7 Test 4 - sky models with point-like and extended objects

7.1 Input configuration

We have chosen exactly the same input point-like sources configuration as in Test 3 and we have added 5 extended objects. They may be regarded as clusters of galaxies at different redshifts with the same $\beta$-profiles and moderate X-ray luminosity $L_{[2{-}10]\,{\rm keV}} \sim 3~10^{44}$ erg/s (cf. Table 2). Now the objective is to estimate the capabilities of the procedures to detect and identify extended objects. The difference from Test 2 is the arbitrary positions of the point-like sources leading to different local and global background properties and to uncontrolled confusion effects.

The input configuration and wavelet filtered and output images are given in Fig. 10.

Figure 10: Test 4. The raw X-ray photon image with point-like and extended objects for 10 ks exposure time (upper left) and its visual representation for much larger exposure and no background (upper right). The corresponding redshifts for the clusters are indicated. The MR/1+SE filtering (lower left) and WAVDETECT both with 10-4 significance threshold (lower right) are shown

7.2 Positional and photometric reconstruction

Results for the point-like sources will not be presented, because the input configuration (position, $\log N-\log S$, background) is exactly the same as in the previous test. It was shown in Test 2 that the presence of a point source even with moderate counts in the vicinity of a faint extended source could lead to confusion and even non-detection. Of course, the presence of a cluster will affect the detection and photometry of the point-like objects in its vicinity, but this effect is of minor concern for this test and has been already discussed (Test 2).

The detection rate, input-detect position offsets, detected counts and detected-to-input counts ratio are shown in Table 7.

 

 

Table 7: Recovery of position and flux of the extended objects

redshift	$\Delta r$	Input	Detect	Detect/Input
	[arcsec]	[counts]	[counts]	[%]
EMLDETECT
0.6	2.1	1316	94	7
1.0	8.0	465	12	3
1.5	12.3	200	161	81
1.8	4.6	136	228	167
2.0	14.8	109	32	29
G+SE
0.6	1.2	1316	1043	79
1.0	5.2	465	355	76
1.5	1.9	200	220	110
1.8	Not detected
2.0	15.3	109	80	73
MR/1+SE
0.6	0.2	1316	1016	77
1.0	2.3	465	340	73
1.5	1.8	200	223	111
1.8	11.8	136	83	61
2.0	10.8	109	185	169
WAVDETECT
0.6	5.8	1316	344	26
1.0	10.6	465	193	41
1.5	0.1	200	39	19
1.8	Not detected
2.0	15.3	109	27	24

As to the positional errors, it was already concluded that the centres of the extended object can be displaced by more than the adopted searching radius for point-like sources (Sect. 5). The differences in positions shown in Table 7, especially for fainter objects, are 3-4 times larger than the one sigma limit for point-sources inside the inner $10\hbox {$^\prime $ }$ of the FOV (Table 6).

It is confirmed again that EMLDETECT and WAVDETECT are not quite successful in charactering extended objects. But note that this time the results for MR/1+SE and G+SE are worse than the results in Test 2 - the rate of lost photons being about 20-30%. Also, the flux of the clusters at z=1.5 and 2 is overestimated, suggesting blending with faint nearby point-like sources.

7.3 Classification

To classify the detected objects we have performed many simulations with only point-like sources as in Test 3. Ten simulated images were generated with the same $\log N-\log S$ and background, but with different and arbitrary positions of the input sources. Exactly the same parameters were used for filtering, detection and characterization.

Two classification parameters were used: the half-light radius (R₅₀) and the stellarity index from SExtractor based procedures. The results are shown in Fig. 11. We do not show results with WAVDETECT and EMLDETECT classification parameters because their unsatisfactory results were confirmed, as in Test 2.

Figure 11: Test 4. Half-light radius R50 (left figures) and stellarity index (right) as a function of the off-axis angle (up) and detected counts (down) for 10 generations. The detection was performed with SExtractor after MR/1 multiresolution filtering. There are in total 1287 detections indicated by points. The extended objects from this test are shown with filled circles

We can see the excellent classification based on the stellarity index and half-light radius: in the inner $10\hbox {$^\prime $ }$, for objects with more than 20 detected counts, stellarity less than 0.1 and $R_{50} \geq 20\hbox{$^{\prime\prime}$ }$ we have 15 incorrect assignments from 1287 detections ($\sim$$1\%$).