Stacked Observation Detections Table
The concept of Stacks are new to CSC 2.0, as discussed on the Catalog Organization page.
Each identified distinct Xray source on the sky is represented in the catalog by one or more "stack detection" entries—one for each stack in which the source has been detected—and a single "master source" entry. The individual stack entries record all of the properties about a detection extracted from a single stack, as well as associated filebased data products, which are stackspecific.
Note: Source properties in the catalog which have a value for each science energy band (type "double[6]", "long[6]", and "integer[6]" in the table below) have the corresponding letters appended to their names. For example, "flux_aper_b" and "flux_aper_h" represent the backgroundsubtracted, aperturecorrected broadband and hardband energy fluxes, respectively.
Note: "Description" entries with a vertical bar running to the left of the text have more information available that will be displayed when the cursor hovers over the column description.
Column Name  Type  Units  Description  

ascdsver  string  software version used to create the Level 3 detect stack event data file  
caldbver  string  calibration database version used to calibrate the Level 3 detect stack event data file  
conf_code  integer 
compact detection may be confused (bit encoded: 1:
background region overlaps another background region; 2:
background region overlaps another source region; 4: source
region overlaps another background region; 8: source region
overlaps another source region; 256: compact detection is
overlaid on an extended detection)
From the Source Flags column descriptions page: The confusion code for a compact detection is a 16bit coded integer that has all bits set to zero if the detection's source and background region ellipses do not overlap another source or background region in any source detection energy band, and the compact detection does not overlay an extended detection. Otherwise, the bits are set as follows:
The confusion code for an extend (convex hull) detection is always NULL. 

crdate  string  creation date/time of the Level 3 detect stack event data file, UTC (yyyymmddThh:mm:ss)  
dec  double  deg 
detection position, ICRS declination
From the Position and Position Errors column descriptions page: 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 inturn determined from the wavdetect and/or mkvtbkg detections, as adjusted by the maximum likelihood estimator (MLE) fits to the observed Xray event distributions. 

dec_aper  double  deg 
center of the source region and background region
apertures, ICRS
declination
From the 'Source Region' section of the Source Extent and Errors column descriptions page: The spatial regions defining a source and its corresponding background are determined by scaling and merging the individual source detection regions that result from all of the spatial scales and source detection energy bands in which the source is detected during the source detection process (wavdetect). The result is a single elliptical source region which excludes any overlapping source regions, and a single, colocated, scaled, elliptical annular background region. The parameter values that define the source region and background region for each source are the ICRS right ascension and signed ICRS declination of the center of the source region and background region; the semimajor and semiminor axes of the source region ellipse and of the inner and outer annuli of the background region ellipse; and the position angles of the semimajor axes defining the source and background region ellipses. 

dec_stack  detect stack tangent plane reference position, ICRS declination  
detect_significance  double[6] 
significance of the stackedobservation detection computed
by the stackedobservation detection algorithm for each science energy band
From the Source Significance column descriptions page: Likelihood, detect significance, and flux significance are reported per band for all sources detected in the valid stack. The likelihood reported is the maximum of the likelihood determined from the MLE fit to all valid stack data, and the likelihoods from each individual observation, per band. The fundamental metric used to decide whether a source is included in CSC 2.0 is the likelihood, \[ \mathcal{L}=\ln{P} \ \mathrm{,} \]where \(P\) is the probability that an MLE fit to a point or extended source model, in a region with no source, would yield a change in fit statistic as large or larger than that observed, when compared to a fit to background only. The likelihood is closely related to the probability, \(P_{\mathrm{Pois}}\), that a Poisson distribution with a mean background in the source aperture would produce at least the number of counts observed in the aperture. This quantity, called detect_significance, is also reported in CSC 2.0. Smoothed background maps are used to estimate mean background, and detect_significance is expressed in terms of the number of \(\sigma\), \(z\), in a zeromean, unit standard deviation Gaussian distribution that would yield an upper integral probability \(P_{\mathrm{Gaus}}\), from \(z\) to \(\infty\), equivalent to \(P_{\mathrm{Pois}}\). That is, \[ P_{\mathrm{Pois}} = P_{\mathrm{Gaus}} \]where \[ P_{\mathrm{Gaus}} = \int_{z}^{\infty} \frac{e^{x^{2}/2}}{\sqrt{2\pi}} dx \] 

detect_stack_id  detect stack identifier (designation of observation stack used for source detection) in the format '{acishrc}fJhhmmsss{+}ddmmss_nnn'  
dither_warning_flag  Boolean 
highest statistically significant peak in the power spectrum
of the detection source region count rate occurs at the
dither frequency or at
a beat frequency of
the dither frequency in
one or more of the stacked observations
From the Source Flags column descriptions page: The dither warning flag for a compact detection is a Boolean that has a value of TRUE if the dither warning flag for any contributing perobservation detection is TRUE. Otherwise, the value is FALSE. The dither warning flag for an extended (convex hull) source is always NULL. 

edge_code  coded byte 
detection position, or source or background region dithered
off a detector boundary (chip pixel mask) during one or more
of the stacked observations (bit encoded: 1: background
region dithers off detector boundary; 2:source region
dithers off detector boundary; 4: detection position dithers
off detector boundary)
From the Source Flags column descriptions page: The edge code for a compact or extended (convex hull) detection is a 16bit coded integer that has all bits set to zero if the detection's position, source region, and background region do not dither off a chip boundary (the edge of the unmasked area of the active region of the ACIS CCD or HRC microchannel plate segment, as appropriate) during the observation. Otherwise, the bits are set as follows:
Note that an extended (convex hull) detection (or associated background region) that extends across more than one chip by definition must dither off the chip boundary. 

err_ellipse_ang  double  deg 
position angle (referenced from local true north) of the
major axis 95% confidence level error ellipse
From the Position and Position Errors column descriptions page: 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 inturn determined from the wavdetect and/or mkvtbkg detections, as adjusted by the maximum likelihood estimator (MLE) fits to the observed Xray event distributions. 

err_ellipse_r0  double  arcsec 
major radius of the 95% confidence level position error
ellipse
From the Position and Position Errors column descriptions page: 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 inturn determined from the wavdetect and/or mkvtbkg detections, as adjusted by the maximum likelihood estimator (MLE) fits to the observed Xray event distributions. 

err_ellipse_r1  double  arcsec 
minor radius of the 95% confidence level position error
ellipse
From the Position and Position Errors column descriptions page: 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 inturn determined from the wavdetect and/or mkvtbkg detections, as adjusted by the maximum likelihood estimator (MLE) fits to the observed Xray event distributions. 

extent_code  integer 
detection is extended, or deconvolved compact detection
extent is inconsistent with a point source at the 90%
confidence level in one or more of the stacked observations
and energy bands (bit encoded: 1, 2, 4, 8, 16, 32:
deconvolved compact detection extent is not consistent with
a point source in the ACIS ultrasoft, soft, medium, hard,
broad, or HRC wide (~0.110.0 keV) energy band,
respectively; 256: extended detection)
From the Source Flags column descriptions page: The extent code for a compact detection is a 16bit coded integer that has all bits set to zero if a wavelet transform analysis of counts in the detection's source region ellipse is consistent with a point source at the 90% confidence level in all science energy bands . Otherwise, the bits are set as follows:
The extent code for an extended (convex hull) detection is always set to 256 (Extended detection). 

flux_aper  double[6]  ergs s^{1} cm^{2} 
aperturecorrected detection net energy flux inferred from
the source region aperture, calculated by counting Xray
events for each science energy band
From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page: Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine backgroundmarginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits. Fluxes are determined for each perobservation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits. The aperture source photon and energy fluxes and associated twosided confidence limits represent the average backgroundsubtracted fluxes in the modified source region (photflux_aper, flux_aper) and in the modified elliptical aperture (photflux_aper90, flux_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure for all valid observations in the stack. The conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. 

flux_aper90  double[6]  ergs s^{1} cm^{2} 
aperturecorrected detection net energy flux inferred from
the PSF 90% ECF aperture, calculated by counting Xray
events for each science energy band
From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page: Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine backgroundmarginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits. Fluxes are determined for each perobservation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits. The aperture source photon and energy fluxes and associated twosided confidence limits represent the average backgroundsubtracted fluxes in the modified source region (photflux_aper, flux_aper) and in the modified elliptical aperture (photflux_aper90, flux_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure for all valid observations in the stack. The conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. 

flux_aper90_hilim  double[6]  ergs s^{1} cm^{2} 
aperturecorrected detection net energy flux inferred from
the PSF 90% ECF aperture, calculated by counting Xray
events (68% upper confidence limit) for each science energy band
From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page: Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine backgroundmarginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits. Fluxes are determined for each perobservation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits. The aperture source photon and energy fluxes and associated twosided confidence limits represent the average backgroundsubtracted fluxes in the modified source region (photflux_aper, flux_aper) and in the modified elliptical aperture (photflux_aper90, flux_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure for all valid observations in the stack. The conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. 

flux_aper90_lolim  double[6]  ergs s^{1} cm^{2} 
aperturecorrected detection net energy flux inferred from
the PSF 90% ECF aperture, calculated by counting Xray
events (68% lower confidence limit) for each science energy band
From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page: Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine backgroundmarginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits. Fluxes are determined for each perobservation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits. The aperture source photon and energy fluxes and associated twosided confidence limits represent the average backgroundsubtracted fluxes in the modified source region (photflux_aper, flux_aper) and in the modified elliptical aperture (photflux_aper90, flux_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure for all valid observations in the stack. The conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. 

flux_aper_hilim  double[6]  ergs s^{1} cm^{2} 
aperturecorrected detection net energy flux inferred from
the source region aperture, calculated by counting Xray
events (68% upper confidence limit) for each science energy band
From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page: Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine backgroundmarginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits. Fluxes are determined for each perobservation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits. The aperture source photon and energy fluxes and associated twosided confidence limits represent the average backgroundsubtracted fluxes in the modified source region (photflux_aper, flux_aper) and in the modified elliptical aperture (photflux_aper90, flux_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure for all valid observations in the stack. The conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. 

flux_aper_lolim  double[6]  ergs s^{1} cm^{2} 
aperturecorrected detection net energy flux inferred from
the source region aperture, calculated by counting Xray
events (68% lower confidence limit) for each science energy band
From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page: Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine backgroundmarginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits. Fluxes are determined for each perobservation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits. The aperture source photon and energy fluxes and associated twosided confidence limits represent the average backgroundsubtracted fluxes in the modified source region (photflux_aper, flux_aper) and in the modified elliptical aperture (photflux_aper90, flux_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure for all valid observations in the stack. The conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. 

