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COS Instrument Science Report 2009-01(v1)

Preliminary Characterization of the PostLaunch Line Spread Function of COS
____________________________ Parviz Ghavamian1, Alessandra Aloisi1, Daniel Lennon1,2, George Hartig1, Gerard A. Kriss1, Cristina Oliveira1, Derck Massa1, Tony Keyes1, Charles Proffitt1,3, Thomas Delker4 and Steve Osterman5
1 2 3 4 5

Space Telescop e Science Institute, Baltimore, MD European Sp ace Agency Science Programs, Co mputer Sciences Corporation Ball Aerospace Technologies Corporation, Boulder, CO University of Colorado , Boulder, CO

2 October 2009 __________________________________________________________________________ ABSTRACT We present a preliminary analysis of the line spread function (LSF) of the Cosmic Origins Spectrograph (COS) using FUV and NUV stellar spectra acquired during the SM4 Servicing Mission Observatory Verification (SMOV). Our results indicate that the on-orbit shape of the COS LSF with the HST optical telescope assembly (OTA) deviates from the profile measured in ground testing due to the appearance of broad non-Gaussian wings. The wings are caused by mid-frequency wave-front errors (MFWFEs) that are produced by the zonal (polishing) errors on the HST primary and secondary mirrors; these errors could not be simulated during ground testing. The MFWFE effects are particularly noticeable in the FUV. While the pre-launch FUV LSF is well described by a Gaussian, the on-orbit FUV LSF has up to 40% of its total power distributed in non-Gaussian wings. The power in these wings is largest at the shortest wavelengths covered by the COS medium-resolution gratings (~ 1150 å). The effect diminishes with increasing wavelength but has a nonnegligible effect on encircled energies even at the longest wavelengths. The effects of the MFWFEs are also present in the COS NUV LSF, particularly for the shorter wavelength gratings (G185M and G225M), although at a lower level than in the FUV. Optical models incorporating the MFWFE effects into the LSF have been calculated for the whole spectral range covered by the FUV and NUV medium-resolution gratings. We show that for the
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FUV, the convolution of these model LSFs with high-resolution STIS echelle spectra yield s an excellent match to the on-orbit COS spectra of the same targets. The model LSFs are available online and can be used by COS observers to assess the impact of the MFWFE broadening on their COS spectra. While these LSF models are not perfect and may not always provide an exact match to the actual on-orbit LSFs, they should prove to be an extremely useful tool for the analysis and interpretation of COS spectra. We anticipate that the effects of the MFWFE wings on the on-orbit LSF will be most important for observations that require the full expected 15 km/s resolution of the G130M, G160M, and G185M gratings, with more modest impacts for science programs targeting broad lines, continuum sources, or which use other COS gratings. However, the impact on the detectability of faint, narrow features is important for all gratings, leading to an increase between 20% and 40% of the minimum detectable equivalent width (these values assume a 3 detection of an unresolved line, superimposed on a continuum with S/N = 10 per pixel). __________________________________________________________________________

Contents:
· · · · · · Introduction (page 2) Discovery of the OTA MFWFE Effects on the On-Orbit COS LSF (page 5) Implications (page 15) Summary (page 20) Change History for COS ISR 2009-01 (page 23) References (page 23)

1. Introduction
The Cosmic Origins Spectrograph (COS) was installed during the most recent servicing mission of the Hubble Space Telescope (SM4) and is the most sensitive ultraviolet spectrograph flown to date. This is particularly true for the far ultraviolet channel of the instrument, which is 10 to 30 times more sensitive than STIS. With its medium-resolution gratings (G130M and G160M, covering 1150 å ­ 1800 å) the FUV channel was designed to reach a spectroscopic resolving power of at least 20,000 (15 km s - 1) across 80% of its passband (STE-63, 2004). The COS near ultraviolet channel was designed to cover the 1750 å ­ 3200 å spectral range with a sensitivity 2-3 times larger than STIS. It utilizes medium-resolution gratings (G185M, G225M and G285M) with spectroscopic resolving power requirements similar to the FUV. 1.1 Spectroscopic Resolution: Ground Testing The pre-launch COS spectral resolving power was measured during thermal vacuum testing in 2003 and 2006 (TV03 and TV06) using spectra from an external PtNe hollow-

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cathode emission line source fed to COS by the Reflective Aberrated Simulator/Calibrator (RAS/Cal). The low-frequency wavefront errors produced by the HST OTA (spherical aberration and astigmatism at the COS field location) were mimicked by the RAS/Cal stimulus (COS IDT OP-01, 2003), but it was not practical to simulate the mid-frequency wavefront errors (MFWFEs) discussed below. Thermal vacuum measurements showed that for the G130M and G160M FUV gratings the LSF of an unresolved line was well approximated by a Gaussian profile with a FWHM of approximately 6.5 pixels, corresponding to = 0.065 å at 1300 å and = 0.079 å at 1600 å. Defining the spectroscopic resolving power, R, as /, where is the FWHM of a Gaussian profile fit to the observed data, the TV06 results for both FUV medium resolution gratings indicated R 20,000-24,000 (see Figures 5.2-5 -5.2-6 in AV-04 (2008)), meeting the specifications defined by STE-63 (2004). The LSFs of the NUV gratings are expected to have broad wings due to the response of the MAMA detector in the NUV (similar to what is seen for the STIS MAMA LSFs). Analysis of the NUV thermal vacuum data was performed by fitting a Gaussian to the core of the LSF; this yielded FWHM widths of about 3 pixels, or ~ 0.11 å at the default central wavelengths of the G185M, G225M and G285M gratings. Measured resolving powers were R 16,000-20,000 for the G185M grating and R 20,000-24,000 for the G225M and G285M gratings (see Figure 5.2-8 in AV-04, (2008)), all meeting the specifications defined by STE-63 (2004).

