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% memo_lsf_lh_1.0.tex
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% Usage:
% latex memo_lsf_lh_1.0.tex
%
% Description:
% This document describes the quality of LSFPARM file for
% TG-unrandomized event datasets.
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% Input:
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% Output:
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% Notes:
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% History:
% 02 May 04, created (v1.0)
%-
\documentclass{article}
\usepackage{cxo-memo-logo}
\usepackage[dvips]{graphics,graphicx}
\usepackage{gea}
\usepackage{psfig}
\newcommand{\lsf}{LSFPARM}
\newcommand{\tgres}{tg\_resolve\_events}
\newcommand{\hpe}{hrc\_process\_events}
\newcommand{\apeb}{acis\_process\_events}
\begin{document}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0. Header
\memobasic{Dale Graessle, CALDB lead}{
Bish K. Ishibashi, SDS }{
Evaluation on the quality of LETG/HRC-S LSFPARM file for unrandomized event datasets}{
1.0 }{http://space.mit.edu/CXC/docs/memo\_lsf\_lh\_1.0.ps}{
/nfs/cxc/h2/bish/CXC\ SDS/LSFDIR/HO\_LSF\_HA/memo\_lsf\_lh\_1.0.tex}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1. Theme
\section{Unrandomized LSFPARM files for LETG/HRC-S Configuration}
\noindent
In Repro {\em{III}}, decisions have been made to turn off data randomization
on TG R/D. This action necessitates rapid development of line spread function
parameter files (LSFPARM) without built-in data randomization. By applying the
similar LSF processing scheme\footnote{See an example in https://icxc.harvard.edu/calco/ard\_updates/ECR/Approved\_ECRs/ECR\_2002\_016.html},
new LSFPARM files for LETG+HRC-S configuration have been developed. This document
describes the quality of the new LSFPARM products.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2. Procedure to build LSFPARM
\section{ Building LSFPARM }
\noindent
Procedures for building a LSFPARM file is described at: \\
\hspace{10mm}{http://space.mit.edu/CXC/LSFX/LSF\_valid2.html} \\
\vspace{3mm}
\noindent
For rapid development, several parts of IDL parameterization routines
are S-Langified for better and faster convergence to optimum fitting
parameters through automated processes.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3. Products
\section{ Data products }
\noindent
Two LSFPARM products are developed: LEG $\pm$ 1$^{st}$ orders
configuration with LETG+HRC-S without data randomization in TG coordinate.
Evaluation of the four products are documented in the following section.
\subsection{ Header Keyword for Data Randomization }
Two new FITS header keywords -- RAND\_TG and CBD60001 -- are included
in each LSFPARM product in order to specify whether LSFPARM products is
for randomized or not. For unrandomized dataset, these header
keywords are set to the values as listed in Table 1. These keywords
would enable to form proper CALDB query expression and to search for
unrandomized LSFPARM products.
\begin{table}
\begin{center}
\begin{tabular}{ccl}
\multicolumn{3}{c}{Table~1. New header keywords for LSFPARM} \\
\hline
\hline
Keyword & Value & Comment \\
\hline
RAND\_TG & 0.0 & No data randomization in TG values \\
CBD60001 & RAND\_TG(0.0) & CALDB query expression \\
\hline
\end{tabular}
\end{center}
\end{table}
\subsection{ Caveats on Data Randomization in HRC data system }
Technically speaking, data randomization adds no effective data blur
when applied onto any dataset taken with HRC detectors\footnote{http://hea-www.harvard.edu/$\sim$jdrake/memo/random/}. Hence the existing LSFPARM for LETG+HRC-S may be
valid to both randomized and unrandomized LETG+HRC-S datasets.
\noindent
However, the old products contain LSFPARM with only one extraction width,
hence limiting the way any LETG+HRC-S dataset is calibrated for analysis.
