Pulse Profiles and Spectroscopy

7 .2 Observations and Analysis

7.2.2 Pulse Profiles and Spectroscopy

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

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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.

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Figure 7.6: Left panel: The phase-averaged pulsed count spectrum of GX 1+4 during the bright spin-up state. Right panel: The corresponding photon spectra of GX 1+4. The vertical bars show the 1 a statistical uncertainties, while the horizontal bars show the widths of the energy channels. Upper limits are quoted at 953 confidence. The solid curve shows the best-fit thermal bremsstrahlung spectrum. The data shown are for MJD 49618-49798 (1994 September 23-1995 March 22).

These data were background-subtracted using the BATSE background model of Rubin et al. 1996 (Rubin et al. 1996). Three intervals were chosen: the bright extended spin- up state during 1994 November-1995 March (MJD 49618-49798), a part of the bright 1993 September flare (MJD 49239-49251), and a relatively quiescent interval during 1993 January-April (MJD 49010-49100). The phase-averaged pulsed count rates were fit with

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Figure 7.7: The pulse profile of GX 1+4 as a function of energy. Data shown are for the same dates as the previous figure.

Table 7.1. BATSE Pulsed Spectrum Fits for GX 1+4

Interval kT dN/dE at 70 keV

Dates MJD (keV) (ph cm-² s-¹ kev-1 ) Remarks

1993 Jan 23-Apr 23 49010-49100 45.2 ± 1.3 (1.86 ± 0.06) x 10-⁵ spin-down, low 1993 Sep 9-21 49239-49251 48.8 ± 2.1 (6.9 ± 0.3) x 10-⁵ spin-down, flare 1994 Sep 23-1995 Mar 22 49618-49798 44.1±0.2 (7.19 ± 0.04) x 10-⁵ spin-up, high

NOTE: These fits assume optically-thin thermal bremsstrahlung pulsed emission.

an optically-thin thermal bremsstrahlung spectrum² of the form dN Co

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where kT is a characteristic thermal energy and 9tr is the velocity-averaged free-free Gaunt factor (Rybicki & Lightman 1979). The best-fit spectral parameters are given in Table 7.1.

The spectral shape did not change appreciably between the different intensity states. The spectrum for the bright spin-up interval is shown in Figure 7.6. The corresponding pulse profiles are shown in Figure 7.7. Pulsed emission is clearly detected at energies up to 160 keV. An additional detection in the 590-745 keV channel has a formal significance of only 2.60".

The spectrum for the 1993 September flare is shown in Figure 7.8. A simultaneous measurement of the total (pulsed+unpulsed) spectrum of GX 1+4 in the 40-200 keV range was made with Compton/OSSE (Staubert et al. 1995). Before comparing the BATSE and OSSE spectra, two adjustments are required. First, a recent recalibration of the low-energy response of the OSSE detectors has found that observations reduced with the previous cal- ibration underestimated the low-energy flux by an energy-dependent factor. The necessary correction factor is :::::: 1.2 at 50 keV and falls to unity at 100 keV (J. E. Grove 1995, per- sonal communication). In addition, an intercomparison of BATSE and OSSE observations of the Crab Nebula has found that the BATSE fluxes are systematically ::::::20% higher than the OSSE fluxes (Much et al. 1996). Note that this is the discrepancy after applying the low-energy correction to the OSSE data; the discrepancy would be worse without the

2 A power-law model did not produce an acceptable fit; the photon spectrum falls too quickly at high energies. We adopted the bremsstrahlung model because it is a convenient parametrization which is in wide use by other observers of this source. However, we emphasize that our data are of insufficient quality to discriminate between thermal bremsstrahlung and other exponential spectra.

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Figure 7.8: Left panel: Photon spectrum of the 1993 September flare of GX 1+4. The crosses show the BATSE measurements of the pulsed flux. The solid curve shows the best- fit thermal bremsstrahlung model for the BATSE observations. The dotted curve shows the best-fit model for simultaneous OSSE observations of the total (pulsed+unpulsed) flux, with corrections applied (see text for details). Right panel: Inferred pulsed fraction of GX 1 +4 as a function of energy. This curve was computed by dividing the best-fit BATSE pulsed spectrum for the 1993 September flare by the best-fit OSSE total spectrum.

100

correction. The origin of this difference in overall normalization is unclear. However, to allow an intercomparison of the GX 1 +4 spectra from the two instruments, we applied the low-energy correction to the Staubert et al. (1995) OSSE spectrum and then multiplied the entire OSSE spectrum by 1.2. This should place both spectra on the same scale, although the overall normalization may be 20% too large.

The best-fit thermal bremsstrahlung model for the OSSE data, corrected as de- scribed, is plotted as a dotted curve in the left panel of Figure 7.8. The BATSE and OSSE fits agree at 120 keV but diverge at lower energies, differing by more than a factor of 2 at 20 keV. (We cannot infer anything from the divergence above 100 keV since the BATSE

spectrum is unconstrained in this region.) The difference between the two spectra is con- sistent with previous observations which showed that pulsed fraction increases with energy for most X-ray pulsars, including GX 1+4 (see Frontera & Dal Fiume 1989). Since OSSE is not an imaging instrument, part of the discrepancy may be due to a problem in the subtraction of the low energy background from the Galactic center region. BATSE, a wide field instrument which is also non-imaging, suffers from the same problem for observations of the total flux. However, by restricting the BATSE analysis to the pulsed flux, we obtain a proper background subtraction automatically. If we assume that the OSSE background is properly subtracted in the Staubert et al. observation, then we can estimate the pulsed fraction of GX 1+4 as a function of energy by simply dividing the BATSE spectral fit by the corrected OSSE spectral fit. The resulting estimate for the 20-100 ke V pulsed fraction, shown in the right panel of Figure 7.8, should be viewed with caution due to the several possible sources of systematic uncertainty.