LETGS and HETGS Dispersion Relation Analysis

LETGS and HETGS Dispersion Relation Analysis

O. Johnson, J. Drake

Last update: 3 July 2000

The absolute wavelength accuracy of the LETGS and HETGS has been investigated by comparison of observed wavelengths with accurate theoretical and experimental values. The primary result of this analysis is that the nominal value of the Rowland diameter appears to be in error by approximately 6 mm. The currently accepted value is 8632.31 +/- 0.50 mm; a value of ~ 8638 mm is required to match observations.

This value is derived from analysis of the following observations of Capella reduced with the latest (U5) version of pipeline processing. Earlier versions of the pipeline included a number of errors which affected the observed dispersion relation.

obsid grating/detector exposure (ksec)
1248 LETG/HRC-S 80
55 LETG/ACIS-S 50
57 HETG/ACIS-S 35


Obsid 63, a 70 ksec observation of Procyon, was also analyzed, but is not included in the derivation of the values below. The Procyon wavelengths were generally consistent with those found for Capella.

An attempt was made to isolate only truly unblended lines for this analysis; the initial linelist can be seen here along with comments on line strength and the quality of the profile. Lines for which the fit clearly did not match the data were omitted and are preceeded in the list with a #. Of the 32 lines originally identified as strong and unblended, 22 were suitably clean for this analysis, giving 44 points between positive and negative orders observed by LETG/HRC-S. The LETG/ACIS-S and HETGS observations include subsets of these lines, due to the limited detector area and energy ranges of these data. Some suspect points still appear on the plot below, and will be investigated individually.

Lorentzian profiles were fit to each line using Vinay Kashyap's IDL routine, grafit. Plots of individual fits can be found in the following directories, with filenames denoting theoretical line wavelength:


The reference centroids were then plotted against the difference of the measured centroids and the reference centroids, as shown below. For LETG/HRC-S lines, there is an overall scaling factor, such that observed wavelengths are ~ 0.11% larger than they should be, which is greater on the outer MCP plates (~0.12%) than on the central one (~0.06%). A similar effect is seen in LETG/ACIS-S and HETGS observations, with an average magnitude of ~0.09%. Linear fits to different subsets of the data are tabulated below.

Causes of wavelength shift due to Capella systemic and binary motions are too small to account for the observed deviations. C.O.G. motion is -14 km/s, which is only a 0.005% effect, and Capella's binary motion, even assuming the extreme case in which all X-ray flux originates from the receeding G1 star, can contribute only an additional 0.008% offset.

Error in detector pixel size could cause the observed multiplicative effect, but is very unlikely to be the same in ACIS and HRC. Similarly, error in grating periods, though unlikely due to good subassembly verification, could be to blame, but would not be identical for the high, medium, and low energy gratings.

While processing error would affect all grating/detector combinations identically, it has been ruled out. A MARX simulation of a monochromatic spectrum was run, resulting in 1st, 2nd, and 3rd order lines in negative and positive orders. The data were fed through U5 processing by hand, and analyzed in the same way as the Capella data. Individual fits can be seen here. The resulting wavelength offsets, denoted by the pink crosses in the figure below , indicate that the 'observed' wavelengths were equal to the input wavelengths to within the errors.

The only other parameter in common to both detectors and all gratings is the Rowland diameter. The observed wavelength errors of order 0.1% suggest the nominal value for the Rowland diameter is too small by several mm, despite its specified accuracy of 0.50 mm. Overplotted on the figure below are lines showing the expected offset of reference wavelength from observed wavelength for various values of the Rowland diameter. Though the higher slopes in the outer plates of the HRC-S are not reproduced, the curve for a Rowland diameter of 8638 mm comes close to fitting the observed data.

The points on the positive order outer plate seem to be shifted vertically from those on the other two plates. One explanation for such a vertical shift is error in that plate's tilt angle, but a 20% error in the nominal value of 1.43 degrees would be necessary. This offset, as well as the slope variation from plate to plate, is still being investigated.





(A similar plot covering the +/- 60 AA wavelength range only is available here .)

data included in fit slope of linear fit (A) error (A) derived value of
Rowland diameter (mm) 		error (mm)
LETG/HRC-S: central plate 0.00063 0.00008 8637.71 0.70
LETG/HRC-S: outer plates 0.00115 0.00002 8642.20 0.25
LETG/HRC-S: negative orders 0.00197 0.00033 8649.30 2.92
LETG/HRC-S: positive orders 0.00090 0.00036 8640.11 3.18
LETG/HRC-S: all 0.00111 0.00003 8641.88 0.30
LETG/ACIS-S 0.00094 0.00009 8640.41 0.77
All ACIS-S points 0.00099 0.00006 8640.85 0.49
HEG/ACIS-S 0.00036 0.00063 8635.42 5.47
MEG/ACIS-S 0.00090 0.00010 8640.10 0.89
Current Rowland diameter value - - 8632.31 0.50