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Home > Data Analysis > XRT > pileup correction

Pile-up

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 ]-β

where, for Swift, r_c ~ 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:

• looking at the spectral distortion - Extract spectra excluding different amounts of the core. If the source is piled-up, the spectrum should be harder (i.e., Γ is a smaller number) than expected. When increasing the inner annular region no longer alters the photon index, the region affected by pile-up will have been excluded.
  
  Using GRB 060124 as an example (see Romano et al. 2006), the plot above shows how the photon index changes as more core pixels are excluded from the extraction for a WT observation (the count rates for PC mode would, of course, be much lower). The orange ellipses indicate the points where pile-up is affecting the data. The spectra at different count rates have been shifted vertically for clarity.
• investigating the grade distribution - Where pile-up is a problem, fewer than expected single pixel (grade 0) events are detected. Making plots of the fraction of grade 0 events against central exclusion region can give an indication of the amount of core which should be excluded.
  
  For typical WT data, between about 100-300 count s^-1, the fraction of grade 0 events stays close to constant, implying little pile-up. The decrease in grade 0 events for count rates below 100 count s^-1 is likely to be due to the PSF being tighter at low (soft) energies. That is, grade 0 events are more likely to be found "closer in" to the centre of the PSF; thus, excluding any of the core will remove a larger fraction of grade 0 events than grade 0-2 ones (assuming there is no pile-up).

These methods are applicable to PC and WT data analysis.