6 Application to Chandra simulations

Our experiments on Chandra simulations allowed us to look at the computational requirements of our method. The detect toolkit (Dobrizycki et al. 1999) was designed for analysis of Chandra X-ray Observatory data. We used a simulation (see Fig. 9) from the HRC-I High Resolution Camera imaging detector. The field of view of HRC-I is 31 arcmin $\times$ 31 arcmin. The background corresponds to a 30 ks exposure. The simulation shows 6 repetitions of an aligned set of unresolved sources of the same intensity. From the first source, the following 5 are spaced at 0.5, 4, 5, 10 and 30 arcsec. From the last of these, at 60 arcsec distance, the same aligned pattern is repeated, but a large extended source is superimposed. The extended source is a Gaussian with sigma 25 arcsec. In addition to the aligned set of sources just described, they are also displayed shifted to the right, in parallel, by 60 arcsec and 120 arcsec, providing three parallel rows. The first row is much clearer: the sources have approximately 200 counts each. The extended source has about 2500 counts. In the second row, the sources are much weaker, having about 30 counts each. The third row is the same as the middle row, except that the sources are changed to disks with diameter 1 arcsec.

Figure 9: Simulated HRC-I image, original of dimensions 2800 $\times$ 2800

Detection of sources which are within 1 arcsec of each other was not achieved by the detection methods described in Dobrzycki et al. (1999) and will not be investigated here either. This implies that of the six sources considered in each half-row of the simulation, in effect four were used. Figure 9 appears, therefore, to have a total of 24 compact sources. Likewise the extended sources were not considered in Dobrzycki et al. (1999), nor by us.

In Dobrzycki et al. (1999), two methods for source detection based on wavelet transforms are described. The first, the celldetect method, is based on a sliding cell or window. Its performance is good, finding 22 of the 24 non-extended sources in the simulation. It is fast but requires a considerable range of parameters to be set by the user. A multiple scale binning procedure is used to handle very large images. It allows for variation in bin size to cater for off-axis detector spatial variation.

We selected an isolated point source, to which we fitted a Gaussian, to define a very approximate PSF. We used an 8 resolution scale B₃ spline à trous wavelet transform, with a Poisson noise model. We worked directly on the 2800 $\times$ 2800 array, with no preprocessing. In view of the faintness of some of the sources which we are trying to detect, we set a very low threshold, 1.5 sigma.

Figure 10 shows ellipses fitted to sources detected. Positions of detections are shown in Fig. 11, and an associated table of parameters contains information on the objects detected. The approach used here, which is based on resolution scale and noise modelling, and in addition carries out deconvolution, requires very little by way of user setting of parameters.

Figure 10: Source detections, marked

Figure 11: Source detections, labelled

The analysis of Chandra data is made difficult by off-axis variation in the PSF, which we have not taken into account. Indeed, the PSF becomes bimodal when far off-axis. The wavdetect procedure provided in the detect image analysis software package is based on a Mexican hat wavelet function. Its storage requirements result in an image size of 1024 $\times$ 1024 being recommended as the practical limit to be used. Our own code incorporates memory management and we analyzed, without prior blocking, a 2800 $\times$ 2800 image.

Examination of a smaller field shown in Fig. 12 allows us to go further, - to distinguish between sources which are within 1 arcsec. Figures 13 and 14 show the objects found and a sub-object analysis.

Figure 12: Part of the larger Chandra simulation

Figure 13: Locations of detected objects

Figure 14: Locations of detected objects, following sub-object analysis, with overplotted ellipses