Table of Contents
Description
Inputs
Step 1: Retrieve the High-Resolution HETG Spectrum
Step 2: Input and Apply the gARF
Step 3: Coadd the HEG and MEG Spectral Data
Step 4: Apply the Zeroth-Order, ACIS-S Aimpoint, or ACIS-I Aimpoint ARF
Step 5: Convolve the Combined HEG+MEG High-Resolution Spectrum to Low-Resolution
Step 6: Compare the Convolved Low-Resolution HEG+MEG Predictions to Actual Extracted Spectra
Download the Convolution Routine
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Description
For comparisons between stellar spectra taking at high-resolution with HETG/ACIS-S and those obtained in ACIS images, we convolve the high-resolution HETG spectrum to the resolution of ACIS. To predict the ACIS spectrum of an HETG observation, we combine the HEG and MEG flux spectra and convolve with either the ACIS-S Aimpoint, ACIS-I Aimpoint, or zeroth-order RMF to obtain a prediction of the ACIS-S Aimpoint, ACIS-I Aimpoint, or zeroth-order spectrum, respectively.

Inputs
High-Resolution HEG and MEG Spectra: The individual HEG and MEG coadded ±1st order PHA2 files produced by the X-Atlas reduction pipeline
Combined gratings ARF (gARF) files for 1st Order HEG and MEG: an X-Atlas pipeline product created along with the PHA2 spectral files during the coaddition of plus and minus grating orders
HEG 1st order gARF for obsid 7189

Figure 1: The 1st Order HEG gARF for obsid 7189.

MEG 1st order gARF for obsid 7189

Figure 2: The 1st Order MEG gARF for obsid 7189.

Zeroth-Order ARF: A pipeline product created in the extraction of the zero-order spectrum, described here.
Zeroth-Order ARF effective area

Figure 3: The Zeroth-Order ARF for obsid 7189

Zeroth-Order RMF: A pipeline product created in the extraction of the zero-order spectrum, described here.
ACIS-S Aimpoint ARF: Available here.
ACIS-S
	    Aimpoint ARF effective area

Figure 4: The ACIS-S Aimpoint ARF Effective Area

ACIS-S Aimpoint RMF: Available here.
ACIS-I Aimpoint ARF: Available here.
ACIS-I
	    Aimpoint ARF effective area

Figure 5: The ACIS-I Aimpoint ARF Effective Area

ACIS-I Aimpoint RMF: Available here.

Step 1: Retrieve the High-Resolution HETG spectrum
Each pha2 file returned by the hires2lowres thread in the Xatlas pipeline corresponds to either the HEG or MEG grating arm and to one of the ±1st, ±2nd, and ±3rd order coadded grating spectra.
a. From the appropriate pha2 files, extract the HEG and MEG HETG spectra. They will be in units of [counts/bin]
b. Define the midpoints of the high-resolution wavelength bins by averaging the high and low bin boundaries (also found in the pha2 file). Define the bin boundaries as [phabin_lo,max(phabin_hi)].
c. For viewing purposes, the high-resolution data can be smoothed in on of two ways. The first is to apply a boxcar average with a range of about 20 data points and then to reapply the same boxcar average to the result. The final smoothed spectrum will be, for practical purposes, very close to a Gaussian smoothing. The second smoothing method involves the PINTofALE adaptive smoothing function, "smoothie." Both methods conserve flux.
d. Calculate the approximate Poisson's error on the wavelength bins with the formula:
Bin Error = (1+sqrt(counts+0.75))2
Step 1 Products: The smoothed and unsmoothed high-resolution HEG and MEG HETG spectra and associated errors.
Units: [counts/bin]

High-Resolution HEG Spectrum of obsid 7189
Figure 6: The high-resolution HEG spectrum of obsid 7189.

High-Resolution HEG Spectrum of obsid 7189
Figure 7: The 2x boxcar-smoothed high-resolution HEG spectrum of obsid 7189.

High-Resolution MEG Spectrum of obsid 7189
Figure 8: The 'smoothie'-smoothed high-resolution HEG spectrum of obsid 7189.

High-Resolution MEG Spectrum of obsid 7189
Figure 9: The high-resolution MEG spectrum of obsid 7189.

High-Resolution MEG Spectrum of obsid 7189
Figure 10: The 2x boxcar-smoothed high-resolution MEG spectrum of obsid 7189.