1.2 Spectroscopic Resolution: On-Orbit Results The COS LSF measured on-orbit with the HST OTA has been found to deviate from the profile measured in TV06. As shown in this report, analysis of stellar spectra obtained during SMOV indicates that the HST OTA produces non-Gaussian wings in the on-orbit COS LSF, and both broadens the core of the profile and lowers its amplitude. The wings are a consequence of mid-frequency wavefront errors (MFWFEs), produced by zonal (polishing) errors on the HST optical telescope assembly (OTA). These features were mapped via a phase-retrieval analysis of WFPC2 imagery by Krist & Burrows (1995). However, the MFWFEs of the HST OTA are not included in RAS/Cal, and are not corrected by the optics of COS or any other HST instrument. Therefore, the beam entering COS on-orbit is slightly different from the beam delivered by RAS/Cal during thermal vacuum testing. The effects of the MFWFEs were not included in pre-launch modeling of the COS LSF. Although the COS FUV channel is more sensitive between 1150 å and 1800 å than any previous spectrograph flown to date and is producing science spectra of exquisite quality, the MFWFEs from the HST OTA result in an LSF with a broader core and nonGaussian wings that impacts the spectral resolving power of the spectrograph. This in turn reduces the detectability of faint, narrow spectral features, as compared to the Gaussian LSF derived from TV06 data. The MFWFE effect is most pronounced at shortest wavelengths (~ 1150 å), where we find that about 60% of the light falls inside the modeled FWHM of the COS LSF (compared to ~ 76% for a Gaussian profile). In addition, at 1150 å, the FWHM of the core of the modelled G130M LSF is about 14% broader than pre-launch expectations .
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While the effects of the MFWFEs on the LSF decrease with increasing wavelength, they remain significant for both the FUV and NUV channels. The NUV LSF also exhibits non-Gaussian wings, but the contribution of the MFWFEs to these wings is smaller than for the FUV, particularly for > 2500 å. The main contributor to the non-Gaussian wings at the longer NUV wavelengths is the blurring produced by the MAMA detector point response function (a feature also present in the STIS MAMA detectors). This latter detector contribution to the LSF wings was also present during thermal vacuum measurements when the COS NUV resolution was measured. We have produced optical models of the COS LSF, taking into account the MFWFEs (as well as the appropriate detector responses). We find that the COS spectra are reproduced very well when high-resolution STIS spectra of the same targets are convolved with our model LSFs. We present these models, and estimate how they will impact observations with COS. We have made these model LSFs available to the astronomical community for use in analyzing COS science spectra and for the planning of future COS observations. They can be found at: http://www.stsci.edu/hst/cos/performance/spectral_resolution/ . 1.3 Impact of the on-orbit LSF on COS Science Some of the COS observations that could potentially be affected by the newly characterized on-orbit LSF are as follows: · Science observations intending to use the full resolution of the FUV G130M and G160M and the NUV G185M medium-resolution gratings will be most seriously affected, (though to some extent the following caveats will apply to data obtained with all COS gratings): - At a given signal-to-noise, weak, narrow features (b < 35 km s-1) will be more difficult to detect. - Closely spaced spectral features may blend and become more difficult to isolate kinematically. - Analysis of saturated lines will require full consideration of the LSF. - Studies requiring measurement of accurate line profile shapes will also require full consideration of the LSF. - Spectral purity will be reduced, resulting in decreased contrast between line cores and wings. · Science observations that are expected to be less affected by the MFWFEs include: - Observations of broad-lines (b > 35 km s-1). - Measurements of continuum fluxes or SEDs. - NUV observations with the G225M and G285M gratings having sufficient S/N to overcome slightly reduced spectral purity should recover the full expected resolution. - For FUV G140L observations, the LSF is broadened at a level comparable to that of the G130M and G160M gratings. However, we expect that most science programs critically depending on accurate measurement of line profiles would use the G130M and/or G160M gratings rather than the G140L. Therefore, we anticipate that most G140L science programs will be minimally affected.

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- For NUV G230L observations, the effects should be similar to that of the NUV medium-resolution gratings at comparable wavelengths.

2. Discovery of the OTA MFWFE Effects on the On-Orbit COS LSF
The OTA MFWFE effects on the COS on-orbit LSF were first recognized while analyzing SMOV data of the star Sk 155 taken with the G130M grating at the 1291 å central wavelength. The data were part of an observing program to verify that the COS + HST OTA resolving power was close to what had been previously measured in the FUV during TV06. 2.1 Choice of the Target The O9 Ib supergiant star Sk 155 in the Small Magellanic Cloud (V=12.4) was observed at one central wavelength each with G130M and G160M during SMOV, under program 11489 entitled "COS FUV External Spectroscopic Performance - Part I" (PI: S. Friedman). An important factor in choosing Sk 155 was that it had been previously observed during Cycle 8 with STIS at very high spectroscopic resolution (E140H, 0.2x0.09 aperture, R 114,000, PID 8145, PI: D. Welty), providing a valuable comparison spectrum. The STIS spectrum covers the range 1165 å ­ 1350 å and has a velocity resolution of approximately 2.7 km s-1. The STIS archival spectrum shows numerous narrow Galactic and SMC absorption components in the FUV along the line of sight to Sk 155 (Welty et al. 2001), spread in velocity out to ~ 300 km s-1. Many of these components are blended, forming wide absorption troughs broader than the instrumental resolution of COS. However, some of these narrow lines are shifted in velocity from the main body of the absorption, and were thought to be useful for measuring the COS instrumental resolution. We identified a number of interstellar absorption features with velocity widths ~ 3-5 km s-1 in the STIS spectra of Sk 155. These narrow absorption lines were expected to provide a straightforward test of the COS G130M and G160M grating resolutions. In our analysis we planned to simply fit these lines with a Gaussian, measure their FWHM and then infer the COS spectral resolving power by subtracting the intrinsic line widths obtained from the STIS spectra in quadrature from the widths observed in the COS spectra. 2.2 Data Acquisition COS spectra of Sk 155 were obtained through the primary science aperture (PSA) with the G130M and G160M gratings (at the 1291 å and 1623 å central wavelengths, respectively). The TIME-TAG observations were split into four separate observations, each shifted in wavelength (FPPOS=AUTO; Soderblom et al. 2007). The FPPOS sequence was obtained with internal wavelength calibrations turned on, with flash intervals specified at the beginning and end of each science exposure. The TIME-TAG data were then processed with CalCOS and the latest available reference files produced during SMOV were used to remove instrumental effects and extract the final onedimensional spectrum (Kaiser et al. 2008). The spectra were co-added by the pipeline to

