| BZs >gnuplot.ps Acta Polytechnica Vol. 51 No. 2/2011 Timing Analysis with INTEGRAL: Comparing Different Reconstruction Algorithms V. Grinberg, I. Kreykenbohm, F. Fürst, J. Wilms, K. Pottschmidt, M. Cadolle Bel, J. Rodriguez, D. M. Marcu, S. Suchy, A. Markowitz, M. A. Nowak Abstract 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-ray sources is highly non-trivial. We present results from a comparison of two commonly employed algorithms, which primarily measure flux from mask deconvolution (ii lc extract) and from calculating thepixel illuminated fraction (ii light). Bothmethodsagreewell for timescales above about10s, thehighest 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. Keywords: timing analysis, instrumentation and methods, lightcurves, data extraction. 1 Introduction The INTEGRAL satellite is one of the few instru- ments 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 radia- tion is modulated by a mask. Each source will cast a shadow image (shadowgram) — the combined shad- owgram is recorded in the detector plane. To ob- tain the original image the detected flux distribution has to be deconvolved in an analytically and compu- tationally non-trivial process which is highly CPU- intensive. For the reconstruction of lightcurves two algo- rithms are commonly employed: ii lc extract de- convolves shadowgrams for each time and energy bin, where the lightcurve is extracted. ii light calcu- lates 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 short- comings (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. 2 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- Fig. 1: Intensity mosaics of the fields of CygX-1 and GRS1915+105 in the 20–40keV band 33 Acta Polytechnica Vol. 51 No. 2/2011 Fig. 2: Scatterplots for countrates obtained with ii lc extract and ii light ing the Cyg X-1 and GRS 1915+105 INTEGRAL key programme in the 20–40 keV energy band with the source in the fully coded field of view (FOV), i.e. to a maximum pointing offset of 4.5◦, from 15 science win- dows (ScWs) from revolution 628 and 26 ScWs from revolution 852, respectively. Cyg X-1 (countrate ∼ 100 cps) is significantly brighter than GRS 1915+105 (∼ 40 cps). While both fields are comparable regard- ing the sources taken into account for our extractions (named boxes, σdetection ≥ 6, cps ∼ 0.5–4.5), the field of GRS 1915+105 is crowded with ∼ 35 weak sources (marked with ×, 1 ≤ σdetection < 6), while the field of Cyg X-1 shows only ∼ 20 of them. Figure 2 shows the correlation between the re- sults 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 (rev- olutions and ScWs as for mosaic images), respec- tively. 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 com- mon for X-ray lightcurves. ii lc extract does not allow for a much higher time resolution than 10s. ii light systematically underestimates the countrate. The 10 s lightcurves (cyan circles) are however well linearly correlated with a best- fit 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 differ- ent 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 aver- age 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 lightunderestimates the countrates by about5%, 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 differ- ences 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. 3 High Time Resolution with ii light For the following section we use all ScWs from revo- lution 628 where Cyg X-1 is in the fully or partially coded FOV, i.e., science windows with a pointing off- set of up to ∼ 15◦. Histograms (width 1 cps) of the ii light light- curves 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 re- sults. 