HETGS Resolution, 2/27/01

Gaussian Fit to MARX 19A LRF Core

Wings of LRF are visible in this log y-axis plot. Orange = simulation Blue = LRF from rmf file

The HETGS Line Response Function, LRF, consists of a Gaussian-like core and extended wings. The resolution of the spectrometer is specified by the FWHM of the core and the core plus wings are relevant to accurate line flux measurements. These properties are captured as resolution (or resolving power, E/dE_fwhm) values and rmf files.

The results of ground testing of the HETG are incorporated into the ray-trace simulator, MARX. The current working hypothesis for the HETGS LRF is that:

If the MARX zeroth-order simulated image agrees with the flight image, then the MARX monochromatic response appropriately processed is the instrument LRF.

In this work a MARX simulation which has a nominal flight zeroth-order width and an input spectrum consisting of monochromatic lines is performed, processed, and fit using ISIS software. The result is the expected HETGS resolution for a nominal point source observation. Specifically the expected FWHM (in Angstroms) is reasonably accurately given by a cubic function of the wavelength (also in Angstroms):

      FWHM  =  c0 + c1*lambda + c2*lambda^2 + c3*lambda^3
  

where the c's for the MEG and HEG are tabulated below and available for cutting/pasting in the IDL procedure fwhm_idl_snippet.pro.

Table 1. FWHM vs Wavelength Coefficients

Grating	c0	c1	c2	c3	Plots
MEG	0.018851868	-0.00033946575	2.9781558e-05	-4.1097023e-07	gif , ps
HEG	0.010019662	-0.00014101982	1.4591413e-05	-1.9632994e-07	gif , ps

	MEG FWHM 0 A to 26 A
	HEG FWHM 0 A to 17 A

These cubic functions are the smooth curves shown in the plots above (the plots are also linked from the right-hand column of Table 1). The discrete FWHM measurements (of the MARX simulation data) that were used to generate the polynomial fits are shown by the asterisk and diamond symbols. These FWHM values are in the range between the values derrived from the pre-flight expectations for optimistic and conservative E/dE, as shown by the dashed and dotted lines in the plots.

These resolution values can be used (and tested) in data analysis of nominal on-axis point source observations when fitting the line core, e.g., to assess line broadening or blending. Some example fits to the cores of Capella lines with the FWHM fixed at these values are given in Table 2 below as a sanity check - note that the 12 A line is a blend and so appears broader than the nominal Gaussian.

Table 2. Flight Capella Lines fit with fixed FWHM Gaussian

ObsID	Obs Date	Grating	9.2 A	12 A*	15 A	19 A
1103	Sept.24 '99	MEGm	9.2 A	12 A*	-	19 A
"	"	HEGm	9.2 A	12 A*	15 A	-
1318	Sept.25 '99	MEGm	9.2 A	12 A*	-	19 A
"	"	HEGm	9.2 A	12 A*	15 A	-
0057	Mar.3 '00	MEGm	9.2 A	12 A*	-	19 A
"	"	HEGm	9.2 A	12 A*	15 A	-
1010	Feb.11 '01	MEGm	9.2 A	12 A*	-	19 A
"	"	HEGm	9.2 A	12 A*	15 A	-

* The 12 A line is a blend as indicated by the MEG and HEG data!
The upper panel of the plots shows the data w/error bars and
the best-fit "fixed-width Gaussian plus constant" model (purple).
The lower panel shows the residuals, data-model, on the same Y-scale
so that the error bars (not plotted) have the same size as above.

Of course more HETGS LRF work needs to be done. Caveats and details of this present work are given below.

