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Cosmic Origins SpectrographInstrument Handbookfor Cycle 23 > Chapter 3: Description and Performance of the COS Optics > 3.3 The COS Line-Spread Function

The COS optics correct for the spherical aberration of the HST primary mirror, but not for the mid-frequency wavefront errors (MFWFEs) due to zonal (polishing) irregularities in the HST primary and secondary mirrors. As a result, the COS spectroscopic line-spread function (LSF) has extended wings and a core that is slightly broader and shallower than a Gaussian. The extended wings of its LSF limit the ability of COS to detect faint, narrow spectral features. The effect is greater at short wavelengths, and it may have consequences for some COS FUV science. The most severely impacted programs are likely to be those that

• Initial results from an analysis of the on-orbit COS LSF at the original lifetime position are reported by Ghavamian et al. (2009) in COS ISR 2009-01. They find that model LSFs incorporating HST MFWFEs are required to reproduce the absorption features observed in stellar spectra obtained with COS. Figure 3.6 shows model LSFs computed for grating G130M at 1309 Å. The solid line represents a model incorporating the spherical aberration of the HST OTA. It is well-fit by a Gaussian with FWHM = 6.5 pixels. The dot-dash line represents a model that includes the MFWFEs at the original lifetime position while the dashed line represents a model that also includes the MFWFEs at the second lifetime position. The model at the original lifetime position has a FWHM of 7.9 pixels, slightly larger than that of the solid curve, and broad non-Gaussian wings. The model at the second lifetime position has a very similar FWHM. The non-Gaussian wings can hinder the detection of closely-spaced narrow spectral features. Model LSFs for all of the COS gratings at the original and second lifetime positions are available on the COS website.Model LSFs for G130M at 1309 Å normalized to a sum of unity. The solid line represents a model LSF that incorporates the spherical aberration of the OTA. It is well fit by a Gaussian with FWHM = 6.5 pixels. The dashed line represents a model that also includes the HST mid-frequency wave-front errors at the second lifetime position. The dot-dash line represents a model that also includes the HST mid-frequency wave-front errors at the original lifetime position. These latter two LSFs show a larger FWHM and broad non-Gaussian wings.When a substantial fraction of the power in an LSF is transferred to its extended wings traditional measures of resolution, such as the FWHM of the line core, can be misleading. For example, an observer assuming that the resolving power R = 16,000 at 1200 Å quoted for the G130M grating represents the FWHM of a Gaussian would mistakenly conclude that COS can resolve two closely-spaced narrow absorption features, when in fact it may not be able to. Nevertheless, the FWHM is a convenient tool, and we use it to describe the COS gratings in tables throughout this handbook. When using these tables keep in mind that the quoted resolving power R is computed from the empirically-determined FWHM of the line core, and careful modeling may be needed to determine the feasibility of a particular observation or to analyze its result.Figure 3.7 shows the resolving power of the FUV gratings for three cases: the first assumes a Gaussian LSF of FWHM = 6.5 pixels with no MFWFEs from the HST OTA (solid lines), the second is an LSF model with the MFWFEs included for the original lifetime position (dot-dash lines), and the third is an LSF model with the MFWFEs included for the second lifetime position (dashed lines). In the second case the FWHM of the LSF is calculated directly from the line profile by taking the width at half the peak (from Table 1 of COS ISR 2009-01). The MFWFEs reduce the resolving power of the G130M and G160M gratings by ~20%. The G140L profile is least affected by the MFWFEs, due to its lower dispersion. Measurements of the resolving power of the G130M grating at λ < 1150 Å are presented in Section 5.1.4.Figure 3.7: Resolving Power of FUV GratingsThe resolving power (R = λ / FWHM) for the three gratings of the COS FUV channel for observations through the PSA aperture. The solid lines represent a Gaussian with FWHM = 6.5 pixels. The dashed lines are the values predicted by the LSF model with the on-orbit MFWFEs included at the second lifetime position. The dot-dash lines are the values predicted by the LSF model with the on-orbit MFWFEs included at the original lifetime position. (The dashed, dot-dash, and solid lines for G140L nearly overlap.)The broad core and extended wings of the COS LSF increase the limiting equivalent width for absorption features in COS spectra. Figure 3.8 shows the limiting equivalent widths as a function of wavelength for a 3σ FUV detection of absorption features at S/N = 10 per