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The procedure

The procedure is based on the Maximum Likelihood method, assuming all noise to be Poissonian. This is necessary in all cases where the number of counts that constitute the spectrum is very small (Cash 1979, ApJ 228, 939). From this assumption the probability for a model of an emission line spectrum to represent the measured spectrum is derived. The likelihood is used as a criterion for optimizing the parameters of the theoretical spectrum in order to obtain extremal likelihood values.
The point of this program is that the instrumental background is never subtracted thus conserving the basic assumption of Poissonian statistics. Instead, the theoretical spectrum is derived by summing up background and lines and comparing the sum with the measured spectrum without background subtraction.

The theoretical emission line spectrum consists of the designated number of lines with the designated profile function $g_{i,j}$ (presently only Gauss, Lorentz or combinations of these). The line positions and widths must be indicated, and will be optimized with an ordinary minimizing procedure (Powell), if desired. Best line fluxes are always calculated iterating the fixed point equation:

\begin{displaymath}
a_{j,_{new}}=\sum^N_{i=1}n_i\frac{a_{j,_{old}}g_{i,j}}{c_{i,_{old}}}\ .
\end{displaymath} (1)

with line fluxes $a_j$, the measured spectrum $n_i$ and the theoretical spectrum $c_i=sbg+bg_i+\sum_{j=1}^{M}a_j g_{i,j}$ with a constant source background $sbg$ and the instrumental background $bg_i$. For more details the draft of a paper is enclosed in the distribution.



Subsections
next up previous contents
Next: Constraining the fit Up: Manual for Cora line Previous: Format summary   Contents
Jan-Uwe Ness
2003-05-23