The new products contains, however, contains ten different extraction widths,
hence making it more versatile for custom extraction by users.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4. Testing
\section{ Testing LSFPARM products}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.1 Procedure for testing
\subsection{ Procedures }
\noindent
Testing of the LSFPARM products are performed with MARX simulated and
real Capella (ObsID 1248) datasets. Two key points of our interests
are (1) line profile and (2) encircled energy fractions (hereafter
EEFRAC).
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.2 Testing with Simulated Datasets
\subsection{ Evaluation I. MARX-Simulated Dataset }
\noindent
Mono-energetic beam simulations are performed with MARX at various
energy values and concatenated together to make a L1 event file.
The L1 file has gone through nominal CIAO processing, except that
pixel randomization in TG space being turned off at {\em{\tgres}}.
Corresponding grating RMF files are generated via {\em{mkgrmf}} command
with the new LSFPARM files and used as a fitting kernel in {\em{ISIS}}
for evaluation. Cash statistics is applied throughout this work.
\subsubsection{ Line Profile Analysis }
\noindent
If the LSFPARM products are valid, simulated line profiles can be
described with a Kronecker delta function folded over grating RMFs.
Figures 1 and 2 show several line profiles fitted with a delta
function. For brevity, selected six of 14 line samples are shown in
each figure for inspection: lines at E = 80, 120, 275, 450, 800, and 1500 eV.
These are representative of the results of other line profile fittings,
resulting in the value of goodness of fit generally less than
1.5 for LEG (these are not meant to be necessarily the best fitting results).
\vspace{3mm}
\noindent
Despite unusually high S/N ratio in these line profile simulations,
the model fitting has resulted in the low ${\chi}^{2}$ values and
hence the results validate that the LSF parameterization works
here just as well as with the HETG configuration system.
\subsubsection{Encircled Energy Fraction}
\noindent
The second key component of LSFPARM products is the value of
encircled energy fraction as a function of energy.
The value EEFRAC is derived from cross-dispersion line
profile of a mono-energetic beam, integrated over arbitrary
extraction width centered around the line peak (or in Chandra's
term, at TG\_D = 0 degree). If derived correctly, EEFRAC will
allow users to correct measured count rates (or fluxes) for
the aperture of the extraction.
\vspace{3mm}
\noindent
The following tests are performed such that the simulated line spectra
(samples shown in Figures 1 and 2) are extracted at three different aperture
widths; then the delta-function model is fitted to 14 mono-energetic lines
in order to derive model line fluxes $F_m$ in counts~s$^{-1}$. ISIS is also
enabled to provide cumulative counts in each line, which is used to derive
a ``observed'' line flux $F_d$. In an ideal condition, both the model
and observed line fluxes should be identical, i.e.,
$$ {F_d \over{F_m}} \approx 1. $$
\vspace{3mm}
\noindent
Two LEG configurations (LEG $\pm$ 1st) are tested and verified
that the new LSFPARM products meet this criterion within a few percentage
(see Tables 2 and 3), presumably better than our knowledge in effective area
of Chandra's HRMA system.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.3 Testing with Real Datasets
\subsection{ Evaluation II. Chandra Dataset }
\noindent
The same four LSFPARM products are tested against real Chandra
observation (Capella, ObsID = 1248) in the similar manner as
performed on the simulated datasets.
\subsubsection{ Line Profile Analysis }
\noindent
Instead of using a delta function, thermal X-ray APED model and simple
Gaussian function are fitted on the emission spectrum of Capella.
Eight to ten bright emission lines -- Mg~XII ($\lambda$ 8.421),
Fe~XVII ($\lambda\lambda$ 15.014 and 103.937), O~VIII ($\lambda$ 18.9),
N~VII ($\lambda$ 24.78), Fe~XIX ($\lambda\lambda$ 45.0328 and 108.37),
Fe~XVI ($\lambda$ 54.728), Fe~XVIII ($\lambda$ 93.923),
and Fe~IX ($\lambda$ 171.073) -- are selected for testing.