flux_significance  double[6] 
significance of the stackedobservation detection determined
from the ratio of the stackedobservation detection photon
flux to the estimated error in the photon flux, for each
science energy band
From the Source Significance column descriptions page: Likelihood, detect significance, and flux significance are reported per band for all sources detected in the valid stack. The likelihood reported is the maximum of the likelihood determined from the MLE fit to all valid stack data, and the likelihoods from each individual observation, per band. Flux significance is a simple estimate of the ratio of the flux measurement to its average error. The mode of the marginalized probability distribution for photflux_aper is used as the flux measurement and the average error, \(\sigma_{e}\), is defined to be: \[ \sigma_{e} = \frac{\mathit{photflux\_aper\_hilim}  \mathit{photflux\_aper\_lolim}}{2} \]which are both used to estimate flux significance. 

grating  string  transmission grating used for the stacked observation: 'NONE', 'HETG', or 'LETG'  
hard_hm  double  ACIS hard (2.07.0 keV)  medium (1.22.0 keV) energy band hardness ratio  
hard_hm_hilim  double  ACIS hard (2.07.0 keV)  medium (1.22.0 keV) energy band hardness ratio (68% upper confidence limit)  
hard_hm_lolim  double  ACIS hard (2.07.0 keV)  medium (1.22.0 keV) energy band hardness ratio (68% lower confidence limit)  
hard_hs  double  ACIS hard (2.07.0 keV)  soft (0.51.2 keV) energy band hardness ratio  
hard_hs_hilim  double  ACIS hard (2.07.0 keV)  soft (0.51.2 keV) energy band hardness ratio (68% upper confidence limit)  
hard_hs_lolim  double  ACIS hard (2.07.0 keV)  soft (0.51.2 keV) energy band hardness ratio (68% lower confidence limit)  
hard_ms  double  ACIS medium (1.22.0 keV)  soft (0.51.2 keV) energy band hardness ratio  
hard_ms_hilim  double  ACIS medium (1.22.0 keV) soft (0.51.2 keV) energy band hardness ratio (68% upper confidence limit)  
hard_ms_lolim  double  ACIS medium (1.22.0 keV)  soft (0.51.2 keV) energy band hardness ratio (68% lower confidence limit)  
instrument  string  instrument used for the observation: 'ACIS' or 'HRC'  
kp_intra_prob  double[6] 
intraobservation Kuiper's test variability probability
(highest value across all stacked observations) for each
science energy band
The GregoryLoredo, KolmogorovSmirnov (KS) test, and Kuiper's test intraobservation variability probabilities represent the highest values of the variability probabilities (var_prob, ks_prob, kp_prob) calculated for each of the contributing observations (i.e., the highest level of variability among the observations contributing to the master source entry). 

ks_intra_prob  double[6] 
intraobservation KolmogorovSmirnov test variability
probability (highest value across all
observations) for each science energy band
The GregoryLoredo, KolmogorovSmirnov (KS) test, and Kuiper's test intraobservation variability probabilities represent the highest values of the variability probabilities (var_prob, ks_prob, kp_prob) calculated for each of the contributing observations (i.e., the highest level of variability among the observations contributing to the master source entry). 

likelihood  double[6] 
loglikelihood of the stackedobservation detection computed
by the Maximum Likelihood
Estimator fit to the photon counts distribution
for each science energy band
From the Source Significance column descriptions page: Likelihood, detect significance, and flux significance are reported per band for all sources detected in the valid stack. The likelihood reported is the maximum of the likelihood determined from the MLE fit to all valid stack data, and the likelihoods from each individual observation, per band. The fundamental metric used to decide whether a source is included in CSC 2.0 is the likelihood, \[ \mathcal{L}=\ln{P} \ \mathrm{,} \]where \(P\) is the probability that an MLE fit to a point or extended source model, in a region with no source, would yield a change in fit statistic as large or larger than that observed, when compared to a fit to background only. The likelihood is closely related to the probability, \(P_{\mathrm{Pois}}\), that a Poisson distribution with a mean background in the source aperture would produce at least the number of counts observed in the aperture. This quantity, called detect_significance, is also reported in CSC 2.0. Smoothed background maps are used to estimate mean background, and detect_significance is expressed in terms of the number of \(\sigma\), \(z\), in a zeromean, unit standard deviation Gaussian distribution that would yield an upper integral probability \(P_{\mathrm{Gaus}}\), from \(z\) to \(\infty\), equivalent to \(P_{\mathrm{Pois}}\). That is, \[ P_{\mathrm{Pois}} = P_{\mathrm{Gaus}} \]where \[ P_{\mathrm{Gaus}} = \int_{z}^{\infty} \frac{e^{x^{2}/2}}{\sqrt{2\pi}} dx \] 

likelihood_class  string  highest detection likelihood classification across all energy bands  
livetime  double  s  effective stacked observation exposure time, after applying the good time intervals and deadtime correction factor; vignetting and dead area corrections are NOT applied  
major_axis  double[6]  arcsec 
1σ radius along the major axis of the ellipse defining
the deconvolved
source extent for each science energy band
From the 'Deconvolved Source Extent' section of the Source Extent and Errors column descriptions page: For stacked observation detections, the deconvolved source extent is a parameterization of the best estimate of the flux distribution defining the PSFdeconvolved source, which is determined in each science energy band from a varianceweighted mean of the deconvolved extent of each source measured in all contributing observations. The parameterization represents the best estimate values and associated errors for the \(1\sigma\) radius along the major axis, the \(1\sigma\) radius along the minor axis, and the position angle of the major axis of a rotated elliptical Gaussian source that has been fitted to the observed source spatial event distribution deconvolved with the raytrace local PSF at the location of that source event distribution. Deconvolving the raw source image with the PSF produces the intrinsic shape of the source. In order to determine whether a source is extended, we first need to realize that the intrinsic size of a point source is, by definition, zero. By performing the fitting described above, srcextent estimates the raw sizes and errors of both the source and the PSF. In what follows, we derive the size and error for the intrinsic size of the source, and then we establish a criterion to flag a source as extended. In principle, one can determine the parameters of the intrinsic source ellipse, \(\{a_{1},a_{2},\phi\}\), by solving a nonlinear system of equations involving the PSF parameters, \(\{a_{1},a_{2},\psi\}\), and the measured source parameters, \(\{\sigma_{1},\sigma_{2},\delta\}\). However, because these equations are based on a crude approximation and because the input parameters are often uncertain, such an elaborate calculation seems unjustified. A much simpler and more robust approach makes use of the identity: \[ \sigma_{1}^{2} + \sigma_{2}^{2} = a_{1}^{2} + a_{2}^{2} + b_{1}^{2} + b_{2}^{2} \ , \]which applies to the convolution of two elliptical Gaussians having arbitrary relative sizes and position angles. Using this identity, one can define a rootsumsquare intrinsic source size: \[ a_{\mathrm{rss}} \equiv \sqrt{a_{1}^2 + a_{2}^{2}} = \sqrt{ \max\{0,(\sigma_{1}^{2} + \sigma_{2}^{2})  (b_{1}^{2} + b_{2}^{2}) \}} \ , \]that depends only on the sizes of the relevant ellipses and is independent of their orientations. This expression is analogous to the wellknown result for convolution of 1D Gaussians and for convolution of circular Gaussians in 2D. Using the equation above, one can derive an analytic expression for the uncertainty in \(a_{\mathrm{rss}}\) in terms of the measurement errors associated with \(\sigma_{i}\) and \(b_{i}\). Because \(\sigma_{i}\) and \(b_{i}\) are nonnegative, evaluating the righthand side of the equation using the corresponding mean values should give a reasonable estimate of the mean value of \(a_{\mathrm{rss}}\). A Taylor series expansion of the righthand side evaluated at the mean parameter values, therefore, yields the uncertainty: \[ \Delta a_{\mathrm{rss}} = \frac{1}{a} \sqrt{ \sigma_{1}^{2} \left(\Delta \sigma_{1} \right)^{2} + \sigma_{2}^{2} \left(\Delta \sigma_{2} \right)^{2} + b_{1}^{2} \left(\Delta b_{1} \right)^{2} + b_{1}^{2} \left(\Delta b_{1} \right)^{2} } \]where \(\left(\Delta X \right)^{2}\) represents the variance in \(X\) and where \[ a \equiv \left\{ \begin{array}{ll} a_{\mathrm{rss}} \ , & a_{\mathrm{rss}} > 0 \ , \\ \sqrt{b_{1}^{2} + b_{2}^{2}} \ , & a_{\mathrm{rss}} = 0 \ . \end{array} \right. \]A source is extended if its rootsumsquare intrinsic size is larger than the rootsumsquare error of this size. Namely, if its derived intrinsic size, that depends on the raw source and PSF sizes and errors, is larger than the fluctuations due to the uncertainty in the determination (different from zero). If \(a_{\mathrm{rss}} > f \Delta a_{\mathrm{rss}}\), then the source is extended at the \(f\sigma\) level. In CSC2, we use \(f = 5\), which implies that sources are flagged as extended if the intrinsic size is determined with a significance of \(5\sigma\). 

