beam, which is more common to a pulsar in its bright state. A phase difference in the pulse profile with the energy was explained by a switch over in the beam pattern for a cylinder of emission at higher luminosity (White et al., 1983). To investigate whether the difference in the pulse fraction in the two energy bands is significant, we have obtained the hardness ratios (ratio of counts in the 20-35 keV range to that in the 20-100 keV range) in the pulsed (phase 0.45 to 1.05 in the pulse profile in the top panel of fig. 1.) and unpulsed (phase 0.05 to 0.45 in the pulse profile) parts of the profile. The derived values are and , respectively for the pulsed and the unpulsed part of the profile. Hence we conclude that there is no clear indication of any change in the pulse fraction with the energy. A detailed analysis of the spectra with the pulse phase has also been done and will be reported separately.
3.2. Spectral analysis
The observed energy spectrum was fitted well with an incident power law spectrum with a photon index (reduced = 1.1). A thermal Bremsstrahlung model gave a temperature of 99 keV. Spectral fits were also attempted with two Compton scattered Bremsstrahlung models. A temperature of 18.5 keV and an optical depth of 7.7 was obtained for the first model while the second model gave a temperature of 17.5 keV and an optical depth of 6.8. Pulse phased spectra for the pulsed and the non-pulsed components of the 122 s spin period were also obtained. These spectra were also fitted well with the power law and the thermal Bremsstrahlung models with similar values of the parameters but somewhat larger error bars. The X-ray luminosity in the 20-100 keV range is deduced to be 2.5 0.3 1037 erg s-1 for a distance of 10 kpc with a uncertainty on the higher side.
3.3. Pulse profile modeling
Very complex changes in the pulse profile with luminosity are seen in many X-ray pulsars. An intensity-dependent widely varying pulse profile was observed in the transient pulsar EXO 2030+375 which was modeled with both the fan and the pencil beams of unequal intensity from the two offset magnetic poles, the most complex modeling of a X-ray pulsar profile done so far (Parmar et al., 1989). The pulse profile observed in the high luminosity state changed as the source strength dropped by a factor of 100 and in a later bright state the initial bright state pulse profile was again seen. In EXO 2030+375 the relative luminosity of the two poles was found to change by a factor of 10. A change by a factor of in the overall luminosity and dominance fan beam emission over pencil beam emission was found when luminosity was erg s-1. At lower luminosity ( erg s-1) the emitting material is in the form of a slab over the polar cap and since it emits more along the local field lines, this results in a pencil beam pattern. At the higher accretion rate, the material goes closer to the pole before it is halted and it is held more like a cylinder. In this case the emission is more in the direction of the magnetic equator, resulting in a fan beam pattern.
The observed change in the GX 1+4 pulse profile from December 1993 to March 1995 can be explained in two ways. One possibility is an activation of the second pole, which is possible if the magnetic field is asymmetric in latitude (so that the distribution of mass accretion onto the two poles depends on the Alfven radius or in turn on the luminosity). The second plausible explanation is a gradual change in the beam pattern, from a pencil beam to a fan beam in spite of a decrease in luminosity by a factor of 3 in 20-100 keV energy band. In our modeling we have assumed a simple fan beam pattern of GX 1+4 with a symmetric magnetic dipole and equal intensity on both sides of the equator with a constant overall emission. The luminosity is maximum towards the magnetic equator from the neutron star center and decays exponentially towards the poles. The sum of the two angles, the angle between the magnetic axis and the spin axis and the angle between the observer line of sight and the spin axis needs to be more than so that the line of sight crosses the magnetic equator twice in one period and shows two peaks. Intensity has two minima, corresponding to the phases when the two poles are closest to the viewing axis. Such simple considerations were used successfully to reproduce roughly the pulse profiles of many pulsars by Leahy(1991). To get the detailed features of pulse profiles, many other possibilities like offset in the two magnetic poles, unequal brightness of the two sides, gravitational bending near the neutron star surface for photons direction not normal to the surface, unequal size of the two emission regions etc. are to be considered. But for a pulse profile with few bins and relatively large errors on the data points, a simple geometry as described above gave reasonably good fit and we obtained the following values for the parameters
and the exponential intensity decay towards the pole has an angular scale of .
The model considered here is actually unable to distinguish between and because of their interchangeability. However the values we have obtained are the same for both the parameters. The constraint is more on the sum of the two angles which defines the closest position of the second pole with the viewing axis and produces the valley in between the two peaks. Similar value of the two angles and ensures that we see very close to the first pole at phase 0.25 and the intensity there is an overall background emission.
Two GINGA observations in 1987 and 1988 in 10-37 keV range discovered two peculiar pulse profiles (Dotani et al., 1989). In the first observation at the peak of the profile, there was a dip with a local maximum in it and the intensity was erg s-1. In the second observation about away from the peak, again there was a dip but without any local maximum there unlike the previous observation and the intensity was erg s-1. A hollow cylinder of accretion column causing resonance scattering at the energy of the cyclotron line explained the first observation. At the center of the column there was no scattering and that resulted in the local maximum. At a higher intensity level in the second observation, the accretion column was full and the local maximum in the dip was absent. For this to happen the observer has to see just through one of the poles and that is supported by nearly the same values of and that we have obtained. The offset of the dip with the peak in the pulse profile as observed in the second GINGA observation is also explained with the present value of and . In the second observation probably a gradual change from fan beam to pencil beam was taking place with an increase in luminosity, and the peak in the second observation is at the place of the two magnetic equator crossings and the dip is at the phase when one is seeing through the first pole. A larger value of can produce the wide peak in the second observation and the valley also may become less significant. GX 1+4 showed both single and double peaked pulse profiles on different occasions (Mony et al., 1991). We have observed both types of pulse profiles on two different occasions with the same X-ray telescope.
The source geometry obtained here with the double peaked pulse profile can generate the single peaked profile observed in 1993 December if a pencil beam emission is considered. Very regular observations of GX 1+4 and accurate measurement of luminosity, pulsation period, period derivatives and epochs may help in establishing this scenario of change in the beaming pattern.
© European Southern Observatory (ESO) 1997
Online publication: July 3, 1998