Characterizing CSC 2.1

Organization of Observations

Source properties are reported at the observation, stack, and master level. CSC 2.1 contains 406,089 compact Master Source records and 1,717 extended Master Source records, derived from data in 14,388 separate ACIS and 1,145 separate HRC observations available in the Chandra Public Archive as of December 31, 2021. Observations with aimpoints within 1′ are co-added into Stacks. All source detection is performed at the stack level. Stacking is done separately for ACIS and HRC observations. There are 10,034 such stacks in CSC 2.1: 9,645 ACIS and 389 HRC. Exposures range from ∼0.6 kiloseconds (ks) to ∼6.7 megaseconds (Ms), with a median of ∼14 ksec. The distributions of number of observations and total exposure time per stack are shown in Figure 1.

Figure 1: Observation Stack Histogram

Figure 1: Observation Stack Histogram

Distribution of number of observations per stack (left) and total exposure per stack (right).

At the Master Source level, source properties may include contributions from multiple observations contained in multiple stacks, even if individual observation aimpoints differ by more than 1′. An example is shown in Figure 2, for master source 2CXO J001120.4-152515. The distribution of the number of stacks contributing to each master source is shown in Figure 3.

Figure 2: Master Source

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Figure 2: Master Source

Master Source 2CXO J001120.4-152515, indicated by the white circle, includes data both from stack acisfJ0011475m152519_001, with FOV shown in green, and stack acisfJ0011407m152147_001, with FOV shown in red. Events from the first stack only are shown.

Figure 3: Stacks per Master Source

Figure 3: Stacks per Master Source

Distribution of number of stacks contributing to each master source.

Because master sources may be located at different off-axis angles in different stacks, source data quality may vary from stack-to-stack. In particular, a source detected in one stack at a large off-axis angle may resolve into multiple sources at smaller off-axis angles in another stack. Such "ambiguous" detections will remain linked to master sources in the database, but only data from unambiguous detections will be used to derive master source properties.

Because of the variable source quality in different observations contributing to a master source, and because many X-ray sources are intrinsically variable, we use a Bayesian Blocks algorithm (c.f. "Combining Aperture Photometry Results from Multiple ObsIDs" and Scargle et al. 2013, ApJ 764 167) to group observations into blocks. In each block, a constant flux is consistent with all individual observation level fluxes. ACIS and HRC observations are grouped into separate blocks, and in ACIS blocks, a constant flux must be consistent with all observations in all energy bands. An example is shown in Figure 4. The block with the longest total exposure is selected as the "best" block, and results from it are reported in the Master Source record's aperture photometry quantities.

Figure 4: Observation MPDFs of Master Source

Figure 4: Observation MPDFs of Master Source

Marginalized probability distributions (MPDFs) for the ACIS broad band energy flux in 7 observations contributing to master source 2CXO J004152.6-092213. The green, blue, and red curves represent the MPDFs for observations included in the three identified flux-ordered Bayesian Blocks. The flux-ordered block with the longest exposure time includes the observations in green. The black curve is the master source "best-estimate" MPDF, which combines data from all observations included in that block.

Distribution on Sky

The distribution of CSC 2.1 stacks on the sky is shown in Figure 5. As suggested in Figures 1 and 3, in most areas of the sky, stacks include only a few observations. However, several targets, such as the Galactic Center and M31, have been observed repeatedly, resulting in a large number of master sources from many observations and stacks.

Figure 5: Stacks in the Sky

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Figure 5: Stacks in the Sky

Distribution of CSC 2.1, stacks on the sky, in galactic coordinates. The dot size indicates the number of sources detected in the stack, and dot color indicates the number of observations.

Flux Distribution

CSC 2.1 fluxes range from below 10^-18 erg cm^-2 sec^-1 (for the deepest exposures) to 10^-10 erg cm^-2 sec^-1; most sources have fluxes of 10^-15–10^-13 erg cm^-2 sec^-1 (b-band, or 0.5–7.0 keV). The distribution of master source fluxes is shown in Figure 6.