major_axis_hilim  double[6]  arcsec 
1σ radius along the major axis of the ellipse defining
the deconvolved detection extent (68% upper confidence
limit) for each science energy band
From the 'Deconvolved Source Extent' section of the Source Extent and Errors column descriptions page: For stacked observation detections, the deconvolved source extent is a parameterization of the best estimate of the flux distribution defining the PSFdeconvolved source, which is determined in each science energy band from a varianceweighted mean of the deconvolved extent of each source measured in all contributing observations. The parameterization represents the best estimate values and associated errors for the \(1\sigma\) radius along the major axis, the \(1\sigma\) radius along the minor axis, and the position angle of the major axis of a rotated elliptical Gaussian source that has been fitted to the observed source spatial event distribution deconvolved with the raytrace local PSF at the location of that source event distribution. Deconvolving the raw source image with the PSF produces the intrinsic shape of the source. In order to determine whether a source is extended, we first need to realize that the intrinsic size of a point source is, by definition, zero. By performing the fitting described above, srcextent estimates the raw sizes and errors of both the source and the PSF. In what follows, we derive the size and error for the intrinsic size of the source, and then we establish a criterion to flag a source as extended. In principle, one can determine the parameters of the intrinsic source ellipse, \(\{a_{1},a_{2},\phi\}\), by solving a nonlinear system of equations involving the PSF parameters, \(\{a_{1},a_{2},\psi\}\), and the measured source parameters, \(\{\sigma_{1},\sigma_{2},\delta\}\). However, because these equations are based on a crude approximation and because the input parameters are often uncertain, such an elaborate calculation seems unjustified. A much simpler and more robust approach makes use of the identity: \[ \sigma_{1}^{2} + \sigma_{2}^{2} = a_{1}^{2} + a_{2}^{2} + b_{1}^{2} + b_{2}^{2} \ , \]which applies to the convolution of two elliptical Gaussians having arbitrary relative sizes and position angles. Using this identity, one can define a rootsumsquare intrinsic source size: \[ a_{\mathrm{rss}} \equiv \sqrt{a_{1}^2 + a_{2}^{2}} = \sqrt{ \max\{0,(\sigma_{1}^{2} + \sigma_{2}^{2})  (b_{1}^{2} + b_{2}^{2}) \}} \ , \]that depends only on the sizes of the relevant ellipses and is independent of their orientations. This expression is analogous to the wellknown result for convolution of 1D Gaussians and for convolution of circular Gaussians in 2D. Using the equation above, one can derive an analytic expression for the uncertainty in \(a_{\mathrm{rss}}\) in terms of the measurement errors associated with \(\sigma_{i}\) and \(b_{i}\). Because \(\sigma_{i}\) and \(b_{i}\) are nonnegative, evaluating the righthand side of the equation using the corresponding mean values should give a reasonable estimate of the mean value of \(a_{\mathrm{rss}}\). A Taylor series expansion of the righthand side evaluated at the mean parameter values, therefore, yields the uncertainty: \[ \Delta a_{\mathrm{rss}} = \frac{1}{a} \sqrt{ \sigma_{1}^{2} \left(\Delta \sigma_{1} \right)^{2} + \sigma_{2}^{2} \left(\Delta \sigma_{2} \right)^{2} + b_{1}^{2} \left(\Delta b_{1} \right)^{2} + b_{1}^{2} \left(\Delta b_{1} \right)^{2} } \]where \(\left(\Delta X \right)^{2}\) represents the variance in \(X\) and where \[ a \equiv \left\{ \begin{array}{ll} a_{\mathrm{rss}} \ , & a_{\mathrm{rss}} > 0 \ , \\ \sqrt{b_{1}^{2} + b_{2}^{2}} \ , & a_{\mathrm{rss}} = 0 \ . \end{array} \right. \]A source is extended if its rootsumsquare intrinsic size is larger than the rootsumsquare error of this size. Namely, if its derived intrinsic size, that depends on the raw source and PSF sizes and errors, is larger than the fluctuations due to the uncertainty in the determination (different from zero). If \(a_{\mathrm{rss}} > f \Delta a_{\mathrm{rss}}\), then the source is extended at the \(f\sigma\) level. In CSC2, we use \(f = 5\), which implies that sources are flagged as extended if the intrinsic size is determined with a significance of \(5\sigma\). 

major_axis_lolim  double[6]  arcsec 
1σ radius along the major axis of the ellipse defining
the deconvolved detection extent (68% lower confidence
limit) for each science energy band
From the 'Deconvolved Source Extent' section of the Source Extent and Errors column descriptions page: For stacked observation detections, the deconvolved source extent is a parameterization of the best estimate of the flux distribution defining the PSFdeconvolved source, which is determined in each science energy band from a varianceweighted mean of the deconvolved extent of each source measured in all contributing observations. The parameterization represents the best estimate values and associated errors for the \(1\sigma\) radius along the major axis, the \(1\sigma\) radius along the minor axis, and the position angle of the major axis of a rotated elliptical Gaussian source that has been fitted to the observed source spatial event distribution deconvolved with the raytrace local PSF at the location of that source event distribution. Deconvolving the raw source image with the PSF produces the intrinsic shape of the source. In order to determine whether a source is extended, we first need to realize that the intrinsic size of a point source is, by definition, zero. By performing the fitting described above, srcextent estimates the raw sizes and errors of both the source and the PSF. In what follows, we derive the size and error for the intrinsic size of the source, and then we establish a criterion to flag a source as extended. In principle, one can determine the parameters of the intrinsic source ellipse, \(\{a_{1},a_{2},\phi\}\), by solving a nonlinear system of equations involving the PSF parameters, \(\{a_{1},a_{2},\psi\}\), and the measured source parameters, \(\{\sigma_{1},\sigma_{2},\delta\}\). However, because these equations are based on a crude approximation and because the input parameters are often uncertain, such an elaborate calculation seems unjustified. A much simpler and more robust approach makes use of the identity: \[ \sigma_{1}^{2} + \sigma_{2}^{2} = a_{1}^{2} + a_{2}^{2} + b_{1}^{2} + b_{2}^{2} \ , \]which applies to the convolution of two elliptical Gaussians having arbitrary relative sizes and position angles. Using this identity, one can define a rootsumsquare intrinsic source size: \[ a_{\mathrm{rss}} \equiv \sqrt{a_{1}^2 + a_{2}^{2}} = \sqrt{ \max\{0,(\sigma_{1}^{2} + \sigma_{2}^{2})  (b_{1}^{2} + b_{2}^{2}) \}} \ , \]that depends only on the sizes of the relevant ellipses and is independent of their orientations. This expression is analogous to the wellknown result for convolution of 1D Gaussians and for convolution of circular Gaussians in 2D. Using the equation above, one can derive an analytic expression for the uncertainty in \(a_{\mathrm{rss}}\) in terms of the measurement errors associated with \(\sigma_{i}\) and \(b_{i}\). Because \(\sigma_{i}\) and \(b_{i}\) are nonnegative, evaluating the righthand side of the equation using the corresponding mean values should give a reasonable estimate of the mean value of \(a_{\mathrm{rss}}\). A Taylor series expansion of the righthand side evaluated at the mean parameter values, therefore, yields the uncertainty: \[ \Delta a_{\mathrm{rss}} = \frac{1}{a} \sqrt{ \sigma_{1}^{2} \left(\Delta \sigma_{1} \right)^{2} + \sigma_{2}^{2} \left(\Delta \sigma_{2} \right)^{2} + b_{1}^{2} \left(\Delta b_{1} \right)^{2} + b_{1}^{2} \left(\Delta b_{1} \right)^{2} } \]where \(\left(\Delta X \right)^{2}\) represents the variance in \(X\) and where \[ a \equiv \left\{ \begin{array}{ll} a_{\mathrm{rss}} \ , & a_{\mathrm{rss}} > 0 \ , \\ \sqrt{b_{1}^{2} + b_{2}^{2}} \ , & a_{\mathrm{rss}} = 0 \ . \end{array} \right. \]A source is extended if its rootsumsquare intrinsic size is larger than the rootsumsquare error of this size. Namely, if its derived intrinsic size, that depends on the raw source and PSF sizes and errors, is larger than the fluctuations due to the uncertainty in the determination (different from zero). If \(a_{\mathrm{rss}} > f \Delta a_{\mathrm{rss}}\), then the source is extended at the \(f\sigma\) level. In CSC2, we use \(f = 5\), which implies that sources are flagged as extended if the intrinsic size is determined with a significance of \(5\sigma\). 

man_add_flag  Boolean 
detection was manually added to the catalog via human review
From the Source Flags column descriptions page: The manual detection addition flag for a compact or extended (convex hull) detection is a Boolean that has a value of TRUE if the stacked observation detection was manually added to the catalog by human review. Otherwise, the value is FALSE. Detections that are manually added must satisfy detection likelihood and other validity checks in order to appear in the final catalog. See also the Manual Source/Detection Inclusion Flag below. 

man_inc_flag  Boolean 
detection manually included to the catalog (detection was
rejected by automated criteria)
From the Source Flags column descriptions page: The manual detection inclusion flag for a compact or extended (convex hull) detection is a Boolean that has a value of TRUE if the stacked observation detection was manually included in this catalog by human review. Otherwise, the value is FALSE. Detections that are manually included are not required to satisfy detection likelihood or other validity checks. Manually included detections may or may not be manually added; if they are manually added then the man_add_flag will also be set to TRUE. See also the Manual Source/Detection Addition Flag above. 

man_pos_flag  Boolean 
best fit detection position was manually modified via
human review
From the Source Flags column descriptions page: The manual detection position flag for a compact detection is a Boolean that has a value of TRUE if the final detection position was manually modified from the fitted position (determined by the maximum likelihood estimator [MLE]) were manually modified by human review. Otherwise, the value is FALSE. The manual detection position flag for an extended (convex hull) detection is set to TRUE if the final detection position was manually modified from the fluxweighted centroid position by human review. Otherwise, the value is FALSE. 

man_reg_flag  Boolean 
source region parameters (dimensions, initial guess position
input to the Maximum Likelihood
Estimator fit) were manually modified via human
review
From the Source Flags column descriptions page: The manual detection region parameters flag for a compact source is a Boolean that has a value of TRUE if any of the detection's region parameters (i.e., the source region ellipse semiaxes and/or rotation angle, and/or position that define the detection region evaluated by the maximum likelihood estimator [MLE]) were manually modified by human review. Otherwise, the value is FALSE. The manual detection region parameters flag for an extended (convex hull) source is set to TRUE if the shape or position of the defining polygon was manually modified by human review. Otherwise, the value is FALSE. 

minor_axis  double[6]  arcsec 
1σ radius along the minor axis of the ellipse defining
the deconvolved
source extent for each science energy band
From the 'Deconvolved Source Extent' section of the Source Extent and Errors column descriptions page: For stacked observation detections, the deconvolved source extent is a parameterization of the best estimate of the flux distribution defining the PSFdeconvolved source, which is determined in each science energy band from a varianceweighted mean of the deconvolved extent of each source measured in all contributing observations. The parameterization represents the best estimate values and associated errors for the \(1\sigma\) radius along the major axis, the \(1\sigma\) radius along the minor axis, and the position angle of the major axis of a rotated elliptical Gaussian source that has been fitted to the observed source spatial event distribution deconvolved with the raytrace local PSF at the location of that source event distribution. Deconvolving the raw source image with the PSF produces the intrinsic shape of the source. In order to determine whether a source is extended, we first need to realize that the intrinsic size of a point source is, by definition, zero. By performing the fitting described above, srcextent estimates the raw sizes and errors of both the source and the PSF. In what follows, we derive the size and error for the intrinsic size of the source, and then we establish a criterion to flag a source as extended. In principle, one can determine the parameters of the intrinsic source ellipse, \(\{a_{1},a_{2},\phi\}\), by solving a nonlinear system of equations involving the PSF parameters, \(\{a_{1},a_{2},\psi\}\), and the measured source parameters, \(\{\sigma_{1},\sigma_{2},\delta\}\). However, because these equations are based on a crude approximation and because the input parameters are often uncertain, such an elaborate calculation seems unjustified. A much simpler and more robust approach makes use of the identity: \[ \sigma_{1}^{2} + \sigma_{2}^{2} = a_{1}^{2} + a_{2}^{2} + b_{1}^{2} + b_{2}^{2} \ , \]which applies to the convolution of two elliptical Gaussians having arbitrary relative sizes and position angles. Using this identity, one can define a rootsumsquare intrinsic source size: \[ a_{\mathrm{rss}} \equiv \sqrt{a_{1}^2 + a_{2}^{2}} = \sqrt{ \max\{0,(\sigma_{1}^{2} + \sigma_{2}^{2})  (b_{1}^{2} + b_{2}^{2}) \}} \ , \]that depends only on the sizes of the relevant ellipses and is independent of their orientations. This expression is analogous to the wellknown result for convolution of 1D Gaussians and for convolution of circular Gaussians in 2D. Using the equation above, one can derive an analytic expression for the uncertainty in \(a_{\mathrm{rss}}\) in terms of the measurement errors associated with \(\sigma_{i}\) and \(b_{i}\). Because \(\sigma_{i}\) and \(b_{i}\) are nonnegative, evaluating the righthand side of the equation using the corresponding mean values should give a reasonable estimate of the mean value of \(a_{\mathrm{rss}}\). A Taylor series expansion of the righthand side evaluated at the mean parameter values, therefore, yields the uncertainty: \[ \Delta a_{\mathrm{rss}} = \frac{1}{a} \sqrt{ \sigma_{1}^{2} \left(\Delta \sigma_{1} \right)^{2} + \sigma_{2}^{2} \left(\Delta \sigma_{2} \right)^{2} + b_{1}^{2} \left(\Delta b_{1} \right)^{2} + b_{1}^{2} \left(\Delta b_{1} \right)^{2} } \]where \(\left(\Delta X \right)^{2}\) represents the variance in \(X\) and where \[ a \equiv \left\{ \begin{array}{ll} a_{\mathrm{rss}} \ , & a_{\mathrm{rss}} > 0 \ , \\ \sqrt{b_{1}^{2} + b_{2}^{2}} \ , & a_{\mathrm{rss}} = 0 \ . \end{array} \right. \]A source is extended if its rootsumsquare intrinsic size is larger than the rootsumsquare error of this size. Namely, if its derived intrinsic size, that depends on the raw source and PSF sizes and errors, is larger than the fluctuations due to the uncertainty in the determination (different from zero). If \(a_{\mathrm{rss}} > f \Delta a_{\mathrm{rss}}\), then the source is extended at the \(f\sigma\) level. In CSC2, we use \(f = 5\), which implies that sources are flagged as extended if the intrinsic size is determined with a significance of \(5\sigma\). 

