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4.9 Cosmic Rays

Cosmic ray events usually deposit significant quantities of charge in more than one pixel. This is due partly to the finite thickness of the CCD detectors, and partly to the less than perfect collection efficiency of each pixel. Figure 4.7 shows a histogram of the number of affected pixels for each cosmic ray event. For the purposes of the figure, a cosmic ray is defined as having a peak pixel value more than 10 DN above the background; and an affected pixel is an attached pixel with a value more than 2 DN above the background. Cosmic ray events do have a clear lower cutoff at around 500 electrons of total signal. The variations in cosmic ray rates caused by orbital position or operating temperature have not been characterized yet.

Cosmic ray events impact scientific imaging with WFPC2 in two different ways. Firstly, the WFPC2 CCDs have an epitaxial thickness of about 10 microns compared to 8 microns for the thinned WF/PC-1 device, and a recombination length of 8-10 microns in the substrate. These facts lead to a higher total number of electrons being deposited per event. WFPC2 CCDs also have lower read noise, and so the number of cosmic ray events apparently differs from that of the WF/PC-1 CCDs, since low amplitude events are detected. In practice, this means that the number of pixels apparently contaminated by cosmic rays in an image is higher in WFPC2, although the underlying event rate is similar to that experienced in WF/PC-1.

Figure 4.7: Histogram of Cosmic Ray Event Sizes.

Secondly, stellar images are undersampled and much more difficult to separate from cosmic rays, as is shown in Figure 4.8. Faint stellar images and low energy cosmic rays are indistinguishable. Long science observations are therefore usually broken into at least two exposures (CR-SPLIT) to ensure that events can be identified.

The average properties of on-orbit cosmic ray events have been determined from examination of several dark exposures, each 2000s long. After bias and dark subtraction, "cosmic rays" were identified in each input frame by first looking for pixels more than 5 sigma above the background, and then including in each event all adjacent pixels more than 2 sigma above the background. Very occasionally, two or more physically separate events will be merged into one as a result of this procedure; visual inspection confirms that in the vast majority of cases, this procedure correctly identifies each event and the area affected by it. The typical value of sigma was 5 to 6 electrons, including both read and dark noise. The region near the borders of each CCD was excluded in order to avoid edge effects, but all results given here are rescaled to the full area of the CCD.

Figure 4.8: Comparison of Star Images and Cosmic Ray Events.

One difficulty in this measurement is caused by hot pixels, for some of which the dark current has significant fluctuations from frame to frame; these can be mistakenly identified as cosmic rays when the dark current is at a maximum. Single-pixel events constitute 10% of the total number of events identified by our procedure, but at least half of them recur in the same position in several frames, thus identifying them as damaged (hot) pixels, rather than true cosmic rays. Also, unlike the majority of cosmic ray events, single-pixel events tend to have very small total signal; the majority have total signal less than 200 electrons, as expected from hot pixels, while the signal distribution of multiple-pixel events peaks around 1000 electrons. For this reason, single-pixel events have been classified as "bad pixels'' rather than "cosmic rays''. While we cannot exclude that some true single-pixel events do occur, they are very rare, probably less than 2% of the total.

Cosmic ray events are frequent, occurring at an average rate of 1.8 events chip^-1 s^-1. The distribution of total signal is shown in Figure 4.9; it has a well-defined maximum at about 1000 electrons, and a cut-off at about 500 electrons. The latter is well above the detection threshold used for the above measurements (25 electrons in the central pixel of the cosmic ray), and is therefore undoubtedly real.

Figure 4.9: Histogram of Cosmic Ray Event Energies.

The histogram in Figure 4.9 shows the distribution of total energy of all cosmic ray events. One encouraging feature is the very small number of events below about 30 DN. This low energy drop is well above the energy level of excluded single-pixel events.

A good approximation to the cumulative distribution of events as a function of total signal is given by a Weibull function with exponent 0.25. This function has the form:

where N is the total number of events which generate a total signal larger than S. The best fit to the observed events gives N₀=1.4 events chip^-1 s^-1, S₀=700 electrons, and . The fit fails below S₀, and should not be extrapolated to low-signal events. The rate of events with total signal below 700 electrons is 0.4 events chip^-1 s^-1 (i.e. total events per CCD per second is N₀+0.4=1.8).

The number of pixels affected by cosmic ray events in a given exposure is a slightly more sensitive function of the threshold used. While there is a clear drop at low signal for both total and peak signal, neighboring pixels can be affected at low levels. Each event (defined as before) affects an average of 6.7 pixels, for about 12 affected pixels chip^-1 s^-1. For a 2000s exposure, this results in about 24,000 affected pixels, or 3.8% of all pixels. As cosmic rays are expected to be randomly placed, a pair of such exposures would have about 900 pixels affected in both exposures; cosmic ray correction is impossible for such pixels. For a pair of 1000s exposures, about 220 pixels will be affected in both frames.

Cosmic ray activity varies as a function of time, geomagnetic latitude of the spacecraft, and other factors. The average numbers given here are subject to change in individual exposures. After studying about one month's worth of dark exposures, we estimate a total range of about a factor of two in cosmic ray rates.