Figure 6: Master Flux Distribution

Figure 6: Master Flux Distribution

Distribution of master source fluxes for CSC 2.1 (left) and CSC 2.0 (right). The upper plots are the distribution for energy fluxes and the lower plots are the distribution for photon fluxes.

The CSC 2.1 distributions appear to extend to lower fluxes, and this is due to improvements to the aperture photometry algorithm used to compute the Bayesian X-ray aperture photometry MPDFs in CSC 2.1. For faint detections where the Sherpa pyBLoCXS algorithm fails to converge, a more robust and computationally expensive MCMC algorithm, the No-U-Turn Sampler (NUTS; Hoffman & Gelman 2014) is used. This improves the reliability of aperture photometry flux computations, particularly in the extreme low-count regime.

Also in CSC 2.1, the ultrasoft band and (to some extent) soft band distributions appear to extend to higher fluxes. This is an artifact of the instrument responses used to compute the catalog photometric properties, which are computed at the monochromatic effective energies of the individual energy bands rather than by integrating the (typically not available a priori) source spectrum over the energy band. For these bands, the ACIS effective area has continued to decrease over time because of buildup of a spatially varying contaminant, and the rate of decrease accelerated after ~2013. Combined with the significant slope of the intrinsic detector's quantum efficiency as a function of energy, for a fixed monochromatic energy this variation of the detector's effective area with time will cause the fluxes in these bands to be overestimated for recent observations.

A more detailed comparison of CSC 2.1 and CSC 2.0 flux distributions is shown in Figures 7a and 7b.

Figure 7a: Master Source Energy Flux Distribution

Figure 7a: Master Source Energy Flux Distribution

Histograms of master source energy fluxes for CSC 2.1 (thick, solid line) and CSC 2.0 (thin, dotted line), normalized to unit area. Top left: ACIS broad band, top right: ACIS hard band, center left: ACIS medium band, center right: ACIS soft band, bottom left: ACIS ultrasoft band, bottom right: HRC wide band.

Figure 7b: Master Source Photon Flux Distribution

Figure 7b: Master Source Photon Flux Distribution

Histograms of master source photon fluxes for CSC 2.1 (thick, solid line) and CSC 2.0 (thin, dotted line), normalized to unit area. Top left: ACIS broad band, top right: ACIS hard band, center left: ACIS medium band, center right: ACIS soft band, bottom left: ACIS ultrasoft band, bottom right: HRC wide band.

Field Background

We compute simple estimates of background, averaged over the field, for each observation in CSC 2.1, by computing the total number of events per detector or chip, and subtracting the total number of source counts provided by aperture photometry. We exclude observations with known extended emission from the analysis. Results are shown in Figure 8 and reveal the expected variation with solar cycle. For ACIS observations, broad band values range from ∼0.15–0.35 counts sec^-1 chip^-1 for the I3 chip and ∼0.3–0.7 counts sec^-1 chip^-1 for the S3 chip. For HRC-I observations, values range from ∼25–125 counts sec^-1.

Figure 8: Average Field Background Rates

Figure 8: Average Field Background Rates

Average field background rates per detector or chip, as a function of observation date. Upper left: ACIS broad band, upper right: ACIS hard band, center left: ACIS medium band, center right: ACIS soft band, lower left: ACIS ultrasoft band, lower right: HRC wide band. In each year bin, boxes represent the inter-quartile range (25%–75%) of the distribution of background rates, and the thick horizontal lines indicate the medians. For ACIS, the rates per chip for the front-illuminated chip I3 (black) and back-illuminated S3 (blue) are shown. Bins include typically ∼200 observations for ACIS and ∼40 for HRC.

Limiting Sensitivity Maps

The limiting sensitivity maps are computed for each stack in all source detection energy bands. The maps are based on stack-level background maps and represent the minimum point source photon flux, \(p_{\mathrm{min}}\), in units of photons cm^-2 sec^-1 satisfying the inequality:

where \(P\) is the cumulative Poisson probability of obtaining more than \(B + 0.9 p_{\mathrm{min}} E\) counts in a 90% ECF aperture with expected background \(B\) and average exposure \(E\) in units of cm² s count photon^-1. \(P^{*}\) is a threshold probability that corresponds to the source detection likelihood threshold, \(\mathcal{L}^{*}=-2\ln{P}\).

