Subsections

• 5.11.1 Preparation of the data
• 5.11.2 Stability of the line profiles
• 5.11.3 Characteristics of the profiles. Comparison to Gaussians.
• 5.11.4 Effect of a lower spectral sampling

5.11 Grating Resolution and Characterisation of the Line
Profiles

5.11.1 Preparation of the data

The study of the grating profile was performed with data obtained over the ISO lifetime for wavelength calibration (see Table 5.12 and Figure 5.22). In order to have a homogeneous sampling, only those data obtained with AOT L01, an oversampling of 8, 6 scans of the full grating range and the same number of forward and backward scans were used.

The data processing was performed with the ISAP software. The standard processing of the selected observations is summarized by the following scheme:

• For each object we selected up to 20 observations well spread all over the mission.
• Each individual scan was checked for the presence of glitches or any anomalous feature. Glitches were removed and anomalous scans discarded.
• Each scan was rebinned to 32 points per resolution element.
• Forward and backward scans were averaged separately.
• In the case of extended sources, the resulting scans were corrected for the presence of fringes.
• The continuum was fitted by a polynomial and subtracted off.
• The profile was normalised so that the peak of all profiles was one.
• The resulting spectra were re-centred to the laboratory wavelength, so that profiles from different velocity sources can be compared.

The products were thus one spectrum per scan direction per spectral line per detector per observation per object.

5.11.2 Stability of the line profiles

In order to define as general a profile as possible, parameters susceptible of inducing profile variations were looked for in a step by step approach. When a parameter had proved not to induce any significant variation, the profiles were averaged over this parameter for the subsequent study.

• Stability with time. All observations of the same line on the same detector for the same object were plotted together to look for time variations. The peak to peak variations in the peak height of the line were as low as 2% for the strong lines and always less than 20% in the worst cases corresponding to the faintest lines used. No trend was found with time so these numbers are representative of the photometric accuracy of the LWS detectors. The variation of the line width with time is in general much smaller than the sampling interval of the observations (8 points per resolution element). We concluded that there are no significant time variations in the instrumental profiles.

• Search for transient effects: comparison of forward and backward scans. Slight differences do exist between the forward and backward scans of the same line from the same object due to transient or memory effects. In the short wavelength detectors the difference in the peak is always less than , while in the long wavelength detectors it can be up to . There is no trend with the flux level. In the base of the line some broadening can be observed, in general on the short wavelength side for forward scans and on the long wavelength side for backward scans. The opposite case is also seen though, possibly due to errors in placing the continuum.

  Because the effect is symmetrical when adding the forward and backward scans together, and because most of the differences between forward and backward scans are seen in the feet of the line, where they are confused with continuum features and thereby will be removed by the baseline subtraction process, our recommendation, as long as no formal transient correction is available, is to use both scan directions together. We have thus averaged forward and backward profiles for the rest of the study.

• Variation of line profile with object and detector. In general the profiles show very little difference from object to object (the differences are less than 4%) and they show no significant differences between lines coming from different detectors.
  There is one exception with the clearly anomalous line at m on detector SW2. It shows a strong asymmetry towards the short wavelengths for some objects. The asymmetry is clearly not real because it does not appear when the same line is observed with the detector SW3. It is not due to the detector either, as two other lines falling on SW2 (at m and m) do not show any anomaly. The m line on detector SW2 has thus been excluded from the derivation of the mean profile obtained by averaging all lines from all detectors in all objects.

• Difference in line profiles from point and extended sources. The profiles from extended sources and from point sources were kept separate to check wether off-centred emission was creating any distortion in the line profiles. The comparison of the mean profiles shows that, if anything, the profiles from the extended sources are more symmetrical and more similar to Gaussians than the point source profiles. We thus concluded that there is no distortion coming from the source extension or off-centring and we have averaged all profiles from point sources and extended sources together.

In conclusion, we have created two mean grating profiles (one for SW and one for LW detectors) which are the average of all lines listed in Table 5.12 except the 57 m line on SW2.

5.11.3 Characteristics of the profiles. Comparison to Gaussians.

When considering all the LWS optical elements and detector characteristics, the wavelength response function is not expected to be Gaussian. It is however always convenient when measuring a line intensity to be able to use a Gaussian aproximation.

Figure 5.24: Measured grating profiles (plus signs) and comparison with a Gaussian fit (solid line). The residuals, i.e. the difference between the measured profile and the Gaussian fit, are also shown (dashed line). Up: profile for short wavelength detectors (SW1 to SW5) ; down: profile for long wavelength detectors (LW1 to LW5).

Figure 5.24 shows the comparison of the measured mean profiles with a Gaussian function fitted to them. It also shows the residuals, i.e. the differences between the two profiles.
Table 5.16 lists the line flux, full width at half maximum (FWHM) and peak heights both for the measured profiles and for the fitted Gaussian. This shows that the error made on the determination of the flux with a Gaussian fit is only of the order of .

Table 5.16: Parameters of the measured grating profiles compared with the results of Gaussian fits.

	Observed mean profile				Gaussian fit to the mean profile
	FWHM	line flux	height		FWHM	line flux	height
	[m]	(normalised			[m]	(normalised
		to peak=1)				to peak=1)
SW detectors			1.00
LW detectors			1.00

The line full widths at half maximum that we measure on our profiles are slightly larger than those measured before launch: 0.31 instead of 0.29 for the short wavelength detectors, and 0.61 instead of 0.60 for the long wavelength detectors. This is likely due to the broadening effect of transients.

5.11.4 Effect of a lower spectral sampling

The above study of the line profile has been conducted with the highest oversampling permitted in the observations, an oversamping of 8, i.e. eight points per spectral element. However, in AOTs L01 and L02, four different oversamplings were permitted: 8, 4, 2 and 1. Following the Nyquist theorem, an oversampling of two or higher allows derivation of the line flux with a precision better than 5% (a sampling of 1 point per spectral resolution element would be clearly insufficient). However, we would like to warn the user that a Gaussian fit to observations obtained with an oversampling of 2 or even 4 might give results with a higher error than the one quoted above for an oversampling of 8. This is due to the fact that when a line is scanned quickly, the transient effects are more important and tend to broaden the line. This effect should be reduced once a transient correction (Section 6.9) is available.