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Next: The Stellar X-ray Polarimeter Up: Determining the Feasibility of Previous: Detection of Point Sources

   
Detection of Spectral Lines

Given the good spectral resolution of SIXA and the high throughput of the SODART mirrors, it is expected that one of the principal uses of SIXA will be in the study of spectral lines. In this case, exposure times sufficient for simple source detection will not be adequate. Rather, the required exposure time will depend on the line strength, continuum, and background. Line strength is expressed in terms of Equivalent Width, W, defined as the ratio of the net counts in the line (summed over some energy range $\Delta E$) to the continuum (in counts keV-1) at the line centroid,

\begin{displaymath}W~=~\frac{n_{line}}{CA_{eff}T}. \end{displaymath}

Here, C is the continuum spectrum, in photons cm-2 s-1 keV-1, and Aeff is the effective area at the line energy. The required exposure time is then given by the solution to

\begin{displaymath}\frac{W}{\sigma_W}~=~N_{\sigma}, \end{displaymath}


where



\begin{displaymath}\sigma_W^2~=~\frac{\sigma_{n_{line}}^2}{(CA_{eff}T)^2}~=~ \fr... ...A_{eff}T\Delta E~+~ B_{inst}A_{geom}T\Delta E}{(CA_{eff}T)^2}. \end{displaymath}

Here, Bx-ray  and Binst  are the cosmic and non-X-ray backgrounds (in counts cm-2 s-1 keV-1), and Ageomis the active geometric area of a SIXA pixel (0.67 cm2). The minimum detectable Equivalent Width is then



\begin{displaymath}W_{min}~=~\frac{N_{\sigma}^2}{2CA_{eff}T}\left(1~+~ \sqrt{1~+... ...\Delta E~+~ B_{inst}A_{geom}T\Delta E)}{N_{\sigma}^2}}\right). \end{displaymath}

Typical results for Fe K lines are shown in Figure 70, for a range of exposure times.


  
Figure 57: Array of 19 SIXA Detector Elements. Individual detector elements are labelled with SIXA pixel numbers.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{sixa/sixadet.eps} \end{figure}


  
Figure 58: SIXA Effective Area
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{sixa/sixa-response.ps} \end{figure}


  
Figure 59: SIXA count rates yielding 1 ASCA SIS c s-1, for a power law spectrum. This and subsequent figures (60 - 67) are contour plots of count rate conversions derived from PIMMS. For conversion factors less than 1, one contour per decade is displayed. For factors greater than 1, contour intervals differ by $\sim $30%, on average.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{sixa/sixa_pl_sis.ps} \end{figure}


  
Figure 60: SIXA count rates yielding 1 ASCA GIS c s-1, for a power law spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{sixa/sixa_pl_gis.ps} \end{figure}


  
Figure 61: SIXA count rates yielding 1 ROSAT PSPC c s-1, for a power law spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{sixa/sixa_pl_pspc.ps} \end{figure}


  
Figure 62: SIXA count rates yielding 1 ASCA SIS c s-1, for a thermal bremsstrahlung spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{sixa/sixa_tb_sis.ps} \end{figure}


  
Figure 63: SIXA count rates yielding 1 ASCA GIS c s-1, for a thermal bremsstrahlung spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{sixa/sixa_tb_gis.ps} \end{figure}


  
Figure 64: SIXA count rates yielding 1 ROSAT PSPC c s-1, for a thermal bremsstrahlung spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{sixa/sixa_tb_pspc.ps} \end{figure}


  
Figure 65: SIXA count rates yielding 1 ASCA SIS c s-1, for a blackbody spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{sixa/sixa_bb_sis.ps} \end{figure}


  
Figure 66: SIXA count rates yielding 1 ASCA GIS c s-1, for a blackbody spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{sixa/sixa_bb_gis.ps} \end{figure}


  
Figure 67: SIXA count rates yielding 1 ROSAT PSPC c s-1, for a blackbody spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{sixa/sixa_bb_pspc.ps} \end{figure}


  
Figure 68: SIXA pulse height spectrum simulated with XSPEC. A 5 ksec SIXA observation of a Raymond-Smith plasma with cosmic abundances, emission integral of 1060 cm-3, temperature of 107.5 K, column density of 1021 cm-2, and distance of 10 kpc is simulated.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{sixa/sixaspec.eps} \end{figure}


  
Figure 69: Minimum Count Rate Detectable by SIXA The minimum count rate for a 5$\sigma $ count rate significance is plotted as a function of exposure time, for 3 different background rates (in c s-1) in the central SIXA pixel, using the formula given in section 6.4.4.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{sixa/sixa-minrate.ps} \end{figure}


  
Figure 70: Minimum Equivalent Width at 6 keV detectable by SIXA The minimum detectable equivalent width at 6 keV is plotted as a function of source continuum, for 5 different exposure times in ksec, using the formula given in section 6.4.5. A 5$\sigma $significance is required and background rates of $3\times 10^{-3}$ counts cm-2 s-1 keV-1 (instrumental) and $6.6\times 10^{-7}$ counts cm-2 s-1 keV-1 pixel-1(cosmic) are assumed.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{sixa/sixa-minew.ps} \end{figure}

next up previous contents
Next: The Stellar X-ray Polarimeter Up: Determining the Feasibility of Previous: Detection of Point Sources
Tomas P. Girnius
1999-01-21