B. Comparison of Wachter and cplinear Background Models

§5.12 describes the Wachter method for modeling the background when the C-statistic is used, and describes the alternative cplinear background model that we use in AE.

We have not invested resources in attempting to fit simulated spectra with the cplinear method to characterize the performance of the method. We have however compared the Wachter and cplinear methods for 900 ACIS sources in the Tr14 star cluster, many of which are weak. For each source, the cplinear model was fit first and those $tbabs*vapec$ model parameters were used as the initial conditions of a second fit using the Wachter model. Figures 11 to 17 compare the $tbabs*vapec$ model parameters and observed fluxes in three bands obtained by the two methods. The general trend is that for many sources the derived plasma temperatures and observed fluxes are lower in the Wachter fit, consistent with the examples shown in Figure 7. The hard band shows the largest flux deficit, consistent with the fit residuals in Figure 7 which tend to be largest in the hard band. The column density results have more scatter, but the Wachter fit tends to give higher values. These experiments do not directly address the biases of each method with regard to the true spectral parameters, but examination of many plots like those in Figure 7 has convinced us that the cplinear fits are a better representation of our ACIS spectra.

Figure 11: Plasma temperatures derived using the Wachter (Y-axis) and cplinear (X-axis) background models for 900 ACIS sources.

Figure 12: Column densities derived using the Wachter (Y-axis) and cplinear (X-axis) background models for 900 ACIS sources. The symbol at $\sim (20,20)$ depicts 98 sources where NH was clipped at its lower bound.

Figure 13: Fluxes (0.5-2 keV, NOT absorption-corrected) derived using the Wachter (Y-axis) and cplinear (X-axis) background models for 900 ACIS sources.

Figure 14: Fluxes (0.5-8 keV, NOT absorption-corrected) derived using the Wachter (Y-axis) and cplinear (X-axis) background models for 900 ACIS sources.

Figure 15: Fluxes (2-8 keV, NOT absorption-corrected) derived using the Wachter (Y-axis) and cplinear (X-axis) background models for 900 ACIS sources.

Figure 16: Hard-band (2-8 keV, NOT absorption-corrected) flux differences between the Wachter and cplinear background models as a function of net counts extracted.

Figure 17: Distributions of flux differences (NOT absorption-corrected) in three bands between the Wachter and cplinear background models.