Ruminations Upon the Modeling of X-ray Foregrounds, Backgrounds and Faint Sources

TL;DR

This work develops a comprehensive forward-modeling framework to account for all soft X-ray foregrounds and backgrounds (SFG, CXB, QPB, OOT) in Chandra and XMM observations of galaxy clusters. Implemented in XSPEC with physically motivated components (APEC, phabs) and a detailed PSF and deprojection treatment, the approach enables binless, Poisson-likelihood analyses and marginalization over systematics. Applied to multiple intermediate-to-high redshift clusters, it yields modest gains for bright clusters and substantial improvements in high-background, low-surface-brightness regimes, while also providing a calibration-corrected path for Chandra data. The results validate the forward-modeling method against traditional blank-sky approaches and highlight its relevance for current analyses and future missions (AXIS, NewAthena) in high-background environments.

Abstract

With the goal of extracting as much information as possible from Chandra and XMM-Newton observations of faint, diffuse sources such as galaxy clusters, as well as those of future X-ray telescopes, we present a strategy for forward modeling all the foreground and background signals present in these data. This work leverages widespread efforts to understand the soft X-ray emission from the Galaxy, as well as the cosmic X-ray background and instrument-specific, particle-induced backgrounds. Statistically, a forward model of the foregrounds and backgrounds is preferable to alternatives because it requires no binning of the data, and allows straightforward marginalization over systematic uncertainties. We apply these methods to several galaxy clusters at intermediate-to-high redshifts, spanning a range of masses and morphologies, using Chandra and/or XMM-Newton data. Our results suggest a modest improvement even for relatively bright clusters at these redshifts, and more substantial advantages in the high-redshift, low-surface-brightness regime. We also discuss and provide a simple correction for a time-dependent miscalibration of the Chandra ACIS detectors identified in archival galaxy cluster data.

Figures (17)

• Figure 1: Visualization of a particular Chandra blank-sky spectrum for a $2"$ radius circle, compared with the corresponding generative model. Green points (corresponding to individual events) show the unbinned spectrum. Blue crosses show the spectrum grouped to a minimum of 1 count per bin using the "group min 1" command to the grppha tool. Pink crosses show the same spectrum binned according to the same grouping procedure applied to the corresponding science spectrum. Error bars on these points show the 68.3 percent credible intervals on the spectrum in each bin, assuming uniform and independent priors over the non-negative real line. The black curve shows the model produced by our modification of the Suzuki2108.11234 procedure (see Section \ref{['sec:chqpb']}).
• Figure 2: Top: RASS diffuse background map in the direction of MACS J1423. Circles show the annulus spanning radii of $0.5^\circ$--$1^\circ$ from the cluster position on which we base the ROSAT SFG model. Bottom: SFG brightness within this annulus, relative to the mean, as a function of azimuth. Dashed lines indicate the standard deviation of these points, which are not consistent with a constant value.
• Figure 3: Top: Chandra image of MACS J1423, combining 2 observations. Cyan ellipses show the sources identified by wavdetect, after removing a spurious source at the cluster center. These are not the masks we use in later analysis, which are ObsID-dependent. Bottom: Map of the expected CXB contamination due to undetected sources in the unmasked regions, from blue to yellow with increasing brightness.
• Figure 4: MOS+pn image of MACS J1423 from a single XMM observation. Cyan circles show masks used to remove emission from point-like sources. Within the Chandra field of view (green squares), these are produced based on the wavdetect source parameters and the XMM PSF model.
• Figure 5: Total source counts required for detection with 99 percent probability with wavdetect as a function of the local density of background counts and the angular distance between the source and the aimpoint, based on Monte Carlo simulations with marx. Source and background counts should both be interpreted as Poisson expectation values. These curves were determined for chip ACIS I3 and are applied to both I2 and I3; similar results are derived for use on chips I0--1 and S1--3.