5 Test 2 - point-like plus extended objects

5.1 Input configuration

This test is similar to Test 1, but we have replaced some of the point-like sources by extended ones generated as described in Sect. 2. The raw photon image with input counts indicated and its representations are shown in Fig. 4.

Figure 4: Test 2. The raw X-ray photon image for 10 ks exposure time (upper left). As in Fig. 2 three cases of separations are indicated, as well as the corresponding input source counts. The extended objects are in the right columns. The Gaussian convolution with $FWHM=20\hbox {$^{\prime \prime }$ }$ (upper right), MR/1 WT filtered image (lower left) and WAVDETECT reconstructed image both with a significance threshold of 10-4 (lower right) are shown

5.2 Detection rate and positional errors

The number of missed and false detections are shown in Table 5. An increase of the searching radius to $20\hbox{$^{\prime\prime}$ }$ was needed: at $\delta r=15\hbox{$^{\prime\prime}$ }$ the blending tends to shift the centroid towards the point-like source. Note that this situation is a clear case for source confusion: if we take the closest neighbour (the point-like source in some cases) as the cross-identification from the input list, we shall overestimate the flux more than two-fold, while the true representation is the extended object.

Some changes were needed for the procedures not based on the wavelet technique in order to avoid splitting of the bright extended objects into sub-objects: increase of the Gaussian convolution FWHM to $20\hbox{$^{\prime\prime}$ }$, and multi-PSF fit for EMLDETECT. In the Gaussian case, the larger smoothing length smears some of the point-like sources, leading to non-detection. EMLDETECT splitting persists even with the maximum number of the PSFs fitted to the photon distribution (currently it is capable of simultaneously fitting up to 6 PSFs).

 

 

Table 5: Test 2 results for the detection rate. The first number in the "Missed'' column is for point sources while the second is for extended ones. The total number of input sources is 24=12+12

Method	Missed	False
EMLDETECT	1+1	89
G+SE $4\sigma$	6+0	1
MR/1+SE	6+0	6
WAVDETECT	6+0	18
EWAVELET	4+2	5

5.3 Photometric reconstruction

The inferred-to-input source counts ratio is shown in Fig. 5.

Figure 5: Test 2. As in Fig. 3 except that the squares now represent extended objects and the point-like sources at fixed counts of 100 (circles) are put beside their corresponding neighbors (rather than being put at 100). Circles with arrows and numbers denote the ratio when it is above 2

We will not consider EWAVELET as its photometric results and detection of extended sources were quite unsatisfactory. The simple correction technique (as in Test 1) based on the PSF does not work - the extended objects profile has different shape from the PSF.

$\delta r=15\hbox{$^{\prime\prime}$ }$.

Only MR/1+SE gives good results for the flux restoration of the extended objects, but overestimating the counts for the faintest one. WAVDETECT misses almost half of the input photons while EMLDETECT splitting leads to very poor results;

$\delta r=30\hbox{$^{\prime\prime}$ }$.

All procedures give bad restoration results with MR/1+SE performing best again for the extended sources. The proximity of the objects leads to an overestimation of the point-like source counts and an underestimation of the extended object counts. There is no simple way to correct for this effect, but can be done using a rather elaborated iterative procedure involving extended object profile fitting;

$\delta r=60\hbox{$^{\prime\prime}$ }$.

Point-like source results are relatively similar with all procedures - the source counts are slightly overestimated due to the extended object halo even at $60\hbox {$^{\prime \prime }$ }$. The problems of WAVDETECT and EMLDETECT and the recovery of the extended objects counts are quite obvious. Again MR/1+SE is the best performing procedure with extended objects flux uncertainty about 25-30%.

5.4 Object classification

An important test is the ability of the procedures to classify objects and to allow further analysis of complicated cases of blending. The MR/1+SE results for the clasification by means of the half-light radius and stellarity index (cf. Sect. 3.5) are shown in Fig. 6, overlayed over the results from 10 simulated images with only point-like sources. Clearly the detected extended objects with MR/1+SE fall into zones not occupied by point-like sources. Note, however, that the two detected point-like sources at $30\hbox {$^{\prime \prime }$ }$ will be mis-clasified as extended objects - the proximity not only influences the source counts, overestimated by more than 4-5 times (Fig. 5), but also the object profile and consequently the classification.

Figure 7 shows the WAVDETECT classification - the ratio of the object size to the PSF size ( $R_{\rm PSF}$). The results are more ambiguous with WAVDETECT (Fig. 7) compared to MR/1+SE. The results with EMLDETECT and its classification parameter (extension likelihood) were very unsatisfactory due to the extended object splitting. More comprehensive discussion of the simulations and the classification is left for Sect. 7.

Figure 6: Test 2. MR/1+SE detection classification based on R50 (left panels) and stellarity (right panels) as a function of the off-axis angle (upper panels) and detected source counts (lower panels). Identified extended (filled circles) and point-like objects (triangles) are plotted over the results from 10 simulated images with only point-like sources (see Sect. 6)

5.5 Discussion

Clearly EMLDETECT and WAVDETECT have problems in restoring the fluxes of extended objects. We have already discussed the splitting difficulties of EMLDETECT. The explanation for WAVDETECT's bad results is that the wavelet scale at which the detected object size is closer to the PSF size defines the source detection cell (in which the flux is computed). If the characteristic size of an object is larger than the PSF size (i.e. an extended object) this procedure will tend to underestimate the flux.

We can safely accept the MR/1+SE procedure as the best performing for detection and characterization both for point-like and extended objects. We must stress however that one cannot rely on the flux measurements when there are extended and point-like sources separated by less than $30\hbox {$^{\prime \prime }$ }$. The proximity affects also the classification of the point-like sources. Using the classification and then performing more complicated analysis like profile fitting and integration for the extended sources can improve a lot the restoration. In realistic situations we can expect very often problems of this kind, especially with XMM-Newton.