• "Resolution" as used here is 2.35 times the sigma of a Gaussian which fits the core of the LRF.
• For the measurements made here the core is the region of 0.050 A (0.030 A) centered about the Gaussian centroid of the MEG (HEG) line response.
• The resolution values given here are based on simulation.
• The simulation is 'tied' to flight performance only through the adjustment to get the broadband (0.5-2keV) zeroth-order 1D FWHM to agree with the long-term nominal value of 37.8 um FWHM.
• Variations in this nominal FWHM are not ruled out at up to the 10% level.
• The zeroth-order is made from all 4 HRMA shell's images, in contrast the HEG and MEG systems use only 2 shells each and the zeroth-order flight performance of these shells is only modelled, not measured.
• The MARX HRMA model does not exactly reproduce SAOSAC ray-trace results; SAOSAC is by definition "the HRMA model."
• Both MARX and SAOSAC seem to produce zeroth-order PSF wings that are of order 60% of actual flight values. This is not so relevant to the core-fitting work presented here, however.
• The FITS event file create by MARX was NOT analyzed with the usual CXC processing software, instead the MARX X and Y columns are the analysis starting point for custom software and several effects are not exactly dealt with. In particular aspect reconstruction, ACIS pixel quantization, and the infamous pixel randomization effects are accounted for here through adjustment of the MARX DitherBlur parameter (to 0.33) to get zeroth-order agreement.
  [In future a MARX-->CIAO-->pha route will be used.]
• A cross-dispersion width of 500 microns was used for the dispersed data, compared to the CXC processing default of 200 um. (Should not make a big difference in the core shape.)
• The source is assumed to be a point source.
• The location of the zeroth-order on the detector (off-axis value) can effect the PSF/LRF: the simulations here are with the MARX SourceOffsetY = -0.33000.
• When detailed LRF analysis is being done it is best not to combine the plus and minus order spectra as a small zeroth-order offset can shift the plus and minus centroids the combined peak is broader than either.
• The shortest wavelength used in the MEG analysis is 3.7 A; the extrapolated curve given can have large errors at much shorter wavelengths.
• You know there are bound to be mistakes and other errors in all this!

A unix script with pset commands was run to setup the marx.par file for the narrow lines simulation and produce output FITS and asol files. MARX version 3.01 was used. The input spectrum of narrow lines came from Narrow_lines.tbl .

Using only energies less than 3 keV, the projected 1D FWHM of the simulation output (X,Y columns from the marx2fits output file) was created with HAK s/w and measured with ISIS as described in the zeroth-order 1D projections technote. This is the same software used for measuring the flight zeroth-order FWHM.

The MARX DitherBlur value was adjusted to get agreement of the simulation to the flight average value of 37.8 microns:

Table 3. Zeroth-order FWHM vs MARX DitherBlur parameter

MARX DitherBlur	Zeroth-order FWHM (um) (E<3keV)
0.35	38.5
0.34	38.2
0.33	37.7 <-- good
0.30	35.6

The MARX simulation diffracted events were binned with custom IDL software to produce the CXC-grid ISIS compatible spectrum files linked in Table 4.

Table 4. Simulated spectra and fitting result files

Grating/Order	ISIS spectrum file	ISIS Fitting output FITS file
MEG -1	fil_Narrow33_MEGm1_isis.dat	fil_Narrow33_bp_megm.fits
MEG +1	fil_Narrow33_MEGp1_isis.dat	fil_Narrow33_bp_megp.fits
HEG -1	fil_Narrow33_HEGm1_isis.dat	fil_Narrow33_bp_hegm.fits
HEG +1	fil_Narrow33_HEGp1_isis.dat	fil_Narrow33_bp_hegp.fits

These spectra were then read into ISIS and the core range (0.050 A for MEG, 0.030 A for HEG) was fit by a Gaussian using the following custom ISIS routines:

• Startup files: start.i , nominal_manyTwabs.model , plot_all_groups.i
  rg_setup.i , bp_list.i , rg_list.i , rg_fit.i , rg_plot.i , bp_read_fits.i , bp_write_fits.i
• Read in the isis.dat files: get_fil_data.i
• Do the fitting: bp_extract.i which calls bp_fit_counts.i to do the fitting.

The output of bp_extract.i consists of a postscript plot for each line showing the fit with residuals in the core range, Table 5, and a FITS file for each spectrum containing a table of the fit results for the lines (center, FWHM, etc.) These FITS fit files are given in the right hand column of Table 4 above.

Table 5. Example ISIS fits of the core region of MARX-simulated lines

Grating	9.2 A	12 A	15 A	19 A
MEGm	9.2 A	12 A	15 A	19 A
HEGm	9.2 A	12 A	15 A	-

These FITS fit files were then read into IDL and used to create the polynomial fit and plots given above, using the procedure bp_examine.pro.

To compare the MARX predicted FWHM with flight data, four Capella data sets were read into ISIS from CXC PHA files using get_pha_data.i. The examples of fitting this real data with a fixed-FWHM Gaussian was carried out with bp_fit_counts_fixfwhm.i as called from demo_fixfwhm.i. Table 2 above consists of plots created in this way.

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