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Advanced Camera for Surveys Instrument Handbook for Cycle 22 > Chapter 9: Exposure-Time Calculations > 9.2 Determining Count Rates from Sensitivities

 9.2 Determining Count Rates from Sensitivities
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 (εf) in the peak pixel, the plate scale, and the dispersions of the grisms and prisms. This information is summarized in Table 9.1 and Table 9.2 for Side 1. For updates please see the ACS webpage.
 Filter Pivot λ (Å) ∫QλTλ dλ/λ ∫Sλ dλ ABMAG zero point Encircled Energy Flux in Central Pixels Background sky rate (per pixel) F435W 4318.9 0.0739 3.14E+18 25.66 0.85 0.22 0.0302 F475W 4746.9 0.1070 5.49E+18 26.06 0.86 0.21 0.0566 F502N 5023.0 0.0033 1.87E+17 22.27 0.86 0.21 0.0019 F550M 5581.4 0.0366 2.60E+18 24.90 0.85 0.22 0.0275 F555W 5361.0 0.0782 5.12E+18 25.72 0.86 0.21 0.0538 F606W 5921.1 0.1593 1.27E+19 26.49 0.85 0.22 0.1270 F625W 6311.4 0.0930 8.44E+18 25.91 0.85 0.22 0.0827 F658N 6584.0 0.0051 5.05E+17 22.76 0.85 0.22 0.0047 F660N 6599.4 0.0019 1.89E+17 21.68 0.85 0.22 0.0018 F775W 7692.4 0.0744 1.00E+19 25.67 0.85 0.21 0.0779 F814W 8057.0 0.0962 1.42E+19 25.94 0.84 0.19 0.1026 F850LP 9033.1 0.0349 6.48E+18 24.84 0.74 0.15 0.0390 F892N 8914.8 0.0036 6.50E+17 22.37 0.77 0.15 0.0040 G800L 7467.8 0.1611 2.05E+19 26.50 -- -- -- CLEAR 6272.4 0.3857 3.46E+19 27.45 0.85 0.22 0.2934
Table 9.2: Useful quantities for the ACS SBC.
 Filter Pivot λ (Å) ∫QλTλ dλ/λ ∫Sλ dλ ABMAG zero point Encircled Energy Flux in Central Pixel Background sky rate (per pixel) F115LP 1406.6 0.0149 6.70E+16 23.92 0.82 0.11 0.0479 F122M 1273.7 0.0010 3.56E+15 20.95 0.82 0.09 0.0085 F125LP 1438.2 0.0123 5.81E+16 23.71 0.83 0.11 0.0053 F140LP 1528.0 0.0069 3.69E+16 23.09 0.83 0.13 0.0001 F150LP 1612.2 0.0038 2.28E+16 22.45 0.84 0.14 0.0000 F165LP 1762.5 0.0010 7.35E+15 21.03 0.85 0.16 0.0000 PR110L 1430.1 0.0121 5.62E+16 23.69 -- -- -- PR130L 1439.4 0.0120 5.67E+16 23.69 -- -- --
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 Fλ or Fν. Q(λ) is the instrument sensitivity and T(λ) is the filter transmission.
 • The integral ∫QλTλ dλ/λ, used to determine the count rate when given the astronomical magnitude of the source.
 • The sensitivity integral, defined as the count rate that would be observed from a constant Fλ source with flux 1 erg/cm2/second/Å.
 • The ABmag zero point, defined as the AB magnitude of a source with a constant Fν that gives 1 count/second with the specified configuration.
 •
 • 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.
Here, we describe how to determine two quantities:
 1 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.
 2 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.
9.2.1 Imaging
Point Source
For a point source, the count rate, C, can be expressed as the integral over the bandpass of the filter:
Where:
 • A is the area of the unobstructed 2.4 meter telescope (i.e., 45,239 cm2)
 • Fλ is the flux from the astronomical source in erg/second/cm2/Å
 • h is Planck’s constant
 • c is the speed of light
 • The factor λ/hc converts units of ergs to photons.
 • QλTλ is the system fractional throughput, i.e., the probability of detecting a count per incident photon, including losses due to obstructions of the full 2.4 meter OTA aperture. It is specified this way to separate out the instrument sensitivity Qλ and the filter transmission Tλ.
 • εf is the fraction of the point source energy encircled within Npix pixels.
 • Sλ is the total imaging point source sensitivity with units ofcounts/second/Å per incident erg/second/cm2/Å.
The peak counts/second/pixel from the point source, is given by:
Where:
 • Fλ and Sλ are as above.
 • εf(1) is the fraction of energy encircled within the peak pixel.
Again, the integral is over the bandpass.
If the flux from your source can be approximated by a flat continuum (Fλ = constant) and εf is roughly constant over the bandpass, then:
We can now define an equivalent bandpass of the filter (Bλ) such that:
Where:
 • Speak is the peak sensitivity.
 • Bλ is the effective bandpass of the filter.
The count rate from the source can now be written as:
In Tables 9.1 to 9.2, we give the value of for each of the filters.
Alternatively, we can write the equation in terms of V magnitudes:
where V is the visual magnitude of the source, the quantity under the integral sign is the mean sensitivity of the detector+filter combination, and is tabulated in Tables 9.1 to 9.2, and ΑΒν is the filter-dependent correction for the deviation of the source spectrum from a constant Fν spectrum. This latter quantity is tabulated for several different astronomical spectra in Tables 10.3.2 to 10.3 in Chapter 10.
Diffuse Source
For a diffuse source, the count rate (C) per pixel, due to the astronomical source can be expressed as:
Where:
 • Iλ = the surface brightness of the astronomical source, in erg/second/cm2/Å/ arcseconds2.
 • Sλ as above.
 • mx and my are the plate scales along orthogonal axes.
Emission Line Source
For a source where the flux is dominated by a single emission line, the count rate can be calculated from the equation
where C is the observed count rate in counts/second, (QT) is the system throughput at the wavelength of the emission line, F(λ) is the emission line flux in units of erg/cm2/second, and λ is the wavelength of the emission line in Angstroms. (QT)λ can be determined by inspection of the plots in Chapter 10. See Section 9.6.4 for an example of emission-line imaging using ACS.
9.2.2 Spectroscopy
Point Source
For a point source spectrum with a continuum flux distribution, the count rate, C, is per pixel in the dispersion direction, and is integrated over a fixed extraction height in the spatial direction perpendicular to the dispersion:
Where:
 •
 • d is the dispersion in Å/pixel.
 • is the fraction of the point source energy within Nspix in the spatial direction.
 • the other quantities are defined above.
For an unresolved emission line at with a flux of in
erg/second/cm2 the total counts recorded over the Nspix extraction height is:
These counts will be distributed over pixels in the wavelength direction according to the instrumental line spread function.
In contrast to the case of imaging sensitivity , the spectroscopic point source sensitivity calibration () for a default extraction height of Nspix is measured directly from observations of stellar flux standards after insertion of ACS into HST. Therefore, the accuracy in laboratory determinations of for the ACS prisms and grisms is NOT crucial to the final accuracy of their sensitivity calibrations.
The peak counts/second/pixel from the point source, is given by:
Where:
 • is the fraction of energy contained within the peak pixel.
 • the other quantities are as above.

Advanced Camera for Surveys Instrument Handbook for Cycle 22 > Chapter 9: Exposure-Time Calculations > 9.2 Determining Count Rates from Sensitivities