Astron. Astrophys. Suppl. Ser. 135, 371-381
DSM/DAPNIA/SAp, Bât. 709, CEA-Saclay,
F-91191 Gif-sur-Yvette, France
Received February 12; accepted December 4, 1998
This paper presents a statistical and analytical analysis of the pile-up phenomenon on X-ray CCD detectors, whereby two incoming X-rays are counted as one. The probability of measuring configurations involving 1, 2, 3 or 4 pixels is written down for a uniform incoming flux, thus allowing the computation of the flux loss (fraction of photons rejected because of pile-up) and of the pile-up fraction (fraction of events with wrong energy).
For detectors with pixels which are small compared to the point spread function (PSF) of the telescope (such as XMM/EPIC-MOS or ASCA/SIS) the formulae can be readily integrated over space to predict and account for pile-up on the total flux of point sources. It is shown that if only single events are selected the total pile-up fraction can never get very high for usual PSF shapes. The main effect is a loss of efficiency which is perfectly quantifiable. It is concluded that taking extreme care to avoid pile-up by adapting the instrument setting (for example restricting the useful area of the CCD) may not be so important after all, although it remains necessary if it is important to collect as many photons as possible from the source.
An extension to the theory is proposed for detectors with pixels comparable to the PSF width (such as AXAF/ACIS), and for extended sources.
Key words: methods: analytical -- methods: statistical -- X-rays: general
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