Timing

7 .2 Observations and Analysis

7.2.1 Timing

BATSE is a nearly continuous all-sky monitor of 20 keV-1.8 MeV hard X-ray/1- ray flux, consisting of eight identical uncollimated detectors arranged on the corners of the Compton spacecraft (see Fishman et al. 1989 for a description). Because the detectors are uncollimated, steady sources are indistinguishable from the background except when occulted by Earth's limb. Bright impulsive transients (e.g., solar flares and gamma ray bursts) are detected because their high intensity and short duration make them easily discriminated from the background. Periodic pulsed sources are also readily detectable. Our standard BATSE pulsed source detection and timing analysis uses the 20-60 ke V channel of the 4 channel/1.024 s resolution DISCLA data type (see Chapter 2). The barycentric pulse frequency history of GX 1+4 from 1991 April to 1995 November (MJD 48362-50031) was determined by dividing the BATSE data into five-day segments and searching the Fourier power spectrum of each segment for the strongest signal in the pulse period range 110 s;::; Ppulse ;::; 130 s.

Figure 7.1 shows the long-term pulse frequency history of GX 1+4, including both previous observations by various instruments as well as our BATSE observations (see Appendix J). During the 1970s, GX 1+4 was spinning up with mean rate

v

^~ 6.0 x 10-¹² Hz s-¹. From 1984 to date, the source has spun down at a mean rate

v

~ -3.7 x 10-¹² Hz s-¹, similar in magnitude to the previous spin-up rate. A close inspection of the pulse frequency data shows significant deviations from simple linear trends. During the spin-up era, the post-1975 measurements were of high precision and show excursions from steady spin-up.

The spin-down data during 1987-1991 (see bottom panel of Figure 7.1) show a clear quadratic trend, with the spin-down torque decreasing on a time scale

Iv/

ⁱⁱ

I

~ 10 yr. Our BATSE observations (shown in detail in Figure 7.2) also display a significant quadratic trend with a similar time scale

Iv/iii

~ 10 yr. However, the two quadratic trends are not consistent. Instead, they meet in a cusp around MJD 48300, indicating that a discontinuous change in the torque history occurred around this time. The SIGMA observations are approximately consistent with both trends. We observed a transition from spin-down to spin-up in 1994 November (Figure 7.3). Steady spin-up was observed for about 100 d followed by a gradual transition back to spin-down. About 20 d after the resumption

Year

1970 1975 1980 1985 1990 1995

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6000 7000 8000 9000 10000

Julian Date - 2,440,000.5

Figure 7.1: Pulse frequency history of GX 1+4 at the solar system barycenter. Top panel:

Long-term history of the source since its discovery. Bottom panel: Detailed spin-down history. The data for both panels are collected in Appendix J. Observations taken by other instruments after the start of BATSE monitoring have been omitted from this figure for clarity, but are also included in Appendix J. These measurements agree with the BATSE data.

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1992 1993 1994 1995

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Julian Date - 2,440,000.5

1996

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Figure 7.2: Detailed view of the BATSE pulse frequency history of GX 1 +4.

of spin-down, there was a dramatic increase in the spin-down rate which then gradually relaxed over the next 100 d.

Despite the overall strong quadratic trend in the BATSE data, our pulse frequency measurements display significant systematic excursions. The BATSE pulse frequency resid- uals with respect to the best-fit quadratic frequency model are shown in Figure 7.4. The oscillatory excursions evident on a ,...., 300 d time scale are too large to be attributed to orbital Doppler shifts. If we take b.v ,...., 5 µHz to be the Doppler amplitude of a ,...., 300 d

.. ··· ...

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Figure 7.3: Pulse frequency history of two recent torque reversals in GX 1+4.

orbit, we obtain for the mass function

( b..v )³ ( Porb )

fx(M) ~ 200 M0 5 µHz 300 d ' (7.1)

too massive for any stellar companion, let alone a red giant. The excursions are most likely due to variations in accretion torque. It is possible that the torques exhibit an orbital modulation, in which case the orbital period may still be ,.._, 300 d. We note that Cutler et al. (1986) suggested the presence of a 304 d periodicity in the torque history of the 1970s spin-up era.

It is useful to characterize the statistical properties of the pulse frequency fluctua- tions. The strong correlations evident on long time scales indicate the presence of a strong

"red noise" component (a power spectral component which rises with decreasing frequency) in the pulse frequency fluctuations. The presence of red noise can bias an unwindowed Fourier analysis of the power spectrum continuum due to power leakage through the broad sidelobe response of sinusoidal basis functions (Deeter & Boynton 1982). Spectral leakage can be suppressed (at a cost in frequency resolution) by judicious use of data windowing

40

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1992

8500

Year

1993 1994 1995

9000

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'

^;,

1996

10000

Figure 7.4: Pulse frequency residuals of GX 1+4 with respect to a best-fit quadratic frequency model.

(Harris 1978). Before computing the power spectrum, we multiplied the pulse frequency residuals by a window function of the form ^Wj

=

cos⁴(j7r/N) with j

=

-N/2, · · ·, N/2, substantially suppressing the sidelobe response of the Fourier transform (Harris 1978). To preserve the proper normalization, we rescaled the power spectrum by a factor N

/I:

w.

The resulting power spectral density of the pulse frequency fluctuations Pv is shown in the left panel of Figure 7.5. The spectrum at analysis frequencies

f <

4 x 10-⁷ Hz varies as Pv ex:

1-

^{2.so±o.17 .} The power spectrum for

f

> 4 x 10-⁷ Hz is dominated by the white noise process caused by the statistical uncertainties in the frequency measurements. (The measurement noise level indicated in the figure is not a fit to the power spectrum data but was calculated from the frequency measurement uncertainties.) Although our measurements were made with pulse frequencies, it is of physical interest to study the fluctuations in pulse frequency derivative since this quantity is proportional to the net torque on the neutron star. The power spectral density of fluctuations in pulse frequency derivative Pv is simply related to Pv by Pv

=

(27r !)² Pv (see, e.g., Boynton 1981). This spectrum is shown in the

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G: Analysis frequency (Hz)

Figure 7.5: Left panel: Power spectrum of fluctuations in the pulse frequency. The white noise level expected for the frequency measurement uncertainties is indicated. Right panel:

Corresponding power spectrum of fluctuations in the pulse frequency derivative fl. Our measurements are consistent with 1/ f noise in the torque fluctuations.

right panel of Figure 7.5. There is evidently a 1/

f

red noise process in the torque fluctuation power for GX 1+4. This is similar to (although an order of magnitude weaker than) the torque fluctuations observed in Cen X-3 (Finger, Wilson, & Fishman 1994), but it is in marked contrast to the white noise torque processes observed in Her X-1 (Boynton 1981), Vela X-1 (Deeter et al. 1989), and 4U 1626-67 (Chapter 6). These systems are the only X-ray pulsars for which a detailed characterization of the torque noise process has been made.