The new COS FUV wavelength dispersion solution reference file (DISPTAB), 05i1639ml_disp.fits, includes updated dispersion coefficients
(zero points and slopes) for data taken at LP1 (i.e. prior to 23 July 2012) with the G130M settings (1291, 1300, 1309, 1318, 1327) and G160M
settings (1577, 1589, 1600, 1611, 1623). No updates have been made at this point to the G140L dispersion solutions. Updates to the LP2
and LP3 dispersion solutions for the G130M and G160M settings will be released in the near future.

Details about how the updated zero points and slopes were derived are given below.

Users interested in COS FUV G130M or G160M data obtained before 23 July 2012, are encouraged to re-retrieve their data from the Hubble Space Telescope Archive, hosted by MAST, at http://archive.stsci.edu/hst/ to ensure they have the highest quality data available.

### Deriving updated zero points and slopes for the G130M and G160M LP1 dispersion relations

The G130M and G160M dispersion relations are given by first order polynomials, i.e. a zero point and a slope, which assign wavelengths based on the corrected pixel position (corrected for thermal, geometrical, and drift effects). Each cenwave has a different dispersion relation. The updated zero points and slopes were derived from a combination of ray-trace modeling and cross-correlation between COS and STIS spectra (with the STIS spectra used as a reference wavelength scale). The HST archive was mined for targets observed both by COS (G130M, G160M) and STIS (E140H, E140M) and 16 unique targets were identified with LP1/G130M and 17 unique targets for LP1/G160M data. For those targets, cross-correlation windows were defined around absorption or emission lines (avoiding the N I, Lyα, and O I airglow regions as well as regions around stellar wind lines) and wavelength offsets between COS and STIS were derived. The wavelength offsets between COS and STIS spectra were fit to a linear solution, and provided preliminary dispersion coefficients (zero-point and slope). The relation between dispersion slope and OSM position is consistent with ray-trace modeling, modulo focus adjustments (see Figure 1). The ray-trace model was created at an arbitrary focus value, implying that the relation between dispersion slope and OSM position in the model is vertically offset by an arbitrary amount compared to on-orbit values. Therefore, the final dispersion slopes were obtained by minimizing the reduced chi-square between dispersion slopes measured from COS-STIS cross-correlations, and the shifted ray-trace model.

Figure 1: Dispersion coefficients (slopes) for G130M (top) and G160M (bottom) as a function of cenwave,
where G130M/1309/FP-POS=3 and G160M/1600/FP-POS=3 are represented by zero (so G130M/1291/FP-POS=3 and G160M/1577/FP-POS=3
correspond to -8 while G130M/1327/FP-POS=3 and G160M/1623/FP-POS=3 correspond to +8). Dispersion coefficients in the
previous DISTAB are shown in black, while dispersion coefficients derived by the COS-STIS cross-correlation are shown
in red. The solid blue line represents the original ray-trace model, while the dashed blue line represents what is
in the new DISPTAB.

The new linear dispersion coefficents were tested by cross-correlating COS exposures with different cenwave and FP-POS settings obtained within the same visit. This prevents bias in the analyses dues to uncertainties in the target acquisition. The COS-COS cross-correlation data set includes 97 unique targets for G130M and 89 for G160M. Like the COS-STIS cross-correlations, cross-correlation windows were defined for each target around absorption or emission lines (avoiding the N I, Lyα, and O I airglow regions as well as regions around stellar wind lines). Figure 2 shows some examples of the results of the COS-COS cross-correlations using the previous DISPTAB (left 4 panels) and the new DISPTAB (right 4 panels). The scatter and residual slopes are substantially reduced compared to the previous dispersion solutions. For most modes, one standard deviation of the residual wavelength offsets is well within +/- 3 pixels.

Figure 2: Examples of the residuals of the COS-COS cross-correlations using the previous DISPTAB (left 4 panels)
and the new DISPTAB (right 4 panels), for G130M/FUVB (top 4 panels) and G160M/FUVA (bottom 4 panels). Both the
means and standard deviations are improved when the new DISPTAB is used.

Figure 3: Mean shifts and standard deviations derived by cross-correlating COS exposures obtained in the same visit
but with different cenwaves, with the old DISPTAB (green) and new DISPTAB (purple). The number of cross-correlation
windows that were used for each reference cenwave is also given.

Due to target acquisition uncertainties, the zero-point of the dispersion solutions derived from COS-STIS cross-correlations and ray-trace modeling are only accurate to +/- 3 pixels. The wavelength zero-points derived from COS-STIS cross-correlations were therefore adjusted using the results of the COS-COS cross-correlations, to ensure that mean offsets between COS exposures taken at different cenwaves average out to zero. Specifically, the COS-COS cross-correlations provided mean and RMS wavelength offsets for 10 different combinations of cenwaves within a grating (e.g.,1327 vs 1291 for G130M) . The offsets were first normalized to the middle cenwave (1309 for G130M, 1600 for G160M). The mean wavelength offsets between each cenwave and the middle cenwave of the grating was then subtracted from the zero-point for this given cenwave. With these zero-point adjustments, the mean wavelength offsets between different cenwaves are < 1 pixel (Figure 3).

Figure 3 summarizes the mean shifts and standard deviations determined by cross-correlating COS exposures obtained in the same visit but with different cenwaves, with the old DISPTAB (green) and new DISPTAB (purple). For most of the G130M and G160M settings there is an improvement in both the mean and standard deviation, indicating that for most settings the overall uncertainties in the wavelength calibration are now within +/- 3 pix (1 sigma). It should be noted that this does not include any target acquistion errors (+/- 3 pixels), which may introduce a constant wavelength offset between different COS spectra. The accuracy of the new dispersion solutions is also limited by detector walk and residual geometric distortion effects. These two effects are currently under study.

Examples of the improvement seen with the targets used in the COS vs STIS cross-correlation can be found here.

With the updated dispersion solutions derived from on-orbit data there is no need for the "D" and "D_TV03” values, which were set to zero for the G130M and G160M cenwaves (see COS ISR 2010-06 for more information about these values). A new header keyword "LIFE_ADJ" has also been added to the new DISPTAB, to account for the lifetime position dependence of the dispersion coefficients.