9.2 Determining Count Rates from Sensitivities
In this Chapter, specific formulae appropriate for imaging and spectroscopic modes are provided to calculate the expected count rates and the signal-to-noise ratio from the flux distribution of a source. The formulae are given in terms of sensitivities, but we also provide transformation equations between the throughput (QT) and sensitivity (S) for imaging and spectroscopic modes.
Throughputs are presented in graphical form as a function of wavelength for the prisms and for the imaging modes in Chapter 10. Given your source characteristics and the sensitivity of the ACS configuration, calculating the expected count rate over a given number of pixels is straightforward, since the ACS PSF is well characterized. The additional required information is the encircled energy fraction (
f) in the peak pixel, the plate scale, and the dispersions of the grisms and prisms. This information is summarized in Table 9.1, Table 9.2, and Table 9.3.
Table 9.1: Useful quantities for the ACS WFC.
Filter |
Pivot  (Ċ) |
|
AB mag zero point |
|
encircled energy |
Flux in central pixel |
Background sky rate |
F435W |
4317.4 |
0.0744 |
25.67 |
3.18E18 |
0.85 |
0.22 |
0.0284 |
F475W |
4744.3 |
0.1070 |
26.07 |
5.53E18 |
0.86 |
0.21 |
0.0609 |
F502N |
5023.0 |
0.0032 |
22.27 |
1.88E17 |
0.86 |
0.21 |
0.0020 |
F550M |
5581.2 |
0.0362 |
24.89 |
2.59E18 |
0.85 |
0.22 |
0.0280 |
F555W |
5359.6 |
0.0775 |
25.72 |
5.11E18 |
0.86 |
0.21 |
0.0545 |
F606W |
5917.7 |
0.1573 |
26.49 |
1.26E19 |
0.85 |
0.22 |
0.1358 |
F625W |
6310.5 |
0.0915 |
25.90 |
8.37E18 |
0.85 |
0.22 |
0.0825 |
F658N |
6583.9 |
0.0050 |
22.75 |
5.00E17 |
0.85 |
0.22 |
0.0045 |
F660N |
6599.4 |
0.0019 |
21.67 |
1.87E17 |
0.85 |
0.22 |
0.0017 |
F775W |
7693.0 |
0.0731 |
25.65 |
9.93E18 |
0.85 |
0.20 |
0.0780 |
F814W |
8059.8 |
0.0948 |
25.94 |
1.41E19 |
0.83 |
0.19 |
0.1044 |
F850LP |
9054.8 |
0.0352 |
24.86 |
6.63E18 |
0.73 |
0.14 |
0.0415 |
F892N |
8914.9 |
0.0036 |
22.37 |
6.48E17 |
0.77 |
0.15 |
0.0039 |
G800L |
7480.7 |
0.1591 |
26.50 |
2.04E19 |
0.86 |
0.17 |
0.1526 |
CLEAR |
6269.8 |
0.3833 |
27.45 |
3.46E19 |
---- |
0.10 |
0.3580 |
Table 9.2: Useful quantities for the ACS HRC.