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mitigate the effects of detector features (e.g. grid wires and maximize the signal-to-noise of the final spectrum. negligibly to the total spectrum so background subtraction extraction. No flat field correction was applied to the FUV 2.3 Data Analysis

other detector features) and to The background contributes was turned off during spectral data.

Figure 1 shows closeup views of several prominent absorption features detected in the COS G130M data, along with the corresponding features in the STIS E140H data. Saturated absorption lines for both Galactic and SMC components are seen in both datasets, but with several important differences. The saturated absorption features in the STIS spectrum follow a step-like shape, with the flux sharply dropping to zero at their centers. In the COS G130M spectrum, on the other hand, the profiles of the same saturated absorption lines are noticeably rounded, with nonzero flux at the cores of the lines. The filling-in effect of the flux is also noticeable for the unsaturated lines ­ for example, there are two sharp, narrow absorption features on the red wings of the 1305 å troughs in the STIS spectrum which nearly disappear into the wings of the nearby saturated absorption lines in the COS spectrum.

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Figure 1 . Compar ison of selected strong absorption featur es in th e FUV spectra of Sk 155, ob tained by STIS (E140H, R 114,000, f irst and third pan els from the top) and by COS (G130M, second and fourth panels from the top).

2.3.1 Inadequacy of Gaussian LSF Models All of the above effects are expected to some degree due to the redistribution of photons by the COS LSF, which should produce a spectrum of nearly 5 times lower resolution than the STIS E140H spectrum. However, we were unable to locate useful isolated, narrow absorption features in the COS spectrum of Sk 155 for a direct Gaussian fitting and FWHM measurement. We therefore used a model-based approach to infer the COS spectral resolving power by comparing STIS data convolved with different LSF models to the COS data. In a first attempt the STIS E140H spectrum was convolved with an LSF similar to that derived for the FUV during TV06, i.e. a Gaussian with a width corresponding to R = 20,000 (Figure 2, dotted line). In Figures 3a and 3b we compare the COS spectrum (black solid line) with that obtained by STIS, convolved with an R = 20,000 Gaussian LSF (blue dashed line). Also shown in Figures 3a and 3b is the STIS spectrum convolved with an MFWFE LSF model appropriate for the wavelengths displayed (solid red line; see Section 2.3.3). This figure clearly shows that the rounded, filled-in absorption cores are not properly reproduced by an R = 20,000 Gaussian LSF, which systematically underpredicts the flux at line centers and produces more boxy shapes for the broad, saturated absorption lines than is observed. While using broader (lower resolution) Gaussian LSFs alleviates the mismatch between the model and the COS G130M spectrum for some features (e.g., reproducing the filled-in absorption cores), it increases the disagreement for others (e.g., merging
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Figure 2. Co mparison between a Gaussian LSF w ith FWH M 6.5 pixels (dotted line), which is consistent with the FUV LSF profiles observed at most waveleng ths of the FUV G130 M and G160M gr atings during TV06, and a model LSF profile that includes th e MFWFEs from the HST OTA (so lid line, calcu lated for a wavelength of 1300 å).

narrow absorption features into the wings of adjacent broad absorption lines). Most importantly, neither the weak sharp features nor the broad line cores are properly fit by single Gaussians. Consequently it is clear that a Gaussian LSF is not the appropriate LSF for modeling on-orbit COS spectra in the FUV, in contrast to the FUV LSF measurements from TV06. Therefore, we first investigated the potential impact of pipeline processing and data acquisition anomalies on the line profiles. 2.3.2 Testing for Registration Errors in the Spectra To verify that the observations of Sk 155 are indeed suitable for measurement of the COS LSF, it is necessary to ensure that the data were properly collected and reduced, as misalignments could in principle occur and artificially broaden the final extracted spectrum. Examining the raw 2-dimensional TIME-TAG data of Sk 155 (i.e, before any processing through CalCOS; Figure 4), we extracted spectra by summing the stellar continuum along the cross-dispersion direction. We examined line profiles from the raw TIME-TAG data at each FPPOS. The absorption line profiles in each FPPOS exposure (this time in counts versus pixels) looked fully consistent with the final flux- and wavelength-calibrated profiles in fully processed CalCOS spectra from each

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Figure 3a Closeup views of promin ent absorption features in the CO S G130M (Segment B) sp ectrum of Sk 155. The STIS E140H spectrum convolved with an R = 20,000 Gaussian is overplo tted in blue, while in red it is presented th e convolu tion of the STIS data with the MFW FE LSF model appropriate to the wavelength r ange shown. The RMS residuals to th e fits are (for an MFWFE LSF and an R = 20,000 Gaussian, resp ectiv ely) RMS = (3.3E-14 ; 5.1E-14) at 1190 å and (3.4E-14; 5.0E-14) at 1260 å (RMS units are ergs/cm^2/s/ å).