The limiting sensitivity map consists of a single FITS format file for each set of stacked observation detections and science energy band including two images, one corresponding to less restrictive likelihood thresholds for sources classified as MARGINAL, and one for a more restrictive threshold for sources classified as TRUE. The MARGINAL and TRUE source detection likelihood thresholds correspond to false source rates of ∼1 and ∼0.1 false sources per stack, respectively, and are determined from simulations. The file is named: 〈i〉〈s〉〈stkpos〉_〈stkver〉N〈v〉_〈b〉_sens3.fits

Here, 〈i〉 is the instrument designation; 〈s〉 is the data source; 〈stkpos〉 is the position component of the stack name, formatted as "Jhhmmsss{p|m}ddmmss"; 〈stkver〉 is the 3-digit version component of the stack name, formatted with leading zeros; 〈v〉 is the data product version number, formatted with leading zeros; and 〈b〉 is the energy band designation.

Figure 9: ACIS Sensitivity Map

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Figure 9: ACIS Sensitivity Map

broad band limiting sensitivity maps for stack acisfJ1509253m585033_001, for MARGINAL (left) and TRUE (right) false source rates.

It should be noted, however, that CSC Release 2.1 source detections are not based on likelihoods derived from Poisson fluctuations, like those in the prior inequality describing the sensitivity maps. Rather, the detection procedure is based on fitting a point source model to image data in the vicinity of candidate sources. For each candidate two 2D spatial models are fit—one consisting of background only, and the other of background plus a point source convolved with the PSF. The best-fit \(C\)-statistic for each model is computed and the probability \(P\) of obtaining an increase in \(C\) at least as large as that observed, in the absence of a real source, is evaluated. The source detection likelihood \(\mathcal{L}\) is computed from this probability.

For the purposes of computing the sensitivity maps, we chose not to use these likelihoods, since that would require constructing PSFs for each sensitivity map pixel (∼4″⨯4″ for ACIS, ∼2″⨯2″ for HRC). Rather we used the simpler aperture quantities described in the inequality, under the assumption that for real point sources, the flux associated with a likelihood derived from aperture quantities is related to the actual flux of a source detected at the source detection likelihood threshold, i.e.,

To calibrate this relation, we selected a sample of isolated CSC Release 2.0 point sources and calculated \(p_{\mathrm{min}}\) from the available aperture quantities, using the actual detection likelihoods. We then compared these to actual photon fluxes and energy fluxes, as reported in the corresponding photflux_aper90 or flux_aper90 columns. Results for the b-band are shown in Figure 10.

Figure 10: Aperture Fluxes vs. Source Detection Likelihoods

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Figure 10: Aperture Fluxes vs. Source Detection Likelihoods

Comparison of flux_aper90_b (left) and photflux_aper90_b (right) values vs. \(p_{\mathrm{min}}\), determined using the sources' detection likelihoods, for a sample of isolated point sources.

For all bands, we find the data are well-fit with relations of the form:

Values of \(m\) and \(c\) are given in Table 1 below and may be used to correct sensitivity map values to true limiting sensitivities, in either energy flux or photon flux, as the detection likelihood thresholds.

Sky Coverage

In addition to stack-level sensitivity maps, all-sky maps of limiting sensitivity are constructed by regridding corrected individual maps in HEALPix nested celestial grid with index=16 \(\left(\theta_{\mathrm{pix}} \approx 3.22^{\prime\prime}\right)\). An example HEALPix map for stack acisfJ1509253m585033_001 is shown in Figure 11.

Figure 11: HEALPix Map

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Figure 11: HEALPix Map

Broad band HEALPix map for stack acisfJ1509253m585033_001, for MARGINAL false source rates.

