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Cosmic Origins SpectrographInstrument Handbook for Cycle 26 > 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 dashed 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 solid black line represents a model that includes the MFWFEs at the original lifetime position, while the solid colored lines represent models that include the MFWFEs at subsequent lifetime positions. The model at the original lifetime position has a FWHM of 7.9 pixels, slightly larger than that of the dashed curve, and broad non-Gaussian wings. The models at subsequent lifetime positions have 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 subsequent lifetime positions are available on theModel LSFs for G130M at 1309 Å normalized to a sum of unity. The dashed 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 solid black line represents a model that also includes the HST mid-frequency wavefront errors at the original lifetime position. The solid colored lines represent models that include the HST mid-frequency wavefront errors at subsequent lifetime positions. These 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 channel for one cenwave in each of the three gratings. The solid lines assume a Gaussian LSF of FWHM = 6.5 pixels with no MFWFEs from the HST OTA, and the other lines show the LSF model with the MFWFEs included for each lifetime position. The MFWFEs markedly reduce the resolving power of the G130M and G160M gratings; the G140L profile is less affected 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 one cenwave in each of 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 other lines show the values predicted by the LSF model with the on-orbit MFWFEs included at each lifetime position.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 4. 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 4. 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 (purple).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 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.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. Values for subsequent lifetime positions are not expected to differ 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 Handbook for Cycle 26 > Chapter 3: Description and Performance of the COS Optics > 3.3 The COS Line-Spread Function