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Photon Counting Mode

If the measured count rate is high (above about 0.6 count s-1 in PC mode is a rough guide), then the easiest way to avoid problems related to pile-up is to extract spectra using an annulus, thus eliminating the counts in the bright core, where pile-up will occur. To estimate the level of pile-up (i.e., how much of the core needs to be excluded), one needs to determine where the observed Point Spread Function (PSF) deviates from the known, un-piled-up PSF. In the absence of pile-up, the Swift PSF can be modelled by a King function:

PSF(r) = [ 1 + (r/rc)2 ]

where, for Swift, rc ~ 5.8 and β ~ 1.55 (Moretti et al., SPIE, 2005, 5898, 360).

A quick and simple method to estimate the size of the annulus required can be performed within XIMAGE. After extracting an image for the time period of interest (orb1.img is used in this example), read into XIMAGE and run the psf command:

> ximage

[XIMAGE> read orb1.img
[XIMAGE> cpd /xtk
[XIMAGE> disp
[XIMAGE> psf/cur

At this point, the user should click first in the centre of the object to be analysed, and then again at the outer edge of the object. This will bring up an interactive plot window, showing two plots: the encircled energy fraction and the PSF as shown below.

The bottom (PSF) profile can be fitted with the King function as described above - but out in the wings, where pile-up will definitely not be an issue (e.g., ignore all the data within about 10 arcsec by using the command rescale x). Noticing all the data will then show where the points begin to lie beneath the extrapolation of the King function; this is the approximate radius which should be excluded to avoid pile-up; see below for an example.

In this example, data within about 7 arcsec (1 XRT pixel = 2.36 arcsec) should be excluded when extracting spectra and light-curves.

Although the ARFs generated using xrtmkarf will correct the flux of the spectrum for the loss of counts caused by using an annulus, the correction for the actual count rate (and, hence, light-curve points) needs to be determined separately. The method (both for creating an ARF and determing the correction factor) is covered in the ARF thread.

Windowed Timing Mode

In general, WT mode data should not be affected by pile-up below intensities of about 100 count s-1. See the appendix of Romano et al. (2006) for more details. Methods for compensating when pile-up does occur are discussed below.

Please note that there are many ways to investigate the level of pile-up, and the details above are only an introduction. Other methods include:

These methods are applicable to PC and WT data analysis.