Analysis Technique

An effective area measurement entails determining the ratio of the X-ray line count rate R_FP measured by the ACIS focal plane detector to the X-ray line flux F_BNDincident on the HRMA as measured by a beam normalization detector.

We define as the effective area A_eff of the HRMA/ACIS combination the quantity:

where A_BND is the area of the BND normalization detector.

The effective area measurements performed at the XRCF were made in a defocused mode with ACIS moved approximately 40 mm away from the optimal focus position in the direction of the X-ray source. Operating in the defocused mode resulted in the reduction of pileup by means of spreading the X-ray image over many CCD pixels. In several measurements the image was defocused onto 2 adjacent segments of a CCD that were read out by different CCD amplifiers. Because of slight differences in the properties of the CCD amplifiers, the spectra corresponding to each amplifier were analyzed separately and the results combined to produce the total detected ACIS event rate over the selected spatial region of interest (ROI).

In the present analyses we have made use of incident source spectra produced by electron impact point sources (EIPS) for photon energies below 3 keV. For photon energies of 3 keV and above we have incorporated incident source spectra produced by the combination of the EIPS with a double crystal monochromator (DCM). The extraction of the X-ray line count rate detected by ACIS simply entails determining the number of counts in a region of interest around the X-ray line. The incident X-ray flux levels were high enough to produce noticeable pile-up in the ACIS spectra despite defocusing. Pile-up occurs whenever two or more photons are incident within either adjacent CCD pixels or with only one empty pixel between events, and are detected within a single CCD readout cycle. In such an instance the ACIS electronics will regard these as a single event with an amplitude given by the sum of the charge in the 3x3 neighborhood of the pixel with the maximum detected charge. The manifestation of pile-up in the ACIS spectra is the appearance of ``pile-up lines'' at energies that are multiples of the incident line energy. In addition to these lines a portion of the charge from the multiple events will not be recorded in the 3x3 island resulting in tails below the pile-up lines. Another consequence of pile-up is grade migration. In grade migration the X-ray events are detected, but the grade distribution is altered by the effects of multiple photons in close proximity.

For the analysis of ACIS spectra we have considered ROI's that include the Si escape peak (if present), the main X-ray line and pile-up lines. The number of events, N_pile-up,n detected in the n'th pile-up line are multiplied by n+1. We estimate the detected ACIS count rate with the expression:
 

 

where t_live in the total integration time. Due to dropped CCD frames t_live is determined as the product of the frame readout time of 3.341 sec and the number of processed CCD frames. For the present analysis we have not made any corrections for grade migration due to pile-up.