# Source Fluxes

Source fluxes are determined by aperture photometry in each science energy band. Aperture photometry measurements are obtained in the source region, and in an elliptical aperture that includes the 90% Encircled Counts Fraction of the PSF at the source location, with corrections applied for the PSF aperture fraction. The correction factor is computed from the ray-trace local PSF under the assumption that the source spatial distribution matches the local PSF.

## Aperture Photometry Fluxes

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 background-marginalized 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 per-observation 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.

### Aperture Total Counts

Per-Observation Detections Table:
cnts_aper, cnts_aperbkg, cnts_aper90, cnts_aper90bkg

The aperture total counts represent the total number of source plus background counts measured in the modified source and background regions (cnts_aper, cnts_aperbkg), and in the modified elliptical aperture and modified elliptical background aperture (cnts_aper90, cnts_aper90bkg), uncorrected by the PSF aperture fraction.

### Aperture Source Counts

Per-Observation Detections Table:
src_cnts_aper, src_cnts_aper90, src_cnts_aper_hilim, src_cnts_aper_lolim, src_cnts_aper90_hilim, src_cnts_aper90_lolim

The aperture source counts represent the net number of background-subtracted 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.

Stack Observations Table:
src_cnts_aper, src_cnts_aper90, src_cnts_aper_hilim, src_cnts_aper_lolim, src_cnts_aper90_hilim, src_cnts_aper90_lolim

The aperture source counts represent the combined net number of background-subtracted 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.

### Elliptical Aperture

Per-Observation Detections Table:
mjr_axis_aper90, mnr_axis_aper90, pos_angle_aper90, mjr_axis1_aper90bkg, mnr_axis1_aper90bkg, mjr_axis2_aper90bkg, mnr_axis2_aper90bkg, pos_angle_aper90bkg

The elliptical apertures for each source are defined as the ellipses that include the 90% encircled counts fraction of the PSF in each science energy band at the source location, which are used to extract the aperture counts, count rates, and photon and energy fluxes. The elliptical apertures are co-located with the source region. The elliptical background apertures for each science energy band are scaled, annular ellipses co-located with the background region for that source. The parameter values that define the elliptical aperture and the elliptical background aperture for each source are the semi-major axis, semi-minor axis, and position angle of the major axis of each, in addition to the inner and outer annuli of the elliptical background aperture.

Note

In the first catalog release, the elliptical aperture is defined on a tangent plane projection. The 0 deg position angle reference is defined on that tangent plane to be parallel to the true North direction at the location of the tangent plane reference (refer to the tangent plane reference right ascension (ra_nom), declination (dec_nom), and roll angle (roll_nom)).

### Modified Elliptical Aperture

Per-Observation Detections Table:
area_aper90, area_aper90bkg

The modified elliptical aperture and modified elliptical background aperture for each source and science energy band are defined as the areas of intersection of the elliptical aperture and elliptical background aperture for that source with the field of view, excluding any overlapping source regions.

### Aperture Source Count Rates

Per-Observation Detections Table:
src_rate_aper, src_rate_aper90, src_rate_aper_hilim, src_rate_aper_lolim, src_rate_aper90_hilim, src_rate_aper90_lolim

The aperture source count rates and associated two-sided confidence limits are defined as the background-subtracted 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.

Stack Observations Table:
src_rate_aper, src_rate_aper90, src_rate_aper_hilim, src_rate_aper_lolim, src_rate_aper90_hilim, src_rate_aper90_lolim

The aperture source count rates and associated two-sided confidence limits are defined as the average background-subtracted 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.

### Aperture Source Energy and Photon Fluxes

Master Sources Table:
photflux_aper, photflux_aper90, photflux_aper_hilim, photflux_aper_lolim, photflux_aper90_hilim, photflux_aper90_lolim, flux_aper, flux_aper90, flux_aper_hilim, flux_aper_lolim, flux_aper90_hilim, flux_aper90_lolim

The aperture source photon and energy fluxes and associated two-sided confidence limits represent the 'best estimate' background-subtracted 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 the Bayesian Block with the largest exposure. 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.

Master Sources Table:
photflux_aper_avg, photflux_aper90_avg, photflux_aper_avg_hilim, photflux_aper_avg_lolim, photflux_aper90_avg_hilim, photflux_aper90_avg_lolim, flux_aper_avg, flux_aper90_avg, flux_aper_avg_hilim, flux_aper_avg_lolim, flux_aper90_avg_hilim, flux_aper90_avg_lolim

The aperture source photon and energy fluxes and associated two-sided confidence limits represent the mean background-subtracted fluxes in the modified source region (photflux_aper_avg, flux_aper_avg) and in the modified elliptical aperture (photflux_aper90_avg, flux_aper90_avg), corrected by the appropriate PSF aperture fractions, livetime, and exposure, for all source observations in which the master source was detected or in the field of view. 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.