FPPOS. They were also consistent with the final FPPOS-combined spectra produced by CalCOS. Other effects such as off-center positioning of the target during the exposures, breathing effects (i.e., small thermally­induced variations in focus due to contractions and expansions of the OTA during an orbital period), drift in the optics select mechanism (OSM, responsible for rotating the grating into place) and earthshine were also eliminated. We measured the widths of emission lines from internal wavelength calibration exposures on orbit and found FUV line widths fully consistent with the values obtained in TV06, thus eliminating the detector itself as the source of the non-Gaussian LSFs. Finally, we noted that the rounded, filled-in saturated profiles are also present in the FUV spectra of other stars observed with COS during SMOV. With all these potential complications eliminated, it was clear that the non-Gaussianity inferred for the on-orbit COS LSF in the FUV is unfortunately real.

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Figure 3b Same as Figure 3a bu t for differen t wav elength r egions (Seg ment A). Th e RMS residuals to the fits are (for an MFWFE LSF and an R = 20,000 Gaussian , respectively) RMS = (4 .3E-14; 7.3 E-14) at 1304 å and (4.0E-14; 7 .0E-14) at 1335 å (RMS units are ergs/cm^2/s/ å). The calculation at 1304 å excludes the r egion around the O I atmospheric absorption at ~ 1306 å.

Figure 4. The two-dimensional raw COS/G130M spectru m of Sk 155 (Segment A). The cores of the saturated absorption f eatures are not comp letely b lack , i.e., there is r esidual flux introduced from the nearby continuum by th e non-Gaussian wings of th e LSF.

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2.3.3 LSF Models: Inclusion of Mid-Frequency Wave Front Errors from the OTA We computed model LSFs for the COS gratings from the expected aberration content of the COS + HST OTA system, OTA pupil geometry, OTA MFWFEs as determined by Krist & Burrows (1995), and estimates of the point response function of the detectors. Due to the caveats affecting our modeling, users should be aware that these LSF models may not always provide an exact match to the actual on-orbit LSFs. However, even with these imperfections, they should still provide a very useful tool for the analysis and interpretation of COS spectra. The LSFs for the FUV channel were produced for each grating by first matching monochromatic images generated by a Code V optical model of the COS + HST OTA system to emission line images from thermal vacuum testing with the RAS/Cal stimulus. In particular, a mean detector-induced blur kernel was estimated by matching a suite of images over the spectrum. The model was then used to generate Zernike aberration coefficients, which, together with the OTA pupil function and the MFWFEs, were employed to compute the expected PSF at a number of wavelengths for each grating. The PSFs were then convolved with the estimated detector blur kernel and integrated in the cross-dispersion direction to form the LSFs. Figures 2 and 5 show that these FUV LSFs are characterized by prominent wings, broader cores and lower central peaks than the nearly Gaussian LSFs computed without the OTA MFWFEs. The FUV LSFs presented here are not ideal, in that they do not account for variations in the intrinsic detector resolution along the length of each detector segment, but utilize an average blur kernel. Thermal vacuum measurements show that the detector resolution is higher near the center of each segment and degrades toward the ends (see AV-04 (2008)), increasing the LSF FWHM by ~20% at the extremes. Future modeling of this effect may improve the LSF accuracy over the full spectrum. The FUV LSF models were calculated at the nominal central wavelength setting of each FUV medium-resolution grating (1309 å and 1600 å respectively, for G130M and G160M) and at intervals of 50 å over the full range of wavelengths covered by each grating (see Fig. 5). Although the aberrations change as the grating is rotated to other settings, our preliminary analysis indicates that the LSF is relatively insensitive to the settings, with only minor variations seen over most of the spectrum. We also produced model LSFs for the COS NUV medium-resolution gratings that incorporate MFWFEs. Since all the NUV gratings are planar and are used with a collimated beam, the NUV optical models assume no variation between gratings or central wavelength settings. The models were computed at intervals of 100 å over the full NUV spectral range. While the optical design of the NUV channel is very well corrected and contains inconsequential residual aberrations, small manufacturing and alignment errors are certain to exist, both internally and with respect to the OTA. We estimated these effects, along with a typical OTA "breathing" focus offset, by including 15 nm RMS WFEs (all in focus) in addition to the OTA MFWFEs. We also convolved the resulting PSFs with a MAMA detector point response function (as taken from STIS NUV MAMA measurements at Ball Aerospace), These detector wings would of course have also been present during ground testing. The relative contributions of the wings from the MAMA detector and the wings produced by the MFWFEs are illustrated in Figure 6, which compares model NUV LSFs with and without the MFWFEs included.

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In the COS data. MFWFEs resolution model whi

next section we will use these model line-spead functions in the analysis of In the FUV we will compare the effects of the full model FUV LSF including to that of a 6.5 pixel Gaussian, which is approximately consistent with the determined during ground testing. For the NUV, we compare the full LSF to a ch omits the MFWFEs, but which is otherwise identical.

Figure 5: Calculated LSFs for the COS FUV medium-r esolution gratings that include th e effects of the MFWFEs are shown as solid lin es. The dotted line shows a Gaussian LSF w ith a 6.5 pixel FWH M. Th is Gaussian profile is consistent w ith the typical FUV LSF observed during TV06.

