7.6 Examples

We present a few examples of how 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. The examples were computed using version 25.2 of the ETC; later versions may return slightly different results.

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 Å for a point source with a flux of 10⁻¹⁵ erg cm⁻² s^–1 Å^–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 illustrate two approaches: one that uses a cenwave for which only Segment A is available under the COS 2025 policy, and one that uses a dual-segment cenwave. In practice, the choice will depend on the user's science goal.

Single-Segment Operation

Here we select the 1309 Å setting. We enter the grating and cenwave into the spectroscopic ETC, select the Primary Science Aperture (PSA), select "Exposure time needed to obtain an 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 F_λ. Make sure the reddening, E(B – V), is set to 0. Normalize the target to 10^–15 erg cm⁻² s⁻¹ Å⁻¹ 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 15,884 s; the total count rate is 43 counts s⁻¹ in detector Segment A, well below the safety limit; the count rate in the brightest pixel has 1.5 × 10⁻⁴ counts s⁻¹, also well within the safe range (but see below); and the buffer time indicated by the ETC is 8,307 seconds (COS.sp.1033055). The results for Segment B can be ignored, since it will be off.

The buffer time of 8,307 seconds assumes that both segments are in use. The correct value for single-segment operation is not reported in version 25.2 of the ETC, but it can be determined by recalling that the buffer time is inversely proportional to the count rate (Section 5.4). We multiply the buffer time returned for both segments by the ratio of the count rate for the entire detector to the count rate in Segment A: 8,307 s × (283.976/43.290) = 54,493 s.

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 (30,000/15,884)^1/2 = (13.7/10.0). That is, the S/N ratio scales as t^1/2, 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 2732 s, considerably less than the medium-resolution case required. Since this cenwave has always been offered in single-segment mode, the ETC returns the correct buffer time for Segment A only.

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 sourceʹs spectrum is of interest, using G130M is more efficient than using G140L.

Dual-Segment Operation

For other science goals, the user may wish to retain the use of both segments by switching to a different cenwave, such as 1222. For this example, we use the same inputs as before, except the cenwave is set to 1222. When this case is computed with the ETC, we find the required time is 16,014 s; the total count rates are 63 and 38 counts s⁻¹ in detector Segments A and B, respectively, well below the safety limit; the count rate in the brightest pixel has 0.008 counts s⁻¹, also well within the safe range; and the buffer time indicated by the ETC is 23,434 seconds (COS.sp.1033327).

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 Å. 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 Å. 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 1,163 s.

Suppose this star is reddened, with E(B − V) = 0.2. We select the Milky Way Diffuse (R_V = 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 2762 s (COS.sp.1033334). The ETC returns a BUFFER-TIME of 3043 s. To be conservative, we scale it by 2/3 to get 2028 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 s⁻¹ or 0.18 Å at 1810 Å, and integrated emission line flux of 1 × 10⁻¹⁴ erg cm⁻² s⁻¹. The measured magnitude of the star is V = 12 mag. The desired exposure time is 1000 s.

In the ETC we select a Kurucz 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 Å, and an integrated flux of 10⁻¹⁴ erg cm⁻² s⁻¹. We specify the normalization as Johnson V = 12 mag. We set the zodiacal light, air glow, and earthshine to be average.

The ETC returns S/N = 16.3 per resel (COS.sp.1033356). The local and global count rates are within safe limits. The recommended buffer time is 2730 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 1820 s.

For this example, the ETC returns a warning that the S/N it calculates for NUV observations may overestimate the S/N in the standard reduction of the data provided by the archive. This is because the ETC uses a narrower extraction box. See COS ISR 2017-03 for details.

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 1291 Å, S/N = 20, and a continuum flux of 10⁻¹⁵ erg cm^–2 s^–1 Å^-1 at 1320 Å. (Note that only FP-POS 3 and 4 are available at this cenwave, but these are sufficient to attain the S/N goal; see Table 5.6.) The indicated exposure time is 63,154 s, or about 21.1 orbits (COS.sp.1033359). The source count rate is 0.001 count s^–1, with a background rate of 6.230 × 10⁻⁵ count s^–1, 16 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 316 count/s, well below any safety limits, and the maximum BUFFER-TIME is 7459 s. Scaling by 2/3 yields 4972 s for the BUFFER-TIME.