6 Rapid variability of the continuum

 

 

Table 4: Characteristic numbers for rapid variability in RXTE data.

Date	Obs	Total	QPO1	QPO1	QPO2	QPO2	f1/2
(day	Id. No.	rms	freq.	rms amp.	freq.	rms amp.
in 2001)			(Hz)		(Hz)		(Hz)
45.7	50138-05-01	25%	--	--	--	--	0.81
47.7	50138-05-02	24%	--	--	0.81	5.3%	0.83
50.8	50138-05-03	23%	0.49	3.1%	1.0	11.2%	0.41
56.8	50138-05-04	23%	--	--	0.98	4.8%	0.95
62.5	50138-05-05	22%	--	--	1.2	9.9%	0.50
68.8	50138-05-06	18%	1.1	4.1%	2.0	6.8%	0.66
77.2	60407-01-01	19%	1.1	4.0%	2.1	7.6%	0.72
86.0	60407-01-02	19%	--	--	2.2	3.1%	1.3
92.8	60407-01-03	13%	--	--	6.9	3.4%	2.9
99.7	60407-01-04	12%	--	--	7.3	1.4%	5.1

We searched the RXTE PCA observations for both coherent pulsations and other incoherent rapid variability such as quasiperiodic oscillations (QPOs). The PCA data are taken in several different modes. For fast timing analysis, data in the "E_125us_64M_0_1s'' mode were used. This mode provides individual X-ray tagged events with 125 $\mu$s time precision and 64 bins of energy information.

Pulsations were searched for using the Fourier Transform technique. The PCA events were selected to be in the 2-60 keV range, and extracted into light curve segments of 1024 s duration, sampled at a frequency of 2048 Hz (i.e., Nyquist frequency of 1024 Hz). Fast Fourier transforms of each light curve were computed and the resulting power spectra were averaged. We searched for pulsations only from days 45-100 of year 2001, where SAX J1711.6-3808 was known to be relatively active, resulting in an exposure time of 20.9 ksec. This selection includes XTE observation IDs 50138-05-01-00 through - 06-00 and 60407-01-01-00 through - 04-00. Above a frequency of 10 Hz, the strongest Leahy-normalized (Leahy et al. 1983) Fourier power is 5.06 at a frequency of 88.53418 Hz. However, the 99% detection limit for 10⁶ trials is a power of 5.48, so no pulsations were detected at 99% confidence. The maximum power measured yields a 95% upper limit to pulsations of 1.5% fractional (rms) in the 2-60 keV band.

We also searched for broader high frequency QPOs. Oscillations in the range 300-1300 Hz have been detected from a multitude of neutron star low mass X-ray binaries, and can be as narrow in frequency as a few Hertz, or as broad as 100 Hz. Power spectra in the same energy band were rebinned in frequency and examined for excess power. We found no significant oscillations. The 95% upper limit to the fractional rms variations is 1.4% for QPOs with a full width half-max (FWHM) of 10 Hz, and 1.5% for a FWHM of 100 Hz.

Strohmayer (2001a & 2001b) has recently shown that in the black hole candidates GRS 1915+105 and GRO J1655-40, significant QPOs are present only in the X-ray band above 13 keV. We thus also divided the X-ray events into two bands, 2-8 keV and 8-60 keV, to search for energy dependent phenomena. No QPOs were detected in the soft and hard bands, with 95% upper limits of 2.1% and 2.3% fractional rms respectively, for a hypothetical QPO with FHWM of 50 Hz.

Below frequencies of 10 Hz the power spectrum is dominated by incoherent red noise (Fig. 12; see also Wijnands & Miller 2002). Generally speaking the power spectrum in the 1 mHz - 128 Hz band has a flat top with power law roll-off ($\propto$f^-1) above about 1 Hz. However, the shape of the spectrum does not perfectly obey this prescription. First of all there are noticeable QPOs and harmonics present, especially in the observations that precede day 100. Also, the power law decline above the cut-off is not a perfect power law but often has a smooth shelf, which is mildly visible in Fig. 12.