Upon fitting the parameter for line width $dv$ (converted to velocity
scale in km~s$^{-1}$) is allowed to vary. Ideally the parameter $dv$
should be $\approx$ 0 km~s$^{-1}$ for thermal APED modeling; however,
for Gaussian fitting, the value $dv$ is expected to be $\ge$ 0~km~s$^{-1}$
as most of these lines are either H-like doublet lines or blended with
other weak atomic lines. The results of fitting with the APED model
is tabulated in Tables 4 and 5; likewise, the results with the Gaussian
model in Tables 6 and 7. Corresponding figures for line profile fit
are shown in Figures 3 and 4 for the APED model and in Figures 5 and 6
for the Gaussian model . These are, once again, not meant to be the best
fitting parameters.
\vspace{3mm}
\noindent
Upon inspection of Tables 4 and 5, it is noted that the measured line
width is consistent with 0 km~s$^{-1}$ for the most of lines. Several
measured lines in the outer plate show non-zero widths, although the
width is below the resolution limit ($\sim$ 0.05\AA). One exception
is a a N~VII $\lambda$ 24.78 that show a broader width ($\sim$ 300km~s$^{-1}$,
including the range of error into consideration) in all of the line measurements.
It is possible that this particular line originates from the extended region
of stellar coronae.
\vspace{3mm}
\noindent
The same practice with the Gaussian model is repeated and their results
show all positive measured line widths, which is expected from blended
lines. However the measured widths are not considerably broad (i.e.,
not greater than ~100~km~s$^{-1}$), except for the N~VII line in LEG -1st order.
\vspace{3mm}
\noindent
Figures 3 -- 6 show the results of line profile fitting. While the
strongest line, Fe~XVII $\lambda$ 15.014, shows some significant
residuals in all the line models, other line profile models
have resulted in a reasonably good fit. It is not clear that my
model for the Fe~XVII is quite adequate; furthermore, the model
fit to the simulated line near 15\AA does not show any significant
residual. Hence this particular line model needs to be re-evaluated
first via a collaboration with LETG+HRC. If the model is determined
to be correct, then the MARX model may need to be improved to account
for the discrepancy.
\vspace{3mm}
\noindent
In any other cases, the LSFPARM products can provide decent description
of the observed line profiles.
\subsubsection{Encircled Energy Fraction}
\noindent
Lastly the model EEFRAC values need to be compared with the observed ones.
Here we first compute the theoretical EEFRAC values at three different aperture
widths based on the new LSFPARM products. Then at the same aperture widths
extract spectra from observed event datasets. The same Capella dataset (ObsID 1248)
is chosen for this exercise. Since absolute spectral energy
distributions of the target is not known, the ratio of two entities
are compared instead. Here in this exercise, the ratio of the observed
spectra ``Extraction B'' (at a width equivalent to EEFRAC = 80\% at E = 1.497keV)
to ``Extraction A'' (similarly at EEFRAC = 90.5\%, or nearly at CIAO default
extraction width) is compared with the theoretical counterpart. The same
exercise is repeated for ``Extraction C'' (at EEFRAC = 60\%) as well.
\vspace{3mm}
\noindent
Due to high detector background noise, the background events are measured and
subtracted out prior to the analysis. Furthermore, the total cumulative counts
in this dataset is fairly low and therefore the ratio value may blow up at
several bins as the numerator being divided by zero. For that reason, the
comparisons are made in a base-10 logarithmic space.
\vspace{3mm}
\noindent
If the EEFRAC values in the LSFPARM products are derived properly,
the ratio (as a function of wavelength) should be consistent to each other.
Figure 7 shows the ratio plots for every LETG configuration derived
with the Capella dataset. As shown in the figure, the model trend agrees fairly
well with the observed trend for all cases.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 5.