2.4 Application of LSF Models to On-Orbit COS Data We tested the new LSF models on Sk 155 by convolving them with the STIS E140H spectra and overlaying the resulting curve onto the COS G130M and G160M data. For each prominent absorption feature we convolved the STIS spectrum with the available LSF model closest in wavelength to that of the feature. The results for G130M are shown in Figures 3a and 3b (red line, segment B and segment A data, respectively), where we overlay the convolved STIS spectra onto Galactic and SMC absorption lines of Si II (1190, 1260, detected in Segment B data) and Galactic and SMC absorption by O I 1302, Si II 1304 and C II 1334 (Segment A data). Using the new LSF models produces a markedly improved fit to the COS spectrum ­ the rounded, filled-in cores of the absorption lines are well matched, while the depths of the narrow absorption features on the wings of the broad lines are no longer overpredicted.

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Figure 6: Model LSFs for the COS NU V gratings w ith (solid black lin es) and without (co lored dash-dot lines) th e eff ects of MFW FEs included. The top panel sho ws the LSF ov er a r ange of +/- 10 pixels w ith a linear in tensity scale, while th e bottom pan el shows a +/- 20 pixel range and a log scaling of the LSF inten sity to better illustr ate the f ar w ings of the LSF.

Figure 7 shows the corresponding results for the COS G160M spectrum of Sk 155. Once again comparably good matches are obtained by using the full LSF, MFWFEs included, convolved with a high-resolution STIS spectrum. The STIS data for that analysis were obtained as part of a supplemental COS Cycle 17 calibration program (PID 12010, PI: P. Ghavamian) and made use of the same E140H grating and 0.2x0.09 aperture as the Cycle 8 observations of Sk 155, but with a different central wavelength setting (1598 å instead of 1271 å).

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Figure 7. Same as Figures 3a and 3b, but shown for the G160M observation of Sk 155. The RMS residuals to th e fits ar e RMS (for MFWFE LSF and R = 20,000 Gaussian , resp ectiv ely) = (2.4E-14; 3 .4E14) at 1527 å and (3.1 E-14; 3.8 E-14) at 1671 å, (RMS units are ergs/cm^2/s/ å) .

Figure 8. Compar ison betw een COS NUV data of G191-B2B (G285M at the centr al w avelength setting of 2617 å; solid r ed line) and STIS h igh-resolu tion data (E230 H at the cen tral w avelength setting of 2663 å, dotted black lin e) convolv ed w ith d ifferen t COS LSFs.

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Similarly, in Figure 8 we compare the COS NUV observations (G285M at the central wavelength setting of 2617 å) of the white dwarf G191-B2B with high-resolution STIS archival data (STIS E230H dataset O6HB30060 at the central wavelength of 2663 å, PID 8915, PI: J. Valenti). As shown in this figure, convolving the STIS spectra with a COS LSF representative of typical on-orbit observation conditions, both with (solid black line) and without (solid blue line) MFWFEs produces profiles that are similar to each other and that match the observed COS data. At this wavelength (2600 å) the non-Gaussian wings of the LSF are dominated by the NUV MAMA detector blur kernel, as expected. This preliminary study is consistent with a lower impact of the MFWFEs in the NUV. We are currently performing a more systematic evaluation of the impact of MFWFEs on the on-orbit LSF for the NUV medium-resolution gratings and will present a more complete analysis in the near future.

3. Implications
The above results indicate that detailed modeling of line profiles in COS spectra must take into account the real shape of the on-orbit LSF of the instrument, including the broadening effects of the MFWFEs from zonal errors in the HST OTA. We have found that by using optical parameters matching the in-focus FUV LSF of TV06, combined with the known MFWFE effects from the HST OTA, we can obtain a good match to the on-orbit COS spectral data. This suggests that the on-orbit FUV focus and alignment of COS is close to what it was during TV06. The situation for the NUV channel is more complex (see section 2.3.3). In this case the LSF is more sensitive to focus and alignment errors, and additional investigation of on-orbit data is needed in order to understand whether the models presented here are a good representation of the on-orbit LSF. Given the non-Gaussian shape of the on-orbit LSFs, the concept of spectral resolution must be defined more carefully. While the profile full width at half-maximum can be determined empirically for the LSFs found on orbit, a resolving power of R = 20,000 has a different meaning for a Gaussian LSF than for the LSFs with MFWFEs included. For this reason, it will be necessary to take these effects into account when planning and analyzing COS spectroscopic observations. 3.1 Impact on Equivalent Width Measurements As mentioned earlier and quantified in this section, two aspects of the modeled onorbit COS LSF make the detection of weak spectral features more difficult compared to pre-launch estimates of the LSFs --- the decreased resolution in the core of the LSF, and the decreased intensity in the core, which moves light out into the wings. For these calculations we will assume that the pre-launch measurements of the FUV LSFs are reasonably well approximated by a Gaussian with an FWHM of 6.5 pixels. For the NUV medium-resolution gratings, as an estimate of the pre-launch expected performance, we will use model LSFs that include the MAMA detector blur but will omit the MFWFEs. Note that for the FUV, the LSF shape is nearly independent of wavelength when the MFWFEs are omitted. However, this is no longer true when the MFWFEs are included.

