5.3 Dark Current, Hot Pixels, and Cosmic Rays
5.3.1 Dark Current
The procedure for creating ACS dark reference files and applying dark subtraction to ACS science data is described in detail in Section 3.4.3. Because it takes a few weeks to collect enough frames to create the dark reference file, the "best" darkfile is typically not available in the pipeline until 2-3 weeks after the date of observation. Users may verify whether the darkfile most appropriate to their observations has been installed for pipeline use by checking the ACS reference file web pages:
http://www.stsci.edu/hst/acs/analysis/reference_files/drkimage_list.html.
Using an old reference file will produce a poor dark correction: either leaving too many hot pixels uncorrected and unflagged, or creating many negative "holes" caused by the correction of hot pixels which were not actually hot in the science data (i.e., if the detectors were annealed in the interim).
WFC/HRC
The dark current is not constant across the CCDs. Figure 5.3 shows the dark current features in the WFC1 (above) and WFC2 (below) chips. These features were observed in pre-flight tests, and have generally remained stable in orbit.
There is a gradient, most noticeable on the WFC1 chip, going from a dark edge in the amplifier A quadrant (upper left) to a bright corner in the amplifier B quadrant (upper right). There are two horizontal bright bands of elevated dark current in the center of the WFC2 chip. Many faint rings are also visible: all concentric with the center of both chips. These features are likely intrinsic to the chips themselves: artifacts embedded in (or on) the silicon during various stages of the CCD manufacturing process.
Figure 5.3: High S/N combination of WFC dark frames illustrating dark current structure 
The WFC1 and HRC histograms in Figure 5.4 and Figure 5.5 show the growth of hot pixels (for more information, refer to Section 5.3.2). A less obvious result is that the peak of the normal pixel (Poisson) distribution (i.e., the mean dark current, excluding the hot pixels) has also increased.
The increase in the mean dark current for WFC has been from 6.8 e-/pixel/hr at launch to 11.1 e-/pixel/hr (an average of 11.4 for WFC1 and 10.8 for WFC2) in April 2004. For HRC the change in dark current has been from 9.3 e-/pixel/hr at launch to 13.4 e-/pixel/hr in April 2004. The dark calibration tracks the mean dark current very closely at 2 week intervals (see Section 3.4.3).
Figure 5.4: WFC dark current histogram for chip 1. Statistics for chip 2 are nearly identical. The figures illustrate the growth of hot pixels over time.
Figure 5.5: HRC dark current histogram 
SBC
The SBC, or ACS MAMA detector, intrinsically has no readout noise and very low detector noise levels which normally will be negligible compared to statistical fluctuations. A dark current image was compiled during ground tests with a total exposure time of 14,400 seconds and remains as the calibration dark image. This has a mean dark count of 3.8x10-5 counts/pixel/second. Approximately once per month since ACS was installed, 1800 second SBC darks have been accumulated. The dark rate for these is typically 2.0x10-5 counts/pixel/second. The principal reason for taking these images is to provide a measure of the health of the SBC. No major fluctuation has been noted. An in-flight super-dark will be constructed from the in-flight measurements.
5.3.2 Hot Pixels
A "hot pixel" is a state of radiation damage affecting the dark current production of an individual pixel. Such pixels likely result from the close interaction of an incident heavy nucleon with Si nuclei in a pixel, creating new Si-SiO2 interface states. Once produced, such pixels almost always remain hot before the next anneal producing a continuum of excess dark current rates more than 1 to 4 orders of magnitude greater than the mean value. Although such pixels have temporarily lost their ability to yield precise measurements of faint photon flux, the majority of such pixels are "healed" in monthly anneals when the CCD temperature is raised by ~100 degrees over operating temperature for ~16 hours.
As seen in Figure 5.4 and Figure 5.5, the dark current distribution is well described by a Gaussian. As expected from experience with earlier HST cameras, very significant tails (all pixels with dark current above the 5 sigma limit [~0.02 e-/sec]) are seen in these distributions. These tails consist of the pixels that have suffered radiation damage. The pixels with values between 0.02 and 0.08 e-/sec are referred to as "warm" pixels and those above 0.08 e-/sec as hot pixels. Figure 5.6 and Figure 5.7 show these tails for WFC and HRC for two different dates. As shown, many thousands (HRC) or tens of thousands (WFC) of pixels have greatly elevated dark current with the number markedly increasing with time.
Figure 5.6: Dark Current Distribution Tails in WFC for March 15, 2002 and March 28, 2002. All pixels with dark current above the 5 sigma limit (~0.02 e-/sec) are due to so-called "warm" and "hot" pixels which have suffered radiation damage. The number of these pixels can be seen to increase rapidly with time.
Figure 5.7: Dark Current Distribution Tails in HRC for March 15, 2002 and March 28, 2002.
Trending
Even with 16 million pixels, the WFC would not be expected to have any pixels with dark current more than 6 standard deviations beyond the mean (i.e., with dark current greater than 0.02 e-/sec) were it not for the effects of radiation damage. To analyze hot pixel trending, we have chosen a conservative limit of twice that, or 0.04 e-/sec for WFC and 0.08 e-/sec for HRC as a threshold above which we consider a pixel to be "hot" and not part of the normal distribution of pixel dark current. Note that even though trending is analyzed at these limits, only pixels above 0.08 e-/sec are flagged in the DQ array.
For WFC we find a growth rate of approximately 1200 new hot pixels per day with dark current greater than 0.04 e-/sec. For HRC the number of new hot pixels per day above the threshold is approximately 90. Because the distribution of dark current in hot pixels is strongly concentrated near the threshold, the specific number of such pixels is necessarily a strong function of the chosen threshold.
