5. False Detection Rates in celldetect

In order to study the rates of false source detections from celldetect , the tool was run on sets of simulated Chandra data that contained only a background-like component. This chapter is provided mainly for users performing statistical analysis of of source detections; it describes the simulations, the celldetect parameter settings used, and the results.

5.2 Description of Simulations

The simulated data were created with MARX . Three sets of simulations, each having a different exposure time, were produced for the ACIS-I and HRC-I detectors. The 10ks and 30ks sets each contained 99 simulations. The 100ks set contained 75 simulations for ACIS-I and 50 for HRC-I . The longer exposure times require longer celldetect run times and greater disk space, which necessitated fewer simulations. Although the 100ks set contained fewer simulations, the statistical significance of the celldetect results is not diminished, as these simulations proportionally yielded more detected sources.

The simulations used a monochromatic source (1.49 keV) with a uniform disk distribution of angular extent greater than the detector field of view. The flux of the disk source was set such that the total detected count rate was $\sim7.2\times10^{-7}$ events s $^{-1}$ pixel $^{-1}$ for ACIS-I and $\sim3.7\times10^{-8}$ events s $^{-1}$ pixel $^{-1}$ for HRC-I . These background rate assumptions are expected on-orbit values based on the Science Instrument Calibration Report for the AXAF CCD Imaging Spectrometer (ACIS), and the HRC Ground Calibration Final Report.

The use of a monochromatic disk as the sole source of photons is a simplified approximation to the expected true background in two ways: (1) such simulations are vignetted, but the true background will contain both a vignetted external component and a non-vignetted internal detector background component, and (2) the true background's vignetted external component will be non-monochromatic. However, we found that radial profiles of counts vs. off-axis angle matched to within $\sim$ 1-2% those obtained for a number of other simulations that had both an external component with a realistic energy spectrum (based on Rosat data) and a flat internal component. This is expected since vignetting is a strong function of energy. Adding a flat component makes relative vignetting smaller, and these effects tend to offset one another at 1.49 keV (near which both detectors have their peak effective areas). In addition, usage of monochromatic simulations provided for simpler and faster simulation generation. Given that the predicted background count rate assumptions used for the simulations are $\pm$ $\sim$ 10%, the $\sim$ 1-2% effects caused by this study's simplified approximations should be acceptable.

5.3 celldetect Settings

celldetect was run on these simulations using the current default settings, which were:

Chapter 6 has further information regarding the celldetect algorithm, and Chapter 7 describes the celldetect parameter settings in detail.

5.4 Results

It is important to keep in mind that since the simulated data contained only a background-like component, all detections are false sources.

Traditionally, the false source rate is expressed per field of view. The field of view is defined here as the entire detector for HRC-I (equivalent to $\sim$ 0.25 deg

) and as the four imaging chips in ACIS-I ( $\sim$ 0.08 deg

). The rates considered in this analysis are 0.1, 1, and 10 false sources per field of view.

The distribution of the signal-to-noise ratio (S/N) values of the false sources was examined in order to establish S/N threshold values for the given rates of false sources. For each exposure time, each false source detection rate, and each off-axis angle bin, the considered false source rate was scaled by the area of that bin and multiplied by the number of simulations. This yielded the number of "allowed'' false source detections for that region in all simulations combined. The S/N values of all false source detections in that bin were sorted, and the S/N value of the last "allowed'' source was identified. This is the S/N threshold value data point for that bin.

This calculation, which introduces angular dependence to the S/N threshold value for a particular false source detection rate, provides for a uniform distribution of false sources over the entire detector field of view.

We found that the S/N threshold for false sources grows with off-axis angle (see Figures 5.1, 5.2, and 5.3). This effect is expected, since the photon statistics in random simulations improve as the size of the detect cell grows with off-axis position. Note, however, that the data begin to flatten at large off-axis angles. This is due to mirror vignetting, which causes a reduction in the number of photons in the outer regions of the field of view. This in turn results in poorer photon statistics, and thus a flattening of S/N threshold values vs. off-axis angle at larger angles. The effect is especially prominent in HRC-I , which has a larger field of view than ACIS-I (see Figure 5.3).

Figures 5.1, 5.2, and 5.3 show the S/N threshold that will yield a particular false source detection rate as a function of the off-axis angle for three exposure times (10ks, 30ks, and 100ks). The tabular data for these figures may be found in Section 5.6.1.

