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Cosmic Origins SpectrographInstrument Handbookfor Cycle 22 > Chapter 7: Exposure-Time Calculator (ETC) > 7.6 Examples

7.6
We present a few examples of the way in which the COS ETCs may be used. They illustrate the information that is returned by the ETCs and how they can be used to plan your observations.
7.6.1 A Flat-Spectrum Source
One often does not know the exact spectrum shape of the object to be observed, so the answer to a simple question is desired: how long will it take to achieve a given signal-to-noise ratio at a given wavelength if the flux at that wavelength is specified? The easiest way to determine this is to use a flat spectrum as input. How long will it take to achieve S/N = 10 per resolution element at 1320 for a point source with a flux of 1015 erg cm2 s–1 -1 using a medium resolution grating?
Only the G130M grating covers the desired wavelength at medium resolution, but several choices of central wavelength are available. We select the 1309 setting. We enter these values into the spectroscopic ETC, select the Primary Science Aperture (PSA), select “Exposure time needed to obtain a S/N ratio of 10.0”, enter the specified wavelength of 1320 , and select “Point Source” as the source type. For the spectrum distribution, choose a flat continuum in Fλ. Make sure the reddening, E(B–V), is set to 0. Normalize the target to 10–15 erg cm2 s1 1 at 1320 . The zodiacal light, earthshine, and airglow were not specified, so we choose average values.
When this case is computed with the ETC, we find the required time is 17,660 s; the total count rates are 66 and 271 count s1 in detector Segments A and B, respectively, well below the safety limit; the count rate in the brightest pixel has 0.096 count s1, also well within the safe range (but see below); and the buffer time indicated by the ETC is 7004 seconds (COS.sp.539442).
What if somewhat higher S/N were desired and one were willing to devote 10 HST orbits to the observation? Assuming that each orbit allows 50 minutes of observing time (ignoring the acquisition time here), we find that in 30,000 seconds we will get S/N = 13.0 per resel. Note that (30,000/17,660)1/2 = (13.0/10.0). That is, the S/N ratio scales as t1/2, as stated in Section 7.3.
If a low-resolution observation is acceptable, then one could switch to the G140L grating. With a grating setting of 1105 and S/N = 10 per resel, we find the required exposure time is 2833 s, considerably less than the medium-resolution case required.
Note that the sensitivity of G130M is higher than that of G140L once resolving power is taken into account. In other words, a G130M spectrum that is rebinned to the same resolution as a G140L spectrum can be obtained in less time for a given S/N, although, of course, with diminished wavelength coverage. If only a limited portion of the source’s spectrum is of interest, using G130M is more efficient than using G140L.
These cases also illustrate that the earthshine and zodiacal light are completely negligible in the FUV, unless the target flux is much lower than that considered here. This is also true of the airglow if the wavelength of interest is far from the airglow lines. Of course, the airglow cannot be ignored in terms of the total count rate on the detector, or the local count rate if the source contributes at the same wavelengths as the airglow lines.
This is a toy example. For most targets, a more realistic model spectrum would be used to estimate exposure times and test for bright-object violations.
7.6.2 An Early-Type Star
We wish to observe an O5V star at medium spectral resolution at a wavelength of 1650 . We know that the star has a magnitude of V = 16. How long will it take to obtain S/N = 15?
We select the G160M grating with a central wavelength of 1623 . We select a Kurucz O5V stellar model and set the normalization to be Johnson V = 16 mag. We find that the required exposure time is 910 s.
Suppose this star is reddened, with E(BV) = 0.2. We select the Milky Way Diffuse (RV=3.1) extinction law, which is shown in Figure 7.3. We must now decide if this extinction is to be applied before or after the normalization. Since the star has a measured magnitude, we want to apply the reddening before normalization. Otherwise, the extinction would change the V magnitude of the stellar model. Making this selection, we find that S/N = 15 can be obtained in 2165 s (COS.sp.539447). The ETC returns a BUFFER-TIME of 2753 s. To be conservative, we scale it by 2/3 to get 1835 s.
7.6.3 A Solar-Type Star with an Emission Line
We want to observe a solar-type star with a narrow emission line. Consider the Si II λ1810 feature with the following parameters: FWHM = 30 km s1 or 0.18 at 1810 , and integrated emission line flux of 1 1014 erg cm2 s1. The measured magnitude of the star is V = 12 mag. The desired exposure time is 1000 s.
In the ETC we select a G2V star and an NUV grating, G185M, set to a central wavelength of 1817 . We request an exposure time of 1000 s and specify that the S/N be evaluated at 1810 . We add an emission line with the line center at 1810 , FWHM=0.18 , and an integrated flux of 1014 erg cm2 s1. We specify the normalization as Johnson V = 12 mag. We set the zodiacal and earthshine to be average.
The ETC returns S/N = 16.4 per resel (COS.sp.539448). The local and global count rates are within safe limits. The recommended buffer time is 2326 s. This BUFFER-TIME exceeds the exposure time of 1000 s, so, following the procedure outlined in Section 5.4 we set the BUFFER-TIME to 2/3 of the BUFFER-TIME value returned by the ETC, which is 1551 s.
7.6.4 A Faint QSO
An important science goal for the design of COS was to obtain moderate S/N spectra of faint QSOs in the FUV. In the ETC, use the FOS-based QSO spectrum (in the Non-Stellar Objects menu) and choose G130M at 1309 , S/N = 20, and a continuum flux of 1015 erg cm–2 s–1 -1 at 1320 . The indicated exposure time is 69,843 s, or about 23.3 orbits (COS.sp.539450). The source count rate is 0.001 count/s, with a background rate of 1.410 104 count/s, seven times less than that of the source. The background is completely dominated by the dark current of the detector. The count rate over the entire detector is 352 count/s, well below any safety limits, and the maximum BUFFER-TIME is 6705 s. Scaling by 2/3 yields 4470 s for the BUFFER-TIME.

Cosmic Origins SpectrographInstrument Handbookfor Cycle 22 > Chapter 7: Exposure-Time Calculator (ETC) > 7.6 Examples

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