minor_axis_hilim  double[6]  arcsec 
1σ radius along the minor axis of the ellipse defining
the deconvolved detection extent (68% upper confidence
limit) for each science energy band
From the 'Deconvolved Source Extent' section of the Source Extent and Errors column descriptions page: For stacked observation detections, the deconvolved source extent is a parameterization of the best estimate of the flux distribution defining the PSFdeconvolved source, which is determined in each science energy band from a varianceweighted mean of the deconvolved extent of each source measured in all contributing observations. The parameterization represents the best estimate values and associated errors for the \(1\sigma\) radius along the major axis, the \(1\sigma\) radius along the minor axis, and the position angle of the major axis of a rotated elliptical Gaussian source that has been fitted to the observed source spatial event distribution deconvolved with the raytrace local PSF at the location of that source event distribution. Deconvolving the raw source image with the PSF produces the intrinsic shape of the source. In order to determine whether a source is extended, we first need to realize that the intrinsic size of a point source is, by definition, zero. By performing the fitting described above, srcextent estimates the raw sizes and errors of both the source and the PSF. In what follows, we derive the size and error for the intrinsic size of the source, and then we establish a criterion to flag a source as extended. In principle, one can determine the parameters of the intrinsic source ellipse, \(\{a_{1},a_{2},\phi\}\), by solving a nonlinear system of equations involving the PSF parameters, \(\{a_{1},a_{2},\psi\}\), and the measured source parameters, \(\{\sigma_{1},\sigma_{2},\delta\}\). However, because these equations are based on a crude approximation and because the input parameters are often uncertain, such an elaborate calculation seems unjustified. A much simpler and more robust approach makes use of the identity: \[ \sigma_{1}^{2} + \sigma_{2}^{2} = a_{1}^{2} + a_{2}^{2} + b_{1}^{2} + b_{2}^{2} \ , \]which applies to the convolution of two elliptical Gaussians having arbitrary relative sizes and position angles. Using this identity, one can define a rootsumsquare intrinsic source size: \[ a_{\mathrm{rss}} \equiv \sqrt{a_{1}^2 + a_{2}^{2}} = \sqrt{ \max\{0,(\sigma_{1}^{2} + \sigma_{2}^{2})  (b_{1}^{2} + b_{2}^{2}) \}} \ , \]that depends only on the sizes of the relevant ellipses and is independent of their orientations. This expression is analogous to the wellknown result for convolution of 1D Gaussians and for convolution of circular Gaussians in 2D. Using the equation above, one can derive an analytic expression for the uncertainty in \(a_{\mathrm{rss}}\) in terms of the measurement errors associated with \(\sigma_{i}\) and \(b_{i}\). Because \(\sigma_{i}\) and \(b_{i}\) are nonnegative, evaluating the righthand side of the equation using the corresponding mean values should give a reasonable estimate of the mean value of \(a_{\mathrm{rss}}\). A Taylor series expansion of the righthand side evaluated at the mean parameter values, therefore, yields the uncertainty: \[ \Delta a_{\mathrm{rss}} = \frac{1}{a} \sqrt{ \sigma_{1}^{2} \left(\Delta \sigma_{1} \right)^{2} + \sigma_{2}^{2} \left(\Delta \sigma_{2} \right)^{2} + b_{1}^{2} \left(\Delta b_{1} \right)^{2} + b_{1}^{2} \left(\Delta b_{1} \right)^{2} } \]where \(\left(\Delta X \right)^{2}\) represents the variance in \(X\) and where \[ a \equiv \left\{ \begin{array}{ll} a_{\mathrm{rss}} \ , & a_{\mathrm{rss}} > 0 \ , \\ \sqrt{b_{1}^{2} + b_{2}^{2}} \ , & a_{\mathrm{rss}} = 0 \ . \end{array} \right. \]A source is extended if its rootsumsquare intrinsic size is larger than the rootsumsquare error of this size. Namely, if its derived intrinsic size, that depends on the raw source and PSF sizes and errors, is larger than the fluctuations due to the uncertainty in the determination (different from zero). If \(a_{\mathrm{rss}} > f \Delta a_{\mathrm{rss}}\), then the source is extended at the \(f\sigma\) level. In CSC2, we use \(f = 5\), which implies that sources are flagged as extended if the intrinsic size is determined with a significance of \(5\sigma\). 

minor_axis_lolim  double[6]  arcsec 
1σ radius along the minor axis of the ellipse defining
the deconvolved detection extent (68% lower confidence
limit) for each science energy band
From the 'Deconvolved Source Extent' section of the Source Extent and Errors column descriptions page: For stacked observation detections, the deconvolved source extent is a parameterization of the best estimate of the flux distribution defining the PSFdeconvolved source, which is determined in each science energy band from a varianceweighted mean of the deconvolved extent of each source measured in all contributing observations. The parameterization represents the best estimate values and associated errors for the \(1\sigma\) radius along the major axis, the \(1\sigma\) radius along the minor axis, and the position angle of the major axis of a rotated elliptical Gaussian source that has been fitted to the observed source spatial event distribution deconvolved with the raytrace local PSF at the location of that source event distribution. Deconvolving the raw source image with the PSF produces the intrinsic shape of the source. In order to determine whether a source is extended, we first need to realize that the intrinsic size of a point source is, by definition, zero. By performing the fitting described above, srcextent estimates the raw sizes and errors of both the source and the PSF. In what follows, we derive the size and error for the intrinsic size of the source, and then we establish a criterion to flag a source as extended. In principle, one can determine the parameters of the intrinsic source ellipse, \(\{a_{1},a_{2},\phi\}\), by solving a nonlinear system of equations involving the PSF parameters, \(\{a_{1},a_{2},\psi\}\), and the measured source parameters, \(\{\sigma_{1},\sigma_{2},\delta\}\). However, because these equations are based on a crude approximation and because the input parameters are often uncertain, such an elaborate calculation seems unjustified. A much simpler and more robust approach makes use of the identity: \[ \sigma_{1}^{2} + \sigma_{2}^{2} = a_{1}^{2} + a_{2}^{2} + b_{1}^{2} + b_{2}^{2} \ , \]which applies to the convolution of two elliptical Gaussians having arbitrary relative sizes and position angles. Using this identity, one can define a rootsumsquare intrinsic source size: \[ a_{\mathrm{rss}} \equiv \sqrt{a_{1}^2 + a_{2}^{2}} = \sqrt{ \max\{0,(\sigma_{1}^{2} + \sigma_{2}^{2})  (b_{1}^{2} + b_{2}^{2}) \}} \ , \]that depends only on the sizes of the relevant ellipses and is independent of their orientations. This expression is analogous to the wellknown result for convolution of 1D Gaussians and for convolution of circular Gaussians in 2D. Using the equation above, one can derive an analytic expression for the uncertainty in \(a_{\mathrm{rss}}\) in terms of the measurement errors associated with \(\sigma_{i}\) and \(b_{i}\). Because \(\sigma_{i}\) and \(b_{i}\) are nonnegative, evaluating the righthand side of the equation using the corresponding mean values should give a reasonable estimate of the mean value of \(a_{\mathrm{rss}}\). A Taylor series expansion of the righthand side evaluated at the mean parameter values, therefore, yields the uncertainty: \[ \Delta a_{\mathrm{rss}} = \frac{1}{a} \sqrt{ \sigma_{1}^{2} \left(\Delta \sigma_{1} \right)^{2} + \sigma_{2}^{2} \left(\Delta \sigma_{2} \right)^{2} + b_{1}^{2} \left(\Delta b_{1} \right)^{2} + b_{1}^{2} \left(\Delta b_{1} \right)^{2} } \]where \(\left(\Delta X \right)^{2}\) represents the variance in \(X\) and where \[ a \equiv \left\{ \begin{array}{ll} a_{\mathrm{rss}} \ , & a_{\mathrm{rss}} > 0 \ , \\ \sqrt{b_{1}^{2} + b_{2}^{2}} \ , & a_{\mathrm{rss}} = 0 \ . \end{array} \right. \]A source is extended if its rootsumsquare intrinsic size is larger than the rootsumsquare error of this size. Namely, if its derived intrinsic size, that depends on the raw source and PSF sizes and errors, is larger than the fluctuations due to the uncertainty in the determination (different from zero). If \(a_{\mathrm{rss}} > f \Delta a_{\mathrm{rss}}\), then the source is extended at the \(f\sigma\) level. In CSC2, we use \(f = 5\), which implies that sources are flagged as extended if the intrinsic size is determined with a significance of \(5\sigma\). 

