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Detection of Point Sources

 

The total background per 2$^{\prime}$ diameter sperture in a $\sim $10 ksec observation is likely to be $\mathrel{\copy\simgreatbox}$100 counts for LEPC and $\mathrel{\copy\simgreatbox}$30 counts for HEPC. Therefore, Gaussian statistics can be used to estimate the minimum count rate, Rmin, required to detect a point source at a given count rate significance, as a function of exposure time T. For a point source on-axis, Rmin is given by the solution to

\begin{displaymath}N_{\sigma}~=~\frac{R_{min}fT}{\sqrt{R_{min}fT~+~R_BT}}, \end{displaymath}


or



\begin{displaymath}R_{min}fT~=~\frac{N_{\sigma}^2}{2}\left(1~+~\sqrt{1~+~\frac{4R_BT}{N_{\sigma}^2}}\right). \end{displaymath}

Here, $N_{\sigma}$ is the signal-to-noise ratio of the net source counts, expressed as number of $\sigma $, f is the encircled energy fraction (0.5 on-axis), and RB is the total background rate in the aperture. Results are shown in Figure 53 for LEPC, and Figure 54 for HEPC, for a range of background rates.


  
Figure 22: HEPC/LEPC Effective Area. The solid curve shows the effective area of one MM with the LEPC and the dashed curve shows the effective area of one MM with the HEPC.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/hepclepc_area.eps} \end{figure}


  
Figure 23: HEPC/LEPC Spatial Response. For an 8 m focal length, 1 mm corresponds to $0.43^{\prime}$.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/spatresp.ps} \end{figure}


  
Figure 24: HEPC count rates yielding 1 ASCA SIS c s-1, for a power law spectrum. This and subsequent figures (25 - 50) are contour plots of count rate conversions derived from PIMMS.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/hepc_pl_sis.ps} \end{figure}


  
Figure 25: HEPC count rates yielding 1 ASCA GIS c s-1, for a power law spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/hepc_pl_gis.ps} \end{figure}


  
Figure 26: HEPC count rates yielding 1 ROSAT PSPC c s-1, for a power law spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/hepc_pl_pspc.ps} \end{figure}


  
Figure 27: HEPC count rates yielding 1 ASCA SIS c s-1, for a thermal bremsstrahlung spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/hepc_tb_sis.ps} \end{figure}


  
Figure 28: HEPC count rates yielding 1 ASCA GIS c s-1, for a thermal bremsstrahlung spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/hepc_tb_gis.ps} \end{figure}


  
Figure 29: HEPC count rates yielding 1 ROSAT PSPC c s-1, for a thermal bremsstrahlung spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/hepc_tb_pspc.ps} \end{figure}


  
Figure 30: HEPC count rates yielding 1 ASCA SIS c s-1, for a blackbody spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/hepc_bb_sis.ps} \end{figure}


  
Figure 31: HEPC count rates yielding 1 ASCA GIS c s-1, for a blackbody spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/hepc_bb_gis.ps} \end{figure}


  
Figure 32: HEPC count rates yielding 1 ROSAT PSPC c s-1, for a blackbody spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/hepc_bb_pspc.ps} \end{figure}


  
Figure 33: LEPC low-band count rates yielding 1 ASCA SIS c s-1, for a power law spectrum. This and subsequent figures (34 - 41) are contour plots of count rate conversions derived from PIMMS.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/lepclo_pl_sis.ps} \end{figure}


  
Figure 34: LEPC low-band count rates yielding 1 ASCA GIS c s-1, for a power law spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/lepclo_pl_gis.ps} \end{figure}


  
Figure 35: LEPC low-band count rates yielding 1 ROSAT PSPC c s-1, for a power law spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/lepclo_pl_pspc.ps} \end{figure}


  
Figure 36: LEPC low-band count rates yielding 1 ASCA SIS c s-1, for a thermal bremsstrahlung spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/lepclo_tb_sis.ps} \end{figure}


  
Figure 37: LEPC low-band count rates yielding 1 ASCA GIS c s-1, for a thermal bremsstrahlung spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/lepclo_tb_gis.ps} \end{figure}


  
Figure 38: LEPC low-band count rates yielding 1 ROSAT PSPC c s-1, for a thermal bremsstrahlung spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/lepclo_tb_pspc.ps} \end{figure}


  
Figure 39: LEPC low-band count rates yielding 1 ASCA SIS c s-1, for a blackbody spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/lepclo_bb_sis.ps} \end{figure}


  
Figure 40: LEPC low-band count rates yielding 1 ASCA GIS c s-1, for a blackbody spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/lepclo_bb_gis.ps} \end{figure}


  
Figure 41: LEPC low-band count rates yielding 1 ROSAT PSPC c s-1, for a blackbody spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/lepclo_bb_pspc.ps} \end{figure}

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Figure 42: LEPC high-band count rates yielding 1 ASCA SIS c s-1, for a power law spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/lepchi_pl_sis.ps} \end{figure}


  
Figure 43: LEPC high-band count rates yielding 1 ASCA GIS c s-1, for a power law spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/lepchi_pl_gis.ps} \end{figure}


  
Figure 44: LEPC high-band count rates yielding 1 ROSAT PSPC c s-1, for a power law spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/lepchi_pl_pspc.ps} \end{figure}


  
Figure 45: LEPC high-band count rates yielding 1 ASCA SIS c s-1, for a thermal bremsstrahlung spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/lepchi_tb_sis.ps} \end{figure}


  
Figure 46: LEPC high-band count rates yielding 1 ASCA GIS c s-1, for a thermal bremsstrahlung spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/lepchi_tb_gis.ps} \end{figure}


  
Figure 47: LEPC high-band count rates yielding 1 ROSAT PSPC c s-1, for a thermal bremsstrahlung spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/lepchi_tb_pspc.ps} \end{figure}


  
Figure 48: LEPC high-band count rates yielding 1 ASCA SIS c s-1, for a blackbody spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/lepchi_bb_sis.ps} \end{figure}


  
Figure 49: LEPC high-band count rates yielding 1 ASCA GIS c s-1, for a blackbody spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/lepchi_bb_gis.ps} \end{figure}


  
Figure 50: LEPC high-band count rates yielding 1 ROSAT PSPC c s-1, for a blackbody spectrum.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/lepchi_bb_pspc.ps} \end{figure}


  
Figure 51: LEPC pulse height spectrum simulated with XSPEC. A 5 ksec LEPC 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{hepclepc/lepcspec.eps} \vspace{0.5in} \end{figure}


  
Figure 52: HEPC pulse height spectrum simulated with XSPEC. A 5 ksec HEPC 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{hepclepc/hepcspec.eps} \vspace{0.5in} \end{figure}


  
Figure 53: Minimum Count Rate Detectable by LEPC. 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 a $2^{\prime }$ diameter aperture on-axis, using the formula given in section 4.4.4.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/lepc-minrate.ps} \vspace{0.5in} \end{figure}


  
Figure 54: Minimum Count Rate Detectable by HEPC. 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 a $2^{\prime }$ diameter aperture on-axis, using the formula given in section 4.4.4.
\begin{figure} \centering\leavevmode \epsfxsize=.95\textwidth \epsfbox{hepclepc/hepc-minrate.ps} \vspace{0.5in} \end{figure}

next up previous contents
Next: The Objective Crystal Spectrometer Up: Determining the Feasibility of Previous: Simulating HEPC/LEPC Spectra
Tomas P. Girnius
1999-01-21