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- 34 Acta Polytechnica Vol. 51 No. 2/2011 0 100 200 # o f d a ta p o in ts −5 0 5 re si − d u a ls 0 500 1000 # o f d a ta p o in ts −5 0 5 re si − d u a ls 0 1000 2000 3000 # o f d a ta p o in ts −400 −200 0 200 400 600 −5 0 5 countrate [cps] re si − d u a ls Fig. 3: Histograms (width 1cps) of the ii light lightcurves of revolution 628 with 10s (upper panel), 1s (middle panel) and 0.1s (lower panel) time resolution and up to ∼ 15◦ pointing offset angle in the 20–40keV band of CygX-1 and Gaussian fits to them. The dotted lines indicate the centers of the Gaussians 5.4439×104 5.44395×104 5.444×104 5.44405×104 5.4441×104 8 0 9 0 1 0 0 1 1 0 1 2 0 time [MJD] co u n tr a te [ cp s] Fig. 4: Fluxes from image extraction (box; deconvolution algorithm consistent with ii lc extract) as well as averaged countrates for individual ScW of the ii light lightcurves with 10s (triangle) 1s (x) and 0.1s (circle) time resolution in the 20–40keV energy band 2 4 6 8 10 12 14 0 .9 1 1 .1 offset angle [deg] ii_ lig h t/ flu x fr o m im a g e e xt ra ct io n Fig. 5: The ratio between averaged countrates for individual ScWs of the ii light lightcurves with 10s (triangle), (x) and 0.1s (circle) time resolution in the 20–40keV energy band to the fluxes from the image extraction in dependency on the pointing offset angle of the science window 35 Acta Polytechnica Vol. 51 No. 2/2011 10−3 0.01 0.1 1 1 0 0 5 0 2 0 0 Fourier Frequency L e a h y P o w e r Fig. 6: Power spectrum densities (PSDs) for CygX-1 presented here for the lightcurves with 10s (red), 1s (blue) and 0.1s (brown) time resolution in the 20–40keV energy band in the Leahy normalization ing that ii light underestimates the source flux — the different time resolutions are, however, consistent among each other and reproduce the shape of the lightcurve well. 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 rms2/Hz. This is consistent with the findings of [1] for Vela X-1, where the Poisson noise contributes as much as 100 rms2/Hz at a given fre- quency. Our PSDs for different time resolutions agree rea- sonably well with each other in shape (for exact timing studies longer periods than a single revolu- tion would be necessary to reduce the uncertainities). Note that [3] also found consistent PSD shapes com- paring ISGRI and RXTE-PCA 15–70 keV data for Cyg X-1. So while a better noise correction is re- quired, ii light lightcurves are still well suited for timing studies with a 10s to 0.1s resolu- tion in the regime above 20keV. 4 Summary and Conclusions We have shown that it is possible to perform tim- ing 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 underesti- mates the countrates when compared to more exact deconvolution algorithms (which do not allow bet- ter 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 be- tween the countrates is linear, with the slope appar- ently 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 dif- ferent time resolutions agree well with each other, the noise does however show anomalous behaviour which has also been observed by [1]. 36 Acta Polytechnica Vol. 51 No. 2/2011 References [1] Fürst, F., Kreykenbohm, I., Pottschmidt, K., et al.: A & A, 519, 37, 2010. [2] Kreykenbohm, I., Wilms, J., Kretschmar, P., et al.: A & A, 492, 511, 2008. [3] Pottschmidt, K., Wilms, J., Nowak, M., et al.: Advances in Space Research, 38, 2006, p. 1 350. V. Grinberg E-mail: Victoria.grinberg@sternwarte.uni-erlangen.de Remeis-Observatory/ECAP/FAU Sternwartstr. 7 D-960 49 Bamberg, Germany USM/LMU, Munich, Germany I. Kreykenbohm Remeis-Observatory/ECAP/FAU Bamberg, Germany F. Fürst Remeis-Observatory/ECAP/FAU Bamberg, Germany J. Wilms Remeis-Observatory/ECAP/FAU Bamberg, Germany K. Pottschmidt CRESST/NASA-GSFC Greenbelt, MD, USA UMBC, Baltimore, MD, USA M. Cadolle Bel ESAC, Madrid, Spain J. Rodriguez DSM/DAPNIA/SAp, CEA Saclay, France D. M. Marcu CRESST/NASA-GSFC Greenbelt, MD, USA UMBC, Baltimore, MD, USA GMU, Fairfax, VA, USA S. Suchy CASS/UCSD, La Jolla, CA, USA A. Markowitz CASS/UCSD, La Jolla, CA, USA M. A. Nowak MIT/Chandra X-ray Center Cambridge, MA, USA 37