\section{ Summary }
\noindent
All the testings show that the quality of these new LSFPARM products
for unrandomized datasets are equally as good as the other LSFPARM
products produced through the same LSF generation scheme. While some
anomalous differences are found in both line profile and EEFRAC analyses,
the difference may originate due to some unidentified calibration issues
not included in the current MARX distribution.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\clearpage
\begin{table}
\begin{center}
\begin{tabular}{rccc}
\multicolumn{4}{c}{Table~2. LEG +1st: the Data-to-Model flux ratio} \\
\hline
\hline
\
Energy & & Widths & \\
(eV) & &(radian)& \\
& 2.79e-4 &1.60e-3 &1.84e-2 \\
\hline
80 & 1.01 & 1.00 & 1.00 \\
90 & 1.01 & 1.05 & 1.00 \\
100 & 1.02 & 1.00 & 1.01 \\
120 & 1.01 & 1.00 & 1.00 \\
200 & 1.01 & 1.00 & 1.00 \\
275 & 1.01 & 1.00 & 1.00 \\
350 & 1.01 & 1.00 & 1.00 \\
450 & 1.00 & 1.00 & 1.00 \\
600 & 1.01 & 1.01 & 1.01 \\
800 & 1.00 & 1.00 & 1.00 \\
1000 & 1.00 & 1.05 & 1.00 \\
1200 & 1.00 & 1.00 & 1.00 \\
1500 & 1.00 & 1.00 & 1.00 \\
2000 & 1.00 & 1.00 & 1.00 \\
\hline
\end{tabular}
\end{center}
\end{table}
\begin{table}
\begin{center}
\begin{tabular}{rccc}
\multicolumn{4}{c}{Table~3. LEG -1st: the Data-to-Model flux ratio} \\
\hline
\hline
\
Energy & & Widths & \\
(eV) & &(radian)& \\
& 2.79e-4 &1.60e-3 &1.84e-2 \\
\hline
80 & 1.01 & 1.01 & 1.01 \\
90 & 1.01 & 1.01 & 1.01 \\
100 & 1.01 & 1.00 & 1.00 \\
120 & 1.01 & 1.01 & 1.01 \\
200 & 1.01 & 1.00 & 1.00 \\
275 & 1.00 & 1.00 & 1.00 \\
350 & 1.00 & 1.00 & 1.00 \\
450 & 1.00 & 1.00 & 1.00 \\
600 & 1.00 & 1.00 & 1.00 \\
800 & 1.00 & 1.00 & 1.00 \\
1000 & 1.04 & 1.02 & 1.02 \\
1200 & 1.00 & 1.00 & 1.00 \\
1500 & 1.00 & 1.00 & 1.00 \\
2000 & 1.00 & 1.00 & 1.00 \\
\hline
\end{tabular}
\end{center}
\end{table}
\clearpage
\begin{table}
\begin{center}
\begin{tabular}{lccccl}
\multicolumn{6}{c}{Table~4. Capella LEG +1st: thermal APED model. } \\
\hline
\hline
\
Element& $\lambda_{lab}$ & $dv$ & $dv$ 3$\sigma$ range & ${\chi}^{2}$ & Comment \\
& (\AA) & (km/s) & & & \\
\hline
Mg~XII & 8.4192 & 0 & 0 -- 200 & 1.34 & H-like doublet lines \\
Fe~XVII& 15.014 & 0 & 0 -- 47.6 & 9.21 & Seems blended with an unidentified line \\
O~VIII & 18.90 & 0 & 0 -- 103 & 3.34 & H-like doublet lines \\
N~VII & 24.78 & 0 & 0 -- 281 & 2.06 & Extended line emission? \\
Fe~XIX & 45.0328 & 0 & 0 -- 135 & 0.994 & blended with Fe~XXIV? \\
Fe~XVI & 54.7280 & 0 & 0 -- 113 & 1.49 & \\
Fe~XVIII& 93.923 & 18.8 & 0 -- 55.4 & 1.54 & \\
Fe~XVII& 103.937 & 73.4 & 34.4 -- 106 & 1.31 & \\
Fe~XIX & 108.37 & 88.0 & 29.8 -- 101 & 1.02 & \\
Fe~IX & 171.073 & 76.6 & 29.5 -- 140 & 1.13 & \\
\hline
\end{tabular}
\end{center}
\end{table}
\begin{table}
\begin{center}
\begin{tabular}{lccccl}
\multicolumn{6}{c}{Table~5. Capella LEG -1st: thermal APED model. } \\
