Only the G130M grating covers the desired wavelength at medium resolution, but several choices of central wavelength are available. We select the 1309 Å 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 Å, 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
at 1320 Å. 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 15,691 seconds; the total count rates are 88 and 301counts s−1
in detector segments A and B, respectively, well below the safety limit; the count rate in the brightest pixel is 0.100 counts s−1
, also well within the safe range (but see below); and the buffer time indicated by the ETC is 6075 seconds (COS.sp.432001).
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
= 13.7 per resel. Note that (30,000/15,692)1/2
= (13.7/10.0). 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 Å and S/N
= 10 per resel, we find the required exposure time is 2591 seconds, considerably less than the medium-resolution case required.
Suppose this star is reddened, with E(B−V)
= 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 1776 seconds (COS.sp.432007). The ETC returns a BUFFER-TIME
of 2401. To be conservative, we scale it by 2/3 to get 1601 s.
We want to observe a solar-type star with a narrow emission line. Consider the Si II λ
1810 feature with the following parameters: FWHM = 30 km s−1
or 0.18 Å at 1810 Å, and integrated emission line flux of 1 ×
. The measured magnitude of the star is V
= 12. The desired exposure time is 1000 seconds.
In the ETC we select a G2V star and an NUV grating, G185M, set to a central wavelength of 1817 Å. We request an exposure time of 1000 s and specify that the S/N
be evaluated at 1810 Å. We add an emission line with the line center at 1810 Å, FWHM=0.18, and an integrated flux of 10−14
. We specify the normalization as Johnson V
= 12. We set the zodiacal and earthshine to be average
The ETC returns S/N
= 16.3 per resel (COS.sp.432008). The local and global count rates are within safe limits. The recommended buffer time is 2525 seconds. This BUFFER-TIME
exceeds the exposure time of 1000 s, so the BUFFER-TIME
should be set to 1000.
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 Å, S/N = 20, and a continuum flux of 10−15
at 1320 Å. The indicated exposure time is 62,046 seconds, or about 20.7 orbits (COS.sp.432009). The source count rate is 0.001 (counts/s), with a background rate of 1.974 ×
counts/s, five times lower than the source. The background is completely dominated by the dark current of the detector. The count rate over the entire detector is 398, well below any safety limits, and the maximum BUFFER-TIME
is 5922 seconds. Scaling by 2/3 yields 3948 seconds for the BUFFER-TIME