Because SAX J1712.6-3739 is also present in the field of view, it potentially contaminates the power spectrum of SAX J1711.6-3808. We have examined the power spectrum of SAX J1712.6-3739  both in the last few observations of this observing program where SAX J1711.6-3808 was known to be quiescent, and in observations from August 1999 (Observation IDs 40428-01-01-00 and -01). In those observations SAX J1712.6-3739 generally appeared to have weak variability, on the order of 8% total fractional rms fluctuations over the entire 0.001-128 Hz band. The average power spectrum of SAX J1712.6-3739 from the 1999 PCA observations is shown in the bottom portion of Fig. 12. It can be seen that the variability of SAX J1712.6-3739 is weak compared to the 20%-25% variability of SAX J1711.6-3808 during the peak of its outburst, but SAX J1712.6-3739 may indeed contribute to the "shelf'' seen around 10 Hz.

Figure 12: Comparison of the XTE PCA power spectrum of MJD 51959.8 (top curve) - which may include flux from both SAX J1711.6-3808 and SAX J1712.6-3739 - with the PCA power spectrum of SAX J1712.6-3739 alone taken in 1999 (bottom curve). The best fitting model including continuum and QPOs is shown as a solid smooth line.

In principle the power spectrum should be dominated by the variability of SAX J1711.6-3808. Unfortunately, the flux of SAX J1712.6-3739 in the time range of interest is a factor of $\sim$2 greater than has been seen before by the PCA. Thus, we have no direct experience regarding the variability of SAX J1712.6-3739 as it existed during the peak of the outburst of SAX J1711.6-3808. As such we will avoid presenting detailed results on the noise continuum and focus on the low frequency QPO features. The continuum model employed consisted of two additive continuum components of the form $A/(1+(f/f_{\rm o})^2)^{\alpha/2}$ where A is the normalization and $\alpha$ is the asymptotic power law index above the break frequency $f_{\rm o}$, plus a constant to represent the Poisson noise level. The two additive components were used in order to capture both the main break in the power spectrum and the "shelf''.

The QPOs are seen between 0.5 and 2.5 Hz, near the break in the noise continuum. When two QPOs are formally detected, they appear to have a 1:2 harmonic relationship, dominated primarily by the 2nd harmonic. Even when the first harmonic is not detected (owing in part to imperfections in the continuum model) there appears subjectively to be some excess noise at the first harmonic position. The centroid frequencies and amplitudes of the first and second harmonics are presented in Table 4 as QPO1 and QPO2 respectively. The "total rms'' column refers to the total fractional rms variability in the observation in the 0.001-128 Hz frequency band. Where a non-detection is listed in Table 4, we refrain from placing upper limits given the above discussions. The FWHM of the lower frequency QPO ranged from 0.06 to 0.36 Hz, while that for the upper peak ranged from 0.08 to 0.95 Hz. The total variability declined as the X-ray flux of SAX J1711.6-3808 declined, and during that time the frequencies of the QPOs were seen to increase slightly.

The "break'' frequency of the continuum level is also indicated in Table 4. The tabulated value is f_1/2, the frequency at which the continuum reaches half its maximum value, for the larger of the two continuum components. This quantity is comparable to the half-width at half-maximum value often quoted when authors fit a zero-centered Lorentzian to the low frequency continuum component of a power spectrum.

The nearby source SAX J1712.6-3739 contributes an appreciable fraction of the total flux observed by the PCA. For PCA observations pointed directly at SAX J1711.6-3808, the collimator response to SAX J1712.6-3739 is approximately 44%. For times before day 100 where it was possible to estimate the fluxes of both sources independently using the on- or off-source PCA slews, SAX J1712.6-3739 contributed between 27% and 46% of the total detected flux, with an average of 37%. Thus, if one were to consider the QPOs to come from SAX J1711.6-3808 alone, the fractional rms upper limits and values quoted above and in Table 4 are slight underestimates and should be revised upward by approximately 25%.

Wijnands & Miller (2002) also presented power spectral parameters of SAX J1711.6-3808, derived from PCA observations in the 60407 series. Where QPOs are detected both in Table 4 and in Wijnands & Miller (2002), there is a reasonably good agreement between in the two values. The values for the break in the continuum differ by a factor of $\sim$2.2, which is not unreasonable because the continuum models were quite different: Wijnands & Miller (2002) use a broken power law. However, we urge extreme caution in interpreting the later observations from the PCA, which are the most likely to be contaminated by SAX J1712.6-3739. For example, observations on days 92.8 and 99.7 have rms variabilities of 13% and 12% respectively. These are quite close to the $\sim$8% variability seen from SAX J1712.6-3739 alone. We also see a general positive trend between the QPO frequency and the break frequency.