High-Resolution MEG Spectrum of obsid 7189
Figure 11: The smoothie-smoothed high-resolution MEG spectrum of obsid 7189.

Step 2: Input and Apply the gARF
a. From the gratings ARF (gARF) files of the appropriate grating arms and orders, extract the effective area arrays (cm2) and find the midpoints of the corresponding energy bins.
b. Convert the gARF energies into wavelength and sort the wavelength and effective area arrays by wavelength.
c. Interpolate the HEG and MEG gARF effective areas onto the spectral range of the appropriate high-resolution data sets.
d. Divide the product of step 1 (high-res. [counts/s/Å]) by the size of the wavelength bins and the exposure time, yielding [counts/bin].
e. Divide the high-resolution HEG and MEG [counts/bin] spectra by the interpolated gARF effective area (cm2) where the gARF is nonzero. Where the gARF is zero, set the high-resolution flux equal to zero.
f. Where the gARF effective area is nonzero, divide the HEG and MEG counts/bin errors to convert them to flux units. Where the gARF effective area is equal to zero, set the errors arbitrarily equal to something large, such as 100 times the errors on the [counts/bin] spectrum.

1st
	    Order MEG flux spectrum for obsid 7189

Figure 12: The adaptively-smoothed high-resolution HEG flux spectrum.

1st
	  Order MEG flux spectrum for obsid 7189

Figure 13: The adaptively-smoothed high-resolution MEG flux spectrum.

Step 2 Products: HEG and MEG high-resolution fluxes and associated errors
Units: [photons/s/bin/cm2]

Step 3: Coadd the HEG and MEG Spectral Data
In order to predict the low-resolution spectrum of the zeroth-order, ACIS-S Aimpoint, or ACIS-I Aimpoint, the high-resolution HEG and MEG spectra must first be combined.
a. The original HEG and MEG high-resolution spectra overlap roughly from 0 to 20 Å. Therefore, the portion of the MEG spectrum over the HEG range must first be isolated. However, each data set has a different wavelength grid over this range. Using the rebinw function from PINTofALE, rebin the MEG [counts/s/bin] spectrum onto the HEG spectral range.
b. To coadd the two grating arms, weight the spectra by the errors in each flux bin (product of Step 2).
c. The HEG and MEG error arrays must now be divided by their appropriate gARFs to convert the errors to units of flux.
d. Finally, the portion of the MEG error over the HEG wavelength range must be isolated and rebinned to the HEG wavelength grid.
e. For each flux bin, we calculate the combined HEG+MEG flux in the bin to be:
Combined HEG + MEG flux = (wHEGfHEG + wMEGfMEG) / (wHEG + wMEG),
where fHEG = HEG flux, fMEG = MEG flux, wHEG = 1/(HEG error), and wMEG = 1/(MEG error).

Coadded
	  HEG+MEG High-Resolution Spectrum

Figure 14: Adaptively-smoothed coadded HEG + MEG high-resolution flux spectrum spectra for obsid 7189.

Product: Combined HEG+MEG high-resolution flux spectrum
Units: [photons/bin/cm2]

Step 4: Apply the Zeroth-Order, ACIS-S Aimpoint, or ACIS-I Aimpoint ARF
Applying the Zeroth-Order ARF will yield a prediction of the zero-order low-resolution spectrum, while applying the ACIS-S or ACIS-I Aimpoint ARFs will produce predictions of the low-resolution spectra at each respective aimpoint.

a. Extract the effective area and energy arrays from the Zeroth-Order, ACIS-S Aimpoint, and ACIS-I Aimpoint ARFs.
b. Convert the energy arrays to wavelength and sort the wavelengths and effective energies by wavelength.
b. Interpolate the effective areas of each ARF onto the spectral range of the combined HEG+MEG high-resolution spectrum.
c. Multiply the combined HEG+MEG high-resolution photons/(bin*cm2) spectrum from Step 5 by the effective area of the appropriate ARF.