mjr_axis1_aperbkg  double  arcsec 
semimajor axis of the inner ellipse of the annular
background region aperture
From the 'Source Region' section of the Source Extent and Errors column descriptions page: The spatial regions defining a source and its corresponding background are determined by scaling and merging the individual source detection regions that result from all of the spatial scales and source detection energy bands in which the source is detected during the source detection process (wavdetect). The result is a single elliptical source region which excludes any overlapping source regions, and a single, colocated, scaled, elliptical annular background region. The parameter values that define the source region and background region for each source are the ICRS right ascension and signed ICRS declination of the center of the source region and background region; the semimajor and semiminor axes of the source region ellipse and of the inner and outer annuli of the background region ellipse; and the position angles of the semimajor axes defining the source and background region ellipses. 

mjr_axis2_aperbkg  double  arcsec 
semimajor axis of the outer ellipse of the annular
background region aperture
From the 'Source Region' section of the Source Extent and Errors column descriptions page: The spatial regions defining a source and its corresponding background are determined by scaling and merging the individual source detection regions that result from all of the spatial scales and source detection energy bands in which the source is detected during the source detection process (wavdetect). The result is a single elliptical source region which excludes any overlapping source regions, and a single, colocated, scaled, elliptical annular background region. The parameter values that define the source region and background region for each source are the ICRS right ascension and signed ICRS declination of the center of the source region and background region; the semimajor and semiminor axes of the source region ellipse and of the inner and outer annuli of the background region ellipse; and the position angles of the semimajor axes defining the source and background region ellipses. 

mjr_axis_aper  double  arcsec 
semimajor axis of the elliptical source region aperture
From the 'Source Region' section of the Source Extent and Errors column descriptions page: The spatial regions defining a source and its corresponding background are determined by scaling and merging the individual source detection regions that result from all of the spatial scales and source detection energy bands in which the source is detected during the source detection process (wavdetect). The result is a single elliptical source region which excludes any overlapping source regions, and a single, colocated, scaled, elliptical annular background region. The parameter values that define the source region and background region for each source are the ICRS right ascension and signed ICRS declination of the center of the source region and background region; the semimajor and semiminor axes of the source region ellipse and of the inner and outer annuli of the background region ellipse; and the position angles of the semimajor axes defining the source and background region ellipses. 

mnr_axis1_aperbkg  double  arcsec 
semiminor axis of the inner ellipse of the annular
background region aperture
From the 'Source Region' section of the Source Extent and Errors column descriptions page: The spatial regions defining a source and its corresponding background are determined by scaling and merging the individual source detection regions that result from all of the spatial scales and source detection energy bands in which the source is detected during the source detection process (wavdetect). The result is a single elliptical source region which excludes any overlapping source regions, and a single, colocated, scaled, elliptical annular background region. The parameter values that define the source region and background region for each source are the ICRS right ascension and signed ICRS declination of the center of the source region and background region; the semimajor and semiminor axes of the source region ellipse and of the inner and outer annuli of the background region ellipse; and the position angles of the semimajor axes defining the source and background region ellipses. 

mnr_axis2_aperbkg  double  arcsec 
semiminor axis of the outer ellipse of the annular
background region aperture
From the 'Source Region' section of the Source Extent and Errors column descriptions page: The spatial regions defining a source and its corresponding background are determined by scaling and merging the individual source detection regions that result from all of the spatial scales and source detection energy bands in which the source is detected during the source detection process (wavdetect). The result is a single elliptical source region which excludes any overlapping source regions, and a single, colocated, scaled, elliptical annular background region. The parameter values that define the source region and background region for each source are the ICRS right ascension and signed ICRS declination of the center of the source region and background region; the semimajor and semiminor axes of the source region ellipse and of the inner and outer annuli of the background region ellipse; and the position angles of the semimajor axes defining the source and background region ellipses. 

mnr_axis_aper  double  arcsec 
semiminor axis of the elliptical source region aperture
From the 'Source Region' section of the Source Extent and Errors column descriptions page: The spatial regions defining a source and its corresponding background are determined by scaling and merging the individual source detection regions that result from all of the spatial scales and source detection energy bands in which the source is detected during the source detection process (wavdetect). The result is a single elliptical source region which excludes any overlapping source regions, and a single, colocated, scaled, elliptical annular background region. The parameter values that define the source region and background region for each source are the ICRS right ascension and signed ICRS declination of the center of the source region and background region; the semimajor and semiminor axes of the source region ellipse and of the inner and outer annuli of the background region ellipse; and the position angles of the semimajor axes defining the source and background region ellipses. 

multi_chip_code  coded byte 
source position, or source or background region dithered
multiple detector chips during one or more of the stacked
observations (bit encoded: 1: background region dithers
across 2 chips; 2: background region dithers across >2
chips; 4: source region dithers across 2 chips; 8: source
region dithers across >2 chips; 16: detection position
dithers across 2 chips; 32: detection position dithers across
>2 chips)
From the Source Flags column descriptions page: The multichip code for a compact or extended (convex hull) detection is a 16bit coded integer that has all bits set to zero if the detection's position, source region, and background region do not dither between two or more chips (ACIS CCDs or HRC microchannel plate segment, as appropriate) during the observation. Otherwise, the bits are set as follows:
Note that an extended (convex hull) detection (or associated background region) that extends across more than one chip by definition must dither across the chips. 

phot_nsrcs  integer[6]  number of detections fit simultaneously to compute aperture photometry quantities  
photflux_aper  double[6]  photons s^{1} cm^{2} 
aperturecorrected detection net photon flux inferred from the source
region aperture, calculated by counting Xray events for
each science energy band
From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page: Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine backgroundmarginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits. Fluxes are determined for each perobservation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits. The aperture source photon and energy fluxes and associated twosided confidence limits represent the average backgroundsubtracted fluxes in the modified source region (photflux_aper, flux_aper) and in the modified elliptical aperture (photflux_aper90, flux_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure for all valid observations in the stack. The conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. 

photflux_aper90  double[6]  photons s^{1} cm^{2} 
aperturecorrected detection net photon flux inferred from
the PSF 90% ECF aperture, calculated by counting Xray
events for each science energy band
From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page: Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine backgroundmarginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits. Fluxes are determined for each perobservation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits. The aperture source photon and energy fluxes and associated twosided confidence limits represent the average backgroundsubtracted fluxes in the modified source region (photflux_aper, flux_aper) and in the modified elliptical aperture (photflux_aper90, flux_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure for all valid observations in the stack. The conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. 

photflux_aper90_hilim  double[6]  photons s^{1} cm^{2} 
aperturecorrected detection net photon flux inferred from
the PSF 90% ECF aperture, calculated by counting Xray
events (68% upper confidence limit) for each science energy band
From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page: Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine backgroundmarginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits. Fluxes are determined for each perobservation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits. The aperture source photon and energy fluxes and associated twosided confidence limits represent the average backgroundsubtracted fluxes in the modified source region (photflux_aper, flux_aper) and in the modified elliptical aperture (photflux_aper90, flux_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure for all valid observations in the stack. The conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. 

photflux_aper90_lolim  double[6]  photons s^{1} cm^{2} 
aperturecorrected detection net photon flux inferred from
the PSF 90% ECF aperture, calculated by counting Xray
events (68% lower confidence limit) for each science energy band
From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page: Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine backgroundmarginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits. Fluxes are determined for each perobservation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits. The aperture source photon and energy fluxes and associated twosided confidence limits represent the average backgroundsubtracted fluxes in the modified source region (photflux_aper, flux_aper) and in the modified elliptical aperture (photflux_aper90, flux_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure for all valid observations in the stack. The conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. 

photflux_aper_hilim  double[6]  photons s^{1} cm^{2} 
aperturecorrected detection net photon flux inferred from
the source region aperture, calculated by counting Xray
events (68% upper confidence limit) for each science energy band
From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page: Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine backgroundmarginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits. Fluxes are determined for each perobservation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits. The aperture source photon and energy fluxes and associated twosided confidence limits represent the average backgroundsubtracted fluxes in the modified source region (photflux_aper, flux_aper) and in the modified elliptical aperture (photflux_aper90, flux_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure for all valid observations in the stack. The conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. 

photflux_aper_lolim  double[6]  photons s^{1} cm^{2} 
aperturecorrected detection net photon flux inferred from
the source region aperture, calculated by counting Xray
events (68% lower confidence limit) for each science energy band
From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page: Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine backgroundmarginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits. Fluxes are determined for each perobservation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits. The aperture source photon and energy fluxes and associated twosided confidence limits represent the average backgroundsubtracted fluxes in the modified source region (photflux_aper, flux_aper) and in the modified elliptical aperture (photflux_aper90, flux_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure for all valid observations in the stack. The conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. 

pileup_flag  Boolean 
ACIS pileup fraction exceeds ~10% in any stacked
observations; detection properties may be affected
From the Source Flags column descriptions page: The pileup warning flag for a compact detection is a Boolean that has a value of TRUE if the pileup fraction exceed ~10% for any contributing ACIS perobservation detections and energy bands. Otherwise, the value is FALSE. The pileup warning flag for an extended (convex hull) detection is always NULL. 

