HETGS Absolute Wavelength - Preliminary July 2000

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Ground calibration values have served to define the HETGS absolute wavelength scale since launch. It is reasonable to update this calibration in light of observations. This note is meant as an input to the process, suggesting a general direction and further work.

The calibration of the HETGS in absolute wavelength depends on (at least) three components which are summarized here:

i) A data analysis method and calibration values which assigns wavelengths to diffracted events. (Includes: periods, pixel sizes and gap geometry, Rowland spacing, zeroth-order location, etc.)

Here, the data analysis was carried out using the HAK code operating on CXC events' Sky X,Y coordinates. The wavelengths assigned by the HAK code are in agreement with with the new CXC level 1.5 wavelengths, version "2.0alpha_000605" [dph].

ii) A set of "known" line wavelengths.

Here, the "known" wavelengths come from Kelly, see the explicit values in the procedure make_theory_lists.pro and the short list below.

iii) A method to measure line centroid locations and errors and correct for errors in zero-order centroid location.

Here, simple Gaussian fits were carried out by the HAK software; this fitting is estimated to be accurate to ~50 ppm compared to other fitting methods (e.g., ISIS). Averaging the plus and minus order locations and determining offsets between observations was done by eye.

Definitive values and versions of the above components will lead to an absolute wavelength calibration with accuracy better than 300 ppm (100 km/s) in the near future.

Preliminary Conclusions

*** Numerical values given below are presented to give an idea of the size and direction of expected calibration parameter changes - they are NOT finalized calibration values. ***

[ ] The HEG energies appear consistently ~ -150 ppmE compared to MEG values. Taking the HEG period as fixed, this suggests modifying the MEG period by increasing it by ~ 150 ppm so that HEG and MEG energies agree.

[ ] On average the MEG and HEG (HAK) measured energies need to be increased by +420 ppmE and +420+150 = +570 ppmE respectively to agree with the Kelly reference values.

These two corrections could be accomplished by increasing the HETGS Rowland spacing value by ~ 570 ppm (8632.65 to 8637.57 mm) and increasing the MEG period by ~ 150 ppm (4001.41 to 4002.01 A).

[ ] Earlier CXC s/w versions produced TG_LAM values that were ~ 500 ppm larger than the new "2.0alpha" version. Combining this analysis error with the calibration values above we have that previous MEG and HEG TG_LAM values need to be decreased by ~ 900 ppm for MEG and ~ 1050 ppm for HEG (and ~ 1100 ppm for LETG/ACIS) in order to be absolutely accurate.

[ ] The observation-to-observation variation of the wavelength scale, e.g., an upper limit on the error of the HETGS absolute energy, is of order +/- 50 ppm for the few Capella observations. Taking more observations of other targets into account (see table below) the range about +/- 200 ppm about the average; this range, however, includes any velocity-produced shifts intrinsic to the sources used in the analysis.

[ ] Based on scant analysis of a single Capella observation (obsid 55) the LETG/ACIS-S (HAK) measured energies also need to be increased by ~+420+200 = +620 ppmE to agree with the reference values. (The +200 ppmE is the correction to convert from LEG/ACIS energies to MEG/ACIS values.) This is very close to the HETG value above (570 ppm) and suggests a single common change to the Rowland spacing value may be in order. Note added 7/25/00: The "200ppm" difference between LEG and MEG is very crude; it may be closer to 400-500 ppm. A better estimate of this HETG/LETG "spacing/period" comparison will be determined from uniformly reprocessed Capella-HETG-ACIS and Capella-LETG-ACIS data sets and by using LEG 3rd-order (or higher) events for better accuracy.

This plot shows the residuals in parts per million (ppm) between the measured line energies and the Kelly reference values. Measured energies for each of the four first-order spectra from the HETG are shown seperately as indicated in the key. Zeroth-order location effects can offset the plus and minus orders; the average of the plus/minus orders can be determined by eye as the mid-point between the open symbols (for MEG) and the x-* symbols (for HEG).

The data here were processed by version "2.0alpha" of the CXC AP processing [thanks Dave!] followed by HAK analysis (with ACIS angular pixel size = 0.49200 arc second.) Artificial red shifts, z, have been used to apply the recommended 420 ppm and 570 ppm corrections to the MEG and HEG energy values. For reference, dotted and dashed lines indicate the specified mechanical repeatability for HETG insertion (33 ppm) and the effect of a 6 mm offset in the Rowland spacing.

Data Analysis

HAK analysis of CXC Level 1 FITS events files creates rdb tables of lines found in MEGm1, MEGp1, HEGm1, and HEGp1 part-orders. The input files are grade selected and S4 destreaked. The Sky X, Y coordinates are used, flipped about Y and rotated to pseudo-detector axes. The Rowland spacing for the HETG is 8632.65 mm. Simple peak finding and simple Gaussian fits to the energy-binned histograms are used.

The line lists for an observation are read in and compared to reference values from another observation or fake lists made from theoretical line wavelengths. Plots are created showing the deviation of the observation and reference line energies in ppm. Procedure used is ~dd/idl/marx/ compare_lines.pro .

The plots show the ppm deviations for the four part-orders listed above. Zeroth-order centroid errors are clearly seen by differences in plus and minus orders' values. The average of plus/minus deviation is estimated by eye for MEG and HEG measurements.

The hc value of 12.3985 is used to convert between wavelength and energy.

Reference Wavelengths

Reference wavelengths are taken from Kelly (1987?) for the bright lines identified in Canizares et al. Capella paper, supplemented by the other two Ne IX lines and removing the Fe line which is close to the Ne X line. Fake rdb line lists are created from these values by the procedure ~dd/idl/marx/ make_theory_lists.pro .

Assembling Results

Agreement with absolute wavelengths and variations from observation to observation are estimated by looking primarilly at the 6 lines used in chip-gap measurements:

 Line    lambda-Kelly   Notes
 O VIII   18.967  A
Fe XVII   15.013  A
Ne X      12.132  A
Mg XI      9.1685 A     highest-energy line of triplet
Mg XII     8.419  A     
Si XIII    6.6477 A     highest-energy line of triplet

The following table summarizes the variation from observation to observation based on these lines - note that it is assumed (perhaps eroneously) that all energy variations are due to an instrumental effect as opposed to source velocity shifts.

HETGS observations:
Obsid Target Obs Date ppmE57 * ppmEMEGRef **
.at 110 C: . ..
62538 HR1099 9/14/99 -270 +150
1103 Capella 9/24/99 -65 +355
1318 Capella 9/25/99 +33 +453
16 AB Dor 10/9/99 +100 +520
1451 II Peg 10/17/99 -280 +140
609 lamda And 12/17/99 -200 +220
.at 120 C: . ..
57 Capella 3/3/00 0 +420
15 TZ CRB 6/18/00 -110 +310

LETG/ACIS-S observation:
Obsid Target Obs Date ppmE57 * ppmEMEGRef **
55 Capella ~11/99 +200 +620

* ppmE57 is correction to be applied to the observation's measured energies in order to have them agree with the values of Capella observation Obsid 57. The "E" is appended to the ppm to indicate that it applies to energy values, wavelength corrections are of the opposite sign.

** ppmEMEGRef is the ppm correction to be applied to the observations' MEG energy values so that they will agree with the "Kelly" reference values, based on a value of +420 ppm for obsid 57 combined with the ppmE57 values. The average value of this correction over all 8 of the HETGS observations here is +321 ppm and all values are within about +/-200 ppm of this value.

Please send any comments to Dan Dewey at dd@space.mit.edu.