The S/N threshold quoted here is the formal S/N as defined in Chapter 6, Eq. (6.7). It should not be mistaken for source "significance.'' The S/N threshold in the center of the image is quite low, especially for low exposure times. This is expected since the background in Chandra observations is very low and the expected number of background counts in small cells in the center of the image is effectively zero. Virtually all false sources identified in the center of the image for low exposure times have no counts in the associated background regions.

The S/N threshold dependence on the off-axis angle can be well approximated with the following function:

Fitted curves using the function from Eq. (5.1) are shown in Figures 5.1, 5.2, and 5.3 as dashed lines for the rate of 0.1, as solid lines for the rate of 1.0, and as dotted lines for the rate of 10.0 false sources per field of view. The fitted values of the function coefficients

, and

are shown in Table 5.3 in Section 5.6.2.

Equation (5.1) works especially well for off-axis angles lower than 10 arcmin (i.e. for the region of the data where PSF sizes are small; see Figures 5.1 and 5.2). This region corresponds to the entire field of view of all four ACIS-I chips and the inner portion of HRC-I .

**Figure 5.1:** ACIS-I Field of View. The S/N threshold that will yield a particular false source detection rate, as a function of the off-axis angle. The rates are shown with the best-fit overlaid: 0.1 (cross, dashed line), 1 (circle, solid line), and 10 (triangle, dotted line) false sources per field of view. The data and the best fit function coefficients may be found in Section 5.6.
$\begin{figure}\centering \includegraphics*{plots/cell_false_results_fig1.ps}\end{figure}$

**Figure 5.2:** Inner Region of HRC-I. The S/N threshold that will yield a particular false source detection rate, as a function of the off-axis angle. The rates are shown with the best-fit overlaid: 0.1 (cross, dashed line), 1 (circle, solid line), and 10 (triangle, dotted line) false sources per field of view. The data and the best fit function coefficients may be found in Section 5.6.
$\begin{figure}\centering \includegraphics*{plots/cell_false_results_fig2.ps}\end{figure}$

**Figure 5.3:** Outer Region of HRC-I. The S/N threshold that will yield a particular false source detection rate, as a function of the off-axis angle. The rates are shown with the best-fit overlaid: 0.1 (cross, dashed line), 1 (circle, solid line), and 10 (triangle, dotted line) false sources per field of view. The data and the best fit function coefficients may be found in Section 5.6.
$\begin{figure}\centering \includegraphics*{plots/cell_false_results_fig3.ps}\end{figure}$

5.5 Summary

The data and curves in Figures 5.1, 5.2, and 5.3 should be utilized in the following way: if from a celldetect run the user selects only those sources that lie above the curve corresponding to

false sources per field of view, then the user can expect to have

false detections among those sources over the entire detector. These detections are distributed uniformly over the field of view; there are no preferred positions for false sources.

In addition, since no single value for the celldetect thresh parameter works universally, it is recommended that the user exercise caution when selecting the value of this parameter for their particular analysis. When S/N threshold is set too low, large numbers of spurious sources may result (which may in turn unnecessarily increase computation time). When this parameter is set too high, real source detection may be significantly impaired.

5.6 Appendix

5.6.1 S/N Threshold Values vs. Off-Axis Angle Data

Each column in the table gives the S/N threshold values, in 1 arcmin bins, above which there would be N false sources in the entire field of view. For example, if the user detected a number of sources and they all have a S/N value higher than the tabulated value for their off-axis angle for

, then the user may expect that 10 of the sources are false detections.

Table 5.1: ACIS-I. S/N thresholds for three exposure times as a function of off-axis angle. Rates are over the full ACIS field of view.

	Exposure time
	10 ks			30 ks			100 ks
Off-axis angle	False source rate			False source rate			False source rate
[arcmin]	0.1	1	10	0.1	1	10	0.1	1	10
0.5	1.19	1.19	0.96	1.50	1.41	1.19	1.87	1.87	1.78
1.5	1.26	1.20	0.99	1.71	1.57	1.38	2.33	2.26	2.07
2.5	1.45	1.30	1.11	1.96	1.78	1.60	2.75	2.59	2.31
3.5	1.72	1.46	1.27	2.23	2.03	1.82	3.05	2.86	2.54
4.5	1.92	1.67	1.49	2.51	2.31	2.05	3.43	3.11	2.77
5.5	2.08	1.84	1.67	2.80	2.54	2.24	3.61	3.30	2.94
6.5	2.23	2.05	1.83	3.06	2.76	2.43	3.79	3.45	3.04
7.5	2.45	2.25	2.00	3.28	2.92	2.56	3.87	3.54	3.06
8.5	2.65	2.45	2.14	3.40	3.04	2.66	3.91	3.53	3.07
9.5	2.77	2.62	2.28	3.53	3.11	2.72	4.07	3.56	3.10
10.5	2.82	2.79	2.42	3.66	3.19	2.80	4.43	3.69	3.18

Table 5.2: HRC-I. S/N thresholds for three exposure times as a function of off-axis angle. Rates are over the full HRC-I field of view.