\hline
\hline
\
Element& $\lambda_{lab}$ & $dv$ & $dv$ 3$\sigma$ range & ${\chi}^{2}$ & Comment \\
& (\AA) & (km/s) & & & \\
\hline
Mg~XII & 8.4192 & 54.0 & 0 -- 651 & 0.99 & H-like doublet lines \\
Fe~XVII& 15.014 & 8.75 & 0 -- 166 & 5.47 & Seems blended with an unidentified line \\
O~VIII & 18.90 & 0 & 0 -- 106 & 3.46 & H-like doublet lines \\
N~VII & 24.78 & 294 & 150 -- 455 & 1.07 & Extended line emission? \\
Fe~XIX & 45.0328 & 0 & 0 -- 141 & 1.11 & blended with Fe~XXIV? \\
Fe~XVI & 54.7280 & -- & -- & -- & chip gap \\
Fe~XVIII& 93.923 & 25.0 & 0 -- 71.5 & 1.33 & \\
Fe~XVII& 103.937 & 66.0 & 0 -- 93.4 & 1.35 & \\
Fe~XIX & 108.37 & 45.4 & 0 -- 77.0 & 1.26 & \\
Fe~IX & 171.073 & -- & -- & -- & out of chip \\
\hline
\end{tabular}
\end{center}
\end{table}
\clearpage
\begin{table}
\begin{center}
\begin{tabular}{lccccl}
\multicolumn{6}{c}{Table~6. Capella LEG +1st: Simple Gaussian model. } \\
\hline
\hline
\
Element& $\lambda_{lab}$ & $dv$ & $dv$ 3$\sigma$ range & ${\chi}^{2}$ & Comment \\
& (\AA) & (km/s) & & & \\
\hline
Mg~XII & 8.4192 & 61.2 & 0 -- 441 & 1.29 & H-like doublet lines \\
Fe~XVII& 15.014 & 42.1 & 0.78 -- 86.4& 11.0 & Seems blended with an unidentified line \\
O~VIII & 18.90 & 9.48 & 0 -- 98.1 & 2.86 & H-like doublet lines \\
N~VII & 24.78 & 10.5 & 9 -- 126 & 1.09 & Extended line emission? \\
Fe~XIX & 45.0328 & 14.0 & 0.20 -- 122 & 0.906 & blended with Fe~XXIV? \\
Fe~XVI & 54.7280 & 0.414 & 0 -- 98.8 & 1.42 & \\
Fe~XVIII& 93.923 & 32.8 & 17.3 -- 51.0& 1.86 & \\
Fe~XVII& 103.937 & 55.1 & 28.5 -- 78.7& 1.35 & \\
Fe~XIX & 108.37 & 64.3 & 49.2 -- 79.7& 0.975 & \\
Fe~IX & 171.073 & 66.4 & 33.9 -- 95.4& 1.12 & \\
\hline
\end{tabular}
\end{center}
\end{table}
\begin{table}
\begin{center}
\begin{tabular}{lccccl}
\multicolumn{6}{c}{Table~7. Capella LEG -1st: Simple Gaussian model. } \\
\hline
\hline
\
Element& $\lambda_{lab}$ & $dv$ & $dv$ 3$\sigma$ range & ${\chi}^{2}$ & Comment \\
& (\AA) & (km/s) & & & \\
\hline
Mg~XII & 8.4192 & 103 & 0 -- 496 & 1.28 & H-like doublet lines \\
Fe~XVII& 15.014 & 3.73 & 0 -- 144 & 3.21 & Seems blended with an unidentified line \\
O~VIII & 18.90 & 112 & 0 -- 171 & 1.72 & H-like doublet lines \\
N~VII & 24.78 & 237 & 109 -- 361 & 1.18 & Extended line emission? \\
Fe~XIX & 45.0328 & 76.2 & 0.21 -- 143 & 0.758 & blended with Fe~XXIV? \\
Fe~XVI & 54.7280 & -- & -- & -- & chip gap \\
Fe~XVIII& 93.923 & 44.7 & 28.8 -- 58.6& 1.55 & \\
Fe~XVII& 103.937 & 47.6 & 21.7 -- 73.8& 1.44 & \\
Fe~XIX & 108.37 & 48.9 & 32.9 -- 65.2& 1.25 & \\
Fe~IX & 171.073 & -- & -- & -- & out of chip\\
\hline
\end{tabular}
\end{center}
\end{table}
\clearpage