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For the NUV, the LSF shape varies with wavelength, with or without including MFWFEs. To assess the impact of these effects on the data, we first establish a formal method for determining the limiting equivalent width (W) for a weak, unresolved spectral feature. This then enables us to quantitatively compare the limiting detectable equivalent width (Wlim) for the pre-launch LSF estimates (no MFWFEs) to our model of the on-orbit COS LSF (MFWFEs included). We emphasize that our calculations are intended to show a relative comparison, not to define limiting equivalent widths in absolute terms. More sophisticated analysis methods, such as profile-weighted summation, can give lower limiting equivalent widths in both cases. For simplicity, we assume a known flat continuum, C0 (cts/å), constant in wavelength, . These rather ideal conditions make the comparison more straightforward. We calculate W for an absorption feature using discrete integration by summing over pixels with uniform weight: W = [ (C0 - Ni) / C0 ) ]/ fc , where Ni is the number of counts in the ith pixel, is the dispersion in ångstroms per pixel and fc is the fractional area of the LSF contained within the region of integration (x pixels) as a function of the number of pixels. The noise in the calculated W is then: (W) = (Ni)1/2 /(C0 fc). To set an upper limit on a weak line, we define a significance threshold N, for Gaussian-distributed errors: Wlim = N * (W). The limiting equivalent width is then: Wlim = N * (Ni)1/2 / (C0 fc). For a very weak line, we make the approximation that the counts in each pixel are the same as in the surrounding continuum (i.e., the feature is undetected). Then, Ni x C0, where x is the size of the region (in pixels) where the sum is peformed. Since the signalto-noise ratio (S/N) per pixel is C0 / sqrt( C0), we can write: Wlim = N * [ / (S/N)] * [x1/2 / fc (x)]. Thus the calculated equivalent width is a function of the size of the region chosen for discrete integration. The ratio [x1/2 / fc (x)] does have a minimum, however, which define as xopt, where x is chosen to minimize the above ratio. The quantity xopt is largest number of pixels that can be summed over a profile before the noise contributi begin to outweigh the flux contributions. the we the ons

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In Tables 1 and 2 (FUV and NUV, respectively) we compare the limiting equivalent widths for unresolved spectral features detected at a 3 significance level (N = 3) for the LSFs without the MFWFEs (approximated by a Gaussian in the FUV) and for the full model of the COS LSFs (MFWFEs included) as a function of grating and wavelength. We assume C0=100 cts/pixel for these calculations (i.e., S/N=10 per pixel). Note that the tabulated results are obtained from a simple summation of counts in the absorption line, and can likely be improved by using profile-weighted summation methods. As can be seen from the results in Tables 1 and 2, the FUV G130M and G160M gratings, as well as the NUV G185M grating, show both decreased resolution in the core of the LSF and decreased spectral purity. The G225M and G285M gratings show more modest increases in the FWHM of the LSF, but the increased power in the wings of the LSF reduces the detectability of faint lines. For this example, we find that including the effects of the MFWFEs increases the limiting equivalent width by 31%-38% for G130M, and by 26%-33% for G160M. For the NUV gratings, the effect is 34%-42% for G185M, 24%-28% for G225M, and ~ 18% for G285M. While the core width of the NUV LSF is less affected by the MFWFEs, there is still a substantial amount of power in the far wings. This reduces the signal in the core of the LSF. In light of these effects, one might qualitatively expect that the impact would be most severe on narrow, unresolved features; lines that are intrinsically broadened should be less impacted. To assess this more quantitatively for the more strongly affected FUV channel, we have convolved a series of Gaussian spectral features with nominal Doppler parameters of b = 0, 10, 25, 50 and 100 km s-1 with both a Gaussian instrumental LSF and our modeled on-orbit COS LSF for the G130M and G160M gratings. Figure 9 below bears out our qualitative expectations. The results would be similar for a plot of NUV equivalent widths as a function of wavelength and line width, although the changes would be somewhat more moderate for the long wavelength G285M grating. In Figure 10 we show the fractional enclosed energy within the LSF, measured from the center of the profile, for both FUV and NUV. The differences between the modelled on-board LSFs (MFWFEs included) and the typical LSFs without MFWFEs as inferred from ground testing can be clearly seen for both spectroscopic channels. At the longer NUV wavelengths, even though the FWHM of the model on-orbit LSFs are only slightly wider when MFWFE effects are included, the extra wings added by the MFWFEs still decrease noticeably the spectral purity and the contrast level of the observed spectra.

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Figure 9. Limiting equivalen t wid ths as a function of wav elength for 3 detections at a S/N of 10 per pixel, shown for spectral features in the FUV with both the full mo lines) and the 6 .5-pixel FWH M Gaussian approximation of the LSF from TV06 different colors correspond to features w ith diff erent intr insic Doppler parameter s b km s-1 (red) , 25 km s-1 (green), 50 k m s-1 (blue) and 100 km s-1 (mag enta) .

of absorption features deled COS LSF (solid (dash ed lines) . The = 0 km s-1 (black), 10

3.2 Impact on Signal-to-Noise Ratios of Detected Features The broadening of the COS LSF due to the MFWFEs occurs at the expense of the amplitude at the line center. For the FUV medium-resolution gratings, the calculations discussed above indicate that the LSF peak of the MFWFE models is 24% - 30% and 22% - 27% lower in G130M and G160M, respectively, than the peak of a Gaussian typical of the TV06 FUV LSF (FWHM = 6.5 pixels). This results in 30% - 40% and 25% -30% lower signal-to-noise in the equivalent width of an unresolved absorption feature for G130M and G160M, respectively, compared to a typical TV06 FUV LSF. However, broad-band continuum measurements should be only minimally affected. For the NUV medium-resolution gratings the LSF peak for the MFWFE models is up to 32% lower in G185M than the peak of similar LSF models without the MFWFEs. For G225M and G285M, the MFWFE effects lower the peak of the LSF by about 20%. For the G185M grating, this results in a 30% - 40% reduction in the signal-to-noise in the equivalent width of an unresolved absorption feature. However, the reduction is only about 20% for G225M and ~ 15% for G285M.

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Figure 10. The enclosed en ergy fraction of the COS LSF f or an unresolved spectral feature, as measured from the center of the profile (co llapsed along the cross-dispersion direction). A Gaussian with FWH M = 6.5 å matches typical FUV results from TV06 ( top panel). For the NUV (bottom panel) w e show model profiles with and without the eff ects of the OTA MFWFEs in cluded.

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4.