Per-Observation Detections Table:
photflux_aper, photflux_aper90, photflux_aper_hilim, photflux_aper_lolim, photflux_aper90_hilim, photflux_aper90_lolim, flux_aper, flux_aper90, flux_aper_hilim, flux_aper_lolim, flux_aper90_hilim, flux_aper90_lolim

The aperture source energy fluxes (flux_aper) and associated two-sided confidence limits represent the background-subtracted fluxes in the modified source region (photflux_aper) and in the modified elliptical aperture (photflux_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure. 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.

Stack Observations Table:
photflux_aper, photflux_aper90, photflux_aper_hilim, photflux_aper_lolim, photflux_aper90_hilim, photflux_aper90_lolim, flux_aper, flux_aper90, flux_aper_hilim, flux_aper_lolim, flux_aper90_hilim, flux_aper90_lolim

The aperture source photon and energy fluxes and associated two-sided confidence limits represent the average background-subtracted 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.

## Aperture Model Energy Fluxes

Master Sources Table:
flux_powlaw_aper, flux_powlaw_aper90, flux_bb_aper, flux_bb_aper90, flux_brems_aper, flux_brems_aper90, flux_apec_aper, flux_apec_aper90, flux_powlaw_aper_hilim, flux_powlaw_aper_lolim, flux_powlaw_aper90_hilim, flux_powlaw_aper90_lolim, flux_bb_aper_hilim, flux_bb_aper_lolim, flux_bb_aper90_hilim, flux_bb_aper90_lolim, flux_brems_aper_hilim, flux_brems_aper_lolim, flux_brems_aper90_hilim, flux_brems_aper90_lolim, flux_apec_aper_hilim, flux_apec_aper_lolim, flux_apec_aper90_hilim, flux_apec_aper90_lolim

The aperture model energy fluxes and associated two-sided confidence limits represent the best estimates of the power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes in the source region (flux_powlaw_aper, flux_bb_aper, flux_brems_aper, flux_apec_aper) and in an elliptical aperture that includes the 90% encircled counts fraction of the PSF at the source location (flux_powlaw_aper90, flux_bb_aper90, flux_brems_aper90, flux_apec_aper90), corrected by the PSF aperture fraction, livetime, and exposure.

Per-Observation Detections Table:
flux_powlaw_aper, flux_powlaw_aper90, flux_bb_aper, flux_bb_aper90, flux_brems_aper, flux_brems_aper90, flux_apec_aper, flux_apec_aper90, flux_powlaw_aper_hilim, flux_powlaw_aper_lolim, flux_powlaw_aper90_hilim, flux_powlaw_aper90_lolim, flux_bb_aper_hilim, flux_bb_aper_lolim, flux_bb_aper90_hilim, flux_bb_aper90_lolim, flux_brems_aper_hilim, flux_brems_aper_lolim, flux_brems_aper90_hilim, flux_brems_aper90_lolim, flux_apec_aper_hilim, flux_apec_aper_lolim, flux_apec_aper90_hilim, flux_apec_aper90_lolim

The aperture model energy fluxes and associated two-sided confidence limits represent the power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes in the modified source region (flux_powlaw_aper, flux_bb_aper, flux_brems_aper, flux_apec_aper) and in the modified elliptical aperture (flux_powlaw_aper90, flux_bb_aper90, flux_brems_aper90, flux_apec_aper90), corrected by the appropriate PSF aperture fractions, livetime, and exposure.

Note

The power law, blackbody, bremsstrahlung, and APEC aperture model energy fluxes are distinct from the spectral model fit fluxes in that they are derived from the binned images, whereas the latter are derived directly from the event data.) The conversion from aperture source count rates to aperture model energy fluxes is performed by scaling from a model spectrum folded through the calibrated response as follows:

• For a source model $$S(E)$$ whose integral over the science band is $$S^{\prime}$$, a corresponding band count rate $$C^{\prime}$$ in counts s-1, can be calculated given the effective area calibration, $$A(E)$$, [and, if available, the RMF, $$R(E^{\prime};E)$$] appropriate to the observation; then the count rate is:

over the energy band, $$E^{\prime}$$. If a diagonal RMF is assumed, as for HRC detections, then:

• Infer the aperture model energy flux, $$F^{\prime}$$, from $$S^{\prime}$$ scaled by the ratio of the measured aperture source count rate, $$C$$, and the modeled aperture count rate over the energy band:

The power law spectral model uses a fixed photon index, $$\gamma$$, defined as $$S \propto E^{-\gamma}$$, equal to 2.0 The blackbody spectral model uses a fixed temperature kT = 0.75 keV, a fixed temperature of kT = 3.5 keV for the bremsstrahlung model, and kT = 6.5 keV for the APEC spectral model. All models use fixed absorbing column density of the Galactic neutral hydrogen density in the direction of the source, $$N_{H}=N_{H}(\mathrm{Gal})$$, cm-2, obtained from Colden.

## PSF Aperture Fractions

Per-Observation Detections Table:
psf_frac_aper, psf_frac_aperbkg, psf_frac_aper90, psf_frac_aper90bkg

The PSF aperture fraction represents the fraction of the PSF that is included in the modified source and background regions (psf_frac_aper, psf_frac_bkgaper), and the modified elliptical aperture and modified elliptical background aperture (psf_frac_aper90, psf_frac_aper90bkg).