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Last modified: 14 December 2012

URL: http://cxc.harvard.edu/csc/why/err_ellipse_cio.html

Source Position Errors in the
Source Observations Table


Summary

In the Source Observations Table, source (RA, DEC) positions are determined by wavdetect, the algorithm employed by the Detect Pipeline of Catalog Processing to identify source candidates in a single observation. wavdetect reports positional errors associated with each source detection, however it has been found that they are underestimates for sources at large off-axis angles. This conclusion is based upon the results of simulation procedures which compared the reference positions of artifically generated sources to their positions determined by wavdetect. The simulation results, which quantify the dependence of positional uncertainties of simulated sources on off-axis angle, were found to be consistent with the more extensive ChaMP (Chandra Multiwavelength Project) simulations. As a result, the ChaMP positional uncerainty relations are used to compute source position errors for sources in individual observations of the CSC:

logPU =
(1) 0.1145θ - 0.4958log(net counts)
        + 0.1932 for  0 < log(net counts) ≤ 2.1393
(2) 0.0968θ - 0.2064log(net counts) - 0.4260 for  2.1393< log(net counts)< 3.3

where positional uncertainty PU is in arcseconds and off-axis angle θ is in arcminutes. The relations were derived to characterize the positional uncertainties at the 95% confidence level of X-ray point sources in the ChaMP X-ray point source catalog, which includes ~6800 X-ray sources detected in 149 Chandra observations covering ~10 deg2. Here, net counts are those reported by wavdetect, since that is what ChaMP used to calibrate the relation.

The specifications for computing positional error ellipses in the Table of Individual Source Observationsare:

1. For each source that has passed through the Detect Pipeline of Catalog Processing, determine off-axis angle θ and net counts. When sources are detected in multiple source detection energy bands and blocking factors, use the net counts from the band with the highest detect significance and the smallest available associated blocking factor (i.e. highest resolution).

2. Compute PU from either equation 1 or 2, depending on the value of net counts.

3. Set the source position error ellipse semi-major and semi-minor axis values to PU. (Note: In the first catalog release, the source position error is circular.)

4. Set the source position error ellipse position angle to 0.

The details of the simulations used to determine uncertainties of wavdetect-reported positions are as follows:

Simulation Procedure

The Chandra Ray Tracer (ChaRT) program, which simulates the Chandra PSF by tracing rays through the Chandra X-ray optics to produce a collection of rays, was used to generate a list of artificial sources for a range of off-axis angles and azimuthal angles. The energy was chosen to be 2.36 keV, which approximates the effective energy of the Level 3 broad band.

θ (') φ (deg) Energy (keV) Ray Density (rays/mm2)
0 0 2.36 5
1 Every 30 starting at 0 2.36 5
5 Every 30 starting at 0 2.36 5
7.5 45, 135, 225, 315 2.36 5
9.5 45, 135, 225, 315 2.36 5
15 112.5 2.36 10
18.5 113.5 2.36 10

The simulated sources were then projected to detector and sky coordinates for an actual Chandra observation, ObsID 2925, which is an ACIS-I observation in which ACIS-S chips S2 and S3 were also included. The simulated event lists contained fields ccd_id, chip, det, sky coordinates, and energy; the real event list for ObsID 2925 was filtered to include the same fields.

For each of the ~100 simulation runs conducted per value of off-axis angle, 100 events were randomly selected from the simulated source event lists and appended to the event list for ObsID 2925. An example of the event list with simulated sources at off-axis angles 0', 1', and 5' is shown in Figure 1.

[L3 event list with simulated sources]

Figure 1. Level 3 event list with simulated sources at θ = 0', 1', 5'

The resulting event list and all associated data products were passed through the Level 3 Detect Pipeline of Catalog Processing, in which wavdetect was run to search the event list for source candidates. The outputs from Catalog Processing were collected and concatenated into a single table listing the wavdetect-reported (x,y) positions of all detected sources, real and artificial. This table was then cross-referenced with a table of (x,y) positions of the simulated sources, which had been converted from (θ, φ ) to (x,y) via the CIAO tool 'dmcoords.' Offsets in x and y between the detected simulated source positions and their reference positions were then computed and tabulated as radial offsets, i.e. the quadrature sum of x and y offsets between detected and reference positions.

Simulation Results

The initial evaluation of the simulation results revealed a dependence of the radial offsets on off-axis angle, while ignoring azimuthal dependence. The positional uncertainty vs. θ results for the simulated sources were then compared to those predicted by the ChaMP relations, as well as to wavdetect-reported position errors vs. θ resulting from earlier test runs of 100 and 200 ACIS-I and ACIS-S ObsIDs. The results of the comparison are displayed in Figure 2.

[Positional Uncertainties versus theta]

Figure 2. Positional Uncertainties vs. off-axis angle for simulated sources (blue),
wavdetect sources (red and green), and ChaMP (cyan curve).
Points labeled "CL95 Upper Limits" are the 95% quantiles
of the distributions of radial offsets at each value of θ.

In the plot in Figure 2, the ChaMP curve represents the 95% Confidence Level errors for a 100 count source (Kim et al. 2007), the wavdetect errors were selected from sources with 50-150 net counts as reported by the program, and all simulated source offsets are plotted. As demonstrated, the simulations, though limited, are in general agreement with the more extensive ChaMP simulations, and both indicate that wavdetect underestimates positional errors for large values of off-axis angle. Therefore, until more extensive simulations can be carried out, the ChaMP relations for computing source positional uncertainties are adopted in the Catalog of Individual Source Observations.

Systematic Errors in ChaMP Positional Uncertainty

The ChaMP relations used to determine uncertainties in the positions of sources, Eq. (1) and Eq. (2) above, do not agree at the boundary where log(net counts) = 2.1393 (~138 counts). This means that for a given value of off-axis angle θ, positional uncertainties will suffer a discontinuous increase as net counts fall below ~138. The following figure displays the magnitude of this systematic error (i.e., Eq. 1 minus Eq. 2) as a function of θ.

[Positional Uncertainty Differences versus       theta]

Figure 2. ChaMP (Eq. 1 - Eq. 2) versus θ

This systematic error is conservative, in the sense that uncertainties in lower-count sources are over-estimated, and negligible below θ ~ 10'; it will be eliminated in future Catalog releases.


Last modified: 14 December 2012
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