All populated HEALPix pixels are collected in the catalog database. If a particular HEALPix pixel occurs in multiple stacks, the highest sensitivity value (i.e., lowest sensitivity value) is used. Users may then query the database for limiting sensitivity values near positions of interest. All-sky maps are generated for all detection energy bands (b, h, m, s, w), for both MARGINAL and TRUE detection thresholds. The total cumulative sky coverage at the MARGINAL detection thresholds is ∼681 deg² for the ACIS instrument (any energy band) and ∼67 deg² for the HRC instrument (implying ~18 deg² overlap) and is shown as a function of energy flux in Figure 12.

Figure 12: Cumulative Sky Coverage

Figure 12: Cumulative Sky Coverage

False Source Rate

We can demonstrate the performance of the likelihood threshold functions by computing the actual false source rates in the various simulation runs. An example simulated event list from the ACIS-I aimpoint four-ObsID simulation set (acisfJ0025384m122430_001) is shown in Figure 13, and the distribution of likelihoods vs. off-axis angle is shown in Figure 14.

Calculated false source rates for all the simulation sets are given in Table 2. In general, all are consistent with desired rates of 1 false source per field for MARGINAL sources and 0.1 per field for TRUE sources, with the exception of the ACIS-S aimpoint four-ObsID simulation set (acisfJ0839591p294814_001). We note that there is an excess of detections in the vicinity of bad columns in Chip 8, as shown in Figure 15. If these detections are excluded, the false source rates for this simulation set agree with those in the other sets.

Figure 13: ACIS-I Aimpoint Simulation Set (acisfJ0025384m122430_001)

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Figure 13: ACIS-I Aimpoint Simulation Set (acisfJ0025384m122430_001)

Example simulated event list for ACIS-I aimpoint simulation set comprising four ObsIDs and a total stack exposure of ∼132.7 ks. FALSE (red), MARGINAL (green), and TRUE (blue) sources for all runs of this simulation are indicated.

Figure 14: Detection Likelihoods from ACIS-I Aimpoint Simulation Set (acisfJ0025384m122430_001)

Figure 14: Detection Likelihoods from ACIS-I Aimpoint Simulation Set (acisfJ0025384m122430_001)

Detection likelihoods for sources detected in ∼150 simulation runs of an ACIS-I aimpoint simulation set comprising four ObsIDs and a total stack exposure of ∼132.7 ks. FALSE (red), MARGINAL (green), and TRUE (blue) detections for all runs are shown.

Figure 15: ACIS-S Aimpoint Simulation Set (acisfJ0839591p294814_001)

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Figure 15: ACIS-S Aimpoint Simulation Set (acisfJ0839591p294814_001)

The ACIS-S aimpoint simulation set comprising four ObsIDs and a total stack exposure of ∼292.0 ks shows an excess of detections in Chip 8. FALSE (red), MARGINAL (green), and TRUE (blue) sources for all runs of this simulation are indicated.

Detection Efficiency

We estimate the detection efficiency in CSC 2.1 by comparing the number of source detections in individual observations that are part of the Chandra Deep Field South Survey to the number of sources reported in that survey's 7 Ms catalog (Luo et al., 2017 ApJS 228 2). The CDFS sources are derived from an analysis of stacked Chandra ACIS-I images, totaling ∼7 Ms, and so can be considered complete at the exposures of individual observations. We have selected three individual ACIS-I observations, ObsIDs 12047, 12054 and 17535, with exposures of ∼10, ∼60, and ∼120 ks, respectively. We extracted the CDFS sources which lie in the fields-of-view of each of these observations and constructed histograms of fluxes in the CDFS "full" band (0.5–7.0 keV). We then constructed similar histograms using only CDFS sources which would be classified as MARGINAL or TRUE in the CSC 2.1 source detection lists for those observations. The ratio of the two distributions provides estimates of the detection efficiency. Examples of detection efficiency curves for sources in two ranges of off-axis angle, \(0 < \theta \leq 6^{\prime}\) and \(\theta > 6^{\prime}\), are shown in Figure 16.

Figure 16: Detection Efficiency vs. Flux

Figure 16: Detection Efficiency vs. Flux

Detection Efficiency for ACIS-I observations of ∼10, ∼60, and ∼120 ks. Typical error bars are indicated for each curve.