A&A 453, 1037-1040 (2006)
A. Baykal1 - S. Ç. Inam2 - E. Beklen1,3
1 - Physics Department, Middle East Technical University, 06531 Ankara, Turkey
2 - Department of Electrical and Electronics Engineering, Baskent University, 06530 Ankara, Turkey
3 - Physics Department, Süleyman Demirel University, 32260 Isparta, Turkey
Received 30 November 2005 / Accepted 2 April 2006
The high mass X-ray binary pulsar 4U 1538-52 was observed between July 31 and August 7, 2003. Using these observations, we determined new orbital epochs for both circular and elliptical orbit models. The orbital epochs for both orbit solutions agreed with each other and yielded an orbital period derivative yr-1. This value is consistent with the earlier measurement of yr-1 at the level and gives only an upper limit to the orbital period decay. Our determination of the pulse frequency showed that the source spun up at an average rate of Hz s-1 between 1991 and 2003.
Key words: X-rays: binaries - stars: neutron - pulsars: individual: 4U 1538-52 - accretion, accretion disks
From RXTE observations, Clark (2000) obtained new orbital parameters of the source that provided marginal evidence of orbital decay, i.e., they found yr-1. In this work, we present new orbital epoch and pulse frequency measurements based on our analysis of archival RXTE observations of 4U 1538-52.
The observations of 4U 1538-52 took place between July 31 and August 7, 2003 (MJD 52851-52858) and accumulated a total nominal exposure of 75 ks. The results presented here are based on data collected with the Proportional Counter Array (PCA, Jahoda et al. 1996). The PCA instrument consists of an array of five collimated xenon/methane multianode proportional counters. The total effective area is approximately 6250 cm2 and the field of view is FWHM. The nominal energy range of the PCA extends from 2 to 60 keV.
|Figure 1: 2-30 keV RXTE-PCA light curve of 4U 1538-52 between July 31 and August 7, 2003. Two 26 s binned 3 ks samples of this light curve corresponding to single RXTE orbits are presented on the upper left and the upper right.|
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Table 1: Orbital parameters of 4U 1538-52.
Background light curves and X-ray spectra were generated by using background estimator models based on the rate of very large events (VLE), detector activation, and cosmic X-ray background. The background light curves were subtracted from the source light curve obtained from the binned Good Xenon data. For 4U 1538-52, X-ray emission coming from the galactic ridge is only a few percent of the total X-ray emission which should not affect our timing analysis (see Makishima et al. 1987), so we did not include an estimation of the galactic ridge emission in our analysis. In Fig. 1, we present the background subtracted light curve. Although the number of active PCUs varied from 1 to 4 during the observations, Fig. 1 shows count rates adjusted as if 5 PCUs had been active using the "correctlc'' tool in HEASOFT 6. For the timing analysis, we corrected the light curve to the barycenter of the solar system. We also corrected this barycentered light curve for binary orbital motion using both circular and elliptical orbital models given in Table 1 (see also Clark 2000). Then a template pulse profile was created by folding the light curve into one master profile. Pulse profiles were also made from each of the 12 independent RXTE observations seen in Fig. 1.
In order to find the pulse frequency and a new orbital epoch, we obtained 12 pulse arrival times through the 2 binary orbits using a cross-correlation technique. In the pulse timing analysis, we used the method of harmonic representation of pulse profiles, which was proposed by Deeter Boynton (1985). In this method, the pulse profiles for each orbit and the master profile are expressed in terms of harmonic series. We used 10-term unweighted harmonic series to cross-correlate the template pulse profile with the pulse profiles for each RXTE observation. The maximum value of the cross-correlation is analytically well-defined and does not depend on the phase binning of the pulses.
The source 4U 1538-52 has a variable pulse profile which affects the pulse timing. In order to estimate the errors in the arrival times, the light curve of each RXTE observation was divided into approximately 4-5 equal subsets and new arrival times were estimated. The standard deviation of the arrival times obtained from each subset of the observation was taken to be the uncertainty in the arrival time for that observation.
Table 2: Orbital epochs by pulse timing analysis.
Arrival time delays may arise from the
change of the pulse frequency during the observation (or
intrinsic pulse frequency derivative) and from the differences
between the assumed and actual orbital and pulse parameters
(Deeter et al. 1981),
Table 1 presents the result of fits for both orbital and pulse parameters.