pos_angle  double[6]  deg 
position angle (referenced from local true north) of the
major axis of the ellipse defining
the deconvolved source extent for
each science energy band
From the 'Deconvolved Source Extent' section of the Source Extent and Errors column descriptions page: For stacked observation detections, the deconvolved source extent is a parameterization of the best estimate of the flux distribution defining the PSFdeconvolved source, which is determined in each science energy band from a varianceweighted mean of the deconvolved extent of each source measured in all contributing observations. The parameterization represents the best estimate values and associated errors for the \(1\sigma\) radius along the major axis, the \(1\sigma\) radius along the minor axis, and the position angle of the major axis of a rotated elliptical Gaussian source that has been fitted to the observed source spatial event distribution deconvolved with the raytrace local PSF at the location of that source event distribution. Deconvolving the raw source image with the PSF produces the intrinsic shape of the source. In order to determine whether a source is extended, we first need to realize that the intrinsic size of a point source is, by definition, zero. By performing the fitting described above, srcextent estimates the raw sizes and errors of both the source and the PSF. In what follows, we derive the size and error for the intrinsic size of the source, and then we establish a criterion to flag a source as extended. In principle, one can determine the parameters of the intrinsic source ellipse, \(\{a_{1},a_{2},\phi\}\), by solving a nonlinear system of equations involving the PSF parameters, \(\{a_{1},a_{2},\psi\}\), and the measured source parameters, \(\{\sigma_{1},\sigma_{2},\delta\}\). However, because these equations are based on a crude approximation and because the input parameters are often uncertain, such an elaborate calculation seems unjustified. A much simpler and more robust approach makes use of the identity: \[ \sigma_{1}^{2} + \sigma_{2}^{2} = a_{1}^{2} + a_{2}^{2} + b_{1}^{2} + b_{2}^{2} \ , \]which applies to the convolution of two elliptical Gaussians having arbitrary relative sizes and position angles. Using this identity, one can define a rootsumsquare intrinsic source size: \[ a_{\mathrm{rss}} \equiv \sqrt{a_{1}^2 + a_{2}^{2}} = \sqrt{ \max\{0,(\sigma_{1}^{2} + \sigma_{2}^{2})  (b_{1}^{2} + b_{2}^{2}) \}} \ , \]that depends only on the sizes of the relevant ellipses and is independent of their orientations. This expression is analogous to the wellknown result for convolution of 1D Gaussians and for convolution of circular Gaussians in 2D. Using the equation above, one can derive an analytic expression for the uncertainty in \(a_{\mathrm{rss}}\) in terms of the measurement errors associated with \(\sigma_{i}\) and \(b_{i}\). Because \(\sigma_{i}\) and \(b_{i}\) are nonnegative, evaluating the righthand side of the equation using the corresponding mean values should give a reasonable estimate of the mean value of \(a_{\mathrm{rss}}\). A Taylor series expansion of the righthand side evaluated at the mean parameter values, therefore, yields the uncertainty: \[ \Delta a_{\mathrm{rss}} = \frac{1}{a} \sqrt{ \sigma_{1}^{2} \left(\Delta \sigma_{1} \right)^{2} + \sigma_{2}^{2} \left(\Delta \sigma_{2} \right)^{2} + b_{1}^{2} \left(\Delta b_{1} \right)^{2} + b_{1}^{2} \left(\Delta b_{1} \right)^{2} } \]where \(\left(\Delta X \right)^{2}\) represents the variance in \(X\) and where \[ a \equiv \left\{ \begin{array}{ll} a_{\mathrm{rss}} \ , & a_{\mathrm{rss}} > 0 \ , \\ \sqrt{b_{1}^{2} + b_{2}^{2}} \ , & a_{\mathrm{rss}} = 0 \ . \end{array} \right. \]A source is extended if its rootsumsquare intrinsic size is larger than the rootsumsquare error of this size. Namely, if its derived intrinsic size, that depends on the raw source and PSF sizes and errors, is larger than the fluctuations due to the uncertainty in the determination (different from zero). If \(a_{\mathrm{rss}} > f \Delta a_{\mathrm{rss}}\), then the source is extended at the \(f\sigma\) level. In CSC2, we use \(f = 5\), which implies that sources are flagged as extended if the intrinsic size is determined with a significance of \(5\sigma\). 

pos_angle_aper  double  deg 
position angle (referenced from local true north) of the
semimajor axis of the
elliptical source
region aperture
From the 'Source Region' section of the Source Extent and Errors column descriptions page: The spatial regions defining a source and its corresponding background are determined by scaling and merging the individual source detection regions that result from all of the spatial scales and source detection energy bands in which the source is detected during the source detection process (wavdetect). The result is a single elliptical source region which excludes any overlapping source regions, and a single, colocated, scaled, elliptical annular background region. The parameter values that define the source region and background region for each source are the ICRS right ascension and signed ICRS declination of the center of the source region and background region; the semimajor and semiminor axes of the source region ellipse and of the inner and outer annuli of the background region ellipse; and the position angles of the semimajor axes defining the source and background region ellipses. 

pos_angle_aperbkg  double  deg 
position angle (referenced from local true north) of the
semimajor axes of the annular background region aperture
From the 'Source Region' section of the Source Extent and Errors column descriptions page: The spatial regions defining a source and its corresponding background are determined by scaling and merging the individual source detection regions that result from all of the spatial scales and source detection energy bands in which the source is detected during the source detection process (wavdetect). The result is a single elliptical source region which excludes any overlapping source regions, and a single, colocated, scaled, elliptical annular background region. The parameter values that define the source region and background region for each source are the ICRS right ascension and signed ICRS declination of the center of the source region and background region; the semimajor and semiminor axes of the source region ellipse and of the inner and outer annuli of the background region ellipse; and the position angles of the semimajor axes defining the source and background region ellipses. 

pos_angle_hilim  double[6]  deg 
position angle (referenced from local true north) of the
major axis of the ellipse defining
the deconvolved detection extent (68%
upper confidence limit)
From the 'Deconvolved Source Extent' section of the Source Extent and Errors column descriptions page: For stacked observation detections, the deconvolved source extent is a parameterization of the best estimate of the flux distribution defining the PSFdeconvolved source, which is determined in each science energy band from a varianceweighted mean of the deconvolved extent of each source measured in all contributing observations. The parameterization represents the best estimate values and associated errors for the \(1\sigma\) radius along the major axis, the \(1\sigma\) radius along the minor axis, and the position angle of the major axis of a rotated elliptical Gaussian source that has been fitted to the observed source spatial event distribution deconvolved with the raytrace local PSF at the location of that source event distribution. Deconvolving the raw source image with the PSF produces the intrinsic shape of the source. In order to determine whether a source is extended, we first need to realize that the intrinsic size of a point source is, by definition, zero. By performing the fitting described above, srcextent estimates the raw sizes and errors of both the source and the PSF. In what follows, we derive the size and error for the intrinsic size of the source, and then we establish a criterion to flag a source as extended. In principle, one can determine the parameters of the intrinsic source ellipse, \(\{a_{1},a_{2},\phi\}\), by solving a nonlinear system of equations involving the PSF parameters, \(\{a_{1},a_{2},\psi\}\), and the measured source parameters, \(\{\sigma_{1},\sigma_{2},\delta\}\). However, because these equations are based on a crude approximation and because the input parameters are often uncertain, such an elaborate calculation seems unjustified. A much simpler and more robust approach makes use of the identity: \[ \sigma_{1}^{2} + \sigma_{2}^{2} = a_{1}^{2} + a_{2}^{2} + b_{1}^{2} + b_{2}^{2} \ , \]which applies to the convolution of two elliptical Gaussians having arbitrary relative sizes and position angles. Using this identity, one can define a rootsumsquare intrinsic source size: \[ a_{\mathrm{rss}} \equiv \sqrt{a_{1}^2 + a_{2}^{2}} = \sqrt{ \max\{0,(\sigma_{1}^{2} + \sigma_{2}^{2})  (b_{1}^{2} + b_{2}^{2}) \}} \ , \]that depends only on the sizes of the relevant ellipses and is independent of their orientations. This expression is analogous to the wellknown result for convolution of 1D Gaussians and for convolution of circular Gaussians in 2D. Using the equation above, one can derive an analytic expression for the uncertainty in \(a_{\mathrm{rss}}\) in terms of the measurement errors associated with \(\sigma_{i}\) and \(b_{i}\). Because \(\sigma_{i}\) and \(b_{i}\) are nonnegative, evaluating the righthand side of the equation using the corresponding mean values should give a reasonable estimate of the mean value of \(a_{\mathrm{rss}}\). A Taylor series expansion of the righthand side evaluated at the mean parameter values, therefore, yields the uncertainty: \[ \Delta a_{\mathrm{rss}} = \frac{1}{a} \sqrt{ \sigma_{1}^{2} \left(\Delta \sigma_{1} \right)^{2} + \sigma_{2}^{2} \left(\Delta \sigma_{2} \right)^{2} + b_{1}^{2} \left(\Delta b_{1} \right)^{2} + b_{1}^{2} \left(\Delta b_{1} \right)^{2} } \]where \(\left(\Delta X \right)^{2}\) represents the variance in \(X\) and where \[ a \equiv \left\{ \begin{array}{ll} a_{\mathrm{rss}} \ , & a_{\mathrm{rss}} > 0 \ , \\ \sqrt{b_{1}^{2} + b_{2}^{2}} \ , & a_{\mathrm{rss}} = 0 \ . \end{array} \right. \]A source is extended if its rootsumsquare intrinsic size is larger than the rootsumsquare error of this size. Namely, if its derived intrinsic size, that depends on the raw source and PSF sizes and errors, is larger than the fluctuations due to the uncertainty in the determination (different from zero). If \(a_{\mathrm{rss}} > f \Delta a_{\mathrm{rss}}\), then the source is extended at the \(f\sigma\) level. In CSC2, we use \(f = 5\), which implies that sources are flagged as extended if the intrinsic size is determined with a significance of \(5\sigma\). 

pos_angle_lolim  double[6]  deg 
position angle (referenced from local true north) of the
major axis of the ellipse defining
the deconvolved detection extent (68%
lower confidence limit)
From the 'Deconvolved Source Extent' section of the Source Extent and Errors column descriptions page: For stacked observation detections, the deconvolved source extent is a parameterization of the best estimate of the flux distribution defining the PSFdeconvolved source, which is determined in each science energy band from a varianceweighted mean of the deconvolved extent of each source measured in all contributing observations. The parameterization represents the best estimate values and associated errors for the \(1\sigma\) radius along the major axis, the \(1\sigma\) radius along the minor axis, and the position angle of the major axis of a rotated elliptical Gaussian source that has been fitted to the observed source spatial event distribution deconvolved with the raytrace local PSF at the location of that source event distribution. Deconvolving the raw source image with the PSF produces the intrinsic shape of the source. In order to determine whether a source is extended, we first need to realize that the intrinsic size of a point source is, by definition, zero. By performing the fitting described above, srcextent estimates the raw sizes and errors of both the source and the PSF. In what follows, we derive the size and error for the intrinsic size of the source, and then we establish a criterion to flag a source as extended. In principle, one can determine the parameters of the intrinsic source ellipse, \(\{a_{1},a_{2},\phi\}\), by solving a nonlinear system of equations involving the PSF parameters, \(\{a_{1},a_{2},\psi\}\), and the measured source parameters, \(\{\sigma_{1},\sigma_{2},\delta\}\). However, because these equations are based on a crude approximation and because the input parameters are often uncertain, such an elaborate calculation seems unjustified. A much simpler and more robust approach makes use of the identity: \[ \sigma_{1}^{2} + \sigma_{2}^{2} = a_{1}^{2} + a_{2}^{2} + b_{1}^{2} + b_{2}^{2} \ , \]which applies to the convolution of two elliptical Gaussians having arbitrary relative sizes and position angles. Using this identity, one can define a rootsumsquare intrinsic source size: \[ a_{\mathrm{rss}} \equiv \sqrt{a_{1}^2 + a_{2}^{2}} = \sqrt{ \max\{0,(\sigma_{1}^{2} + \sigma_{2}^{2})  (b_{1}^{2} + b_{2}^{2}) \}} \ , \]that depends only on the sizes of the relevant ellipses and is independent of their orientations. This expression is analogous to the wellknown result for convolution of 1D Gaussians and for convolution of circular Gaussians in 2D. Using the equation above, one can derive an analytic expression for the uncertainty in \(a_{\mathrm{rss}}\) in terms of the measurement errors associated with \(\sigma_{i}\) and \(b_{i}\). Because \(\sigma_{i}\) and \(b_{i}\) are nonnegative, evaluating the righthand side of the equation using the corresponding mean values should give a reasonable estimate of the mean value of \(a_{\mathrm{rss}}\). A Taylor series expansion of the righthand side evaluated at the mean parameter values, therefore, yields the uncertainty: \[ \Delta a_{\mathrm{rss}} = \frac{1}{a} \sqrt{ \sigma_{1}^{2} \left(\Delta \sigma_{1} \right)^{2} + \sigma_{2}^{2} \left(\Delta \sigma_{2} \right)^{2} + b_{1}^{2} \left(\Delta b_{1} \right)^{2} + b_{1}^{2} \left(\Delta b_{1} \right)^{2} } \]where \(\left(\Delta X \right)^{2}\) represents the variance in \(X\) and where \[ a \equiv \left\{ \begin{array}{ll} a_{\mathrm{rss}} \ , & a_{\mathrm{rss}} > 0 \ , \\ \sqrt{b_{1}^{2} + b_{2}^{2}} \ , & a_{\mathrm{rss}} = 0 \ . \end{array} \right. \]A source is extended if its rootsumsquare intrinsic size is larger than the rootsumsquare error of this size. Namely, if its derived intrinsic size, that depends on the raw source and PSF sizes and errors, is larger than the fluctuations due to the uncertainty in the determination (different from zero). If \(a_{\mathrm{rss}} > f \Delta a_{\mathrm{rss}}\), then the source is extended at the \(f\sigma\) level. In CSC2, we use \(f = 5\), which implies that sources are flagged as extended if the intrinsic size is determined with a significance of \(5\sigma\). 