pixel at lifetime position 2. A series of Gaussian spectral features with nominal Doppler parameters of b = 0, 10, 25, 50, and 100 km/s have been convolved with both a Gaussian instrumental LSF and the modeled on-orbit COS LSF for the G130M and G160M gratings. The results are similar for the NUV gratings, although the effect of the MFWFEs is more moderate for the long-wavelength G285M grating.Limiting equivalent width as a function of wavelength for 3σ detections of absorption features at a S/N of 10 per pixel at lifetime position 2. Dashed lines represent the full on-orbit LSFs including MFWFEs. Solid lines represent Gaussian LSFs without MFWFEs. The colors correspond to features with intrinsic Doppler parameters b = 0 km s-1 (black), 10 km s-1 (red), 25 km s-1 (green), 50 km s-1 (blue) and 100 km s-1 (magenta).The LSF models of Ghavamian et al. (2009) successfully characterize the basic profile and integrated properties of narrow spectral features in COS spectra. However, scientific investigations that depend on characterizing the depth of saturated or nearly-saturated absorption features may require a more careful treatment of the light scattered into the wings of the LSF. To address this concern Kriss (2011) has developed empirical LSF models for the G130M and G160M gratings. These models differ in two ways from the preliminary models discussed above. First, while the preliminary models extend only ±50 pixels from the line center, the new models extend ±100 pixels, which is the full width of the geocoronal Lyman-α line. Second, the new models include scattering due to the micro-roughness of the surface of the primary mirror, an effect that transfers an additional 3% of the light from the center of the line into its extended wings (Figure 3.9). For details, see COS ISR 2011-01. The LSF models computed by Ghavamian et al. (2009), the empirical models of Kriss (2011), and predicted LSFs for the lifetime positions are available on the COS website.Comparison between a simple Gaussian LSF model (red line, FWHM = 6.5 pixels), the LSF profile from Ghavamian et al. (2009) that includes MFWFEs from the HST OTA (blue line, calculated at 1200 Å), and the new LSF that includes power-law scattering wings of index −2.25 extending ± 100 pixels from line center (Kriss et al., 2011;black line). In the latter two cases solid lines represent the original lifetime position and the dot-dash lines represent the second lifetime position. Figure based on figure 2 from Kriss (2011).Figure 3.10 shows the fraction of enclosed energy within the LSF, measured from the center of the profile, for both the FUV and NUV channels. The differences between the modeled on-orbit LSFs (MFWFEs included) and the Gaussian LSFs without MFWFEs are apparent in both spectroscopic channels. Though inclusion of the MFWFEs at longer NUV wavelengths widens the FWHM of the on-orbit LSF models only slightly, the wider wings decrease noticeably the spectral purity and the contrast level of the observed spectra.The enclosed energy fraction of the COS LSF for an unresolved spectral feature as measured from the center of the profile (collapsed along the cross-dispersion direction). The top panel shows a Gaussian with FWHM = 6.5 Å and FUV model profiles with and without scattering due to micro roughness on the surface of the HST primary mirror (Kriss 2011). The 1150 Å data (blue) use the G130M grating while the 1450 Å (green) and 1750 Å (red) data use the G160M grating. The solid lines indicate results for the original lifetime position while the dot-dash lines indicate data for the second lifetime position. In the bottom panel, NUV model profiles with and without the effects of the OTA MFWFEs are shown (Ghavamian et al. 2009). The 1700 Å data (blue) use the G185M grating, the 2500 Å data (green) use the G225M grating, and 3200 Å data (red) use the G285M grating.Table 3.2: Distance from Line Center (in Pixels) Versus Enclosed Energy Fraction and Wavelength for the G130M Grating.^{1}

Table 3.3: Distance from Line Center (in Pixels) Versus Enclosed Energy Fraction and Wavelength for the G160M Grating.^{2}

Table 3.4: Distance from Line Center (in Pixels) Versus Enclosed Energy Fraction and Wavelength for the G140L Grating^{3}.

Table 3.2, Table 3.3, and Table 3.4 present the enclosed-energy fractions for gratings G130M, G160M, and G140L respectively. The G130M and G160M data include the effects of scattering and are for both the original and the second lifetime position. Information on values for the third lifetime position will be made available in the future, but are not expected to change appreciably. The G140L data are taken from Ghavamian et al. (2009) and are for the original lifetime position. The G140L data do not include the effects of micro-roughness.

Cosmic Origins SpectrographInstrument Handbookfor Cycle 23 > Chapter 3: Description and Performance of the COS Optics > 3.3 The COS Line-Spread Function