Timing analysis with INTEGRAL : comparing different reconstruction algorithms

INTEGRAL is one of the few instruments capable of detecting X-rays above 20keV. It is therefore in principle well suited for studying X-ray variability in this regime. Because INTEGRAL uses coded mask instruments for imaging, the reconstruction of light curves of X-rav sources is highly non-trivial. We present results from the comparison of two commonly employed algorithms, which primarily measure flux from mask deconvolution (ii-lc-extract) and from calculating the pixel illuminated fraction (ii-light). Both methods agree well for timescales above about 10 s, the highest time resolution for which image reconstruction is possible. For higher time resolution, ii-light produces meaningful results, although the overall variance of the lightcurves is not preserved.


Introduction
The INTEGRAL satellite is one of the few instruments designed for the detection of X-rays above 20 keV with a good time resolution.It offers a unique opportunity for timing studies in this regime, though the exact analysis at high time resolution remains a challenge.In coded mask instruments like the IBIS telescope aboard the INTEGRAL the source radiation is modulated by a mask.Each source will cast a shadow image (shadowgram) -the combined shadowgram is recorded in the detector plane.To obtain the original image the detected flux distribution has to be deconvolved in an analytically and computationally non-trivial process which is highly CPUintensive.
For the reconstruction of lightcurves two algorithms are commonly employed: ii lc extract deconvolves shadowgrams for each time and energy bin, where the lightcurve is extracted.ii light calculates the lightcurves primarily from the pixel illumi-nated fraction (PIF, number between 0 and 1 for a given source expressing the degree of illumination of a detector pixel).Both are included in the INTEGRAL Off-line Scientific Analysis (OSA) software package.
In the following we compare the two extraction mechanisms and discuss their advantages and shortcomings (Sec.2), and then assess the suitability of ii light for high time resolution analysis (Sec.3).A short summary of the results and the implications for further timing analysis with INTEGRAL are given in Sec. 4.

Comparison between different lightcurve extraction algorithms
To reduce the influence of the selected field on the results of the lightcurve extraction, we perform the comparison on two different fields.Figure 1 shows a comparison of significance mosaics obtained dur- Figure 2 shows the correlation between the results obtained with ii light (OSA 7 version) and ii lc extract (OSA 8 version) for sources in the fully coded field of view in the 18-50 keV and 20-50 keV band for Cyg X-1 and GRS 1915+105 (revolutions and ScWs as for mosaic images), respectively.Note that the ii light algorithm was not included into OSA 8 release; we therefore used the newest version of both algorithms available at the time of writing.At a 10 s time resolution ii lc extract fails to detect the respective sources in several timebins, resulting in datapoints with zero countrate and error (red circles), which are excluded from our analysis.Negative countrate values are an artifact of the background extraction and common for X-ray lightcurves.ii lc extract does not allow for a much higher time resolution than 10 s. ii light systematically underestimates the countrate.The 10 s lightcurves (cyan circles) are however well linearly correlated with a bestfit slope of 1.05 ± 0.01 for Cyg X-1 and 1.15 ± 0.01 for GRS 1915+105.Fits to individual ScW-averaged countrates (black circles) in both cases show a different linear correlation with a lower slope and a sig-nificant offset.Given the good correlation for the non-averaged lightcurves and the fact, that the average datapoints lie well on the 10 s lightcurve fits, we are inclined to attribute this to the low number of ScWs analysed.More data covering a greater range in countrates will shed light on this issue.
The performance of ii light on all available IN-TEGRAL Crab data was analysed by [2], who found that ii light underestimates the countrates by about 5 %, consistent with our results.We attribute the different ratios of ii light and ii lc extract results for Cyg X-1 and GRS 1915+105 to the differences in the fields: in a more crowded field like the one of GRS 1915+105, a signal is more likely to be assigned to the wrong source.

High Time Resolution with ii light
For the following section we use all ScWs from revolution 628 where Cyg X-1 is in the fully or partially coded FOV, i.e., science windows with a pointing offset of up to ∼ 15 • .Histograms (width 1 cps) of the ii light lightcurves for Cyg X-1 (Fig. 3) and Gaussian fits to them show that though the scatter increases with the time resolution, the routine produces meaningful results.The centers of the Gaussians fit components (dashed lines) are well consistent with each other.The FWHM of the Gaussians increases by a factor of ∼ 3 for one order of magnitude increase in time resolution, consistent with the decreasing SNR.The deviations from the Gaussian shape are explained by the high intrinsic variability of the source of > 25 % over the 3 days of the INTEGRAL revolution 628, as seen in Fig. 4. Note also that Fig. 4 supports the find- Comparing the ratio between averaged countrates for individual ScWs of the ii light lightcurves to the fluxes from the image extraction, we see no offset angle dependency, as reported by [2], cf.Fig. 5.The respective means of the ratios (dotted lines) agree well and indicate an offset of ∼ 5 %, consistent with the linear correlation presented above for the fully coded FOV.
The power spectrum densities (PSDs) calculated from the above discussed ii light lightcurves are shown in Fig. 6.For such PSDs calculated in Leahy normalizazion, the Poisson noise level should be equal to 2, independent of the countrate of the source.It can, however, clearly be seen here that even at as high frequencies as a few Hz, the PSD flattens out at a value of ∼ 80 rms 2 /Hz.This is consistent with the findings of [1] for Vela X-1, where the Poisson noise contributes as much as 100 rms 2 /Hz at a given frequency.
Our PSDs for different time resolutions agree reasonably well with each other in shape (for exact timing studies longer periods than a single revolution would be necessary to reduce the uncertainities).Note that [3] also found consistent PSD shapes comparing ISGRI and RXTE-PCA 15-70 keV data for Cyg X-1.So while a better noise correction is required, ii light lightcurves are still well suited for timing studies with a 10 s to 0.1 s resolution in the regime above 20 keV.

Summary and Conclusions
We have shown that it is possible to perform timing studies with a resolution of up to 0.1 s with IN-TEGRAL when using the ii light tool.Although ii light (OSA 7 version) systematically underestimates the countrates when compared to more exact deconvolution algorithms (which do not allow better time resolution than 10 s even for bright sources such as Cyg X-1), the differences can in principle be assessed and taken into account.The correlation between the countrates is linear, with the slope apparently depending on the field under consideration.A more detailed analysis of sources in different fields will allow to better quantify this linear correlation.
The countrates of the ii light lightcurves follow a Gaussian distribution around the mean value.We do not see a dependency on the pointing offset angle of the observation.
PSDs calculated from these lightcurves with different time resolutions agree well with each other, the noise does however show anomalous behaviour which has also been observed by [1].

Fig. 3 :Fig. 4 :Fig. 6 :
Fig. 3: Histograms (width 1 cps) of the ii light lightcurves of revolution 628 with 10 s (upper panel), 1 s (middle panel) and 0.1 s (lower panel) time resolution and up to ∼ 15 • pointing offset angle in the 20-40 keV band of Cyg X-1 and Gaussian fits to them.The dotted lines indicate the centers of the Gaussians