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INTEGRAL observations are performed in individual pointings called Science Windows (ScW) that have a typical duration of ∼2000 s. Each ScW is de-convolved by the OSA software and a sky image produced in a specified energy band. The nominal energy band used in the analysis of SFXTs here is 18−60 keV unless stated otherwise. A ScW resolution light curve is produced by extracting the count rate and uncertainty at the best known position of a source from each IBIS image where the source is within the FOV. It is IBIS ScW light curves produced in this manner that underpin much of the INTEGRAL analysis of SFXTs presented in this work. The main effect of the coded aperture imaging used by IBIS is that imperfect reconstructions of the sky images results in a higher level of positionally dependant systematic uncertainty and a deviation from the typical Poissonian statistics encountered in conventional focusing optics systems. Additionally as the flux from each source in the FOV is spread across the whole detector plane every source acts as a source of background for every other source. This enhanced background contribution fundamentally limits the sensitivity of coded aperture instruments compared to focusing optics where the flux from each source is concentrated on a specific region of the detector plane. Figure 2.3 shows an example de-convolved sky significance map from a single ScW of the region around the SFXT IGR

J17544−2619. IGR J17544−2619 is clearly detected during an outburst in the image along with several other bright point sources. The logarithmic colour scale

Figure 2.3: A significance map of the region around the SFXT IGR J17544−2619 from a single ScW in the 18−60 keV band using a logarithmic colour scale. Several bright sources, indicated by the white squares, are detected at > 5σ along with lower significance artefacts seen across the whole image and systematic noise in the outer regions resulting from the imperfect de-convolution of the shadowgram accumulated on the detector plane.

also illustrates the large number of artefacts present in this single image as well as systematic noise structures present in the outer regions of the image. These

artefacts and structures, which are of particular concern when they stack on top of each other in successive ScWs, present difficulties that have to be overcome when analysing source light curves derived from such images.

In the case of detected sources the magnitude of the uncertainty on the count rates extracted from each image increases as a source moves to larger off-axis angles as the source projects an incomplete section of the mask pattern onto the detector, thus accumulating an incomplete shadowgram on which to perform deconvolution. Sources at off-axis angles of less than 4.5o project a full mask pattern on to the detector plane and are in the ‘Fully Coded Field of View (FCFOV)’ where the uncertainties in the flux detected in each pixel approximate to being purely statistical. At larger off-axis angles, however, sources are in the ‘Partially Coded Field of View (PCFOV)’ where there is an increasing systematic contribution to the uncertainties in each pixel. The origin of this uncertainty is two fold. The first effect is a result of sources at larger off-axis angles projecting an in-complete mask pattern on to the detector plane such that the deconvolution is intrinsically less well defined, resulting in an increased count rate uncertainty. The second effect is a result of the imperfectly modelled energy response of IBIS for sources at large off-axis angles resulting from the effect of photons interacting with different surfaces of multiple pixels in the detector plane. Due to computational limitations these effects cannot be modelled for the production of each image resulting in an

additional source of systematic uncertainty in the derived count rates at the level of ∼2%. At sky positions where a source is not detected, however, the image is

dominated by artefacts that result from random fluctuations in the correlation of the mask pattern to regions of noise in the detector plane. For a sky position free of X-ray sources these random correlations are equally as likely to be negative as positive and hence the light curve of an empty region of sky will consist of a

distribution of positive and negative count rates centred on, and with an average of, zero. When studying persistent sources these random correlations are of little concern as the count rates at the source position are dominated by the detected flux. In the case of transient sources, however, extracted light curves contain epochs where the count rates are extracted from both flux-dominated and random

artefact-dominated images. Hence caution must be taken in the analysis of these light curves to avoid the identification of false positive outbursts resulting from the random fluctuation of artefacts at the source position whilst the source is in a dormant state. In all cases short exposures (∼ a few hundred seconds) also result in count rates with large uncertainties as insufficient detail can be accumulated in the detector plane shadowgram to allow effective deconvolution and the production of a well modelled sky image during such short observations.

IGR J17544−2619 extracted from each ScW in which the source was in the IBIS FOV between MJD 52698.174 and MJD 55698.030. The ScWs with a short

exposure and/or where IGR J17544−2619 was at a large off-axis angle can be easily identified by the data points with the large uncertainties. Large negative points are also observed, indicating the anti-correlations that can occur during the

de-convolution process. Additionally the distribution of count rate uncertainties (in logarithmic space) as a function of the off-axis angle of the observations are

illustrated in Fig. 2.5, where the red points illustrate observations with an exposure of greater than 200 s and where IGR J17544−2619 was at an off-axis angle of less than 12o (see Section 2.3) and the black points are the observations of lower exposure length and/or larger off-axis angle. The systematic increase in the magnitude of the uncertainty as a function of the off-axis angle is clearly observed with the increasing curvature of the distribution at the higher end of the angle range indicating the increasing influence of the poorly modelled IBIS response for sources at the edge of the FOV. The distribution of points in the vertical direction for any given off-axis angle is a combination of two factors. The first, and more dominant factor is the exposure length of the individual ScWs where longer exposures provide better constrained uncertainties due to the higher photon

statistics achieved. Conversely the black points at lower off-axis angles illustrate the shortest exposures where the de-convolution could not be performed effectively even for sources in the FCFOV. The second factor is the influence of the varying photon statistics of a transient source detected at different intensity levels with detections of the source in a brighter state having a larger √N uncertainty, despite being detected at higher significance, than when the source is in a fainter state. The following section discusses how these effects are accounted for in subsequent analyses of the IBIS light curves of SFXTs.