Summary

Analysis of FUV spectra obtained during SMOV indicates that the LSF of COS with the HST OTA departs from the Gaussian profile observed during ground testing. It exhibits a broadened central core and strong, broad wings, where a significant fraction of the flux (up to 40%, depending on the wavelength) is redistributed. The reason for the difference is that zonal (polishing) errors on the HST OTA introduce MFWFEs into the beam entering the COS spectrograph, which in turn diverts more light from the core of the LSF into the wings. The MFWFEs could not be included in the RAS/Cal stimulus that was used in the pre-launch testing, and their impact on the on-orbit LSF was not expected to be large. We performed optical modeling of the COS LSF with the MFWFEs included, and tested these new models on COS data obtained during SMOV. We found that convolving these LSF models with very high-resolution STIS E140H spectra leads to an excellent match to the observed COS FUV spectra, in contrast to the poor fit resulting from the convolution with Gaussian LSFs. This indicates that the impact of the MFWFEs on the COS LSF is larger than had been anticipated. The size of the MFWFEs in the HST OTA (~ 18 nm Krist & Burrows 1995) are smaller than the wavelengths of light observed by HST, and this reduces their importance at longer wavelengths. The fraction of light diverted into the wings of the LSF is therefore smaller in the NUV channel of COS than in the FUV channel, and decreases toward longer wavelengths, as the LSF wings progressively shrink moving into the NUV. However, the effects of the MFWFE remain signficant at all wavelengths covered by COS. Further characterization of the observed on-orbit COS LSF in the NUV is in progress and results will follow in a subsequent report. We computed a series of LSF models with MFWFEs included for all FUV and NUV gratings; these models are provided online to the astronomical community. For the FUV channel a single (default) central wavelength setting per grating was considered, namely 1309 å for G130M and 1600 å for G160M. For each of these settings, LSFs are provided at intervals of 50 å. For the NUV medium-resolution gratings (G185M, G225M and G285M) a single model as a function of wavelength covering the whole NUV spectral range was instead calculated at 100 å intervals. For a given FUV grating there are actually slight differences among the LSFs of each central wavelength setting calculated at the same wavelength. These differences reflect slight discrepances in the aberration content of each setting. In the NUV there are practically no differences between different gratings and central wavelengths. We are currently in the process of computing LSFs for all FUV central wavelengths using the aberration constants appropriate to each central wavelength setting. We will provide this more extensive library of LSFs to the astronomical community as soon as they become available. The optical path and aberrations for all of the NUV gratings, including the G230L, are very similar. The encircled energy as a function of pixel offset should be the same for all gratings at a given wavelength, and so the LSFs calculated for the medium resolution NUV gratings can be used for the G230L as well. For the G140L, the changes to the LSF will be qualitatively similar to those for the medium-resolution FUV gratings, but will differ in detail because of variations in the aberration constants. We have provided LSFs for the G140L, but they will be discussed in a later report. The LSF models can be used by COS observers to assess the impact of the on-orbit

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COS LSF on their planned science observations and/or to analyze data acquired on-orbit. We already anticipate that the MFWFE effects are most important for science with the medium-resolution FUV gratings, G130M and G160M, and with the G185M NUV grating. In contrast, due to the nature of the science likely to be conducted with the low dispersion G140L and G230L gratings, we expect that the MFWFE effects on most science conducted with them will be minimal. Detailed on-orbit LSF characterization and modelling for the G140L and G230L will be provided in the near future. Tables 1 and 2 provide quantitative estimates of the model LSF properties that can also be used by COS observers to assess the impact of the observed on-orbit LSF on their planned science.
Table 1: Li miting equivalent widths for unresolved FUV absorption lines superposed on a bright continuum (C0 = 100 cts/pixel, corresponding to S/ N=10 per pixel)1 LSF Fraction within F WHM LSF Fraction within 6.5 pixels

Grating

(å)

LSF Peak

LSF F WHM (pixels)

opt(3) (må)

Wlim(3) (må)

G130M G130M G130M G130M G130M G130M G130M G160M G160M G160M G160M G160M G160M G160M G160M
1

GAUSS 6.5 pixel 1150 1200 1250 1300 1350 1400 GAUSS 6.5 pixel 1450 1500 1550 1600 1650 1700 1750

0.1445 0.0990 0.1013 0.1026 0.1042 0.1067 0.1085 0.1445 0.1047 0.1067 0.1075 0.1086 0.1099 0.1116 0.1120

6. 7. 7. 7. 7. 6. 6. 6. 7. 7. 7. 7. 6. 6. 6.

50 43 28 21 12 97 89 50 25 10 06 01 96 91 98

0.761 0.586 0.587 0.589 0.591 0.592 0.596 0.761 0.607 0.607 0.607 0.609 0.613 0.618 0.626

0.761 0.536 0.545 0.551 0.557 0.566 0.574 0.761 0.565 0.572 0.575 0.579 0.585 0.593 0.598

75.77 93.72 91.72 91.72 89.73 87.74 85.74 92.95 110.07 107.62 107.62 107.62 105.18 105.18 105.18

9.9 13.7 13.5 13.4 13.3 13.1 13.0 12.1 16.1 15.9 15.9 15.8 15.6 15.4 15.3

Table 1 columns are (1) the FUV grating chosen, (2) indication of a Gaussian LSF (as an approximation for TV06 results) or of the modeled wavelength for the on-orbit LS F (MFWFEs included), (3) the pea k intensity of the LSF (nor malized to an area of unity), (4) the FWHM of the LSF in pixels, (5) the fraction of the LSF area cont ained within the FWHM as indicated by column 4, (6) the fraction of the LSF ar ea contained within the nominal resolution element ­ FWHM of the Gaussian observed during TV06, (7 ) the optimum width for the region of integration, opt, in må for a feature detect ed at a 3 significance level (N = 3), and (8) the calculated limiting equivalent width for a 3 detection feature.