Filter |
Pivot  (Ċ) |
|
AB mag zero point |
|
encircled energy |
Flux in central pixel |
Background sky rate |
F220W |
2255.3 |
0.0106 |
23.55 |
1.23E17 |
0.79 |
0.17 |
0.0001 |
F250W |
2715.8 |
0.0123 |
23.72 |
2.09E17 |
0.82 |
0.16 |
0.0003 |
F330W |
3362.7 |
0.0172 |
24.08 |
4.47E17 |
0.84 |
0.16 |
0.0006 |
F344N |
3433.7 |
0.0017 |
21.59 |
4.67E16 |
0.84 |
0.16 |
0.0001 |
F435W |
4311.0 |
0.0436 |
25.09 |
1.86E18 |
0.86 |
0.17 |
0.0043 |
F475W |
4775.7 |
0.0650 |
25.53 |
3.40E18 |
0.85 |
0.17 |
0.0120 |
F502N |
5022.9 |
0.0021 |
21.82 |
1.24E17 |
0.85 |
0.17 |
0.0003 |
F550M |
5579.8 |
0.0234 |
24.42 |
1.67E18 |
0.85 |
0.15 |
0.0048 |
F555W |
5356.0 |
0.0503 |
25.25 |
3.31E18 |
0.85 |
0.16 |
0.0099 |
F606W |
5888.0 |
0.0983 |
25.98 |
7.82E18 |
0.85 |
0.14 |
0.0238 |
F625W |
6295.5 |
0.0557 |
25.36 |
5.07E18 |
0.84 |
0.13 |
0.0148 |
F658N |
6583.7 |
0.0030 |
22.18 |
2.98E17 |
0.83 |
0.13 |
0.0008 |
F660N |
6599.1 |
0.0011 |
21.11 |
1.11E17 |
0.83 |
0.13 |
0.0003 |
F775W |
7665.1 |
0.0380 |
24.94 |
5.13E18 |
0.78 |
0.11 |
0.0111 |
F814W |
8115.3 |
0.0521 |
25.29 |
7.88E18 |
0.76 |
0.10 |
0.0161 |
F850LP |
9145.2 |
0.0228 |
24.39 |
4.37E18 |
0.68 |
0.08 |
0.0075 |
F892N |
8916.1 |
0.0022 |
21.87 |
4.09E17 |
0.73 |
0.09 |
0.0007 |
G800L |
7506.4 |
0.0924 |
25.91 |
1.20E19 |
0.81 |
0.07 |
0.0250 |
PR200L |
5650.2 |
0.2756 |
27.10 |
2.02E19 |
0.80 |
0.16 |
0.0624 |
CLEAR |
5472.0 |
0.3205 |
27.26 |
2.20E19 |
---- |
0.12 |
0.0683 |
Table 9.3: Useful quantities for the ACS SBC.
Filter |
Pivot  (Ċ) |
|
AB mag zero point |
|
encircled energy |
Flux in central pixel |
Background sky rate |
F115LP |
1406.1 |
0.0147 |
23.92 |
6.70E16 |
0.83 |
0.11 |
0.0238 |
F122M |
1273.8 |
0.0010 |
20.95 |
3.56E15 |
0.82 |
0.09 |
0.0042 |
F125LP |
1437.5 |
0.0122 |
23.71 |
5.80E16 |
0.83 |
0.12 |
0.0027 |
F140LP |
1527.0 |
0.0069 |
23.09 |
3.68E16 |
0.84 |
0.13 |
0.0000 |
F150LP |
1610.7 |
0.0038 |
22.45 |
2.27E16 |
0.84 |
0.14 |
0.0000 |
F165LP |
1757.9 |
0.0010 |
21.02 |
7.29E15 |
0.85 |
0.16 |
0.0000 |
PR110L |
1429.4 |
0.0120 |
23.69 |
5.62E16 |
0.86 |
0.26 |
0.0129 |
PR130L |
1438.8 |
0.0120 |
23.68 |
5.66E16 |
0.87 |
0.28 |
0.0027 |
In each Table, the following quantities are listed:
- The pivot wavelength, a source-independent measure of the characteristic wavelength of the bandpass, defined such that it is the same if the input spectrum is in units of F
or F
:
- The integral
Q
T
d
/
, used to determine the count rate when given the astronomical magnitude of the source.
- The ABmag zero point, defined as the AB magnitude of a source with a constant F
that gives 1 count/second with the specified configuration.
- The sensitivity integral, defined as the count rate that would be observed from a constant F
source with flux 1 erg/cm/second/Ċ.
- The encircled energy, defined as the fraction of PSF flux enclosed in the default photometry aperture 0.2 arcseconds for the WFC and HRC, and 0.5 arcseconds for the SBC. These correspond approximately to 5 ×5, 9 ×9, and 15 ×15 box-sizes respectively.
- The fraction of PSF flux in the central pixel, useful for determining the peak count rate to check for overflow or bright object protection possibilities.
- The sky background count rate, which is the count rate that would be measured with average zodiacal background, and average earthshine. It does not include the contribution from the detectors, tabulated separately in Table 9.5.
Here, we describe how to determine two quantities:
- The counts/second (C) from your source over some selected area of Npix pixels, where a signal of an electron on a CCD is equivalent to one count.
- The peak counts/second/pixel (Pcr) from your source, which is useful for avoiding saturated CCD exposures, and for assuring that SBC observations do not exceed the bright-object limits.
We consider the cases of point sources and diffuse sources separately in each of the imaging and spectroscopy sections following.
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