	Exposure time
	10 ks			30 ks			100 ks
Off-axis angle	False source rate			False source rate			False source rate
[arcmin]	0.1	1	10	0.1	1	10	0.1	1	10
0.5	1.06	1.06	1.00	1.31	1.31	1.20	1.81	1.81	1.73
1.5	1.19	1.17	1.11	1.56	1.55	1.47	2.22	2.22	2.05
2.5	1.46	1.43	1.32	1.91	1.88	1.79	2.64	2.64	2.43
3.5	1.77	1.70	1.54	2.37	2.28	2.12	3.11	3.07	2.85
4.5	2.05	2.00	1.78	2.75	2.65	2.44	3.52	3.44	3.14
5.5	2.38	2.22	2.01	3.17	3.02	2.70	3.75	3.65	3.30
6.5	2.71	2.55	2.27	3.40	3.25	2.87	3.87	3.76	3.37
7.5	3.02	2.79	2.49	3.67	3.46	3.02	3.99	3.82	3.42
8.5	3.16	2.99	2.63	3.83	3.52	3.08	4.08	3.89	3.45
9.5	3.38	3.12	2.74	4.01	3.63	3.15	4.18	3.95	3.43
10.5	3.50	3.23	2.82	4.20	3.66	3.14	4.07	3.90	3.40
11.5	3.69	3.29	2.86	4.17	3.64	3.13	4.07	3.90	3.35
12.5	3.84	3.34	2.89	4.18	3.59	3.11	3.99	3.81	3.29
13.5	3.85	3.34	2.89	4.06	3.58	3.10	4.00	3.79	3.23
14.5	3.84	3.32	2.88	4.00	3.57	3.08	3.90	3.63	3.15
15.5	3.79	3.31	2.80	4.02	3.58	2.97	3.84	3.59	3.09
16.5	3.74	3.26	2.69	3.80	3.44	2.84	3.72	3.45	3.02
17.5	3.58	3.19	2.55	3.75	3.34	2.68	3.62	3.36	3.00
18.5	3.45	3.11	2.47	3.67	3.21	2.56	....	....	....
19.5	3.55	3.12	2.44	....	....	....	....	....	....

5.6.2 Fitted Function Coefficients

Table 5.3 shows the fitted values of the coefficients in Equation (5.1) for all exposure times and false source rates analyzed here.

Table 5.3: Coefficients for best fits to Eq. (5.1) for three exposure times. The false source rates are over the full field of view of each detector (0.08 deg

for ACIS-I, 0.25 deg

for HRC-I).

		Exposure time
		10 ks			30 ks			100 ks
		False source rate			False source rate			False source rate
Detector	Coeff.	0.1	1	10	0.1	1	10	0.1	1	10
ACIS-I		1.0153	1.0378	0.7850	1.2899	1.1969	1.0385	1.7867	1.7674	1.6772
Whole		0.2035	0.1286	0.1574	0.2956	0.2675	0.2440	0.3719	0.3315	0.2700
FOV		0.0008	0.0017	0.0000	0.0015	0.0018	0.0020	0.0024	0.0029	0.0029
HRC-I		0.7909	0.8156	0.7924	1.0139	1.0139	0.9833	1.5840	1.6203	1.5541
Inner		0.3009	0.2747	0.2362	0.4097	0.3991	0.3525	0.4592	0.4347	0.3817
Region		0.0009	0.0010	0.0011	0.0020	0.0027	0.0031	0.0035	0.0035	0.0037
HRC-I		0.7611	0.8361	0.7961	1.1268	1.2286	1.1892	1.8950	1.9315	1.9064
Whole		0.3205	0.2758	0.2425	0.3706	0.3127	0.2666	0.3210	0.2969	0.2381
FOV		0.0013	0.0014	0.0015	0.0017	0.0017	0.0018	0.0018	0.00019	0.0018