# Source Position and Position Errors

Source positions and positional uncertainties in the Master Sources Table are computed by statistically averaging the positions and positional uncertainties of stacked observation detections of the same source, including a correction for the average absolute astrometric uncertainty of the catalog. In the Stacked Observation Detections Table, positions and positional uncertainties are determined from the maximum likelihood estimator (MLE) fits to the detections' X-ray event distributions.

## Equatorial Coordinates

**Master Sources Table**

*ra*,

*dec*,

*err_ellipse_r0*,

*err_ellipse_r1*,

*err_ellipse_ang*

The equatorial coordinates of a source in the Master Sources Table are the best estimates of the ICRS celestial position of the source, determined by statistically averaging the positions of detections from the individual stacked observations that are uniquely matched (i.e., those that have match_type="u") to the source. The calculation of the averaged positions and position uncertainties is described in detail in the How and Why topic 'Source Position Errors in the Master Sources Table'.

The statistically averaged source position uncertainties
are expressed in the form of an error ellipse centered on
the source position, projected from the celestial sphere
onto a common tangent plane. The parameters specifying the
geometry of the error ellipse are the radii of the
semi-major and semi-minor axes (*err_ellipse_r0*,
*err_ellipse_r1*), and the astronomical position
angle of the major axis of the ellipse
(*err_ellipse_ang*). The radii of the semi-major and
semi-minor axes correspond to the 95% confidence intervals
along these axes.

Source position error ellipses in the Master Sources Table
include a component to account for the absolute uncertainty
in the astrometry relative to the ICRS reference frame.
This uncertainty, 0.71 arcsec (95% confidence) *in each axis*, is
derived from comparisons of source positions from release
2.0 detections relative to the Sloan Digital Sky Survey, and
is added in quadrature to the statistically averaged
position uncertainties from the stacked observation
detections. While the true positional uncertainty should be
consistent with the reported positional uncertainty for ~90%
of the sources, the ~10% of sources for which this is not
the case are not distributed randomly. There are a small
number of observation stacks for which the absolute error
may be significantly larger than 0.71 arcsec (up to a
maximum of ~2.0 arcsec).

**Stacked Observation Detections Table:**

*ra*,

*dec*,

*err_ellipse_r0*,

*err_ellipse_r1*,

*err_ellipse_ang*

The position of each stacked observation detection is defined by the ICRS right ascension and declination of the center of the source region in which the detection is located, which is in-turn determined from the wavdetect and/or mkvtbkg detections, as adjusted by the maximum likelihood estimator (MLE) fits to the observed X-ray event distributions.

The detection position uncertainties are expressed in the
form of an error ellipse centered on the detection position,
projected from the celestial sphere onto the stacked
observation's common tangent plane (located at ICRS
coordinates [*ra_stack*, *dec_stack*]). The
error ellipse is typically
the best-fitting ellipse to the
position-uncertainty–fit-statistic surface computed from the
MLE's Markov
chain Monte Carlo draws. If the MCMC draws do
not converge then an error circle, rather than error
ellipse, is used. The parameters specifying the geometry of
the error ellipse are the radii of the semi-major and
semi-minor axes (*err_ellipse_r0*,
*err_ellipse_r1*), and the astronomical position
angle of the major axis of the ellipse
(*err_ellipse_ang*). The radii of the semi-major and
semi-minor axes correspond to the 95% confidence intervals
along these axes.

In release 2 of the catalog, the astronomical position
angle (measured from North through East) of the major axis
of the ellipse (*err_ellipse_ang*) is defined with
respect to *local* North at the position of the
source, rather than with respect to tangent plane North
that was used in release 1.

## Off-Axis Angles

**Per-Observation Detections Table:**

*theta*,

*phi*

The angular location of the source region aperture that includes a detection, relative to the optical axis of the individual observation, 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}, computed by averaging the
off-axis angles θ 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 for an observation 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 in the determination of the detection'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.