ra  double  deg 
detection position, ICRS right
ascension
From the Position and Position Errors column descriptions page: 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 inturn determined from the wavdetect and/or mkvtbkg detections, as adjusted by the maximum likelihood estimator (MLE) fits to the observed Xray event distributions. 

ra_aper  double  deg 
center of the source region and background region
apertures, ICRS right
ascension
From the 'Source Region' section of the Source Extent and Errors column descriptions page: The spatial regions defining a source and its corresponding background are determined by scaling and merging the individual source detection regions that result from all of the spatial scales and source detection energy bands in which the source is detected during the source detection process (wavdetect). The result is a single elliptical source region which excludes any overlapping source regions, and a single, colocated, scaled, elliptical annular background region. The parameter values that define the source region and background region for each source are the ICRS right ascension and signed ICRS declination of the center of the source region and background region; the semimajor and semiminor axes of the source region ellipse and of the inner and outer annuli of the background region ellipse; and the position angles of the semimajor axes defining the source and background region ellipses. 

ra_stack  detect stack tangent plane reference position, ICRS right ascension  
region_id  integer  detection region identifier (component number)  
sat_src_flag  Boolean 
detection is saturated in all stacked observations (strong
ACIS pileup); detection properties are unreliable
From the Source Flags column descriptions page: The saturated detection flag is for a compact detection is a Boolean that has a value of TRUE if all contributing observations are ACIS observations and all perobservation detections are significantly piledup, i.e., sat_src_flag is TRUE for all of the contributing perobservation detections. Detection properties (including the pileup warning flag) are unreliable for all ACIS energy bands. Otherwise, the value is FALSE. sat_src_flag for an extended (convex hull) source is always NULL. 

src_area  double[6]  sq. arcseconds  area of the deconvolved detection extent ellipse, or area of the detection polygon for extended detections for each science energy band  
src_cnts_aper  double[6]  counts 
aperturecorrected detection net counts inferred from the source
region aperture for each science energy band
From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page: Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine backgroundmarginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits. Fluxes are determined for each perobservation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits. The aperture source counts represent the combined net number of backgroundsubtracted source counts in the modified source region (src_cnts_aper) and in the modified elliptical aperture (src_cnts_aper90), corrected by the appropriate PSF aperture fractions, for all valid source observations in the stack. 

src_cnts_aper90  double[6]  counts 
aperturecorrected detection net counts inferred from the
PSF 90% ECF aperture for each science energy band
From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page: Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine backgroundmarginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits. Fluxes are determined for each perobservation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits. The aperture source counts represent the combined net number of backgroundsubtracted source counts in the modified source region (src_cnts_aper) and in the modified elliptical aperture (src_cnts_aper90), corrected by the appropriate PSF aperture fractions, for all valid source observations in the stack. 

src_cnts_aper90_hilim  double[6]  counts 
aperturecorrected detection net counts inferred from the
PSF 90% ECF aperture (68% upper confidence limit) for each
science energy band
From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page: Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine backgroundmarginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits. Fluxes are determined for each perobservation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits. The aperture source counts represent the combined net number of backgroundsubtracted source counts in the modified source region (src_cnts_aper) and in the modified elliptical aperture (src_cnts_aper90), corrected by the appropriate PSF aperture fractions, for all valid source observations in the stack. 

src_cnts_aper90_lolim  double[6]  counts 
aperturecorrected detection net counts inferred from the
PSF 90% ECF aperture (68% lower confidence limit) for each
science energy band
From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page: Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine backgroundmarginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits. Fluxes are determined for each perobservation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits. The aperture source counts represent the combined net number of backgroundsubtracted source counts in the modified source region (src_cnts_aper) and in the modified elliptical aperture (src_cnts_aper90), corrected by the appropriate PSF aperture fractions, for all valid source observations in the stack. 

src_cnts_aper_hilim  double[6]  counts 
aperturecorrected detection net counts inferred from the
source region aperture (68% upper confidence limit) for each
science energy band
From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page: Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine backgroundmarginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits. Fluxes are determined for each perobservation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits. The aperture source counts represent the combined net number of backgroundsubtracted source counts in the modified source region (src_cnts_aper) and in the modified elliptical aperture (src_cnts_aper90), corrected by the appropriate PSF aperture fractions, for all valid source observations in the stack. 

src_cnts_aper_lolim  double[6]  counts 
aperturecorrected detection net counts inferred from the
source region aperture (68% lower confidence limit) for each
science energy band
From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page: Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine backgroundmarginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits. Fluxes are determined for each perobservation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits. The aperture source counts represent the combined net number of backgroundsubtracted source counts in the modified source region (src_cnts_aper) and in the modified elliptical aperture (src_cnts_aper90), corrected by the appropriate PSF aperture fractions, for all valid source observations in the stack. 

src_rate_aper  double[6]  counts s^{1} 
aperturecorrected detection net count rate inferred from the source
region aperture for each science energy band
From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page: Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine backgroundmarginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits. Fluxes are determined for each perobservation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits. The aperture source count rates and associated twosided confidence limits are defined as the average backgroundsubtracted source count rates in the modified source region (src_rate_aper) and in the modified elliptical aperture (src_rate_aper90), corrected by the appropriate PSF aperture fractions and livetime, for all valid source observations in the stack. 

src_rate_aper90  double[6]  counts s^{1} 
aperturecorrected detection net count rate inferred from
the PSF 90% ECF aperture for each science energy band
From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page: Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine backgroundmarginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits. Fluxes are determined for each perobservation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits. The aperture source count rates and associated twosided confidence limits are defined as the average backgroundsubtracted source count rates in the modified source region (src_rate_aper) and in the modified elliptical aperture (src_rate_aper90), corrected by the appropriate PSF aperture fractions and livetime, for all valid source observations in the stack. 

src_rate_aper90_hilim  double[6]  counts s^{1} 
aperturecorrected detection net count rate inferred from
the PSF 90% ECF aperture (68% upper confidence limit) for
each science energy band
From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page: Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine backgroundmarginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits. Fluxes are determined for each perobservation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits. The aperture source count rates and associated twosided confidence limits are defined as the average backgroundsubtracted source count rates in the modified source region (src_rate_aper) and in the modified elliptical aperture (src_rate_aper90), corrected by the appropriate PSF aperture fractions and livetime, for all valid source observations in the stack. 

src_rate_aper90_lolim  double[6]  counts s^{1} 
aperturecorrected detection net count rate inferred from
the PSF 90% ECF aperture (68% lower confidence limit) for
each science energy band
From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page: Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine backgroundmarginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits. Fluxes are determined for each perobservation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits. The aperture source count rates and associated twosided confidence limits are defined as the average backgroundsubtracted source count rates in the modified source region (src_rate_aper) and in the modified elliptical aperture (src_rate_aper90), corrected by the appropriate PSF aperture fractions and livetime, for all valid source observations in the stack. 

src_rate_aper_hilim  double[6]  counts s^{1} 
aperturecorrected detection net count rate inferred from
the source region aperture (68% upper confidence limit) for
each science energy band
From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page: Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine backgroundmarginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits. Fluxes are determined for each perobservation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits. The aperture source count rates and associated twosided confidence limits are defined as the average backgroundsubtracted source count rates in the modified source region (src_rate_aper) and in the modified elliptical aperture (src_rate_aper90), corrected by the appropriate PSF aperture fractions and livetime, for all valid source observations in the stack. 

src_rate_aper_lolim  double[6]  counts s^{1} 
aperturecorrected detection net count rate inferred from
the source region aperture (68% lower confidence limit) for
each science energy band
From the 'Aperture Photometry Fluxes' section of the Source Fluxes column descriptions page: Aperture photometry quantities are derived from counts in source regions or elliptical apertures, with background estimated from counts in surrounding background regions. Corrections are made for PSF aperture fractions, livetime, and exposure. In the case of energy fluxes, the conversion from photons s^{1} cm^{2} to ergs s^{1} cm^{2} is performed by summing the photon energies for each incident source photon and scaling by the local value of the ARF at the location of the incident photon. For all aperture photometry quantities, a Bayesian statistical analysis is performed to determine backgroundmarginalized posterior probability distribution for the flux quantity, and the mode and 68% percentiles of the distribution are reported as the flux value and confidence limits. Fluxes are determined for each perobservation detection, for each stack, and for the master source. At the stack level, aperture data from all valid source observations in the stack are combined. At the master source level, a Bayesian Blocks analysis is performed to determine the sets of source observations consistent with a constant source flux. Aperture data from the set with the largest total exposure are then combined to determine master source 'best estimate' fluxes and confidence limits. In addition, aperture data from all source observations in which the master source was detected or in the field of view are combined to determine master source average fluxes and confidence limits. The aperture source count rates and associated twosided confidence limits are defined as the average backgroundsubtracted source count rates in the modified source region (src_rate_aper) and in the modified elliptical aperture (src_rate_aper90), corrected by the appropriate PSF aperture fractions and livetime, for all valid source observations in the stack. 

streak_src_flag  Boolean 
detection located on an ACIS readout streak in all stacked
observations; detection properties may be affected
From the Source Flags column descriptions page: The streak detection flag for a compact detection is a Boolean that has a value of TRUE if all contributing observations are ACIS observations and all perobservation source regions overlap a defined region enclosing an identified readout streak, i.e., streak_src_flag is TRUE for all of the contributing perobservation detections. Otherwise, the value is FALSE. The streak source flag for an extended (convex hull) detection is TRUE if any contributing observations are ACIS observations and any perobservation detection source region overlaps a defined region enclosing an identified readout streak . Otherwise, the value is FALSE. 

