13.2 Using the Information in this Chapter

13.2.1 Grating Parameters

For each grating, the resolving power and dispersion are taken from Table 5.1. Plate scales are derived from data obtained during SMOV.

13.2.2 Wavelength Ranges

For each grating, we plot the wavelengths sampled by each central-wavelength setting. For the NUV gratings, the central wavelength is the approximate midpoint of Stripe B. For the FUV gratings, the central wavelength is (approximately) the shortest wavelength recorded on Segment A. Wavelength ranges for each central wavelength at FP-POS=3 are provided in tabular format in Table 5.3 and Table 5.4.

For the FUV gratings, the wavelength ranges sampled at each FP-POS position are plotted separately. For the NUV gratings, the total wavelength range sampled by all FP-POS positions is plotted for each central-wavelength setting.

Figure 13.1 shows how some wavelengths are covered by multiple modes, but on different parts of the FUV detectors. At LP4 and LP5, the FUVB cenwaves shown with dotted lines are unavailable, while the one shown with a dashed line (1291) is available only at FP-POS=3 and 4.

13.2.3 Grating Sensitivities and Effective Areas

This section presents sensitivities and effective areas as a function of wavelength for each grating. The target is assumed to be a point source centered in the PSA. For both the FUV and NUV detectors, the total systemic¹ spectroscopic point-source sensitivity, $//<![CDATA[ \begin{array}{l}\small{S\,^p_\lambda}\end{array} //]]>$, has units of counts pix_λ⁻¹ s⁻¹ per incident erg cm^-2 s⁻¹ Å⁻¹, where:

• pix_λ = a pixel in the dispersion direction, and

• counts refer to the total counts from a point source integrated over the PSF in the direction perpendicular to the dispersion.

The count rate per pixel is simply the product of the target flux and the point-source sensitivity at a given wavelength. To estimate the signal-to-noise ratio (S/N ) achieved at a given count rate and exposure time, follow the directions in Section 7.3 or use the S/N  plots in this chapter.

The effective area has units of cm².

13.2.4 Signal-to-Noise Plots

For each grating, a plot is provided to help you estimate the S/N  that can be achieved from a point source observed at a fiducial wavelength near the peak of the effective-area curve. The fiducial wavelength is indicated in the ordinate label of each plot. To estimate the S/N  at other wavelengths, scale your source flux or magnitude by the relative sensitivities at the wavelength of interest and at the fiducial. The plots show S/N  as a function of F_λ and of STMAG for a range of exposure times. STMAG_λ is the color-dependent correction from V magnitude to STMAG at wavelength λ. Values of STMAG_λ for various stellar and extragalactic sources are presented in Table 13.1 and Table 13.2, respectively. In producing these plots, we assumed an average sky background (as described in Chapter 7) and the dark current appropriate for each detector. These plots should be used only for rough estimates of exposure times. When constructing your proposal, use the COS ETC to estimate S/N  values.

Note the following:

• The point source S/N  has been calculated per resolution element and has been integrated over the PSF to contain all of the flux in the cross-dispersion direction.
• The symbols in the S/N  figures delineate regions of parameter space where the dark current contributes more than half the source counts.
• The vertical shaded area indicates the bright-object screening limit given in Table 10.1.

Follow these steps to use the S/N  plots.

1. Look up, in Table 13.1, the effective temperature and wavelength region of interest (e.g., 5000 K at 2000 Å). Interpolate in the table to get STMAG_λ.
2. Add the V magnitude of the target to get STMAG.

3. Find the appropriate plot for the desired grating and locate STMAG on the horizontal axis. Read off the S/N for the desired exposure time, or vice-versa. Alternatively, use F_λ directly on the horizontal axis.

4. To get accurate values for repeated, or FP-POS, exposures use the sub-exposure time when consulting the plot, and then multiply the resulting S/N  by $//<![CDATA[ \begin{array}{l}\small{\sqrt{N}}\end{array} //]]>$, where N is the number of sub-exposures to be averaged.

For example, consider a V = 15 mag star of spectral type B0V, for which we want to derive the S/N  achieved in a 100 s exposure using the NUV grating G230L. The S/N  calculations for G230L are presented in Figure 13.28, where we learn that the fiducial wavelength for this grating is 3001 Å. Assuming an effective temperature of 30,000 K, we obtain STMAG_λ ~ –2.1 at 3000 Å from Table 13.1, making STMAG = 12.9. Returning to Figure 13.28, we find this value on the horizontal axis. For an exposure time of 100 s, we find S/N ~ 9.5.

Table 13.1: STMAG_λ as a Function of Wavelength for Stellar Objects.

Table 13.2: STMAG_λ as a Function of Wavelength for Non-Stellar Objects.

The STMAG_λ values of Table 13.1 are derived from the stellar models of Castelli and Kurucz (2003, 2004), assuming solar metallicity ([Fe/H] = 0.0) and a surface gravity of log(g) = 4.5. The STMAG_λ values of Table 13.2 are based on observed spectra of each object type.

¹ COS plus HST Optical Telescope Assembly (OTA).