Subtraction of a superdark frame from a science image can remove the dark current from hot pixels just as it does for normal pixels. However, hot pixels are often orders of magnitude noisier than normal pixels, which in many cases limits their ability to provide useful measurements of flux. For the hottest pixels, the observed noise exceeds even the Poisson noise by an order of magnitude. Observations which do not employ contemporaneous superdarks will suffer from uncorrected and unflagged hot pixels, a particular concern to programs whose aim is to search for astrophysical transients or broad-band drop-outs. The problems associated with hot pixels can be mitigated by using the best reference files (usually necessitating recalibration with OTFR several weeks after the data were obtained), flagging and discarding data from hot pixels, and dithering observations to provide additional sampling of pixel positions on the sky and allow rejection of hot pixels.
Figure 5.8: Hot pixel growth rate for HRC (top) and WFC (bottom)
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The anneal rate of new hot pixels (dark current > 0.04 e-/sec) on the ACS WFC has been disappointingly low: ~60% in the first eight monthly anneal cycles of the instrument. This rate is significantly lower than the observed and characteristic value for other HST CCDs: 80-85% for WFPC2, STIS, and ACS HRC. The anneal rate is significantly less than 60% for pixels which are much hotter than 0.04 e-/sec. The consequence of poor annealing is a greater fractional coverage of the camera by pixels with elevated dark current than was the experience of other HST CCDs. Figure 5.8 shows the observed growth of hot pixels on both HRC and WFC. The saw-tooth appearance is due to regular anneals. For WFC hot pixel coverage is more than cosmic ray coverage in a typical exposure. By the end of the decade one in every 16 pixels is predicted to be hot on WFC. For more details see ACS ISR 02-09.
5.3.3 Cosmic Rays
Like all HST cameras before it, the ACS HRC and WFC fields of view are heavily peppered by cosmic rays in even the shortest of exposures. For full orbit integrations, approximately 5% of the pixels receive significant charge from cosmic rays via direct deposition or from diffusion from nearby pixels. Great care must be taken in planning and analyzing HST ACS observations to minimize the impact of cosmic rays on science images.
Fractional Coverage
For most users of the HRC and WFC, the most important characteristic of cosmic rays is simply the fraction of pixels they impact. This number provides the basis for assessing the risk that the target(s) in any set of exposures will be compromised. For ACS the observed rate of cosmic ray impacts on an individual frame varies by a factor of two depending on the proximity of the spacecraft to the confluence of the Earth's magnetic field lines (e.g., the South Atlantic Anomaly). For a 1000 second exposure the fraction of pixels affected by cosmic rays (in non-SAA passages) varies between 1.5% and 3%. This fraction is the same for the WFC and HRC despite their factor of two difference in pixel areas, because the census of affected pixels is dominated by charge diffusion, not direct impacts. This fraction is also consistent with what is observed for WFPC2. For most science observations, a single CR-split (i.e., two exposures) is sufficient to insure that measurements of the targets are not compromised by cosmic rays.
More consideration is required for survey-type observations with WFC, a bonafide survey instrument. Observers seeking rare or serendipitous objects as well as transients may require that every single WFC pixel in at least one exposure among a set of exposures is free from cosmic ray impacts. For the cosmic ray fractions of 1.5% to 3% in 1000 sec, a single ~2400 second orbit must be broken into 4 exposures (4 CR-splits of 500 to 600 sec each) to reduce the number of uncleanable pixels to 1 or less. (It is also recommended that users dither these exposures to remove hot pixels as well.)
Cosmic Ray Events
Many science observations require a careful consideration of individual cosmic rays events. To either remove cosmic rays events or distinguish them from astrophysical sources users might consider the distributions of observed cosmic ray fluxes, sizes, anisotropies, and the number of attached pixels per event.
Electron Deposition
The flux deposited on the CCD from an individual cosmic ray does not depend on the energy of the cosmic ray but rather the length it travels in the silicon substrate. As a result the deposition distribution has a well-defined minimum with few events of less than 500 electrons (where such low-electron events correspond to cosmic rays which pass through the CCD at a normal angle of incidence). As seen in Figure 5.9, the median charge deposited for WFC and HRC is about 1000 electrons, the same as for WFPC2.
A useful characteristic of the deposition distribution is its well-defined minimum; e.g., multi-pixel events which have an apparent magnitude of 25th or fainter, in a 500 second broad-band exposure, are unlikely to be caused by cosmic rays. Such information can help with the removal of false positives from searches for faint transients (e.g., high-redshift SNe).
Figure 5.9: Electron deposition by cosmic rays on HRC (top) and WFC (bottom). A minimum deposition of ~500 e is seen corresponding to CR's with normal incidence. The median deposition is ~1000 e. 
Attached Pixels
As seen in Figure 5.10 for HRC and WFC the salient features of electron deposition are a strong peak in the distribution function at 4 to 5 pixels. On the smaller side there is a sharp decline in events. Although a few events are seen which encompass only one pixel, examination of these events indicate that at least some and maybe all of these sources are actually transient hot pixels or unstable pixels which can appear hot in one exposure (with no charge diffusion) and normal in the next. Such pixels are very rare but do exist. There is a long tail in the direction towards increasing numbers of attached pixels. Some of these are likely due to two individual events associated by their chance superposition, but more are from oblique incidence cosmic rays which skim the surface of the CCD leaving a long trail (which is wider near the surface). Unfortunately the number of attached pixels is not a very useful characteristic to distinguish cosmic rays from unresolved astrophysical sources.
Figure 5.10: Distribution of the number of pixels associated with a single CR event for the HRC (top) and WFC (bottom). Some bias exists for events >6 pixels which may be composed of two events with chance superposition. 