\begin{figure}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/SIML/leg_lp9800_lp1_155AA.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/SIML/leg_lp9800_lp1_103AA.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/SIML/leg_lp9800_lp1_45AA.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/SIML/leg_lp9800_lp1_27AA.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/SIML/leg_lp9800_lp1_15AA.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/SIML/leg_lp9800_lp1_8AA.ps}
\caption{LEG +1st-order line profiles, fitted with a Kronecker delta function (red) folded
over LEG +1st through +11st multi-order grating RMFs: (top right) line profile at E = 80~eV,
with a goodness of fit ${\chi}^2$ = 1.38; (top left) E = 120~eV, ${\chi}^2$ = 1.40;
(middle left) E = 275~eV, ${\chi}^2$ = 1.47; (middle right) E = 450~eV, ${\chi}^2$ = 1.40;
(bottom right) E = 800~eV,${\chi}^2$ =2.00; and (bottom left) E = 1500~eV, ${\chi}^2$ = 0.966.
The delta function model describes simulated line profiles fairly well.
\label{fig1}}
\hfil
\end{figure}
\begin{figure}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/SIML/leg_lp9800_lm1_155AA.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/SIML/leg_lp9800_lm1_103AA.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/SIML/leg_lp9800_lm1_45AA.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/SIML/leg_lp9800_lm1_27AA.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/SIML/leg_lp9800_lm1_15AA.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/SIML/leg_lp9800_lm1_8AA.ps}
\caption{LEG +1st-order line profiles: (top right) line profile at E = 80~eV,
with a goodness of fit ${\chi}^2$ = 1.21; (top left) E = 120~eV, ${\chi}^2$ = 1.68;
(middle left) E = 275~eV, ${\chi}^2$ = 1.27; (middle right) E = 450~eV, ${\chi}^2$ = 1.29;
(bottom right) E = 800~eV,${\chi}^2$ =1.12; and (bottom left) E = 1500~eV, ${\chi}^2$ = 1.53.
\label{fig2}}
\hfil
\end{figure}
\clearpage
\begin{figure}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/REAL/CAPELLA/mgxii_aped_lp1.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/REAL/CAPELLA/fexvii_aped_lp1.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/REAL/CAPELLA/oviii_aped_lp1.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/REAL/CAPELLA/nvii_aped_lp1.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/REAL/CAPELLA/fexix2_aped_lp1.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/REAL/CAPELLA/feix_aped_lp1.ps}
\caption{Selected LEG +1st-order Capella line profiles; (top left) Mg~XII line,
fitted with an APED thermal model (red) and its goodness of fit ${\chi}^2$ = 1.34; (top right)
Fe~XVII with ${\chi}^2$ = 9.21; (middle left) O~VIII with ${\chi}^2$ = 3.34;
(middle right) N~VII with ${\chi}^2$ = 2.06;
(bottom left) Fe~XIX with ${\chi}^2$ = 1.02; and (bottom right) Fe~IX with ${\chi}^2$ = 1.13.
This simplified APED model (not necessarily the best fit) adequately describes the Capella
line spectra, though the atomic model may be lacking in its accuracy, which lead to higher
${\chi}^2$ values.