HEG+MEG High-Resolution Zeroth-Order Prediction
	  (Adaptively Smoothed)

Figure 15: The adaptively smoothed HEG+MEG High-Resolution Prediction of the Zeroth-Order Counts Spectrum

HEG+MEG High-Resolution ACIS-S Prediction (smoothie)

Figure 16: The adaptively smoothed HEG+MEG High-Resolution Prediction of the ACIS-S Aimpoint Counts Spectrum

HEG+MEG High-Resolution ACIS-I Prediction (smoothie)

Figure 17: The adaptively smoothed HEG+MEG High-Resolution Prediction of the ACIS-I Aimpoint Counts Spectrum

Step 4 Products: The combined HEG+MEG high-resolution prediction at zero-order, the ACIS-S Aimpoint, or the ACIS-I Aimpoint.
Units: [counts/bin]

Step 5: Convolve the Combined HEG+MEG High-Resolution Spectrum to Low-Resolution
conv_rmf, a PINTofALE program, will convolve the combined HEG+MEG high-resolution spectrum with a Response Matrix Function (RMF), outputting a low-resolution spectrum. The required inputs are the combined HEG+MEG high-resolution counts/bin*s array (Step 4), the HEG+MEG high-resolution energy array, and the appropriate RMF (either the Zeroth-Order, ACIS-S Aimpoint, or ACIS-I Aimpoint RMF). Outputs are low-resolution counts/bin*s and low-resolution energies (keV).
a. Convert high-resolution wavelengths (A) to energies (keV), using the conversion:
Energy (keV) = 12.3985/Wavelength (A).
b. Run conv_rmf on either the zero-order, ACIS-S Aimpoint, or ACIS-I Aimpoint high-res. spectrum. Calling sequence is:
conv_rmf, heg+meg_enrg_hi, heg+meg_cts_hi, enrg_low, cts_low, rmf
where rmf is the output of rd_ogip_rmf().
c. Convert the outputted low-resolution energy array to wavelength and calculate the width of the wavelength bins.
d. Divide the low-resolution counts/bin spectrum by the exposure time and the width of the low-resolution wavelength bins to create the low-resolution counts/(s*Å) spectrum.

Adaptively Smoothed HEG+MEG High-Resolution
	  Zeroth-Order Prediction

Figure 17: The adaptively smoothed HEG+MEG low-resolution prediction of the zeroth-order spectrum

adaptively smoothed HEG+MEG Low-Resolution ACIS-S Prediction

Figure 18: The adaptively smoothed HEG+MEG Low-Resolution Prediction of the ACIS-S Aimpoint Spectrum

adaptively smoothed HEG+MEG Low-Resolution ACIS-I Prediction

Figure 19: The adaptively smoothed HEG+MEG low-resolution prediction of the ACIS-I Aimpoint spectrum

Product: The convolved low-resolution spectrum, a prediction of the low-resolution zero-order, ACIS-S Aimpoint, or ACIS-I Aimpoint spectrum
Units: [counts/s/Å]

Step 6: Compare the Convolved Low-Resolution HEG+MEG Predictions to Actual Extracted Spectra
a. First, we can compare the predicted zero-order low-resolution HEG+MEG spectrum (step 5) with the actual zero-order spectrum.

Smoothed Predicted and Actual Zeroth-Order Spectra for obsid
	  7189

Figure 20: The Adaptively Smoothed Convolved HEG+MEG Zeroth-Order Predicted Spectrum and the Actual Zeroth-Order Spectrum.

Errors for Smoothed Flux for obsid
	  7189

Figure 21: The Adaptively Smoothed HEG Flux Errors and the Adaptively Smoothed MEG Flux Errors.

Smoothed Convolved HEG+MEG, HEG, and MEG Zeroth-Order
	  Low-Resolution Prediction for obsid 7189

Figure 22: The Adaptively Smoothed Convolved Low-Resolution HEG+MEG Zeroth-Order Spectrum Prediction the Adaptively Smoothed Convolved HEG Zeroth-Order Low-Resolution Spectrum Prediction, and the Adaptively Smoothed Convolved MEG Zeroth-Order Low-Resolution Spectrum Prediction.

Predicted and Actual Zeroth-Order Spectra for obsid
	    7189

Figure 23: The Convolved Low-Resolution HEG+MEG ACIS-S Aimpoint Spectrum Prediction the Convolved HEG ACIS-S Aimpoint Low-Resolution Spectrum Prediction, and the Convolved MEG ACIS-S Aimpoint Low-Resolution Spectrum Prediction.
Download hires2lowres.pro
hires2lowres.pro - Convolve a high-resolution HETG spectrum with the ACIS response matrix
make_lowres.pro - Wrapper to store the output of hires2lowres.pro in fits and text format

Latest Modification
Webpage updated on Monday, 09-Jul-2007 15:43:40 EDT by Owen Westbrook