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Table 2. Li miting equivalent widths for unresolved NUV absorption lines superposed on a bright continuum (C0 = 100 cts/pixel, corresponding to S/ N=10 per pixel) LSF LSF LSF Fraction Fraction opt(3) F WHM within within 3 (må) (pixels) FWHM pixels
w ithout MFW FEs 0.805 88.80 and MFW FEs 0.572 98.67 0.585 98.67 0.596 98.67 0.606 98.67 without MFWF 0.783 and MFW FEs 0.615 0.622 0.628 0.633 0.638 Es 81.4 8 8 8 8 8 8 8 8 8 8 .0 .0 .0 .0 .0 0 0 0 0 0

Grating

1

(å)

LSF Peak

Wlim(3) (må)

G185M G G G G 1 1 1 1 8 8 8 8 5 5 5 5 M M M M

1700 1700 1800 1900 2000

LSF including 0.423 LSFs inclu 0.285 0.291 0.297 0.303

G225M G G G G G 2 2 2 2 2 2 2 2 2 2 5 5 5 5 5 M M M M M

2500 2100 2200 2300 2400 2500

G285M G G G G G G G
1

3200 2600 2700 2800 2900 3000 3100 3200

2 2 2 2 2 2 2

8 8 8 8 8 8 8

5 5 5 5 5 5 5

M M M M M M M

G185M detector blur, bu t 1.90 0.645 ding d etector blur 2.07 0.468 2.05 0.478 2.04 0.487 2.04 0.494 G225M LSF including detector blur but 0.405 1.94 0.629 LSFs including d etector blur 0.309 2.04 0.501 0.312 2.04 0.507 0.315 2.04 0.512 0.315 2.04 0.516 0.318 2.05 0.520 G285M LSF including detector blur but 0.384 1.99 0.615 LSFs including d etector blur 0.318 2.05 0.523 0.321 2.06 0.526 0.321 2.06 0.528 0.321 2.07 0.529 0.321 2.08 0.531 0.318 2.08 0.532 0.318 2.09 0.533

23.7 3 3 3 3 3 3 2 1 .7 .0 .3 .8

21.8 27.9 27.6 27.4 27.1 27.0

without MFWFEs 0.757 104 and MFW FEs 0.641 106 0.644 106 0.645 109 0.647 109 0.648 109 0.648 112 0.648 112

.00 .6 .6 .3 .3 .3 .0 .0 7 7 3 3 3 0 0

27.4 3 3 3 3 3 3 3 2 2 2 2 2 2 2 .5 .4 .3 .3 .2 .2 .2

Table 2 colu mns are (1) the NUV grating chosen, (2 ) indication of the wavel ength for the LS F calculations; note that results depend much less strongly on wavelength when the OTA MFWFEs are omitted, (3) the peak intensity of the LSF (normalized to an area of unity), (4) the FWHM of the LSF in pixels, (5) the fraction of the LSF area contained within the FWHM as indicated by column 4 , (6 ) the fraction of the LS F within 3 pixels (r esolution estimate from TV06; see Section 1.1), (7) the opti mu m width for the region of integration, opt, in må for a feature detected at a 3 significance level (N = 3), and (8) the calculated limiting equivalent width for a 3 detection feature.

We also assessed the impact of the newly characterized on-orbit LSF on the

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detectability of absorption lines (see Tables 1 and 2). For a weak unresolved absorption line superposed on a bright (S/N=10 per pixel) continuum, we obtain a limiting equivalent width for a 3 detection that is at worst 40% higher than the value obtained assuming the thermal vacuum LSF for the G130M grating, and up to 30% higher for the G160M grating (the results can likely be improved by using a flux-weighted summation, rather than the straight pixel sum assumed here). Similarly, we obtain values up to 40%, 30%, and 20% higher for the G185M, G225M and G285M NUV gratings, respectively, compared to a typical NUV LSF without the MFWFE effects. So while the G225M and G285M resolution, as determined by a formal measurement of the FWHM is minimally impacted by the MFWFEs, the NUV limiting equivalent widths are still significantly affected. In general, spectra in all COS gratings will provide reduced contrast of spectral features and reduced spectral purity as compared with pre-launch estimates. ASCII text files containing the tabulated LSFs dicussed in this report are available at: http://www.stsci.edu/hst/cos/performance/spectral_resolution/ .

5. Change History for COS ISR 2009-01
Version 1: 2 October 2009 - Original Document

References
COS IDT, "Cosmic Origins Spectrograph (COS) Science Operations Requirements Document (OP-01)," (2003) COS IDT, "COS Pre-Launch Calibration Data" Document (AV-04)," (2008) "Hubble Space Telescope Cosmic Origins Spectrograph Contract End Item (CEI) Specification" (STE-63) (2004) Kaiser, M. B., et al. 2008, SPIE 7014, 214 Krist, J. E. & Burrows, C. J. 1995, Applied Optics, 34, v22, p 4951 Soderblom, D. R., et al. 2007, "The Cosmic Origins Spectrograph Instrument Handbook, version 1.0", (Baltimore, STScI) Welty, D. E., Lauroesch, J. T., Blades, J., Hobbs, L. M. & York, D. G. 2001, ApJ 554, L75

Acknowledgements
We thank Matt Lallo for helpful discussions on the HST optics, and the following people for thoughtful comments on various stages of the draft: Kenneth Sembach, Knox Long, Tom Brown, Jason Tumlinson, Thomas Ake, Christopher Thom, Cynthia Froning, Dave Sahnow, and Steve Penton.

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