We also reestimated the orbital epochs by varying the
projected orbital radius
in the range of its uncertainty (
found that the resulting orbital epochs are consistent with the best fit
value at the 1
level. The error in the orbital epoch
due to an error in
also be expressed (Deeter et al. 1981) as
As seen from Table 1, the orbital epochs for circular and elliptical orbital models agree with each other at the 1 level. In order to check our technique, we extracted observations of 4U 1538-52 done in 1997 (MJD 50449.93-50453.69) and estimated orbital epochs for those observations. The results agreed with the orbital epochs given by Clark (2000).
In Table 2, we present the orbital epoch measurements from different observatories and orbital cycle number (n). In Fig. 3, we present observed minus calculated values of orbital epochs ( ) relative to the constant orbital period ( days). A quadratic fit to the epochs from all experiments yielded an estimate of the rate of period change yr-1. In Fig. 4, we display the long-term pulse frequency history of the source.
|Figure 2: ( Top) Pulse arrival time delays and best-fit elliptical orbital model given in Table 1. (Note that pulse profiles are obtained with respect to the reference time 52855.0585 MJD.) ( Below) Residuals after removing best orbital model.|
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|Figure 3: The phase residuals of orbital epoch for 4U 1538-52. The orbital phases are estimated relative the constant orbital period , where n is the orbital cycle number (see Table 2). The rightmost point corresponds to the most recent RXTE observation of ID 80016.|
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|Figure 4: Pulse frequency history of 4U 1538-52. The rightmost point corresponds to the most recent RXTE observation of ID 80016.|
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Before CGRO observations, 4U 1538-52 had been found to have a long-term spin down trend. A linear fit to pre-CGRO pulse frequency history gives and a linear fit to CGRO and our RXTE result yields . Rubin et al. (1997) constructed the power spectrum of pulse frequency derivative fluctuations. Their analysis showed that the pulse frequency derivative fluctuations can be explained on timescales from 16 to 1600 days with an average white noise strength of (Hz s-1)2 Hz-1. A random walk in pulse frequency (or white noise in pulse frequency derivative) can be explained as a sequence of steps in pulse frequency with an rms value of which occur at a constant rate R. Then the rms variation of the pulse frequency scales with elapsed time as (Hz), where is defined as noise strength. Then, rms scaling for the pulse frequency derivatives can be obtained as . As seen from Table 1, in our fits, upper limits on intrinsic pulse frequency derivatives are 7-10 times higher than the long-term spin up rates. If white noise in the pulse frequency derivative can be interpolated to a few days, then the upper limit on the change of frequency derivative obtained from a 1 week observation should typically have a magnitude that can be estimated from . This value is 15/7-15/10 times higher than the measured upper limit values. Therefore the measured upper limits on the intrinsic pulse frequency derivatives for 1 week are consistent with the values from the extrapolation of the power spectrum within a factor of a few.
The previous marginal measurement of change in the orbital period was yr-1 (Clark 2000), and our new value for the orbital period change, yr-1, are consistent with zero. These two measurements are consistent with each other in level.
In most of the X-ray binaries with accretion powered pulsars, the evolution of the orbital period seems to be too slow to be detectable. Yet there are still some such systems in which this evolution was measured and were reported. These systems include Cen X-3 with yr-1(Kelley et al. 1983; Nagase et al. 1992), Her X-1 with 10-8 yr-1 (Deeter et al. 1991), SMC X-1 with yr-1 (Levine et al. 1993), Cyg X-3 with yr-1 (Kitamoto et al. 1995), 4U 1700-37 with yr-1 (Rubin et al. 1996), and LMC X-4 with yr-1 (Levine et al. 2000). Change in the orbital period of Cyg X-3 was associated with the mass loss rate from the Wolf-Rayet companion star. For 4U 1700-37, the major cause of orbital period change was also thought to be mass loss from the companion star. For Her X-1, mass loss and mass transfer from the companion were proposed to be the reasons for the change in the orbital period of the system.
On the other hand, for the high mass X-ray binary systems Cen X-3, LMC X-4 and SMC X-1, the major cause of change in the orbital period is likely to be tidal interactions (Kelley et al. 1983; Levine et al. 2000; Levine et al. 1993). For these three systems, the orbital period decreases (i.e. the derivative of the orbital period is negative). Our new measurement of orbital period change () gives the value of about -10-6 yr-1 which is similar to the observed values of SMC X-1 and Cen X-3. Further observations can give more information about the orbital period change of this source.
We thank the anonymous referee for useful suggestions and comments. A.B. and S.C.I. acknowledge research project TBAG 106T040 of the Scientific and Technological Research Council of Turkey (TUBITAK).