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

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

Figure 3: The Zeroth-Order ARF for obsid 7189

Figure 4: The ACIS-S Aimpoint ARF Effective Area

Figure 5: The ACIS-I Aimpoint ARF Effective Area

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]

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

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

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

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

Figure 10: The 2x boxcar-smoothed 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.

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

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 = (w_HEGf_HEG + w_MEGf_MEG) / (w_HEG + w_MEG),

where f_HEG = HEG flux, f_MEG = MEG flux, w_HEG = 1/(HEG error), and w_MEG = 1/(MEG error).

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.

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

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

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

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

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

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

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

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

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.

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.