EPIC photon pile-up

Photon pile-up, i.e., the arrival of more than one X-ray photon in one camera pixel before it is read out, can affect both the spectral response of EPIC and its PSF:

The spectral response is compromised, because the charge deposited by more than one photon is added up before being read out, thus creating artifical ``hard'' photons where there have actually been two or more soft photons.

The PSF is influenced by pile-up, because in the core of the PSF many photons arrive at almost the same time (within one readout frame), creating multi-pixel photon patterns which, for the MOS camera, are then rejected by the onboard event reconstruction software (which is supposed to suppress spurious events, such as cosmic rays). This leads, in the most extreme case, to a PSF with an artificial ``hole'' at its centre, as displayed in Fig. 27. For the pn camera, event reconstruction is performed offline in the SAS.

**Figure 27:** SciSim simulation of the EPIC MOS PSF with increasing photon count rate per frame. The panels are arranged clockwise, with the lowest count rate (and thus pile-up rate) in the upper left and the highest in the lower left. The simulated count rates are 0.37, 5.92, 12.6 and 23.7 counts/s, respectively.
$\begin{figure} \begin{center} \leavevmode \epsfig{width=0.9\hsize, file=figs/pileholes.ps} \end{center} \end{figure}$

As an example for the influence of pile-up on spectral analyses, a kT = 1 keV Raymond-Smith model spectrum with $N_H\ = 3\times10^{20}$ cm^-2 has been fed into SciSim and the fit to the resulting ``observed'' spectrum compared with the input for EPIC MOS observations in the full window mode (Tab. 8). One can see how the best-fitting N_H, kT and normalisation vary as a function of input source flux (and thus count rate per frame). Note that, because of the photon pile-up, one apparently loses soft photons (whose charge combines and is then seen at higher energies), thus requiring a higher N_H and also a higher kTto reach the minimum $\chi^2$ for the fit. Therefore, the change in the relative normalisation (right column) is not the only, and also not the most severe problem in an attempt to provide the best possible spectro-photometric calibration. The peculiarity that for low fluxes the fitted kT is a bit lower than the input value is explained by the fact that the SciSim simulation was performed without event reconstruction. What is important to note is the relative change in kT. A similar change is also caused in the best-fitting slope of a power law, as displayed in Fig. 28. The effect of pile-up on the PSF has been taken into account in these simulations by choosing an appropriately large photon extraction region for the spectral analysis.

Note: No error bars are provided in Tab. 8, because the input spectrum is a numerical model spectrum without noise. Differences in the output ``fit'' spectrum with respect to the noise-free input occur only because of re-grouping of photons due to pile-up. The relevance of the effect depends on the scientific goal of the observing programme. For up to 2 counts per MOS frame, the error in N_H stays below 10%, that of kT and the normalisation at a level of 2%, which in many cases will be below the uncertainty of the spectral fit anyway.

**Table 8:** *The effect of pile-up on spectral fits*
$\textstyle \parbox{1cm}{{\bf Input flux$^1$ }}$	$\textstyle \parbox{1.4cm}{{\bf Output count rate [s$^{\bf -1}$ ]}}$	$\textstyle \parbox{1.4cm}{{\bf Counts per MOS frame}}$	$\textstyle \parbox{2cm}{{\bf N$_{\bf H}$ [10$^{\bf 20}$ ~cm$^{\bf -2}$ ]}}$	$\textstyle \parbox{2cm}{{\bf kT [keV]}}$	$\textstyle \parbox{2cm}{{\bf Norm./ expect}}$
4.05	1.08	0.22	3.0	0.967	1
13.4	3.56	0.71	3.05	0.972	1
40.5	10.5	2.1	3.2	0.979	0.98
134	33.3	6.65	3.5	1.010	0.95
405	85.4	17.1	4.1	1.022	0.80

**Figure 28:** *The best-fitting power law slope,* $\alpha$ *, for an* $\alpha = 1.7$ *input spectrum into SciSim, with different input count rates, leading to different levels of pile-up.*
$\begin{figure} \begin{center} \leavevmode \epsfig{width=0.8\hsize, file=figs/hardens.ps} \end{center} \end{figure}$

Table 4 provides estimates of count rates for the different EPIC instrument modes for which pile-up should not be a problem. For the MOS full imaging mode, e.g., ca. 0.7 counts/s should not be exceeded.

A quantitative comparison of both types of EPIC cameras with the AXAF ACIS-I instrument in this respect is provided in § 3.7.1.3.

XMM Users' Handbook

EPIC photon pile-up