Mn K $\alpha _{1,2}$:L complex ratio

Code was written to ensure that the K:L would be calculated the same way for each additional measurement. For the FI chip S2 this involves fitting a gaussian model to the Mn K $\alpha _{1,2}$ line and a gaussian model to the combined Mn-Fe L feature. The K:L ratio is simply the ratio of the gaussian areas. For the BI chip S3 a gaussian was also fit to the Mn K $\alpha _{1,2}$ line. The poorer low energy spectral response required a more complicated function to accurately fit the L complex: a gaussian model with constant, linear and quadratic terms. The K:L ratio is still the ratio of the gaussian areas.

  

Figure 4.113: Contour map of ICM Mn K $\alpha _{1,2}$ events from three different measurements.

Table 4.79 presents the ratios for one S2 quadrant and three S3 quadrants from three different measurements. The quoted errors are 1 $\sigma$ Poisson errors. For S2, the ratios are consistent within the errors, while for S3 the values show a larger than statistical variation. The mean and standard deviation of the nine points are 106.6 $\pm$ 5.16, clearly demonstrating that there is some unaccounted for systematic effect. If we disregard the highest and lowest values, the mean and standard deviation are 106.0 $\pm$ 2.30, closer to, but still higher than statistical fluctuations. The large difference between the BI and FI ratio is due to the BI's higher low energy quantum efficiency. Since we know the QE of both chips, the intrinsic K:L ratio can be calculated from both sets of data and compared as an additional check. We measure

$$\begin{eqnarray*}R_{FI} = \frac{QE^{FI}_{Mn K\alpha}}{QE^{FI}_{L complex}} \time... ...{QE^{BI}_{Mn K\alpha}}{QE^{BI}_{L complex}} \times \frac {K}{L} \end{eqnarray*}$$

where R_i is the K:L ratio for the BI or FI chip, QEⁱ_j is the quantum efficiency for the i^th chip at energy j, and $\frac{K}{L}$ is the intrinsic Mn K $\alpha _{1,2}$ to Mn-Fe L complex ratio. Since the L complex is a blend of lines, we approximate the low energy QE as the average of the mean QE's at Mn L and Fe L, which themselves are weighted averages of the various L lines. Table 4.80 lists the appropriate quantum efficiencies, the measured ratios, and the calculated intrinsic ratios. While the ratios are much closer to agreeing, there is still a $\sim$15% discrepancy. If we then consider that BI $\frac{K}{L}$ value should be higher, due to the addition of the O K$\alpha$and Cr L flux in the L complex (see Section 2 for details), the discrepancy becomes larger. At the same time, however, our approximation laden method clearly over-simplifies the situation. Our averaging of discrete QE values over a wide energy pass band introduces errors into the low energy QE. Also, our simplistic gaussian + background model of the L complex cannot account for the complicated spectral redistribution function of the BI. A reliable, exact comparison demands that an accurately modeled ICM source spectrum be folded through both the BI and FI response matrices.

 

Table 4.79: Mn K $\alpha _{1,2}$:Mn-Fe L complex ratios

		S2	S3
Location	Date	Quad D	Quad A	Quad B	Quad C
XRCF-I	01Jun97	293.9 $\pm$ 5.82	109.1 $\pm$ 1.04	103.8 $\pm$ 0.97	105.7 $\pm$ 1.20
ISIM-TV2	16Jan98	278.8 $\pm$ 9.65	104.3 $\pm$ 1.74	108.9 $\pm$ 1.85	117.8 $\pm$ 2.55
AXAF-TV	16May98	287.3 $\pm$ 3.81	106.5 $\pm$ 0.68	99.33 $\pm$ 0.62	103.6 $\pm$ 0.80

 

 

Table 4.80: The intrinsic strength of the Mn K $\alpha _{1,2}$ line to the L complex

	Quantum Efficiency		Measured	Intrinsic
Chip	<0.674 keV >	5.895 keV	Ratio (R)	Ratio ( $\frac{K}{L}$)
FI	0.365	0.910	287	115
BI	0.952	0.747	106	135