\label{fig3}}
\hfil
\end{figure}
\begin{figure}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/REAL/CAPELLA/mgxii_aped_lm1.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/REAL/CAPELLA/fexvii1_aped_lm1.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/REAL/CAPELLA/oviii_aped_lm1.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/REAL/CAPELLA/nvii_aped_lm1.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/REAL/CAPELLA/fexix_aped_lm1.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/REAL/CAPELLA/fexvii2_aped_lm1.ps}
\caption{Selected LEG -1st-order Capella line profiles; (top left) Mg~XII
line, fitted with an APED thermal model (red) and its goodness of fit ${\chi}^2$ = 0.99; (top right)
Fe~XVII with ${\chi}^2$ = 5.47; (middle left) O~VIII with ${\chi}^2$ = 3.46;
(middle right) N~VII with ${\chi}^2$ = 1.07;
(bottom left) Fe~XIX with ${\chi}^2$ = 0.758; and (bottom right) Fe~XVII with ${\chi}^2$ = 1.35.
\label{fig4}}
\hfil
\end{figure}
\begin{figure}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/REAL/CAPELLA/fevii_lp1_gau.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/REAL/CAPELLA/oviii_lp1_gau.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/REAL/CAPELLA/nvii_lp1_gau_custom.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/REAL/CAPELLA/fexviii_lp1_gau.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/REAL/CAPELLA/fexix2_lp1_gau.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/REAL/CAPELLA/feix_lp1_gau.ps}
\caption{Selected LEG +1st-order Capella line profiles; (top left) Fe~XVII
line, fitted with a single Gaussian function (red; velocity width $dv \approx$ 42km~s$^{-1}$)
and its goodness of fit ${\chi}^2$ = 11.0;(top right) O~VIII ($dv \approx$ 9.5km~s$^{-1}$)
with ${\chi}^2$ = 2.86; (middle left) N~VII ($dv \approx$ 11km~s$^{-1}$) with ${\chi}^2$ = 1.09;
(middle right) Fe~XVIII ($dv \approx$ 33km~s$^{-1}$) with ${\chi}^2$ = 1.86;
(bottom left) Fe~XIX ($dv \approx$ 64km~s$^{-1}$) with ${\chi}^2$ = 0.975;
and (bottom right) Fe~IX ($dv \approx$ 66km~s$^{-1}$)with ${\chi}^2$ = 1.12.
\label{fig5}}
\hfil
\end{figure}
\begin{figure}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/REAL/CAPELLA/fevii_lm1_gau.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/REAL/CAPELLA/oviii_lm1_gau.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/REAL/CAPELLA/nvii_lm1_gau.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/REAL/CAPELLA/fexviii_lm1_gau.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/REAL/CAPELLA/fexix2_lm1_gau.ps}
\includegraphics[keepaspectratio=true,angle=-90,width=8cm]{PS/REAL/CAPELLA/fexvii2_lm1_gau.ps}
\caption{Selected LEG -1st-order Capella line profiles; (top left) Fe~XVII
line, fitted with a single Gaussian function (red; velocity width $dv \approx$ 3.7km~s$^{-1}$)
and its goodness of fit ${\chi}^2$ = 3.21;(top right) O~VIII ($dv \approx$ 112km~s$^{-1}$)
with ${\chi}^2$ = 1.72; (middle left) N~VII ($dv \approx$ 237km~s$^{-1}$) with ${\chi}^2$ = 1.18;
(middle right) Fe~XVIII ($dv \approx$ 45km~s$^{-1}$) with ${\chi}^2$ = 1.55;
(bottom left) Fe~XIX ($dv \approx$ 49km~s$^{-1}$) with ${\chi}^2$ = 1.25;
and (bottom right) Fe~XVII ($dv \approx$ 48km~s$^{-1}$)with ${\chi}^2$ = 1.44.
\label{fig6}}
\hfil
\end{figure}
\begin{figure}
\includegraphics[keepaspectratio=true,angle=90,width=9cm]{PS/REAL/CAPELLA/eef_val_lp1_80to90.ps}
\includegraphics[keepaspectratio=true,angle=90,width=9cm]{PS/REAL/CAPELLA/eef_val_lp1_60to90.ps}
\caption{Ratio plots of theoretical (gray) and Capella's observed (black) EEFRAC values:
(left) LEG $\pm$1st, the ratio of Extraction B to A; (right) LEG $\pm$1st, the ratio of
Extraction C to A.
\label{fig7}}
\hfil
\end{figure}
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\end{document}