# Source Position and Position Errors

Source positions and positional uncertainties in the Master Sources Table are computed by statistically averaging observations of the same source using a multi-variate optimal weighting formalism. In the Stacked Observation Detections Table, source positions and uncertainties are determined from the wavdetect algorithm and adjusted by the MLE fit.

## Equatorial Coordinates

**Master Sources Table**

*ra*,

*dec*,

*err_ellipse_r0*,

*err_ellipse_r1*,

*err_ellipse_ang*

Source positions in the Master Sources Table are the best estimate of the ICRS celestial position of the source at the epoch of observation. The positions are derived from the resuts of the wavelet source detection algorithm (wavdetect) and adjusted by the maximum likelihood estimator fit. The ICRS equatorial coordinates of each source (ra, dec) are determined with an absolute uncertainty that is not to exceed 1.0 arcsecond (1σ) for an isolated point source with at least 10 counts located within 3.0 arcminutes of the optical axis; 2.0 arcseconds (1σ) for an isolated point source with at least 30 counts located within 10.0 arcminutes of the optical axis; and 5.0 arcseconds (1σ) for an isolated point source with at least 50 counts located within 15.0 arcminutes of the optical axis.

The statistically averaged source position uncertainties
are expressed in the form of error ellipses centered upon
the source positions, projected from the celestial sphere
onto a common tangent plane; calculation of the position
errors are described in the How and Why topic
'Position Errors in the Master
Chandra Source Table'. Three of the parameters
specifying the geometry of each error ellipse are the
semi-major and semi-minor radii
(*err_ellipse_r0*, *err_ellipse_r1*), and the
position angle θ that the major axis of the ellipse
makes with respect to the tangent plane *y* axis
(*err_ellipse_ang*). The semi-major and semi-minor
radii correspond to the 95% confidence intervals along these
axes.

**Stacked Observation Detections Table:**

*ra*,

*dec*,

*err_ellipse_r0*,

*err_ellipse_r1*,

*err_ellipse_ang*

The position of each detection in an observation stack is defined by the ICRS right ascension and declination of the center of the source region in which it is located, determined by the MLE-adjusted wavdetect result, and the major and minor radii, and position angle of the error ellipse, parameterized by the MLE's Markov chain Monte Carlo draws, defining the uncertainty in the source position.

The 95% confidence level error ellipse of the source position will be approximated by a 95% confidence level error circle in the first catalog release. This limitation will be lifted in a future release.

The 95% confidence level error ellipse is defined on a tangent plane projection. The 0 deg position angle reference is defined on that tangent plane to be parallel to the true North direction at the location of the tangent plane reference (refer to the tangent plane reference right ascension (ra_nom), declination (dec_nom), and roll angle (roll_nom)).

## Off-Axis Angles

**Per-Observation Detections Table:**

*theta*,

*phi*

The angular location of the source region (that includes a source) relative to the optical axis is defined by the off-axis angle θ and azimuthal angle φ.

**Stacked Observation Detections Table:**

*theta_mean*

The mean source region aperture off-axis angle,
θ_{mean}, from all observations in a
stack.

## Chip Coordinates

**Per-Observation Detections Table:**

*chipx*,

*chipy*

The location of the source region (that includes a detection) in chip coordinates is defined by the effective CHIPX and CHIPY pixel positions corresponding to the off-axis angles (θ, φ).

The effect of the mean dy, dz, dtheta offsets from the aspect solution are included to determine the source's chip coordinates in CSC2. While this does not have a large impact on many observations in the archive, for more recent observations, as the mission has progressed the offsets have become significant and now the offsets are of order 15 arcsec range (~30 ACIS pixels) in both the dy and dz directions, and need to be accounted for.