theta_mean  double  arcmin 
mean source region aperture offaxis angle from all stacked
observations
From the Position and Position Errors column descriptions page: The mean source region aperture offaxis angle, θ_{mean}, computed by averaging the offaxis angles θ from all observations in a stack. 

var_flag  Boolean 
detection displays flux variability within one or more of
the stacked observations, or between stacked observations in
one or more energy bands
From the Source Flags column descriptions page: The variability flag is a Boolean that has a value of TRUE if variability is detected within any single observation in any science energy band in any of the observations contributing to the stacked detection. Otherwise, the value is FALSE. 

var_inter_hard_flag  Boolean 
detection hardness ratios are statistically inconsistent
between two or more of the stacked observations
From the Source Flags column descriptions page: The interobservation variable hardness ratio flag for a compact detection is a Boolean that has a value of TRUE if one or more of the hardness ratios computed for any of the contributing observation detections is statistically inconsistent with the corresponding hardness ratios computed for any other contributing observation detections. Otherwise, the values is FALSE. From the Source Variability column descriptions page: A Boolean set to FALSE if var_inter_hard_prob is below 0.3 for all three hardness ratios, and set to TRUE otherwise. 

var_inter_hard_prob_hm  double 
interstackedobservation ACIS hard (2.07.0 keV)  medium (1.22.0 keV)
energy band hardness
ratio variability probability
From the Source Variability column descriptions page: The interobservation spectral variability probability (var_inter_hard_prob) is a value that records the probability that the source region hardness ratios varied between the contributing observations, based on the hypothesis rejection test described in the hardness ratios and variability memo. The definition of this probability is identical to that of the interobservation source variability (var_inter_prob), and also utilizes the same hypothesis rejection test, but based on the probability distributions (PDFs) for the hardness ratios, rather than the probability distributions for the fluxes. The definition of the hardness ratio PDFs can be found in the memo, and also in the hardness ratios columns page. High values of var_inter_hard_prob indicate that the source is spectrally variable in the corresponding combination of bands. 

var_inter_hard_prob_hs  double 
interstackedobservation ACIS hard (2.07.0 keV)  soft (0.51.2 keV)
energy band hardness
ratio variability probability
From the Source Variability column descriptions page: The interobservation spectral variability probability (var_inter_hard_prob) is a value that records the probability that the source region hardness ratios varied between the contributing observations, based on the hypothesis rejection test described in the hardness ratios and variability memo. The definition of this probability is identical to that of the interobservation source variability (var_inter_prob), and also utilizes the same hypothesis rejection test, but based on the probability distributions (PDFs) for the hardness ratios, rather than the probability distributions for the fluxes. The definition of the hardness ratio PDFs can be found in the memo, and also in the hardness ratios columns page. High values of var_inter_hard_prob indicate that the source is spectrally variable in the corresponding combination of bands. 

var_inter_hard_prob_ms  double 
interstackedobservation ACIS medium (1.22.0 keV)  soft (0.51.2 keV)
energy band hardness
ratio variability probability
From the Source Variability column descriptions page: The interobservation spectral variability probability (var_inter_hard_prob) is a value that records the probability that the source region hardness ratios varied between the contributing observations, based on the hypothesis rejection test described in the hardness ratios and variability memo. The definition of this probability is identical to that of the interobservation source variability (var_inter_prob), and also utilizes the same hypothesis rejection test, but based on the probability distributions (PDFs) for the hardness ratios, rather than the probability distributions for the fluxes. The definition of the hardness ratio PDFs can be found in the memo, and also in the hardness ratios columns page. High values of var_inter_hard_prob indicate that the source is spectrally variable in the corresponding combination of bands. 

var_inter_hard_sigma_hm  double 
interstackedobservation ACIS hard (2.07.0 keV)  medium (1.22.0 keV)
energy band hardness
ratio variability standard deviation
From the Source Variability column descriptions page: Similarly to var_inter_sigma, the interobservation hardness ratio variability parameter (var_inter_hard_sigma) is the absolute value of the difference between the error weighted mean of the source region hardness ratio PDF when a single hardness ratio is assumed, and the mean of the source region hardness ratio PDF for the individual observation that maximizes the absolute value of the difference: \[ \left hard_{\left\langle band_{1}band_{2}\right\rangle}^{\mathrm{max}}  hard_{\left\langle band_{1}band_{2}\right\rangle}^{\mathrm{i,max}} \right \]Of all contributing observations, the observation that yields the highest value for this equation, is used in computing this value, which is recorded in var_inter_hard_sigma. Intuitively, this quantity can be interpreted as the variance of the individual observation hardness ratios. 

var_inter_hard_sigma_hs  double 
interstackedobservation ACIS hard (2.07.0 keV)  soft (0.51.2 keV)
energy band hardness
ratio variability standard deviation
From the Source Variability column descriptions page: Similarly to var_inter_sigma, the interobservation hardness ratio variability parameter (var_inter_hard_sigma) is the absolute value of the difference between the error weighted mean of the source region hardness ratio PDF when a single hardness ratio is assumed, and the mean of the source region hardness ratio PDF for the individual observation that maximizes the absolute value of the difference: \[ \left hard_{\left\langle band_{1}band_{2}\right\rangle}^{\mathrm{max}}  hard_{\left\langle band_{1}band_{2}\right\rangle}^{\mathrm{i,max}} \right \]Of all contributing observations, the observation that yields the highest value for this equation, is used in computing this value, which is recorded in var_inter_hard_sigma. Intuitively, this quantity can be interpreted as the variance of the individual observation hardness ratios. 

var_inter_hard_sigma_ms  double 
interstackedobservation ACIS medium (1.22.0 keV)  soft (0.51.2 keV)
energy band hardness
ratio variability standard deviation
From the Source Variability column descriptions page: Similarly to var_inter_sigma, the interobservation hardness ratio variability parameter (var_inter_hard_sigma) is the absolute value of the difference between the error weighted mean of the source region hardness ratio PDF when a single hardness ratio is assumed, and the mean of the source region hardness ratio PDF for the individual observation that maximizes the absolute value of the difference: \[ \left hard_{\left\langle band_{1}band_{2}\right\rangle}^{\mathrm{max}}  hard_{\left\langle band_{1}band_{2}\right\rangle}^{\mathrm{i,max}} \right \]Of all contributing observations, the observation that yields the highest value for this equation, is used in computing this value, which is recorded in var_inter_hard_sigma. Intuitively, this quantity can be interpreted as the variance of the individual observation hardness ratios. 

var_inter_index  integer[6] 
interstackedobservation variability index in the range
[0, 10]: indicates whether the source region photon flux is
constant between observations for each science energy band
From the Source Variability column descriptions page: The interobservation variability index (var_inter_index) is an integer value in the range \([0,8]\) that is derived according to the estimated value of the quantity \(D/(N1)\) defined above. It is used to evaluate whether the source region photon flux is constant between the observations. The degree of confidence in variability expressed by this index is similar to that of the intraobservation variability index. Below we tabulate the association between the value of \(D/(N1)\) and interobservation variability index.


var_inter_prob  double[6] 
interstacked observation variability probability,
calculated from the χ^{2} distribution of the photon fluxes
of the individual observations for each science energy band
The interobservation variability probability (var_inter_prob) is a value that records the probability that the source region photon flux varied between the contributing observations, based on the hypothesis rejection test described in the hardness ratios and variability memo. Given the \(N\) individual Bayesian probability distribution of the aperture fluxes for the same source in \(N\) different observations (their means and standard deviations), we estimate for each band the maximum likelihood \(\mathcal{L}_{1}^{\mathrm{max}}\) and the corresponding maximizing arguments \(F_{\left\langle band \right\rangle}^{i,\mathrm{max}}\), of the observed fluxes assuming a different flux for each observation, as well as the maximum likelihood \(\mathcal{L}_{2}^{\mathrm{max}}\) and the corresponding maximizing argument \(F_{\left\langle band \right\rangle}^{\mathrm{max}}\) of the observed fluxes assuming a single flux (the latter is the null hypothesis of no variability). As per Wilks' theorem, the quantity: \[ D \equiv 2 \left( \log{\mathcal{L}_{1}^{\mathrm{max}}}  \log{\mathcal{L}_{2}^{\mathrm{max}}} \right) \]follows \(\chi^{2}\) distribution with \(N1\) degrees of freedom, under the null hypothesis. Therefore, the null hypothesis (nonvariability) is rejected with a probability proportional to the cumulative distribution of the \(\chi^{2}\) statistic for values smaller than the estimated \(D\). The quantity var_inter_prob represents this cumulative probability, and therefore gives the probability that the source is variable. The reason for this careful definition is that the probabilities for intraobservation and interobservation variability are, by necessity, of a different nature. Whereas one can say with reasonable certainty whether a source was variable during an observation covering a contiguous time interval, when comparing measured fluxes from different observations one knows nothing about the source's behavior during the intervening interval(s). Consequently, when the interobservation variability probability is high (e.g., var_inter_prob > 0.7), one can confidently state that the source is variable on longer time scales, but when the probability is low, all one can say is that the observations are consistent with a constant flux. 

var_inter_sigma  double[6]  photons s^{1} cm^{2} 
interstackedobservation
flux variability standard
deviation; the spread of the individual
observation photon fluxes about the error weighted mean for
each science energy band
From the Source Variability column descriptions page: The interobservation flux variability (var_inter_sigma) is the absolute value of the difference between the error weighted mean of the source region photon flux density PDF when a single flux is assumed \(\left( F_{\left\langle band \right\rangle}^{\mathrm{max}} \right)\), and the mean of the source region photon flux density PDF for the individual observation that maximizes the absolute value of the difference \(\left( F_{\left\langle band \right\rangle}^{i,\mathrm{max}} \right)\): \[ \left F_{\left\langle band \right\rangle}^{\mathrm{max}}  F_{\left\langle band \right\rangle}^{i,\mathrm{max}} \right \]Of all the contributing observations, the observation that yields the highest value for this equation, is used in computing this value, which is recorded in var_inter_sigma. Intuitively, this quantity can be interpreted as the variance of the individual observation fluxes. 

var_intra_index  integer[6] 
intraobservation GregoryLoredo variability index
in the range [0, 10]: indicates whether the source region
photon flux is constant within an observation (highest value
across all stacked observations) for each science energy band
The intraobservation variability index (var_intra_index) represents the highest value of the variability indices (var_index) calculated for each of the contributing observations. 

var_intra_prob  double[6] 
intraobservation GregoryLoredo variability
probability (highest value across all stacked
observations for each science energy band
The GregoryLoredo, KolmogorovSmirnov (KS) test, and Kuiper's test intraobservation variability probabilities represent the highest values of the variability probabilities (var_prob, ks_prob, kp_prob) calculated for each of the contributing observations (i.e., the highest level of variability among the observations contributing to the master source entry). 