1. Timing analysis

The apparent pulse period was obtained by epoch folding and found to be 4.81250$\pm$0.00074 s. Barycentric corrections were applied to this period and it was then corrected for the orbital motion of the neutron star using the ephemeris of Nagase et al. (1992). The inertial pulse period is 4.81823$\pm$0.00074 s. When this is combined with previous measurements (Nagase et al. (1992) and references therein) the average rate of change of the pulse period from a weighted fit is $\dot{P}$/P = - 2.26 x 10^-4 yr^-1. The long-term behavior of the pulse period is shown in Figure 2.1. The spin up rate exhibits short term fluctuations which have been attributed to variations in the accretion rate (van der Klis et al. (1980)).

Figure 1: The long-term behavior of the pulse period of Cen X-3. The overall trend is a secular spin up at an average rate of $\dot{P}$/P = - 2.26 x 10^-4 yr^-1.

The average pulse profile in the energy range 1-12 keV obtained from BBXRT is shown in Figure 2.1. The dependence of the pulse shape on energy was investigated by binning the event data into 1 keV energy bins and folding it with the pulse period. The profile was found to become slightly less double-peaked at low energies. Figure 2.1 shows the folded light curves over different energy bands.

Figure 2: The average pulse profile in the energy range 1-12 keV. The profile is single peaked with a small interpulse which is slightly less prominent at low energies.

Figure 3: Energy resolved pulse profiles. The A0 data were binned into 1 keV energy bins and folded with the pulse period.

As shown in Figure 2.1, the previously observed QPO (Takeshima et al. (1991)) is evident in the BBXRT data. The QPO peak is well fit by a Lorentzian with centroid 40.7$\pm$1.1 mHz and FWHM 4.6$\pm$3.4 mHz. The values obtained by Takeshima et al. for the centroid and FWHM were 35$\pm$2 and 10$\pm$5 mHz, respectively. To test for variations in the QPO power with energy the data were binned into 1 keV energy bins between 1 and 7 keV. Data between 7 and 12 keV were included in a single 5 keV energy bin to improve the counting statistics. The power spectra were obtained and fit to a Lorentzian centered at $\nu$ = 0, a power law, a Lorentzian for the QPO, and three narrow Lorentzians for the fundamental and first and second harmonics of the 4.8 s pulse period. The integrated power in the QPO was divided by the total integrated power (up to the Nyquist frequency) to obtain the relative intensity of the QPO. It was found that the relative intensity was well fit by a constant in energy, with $\chi^{2}_{}$ = 6.3 for six degrees of freedom. The value thus obtained for the relative intensity of the QPO was 7.8$\pm$1.2 %.

Figure 4: Average power spectrum of Cen X-3 in the energy range 1-12 keV. The A0 data have been fit with a Lorentzian centered at $\nu$ = 0, a power law, and four Lorentzians for the QPO, fundamental, and harmonics, in increasing order of frequency.