Residual Dark Distribution (RDD)

Last update: 2000 July 16

1. What is RDD?

RDD (Residual Dark Distribution) was originally defined as a distribution of the pixel levels calculated after the DFE (Dark Frame Error) correction. However, it may be simply regarded as the distribution of the dark current (including a readout noise), because the DFE correction does not change the RDD shape largely.

It is known that radiation damage increases the dark current of a ccd. This means that excess charge is accumulated in a pixel even if it gets neither X-ray photons nor charged particles. However, such excess charge might not have any impact on the X-ray data if it were same for all the pixels. Such uniform charge will be subtracted in the course of on-board data processing, because the amount of charge accumulated in a pixel is measured from the local mean, which is defined in 16x16 pixels in the case of ASCA. However, increase of the dark current due to the radiation damage is not uniform. In fact, it varies largely from pixel to pixel. Analysis of the frame mode data showed that most of pixels show moderate increase of the dark current, but some show large increase. Thus, the distribution of the dark current shows a tail toward higher pulse height. The distribution becomes gradually wider with the accumulation of the radiation damage. Because the distribution is remained even after the correction of the DFE error in the ground data analysis, it is called residual dark distribution (RDD). Note that, when there is no dark current, RDD coincides the distribution of the readout noise.

2. What determines RDD?

I list below the parameters on which RDD depends. However, among the parameters, we ignore the position dependence and light leak dependence of RDD in the SIS calibration. Dependence on these parameters is small. We ignore the temperature dependence of RDD in some degree. When we model the RDD, we use data obtained when the CCD temperature was close to the nominal value (-61.7°C). However, current model of RDD does not reproduce the temperature dependence. This may introduce excess systematic error for 4 ccd mode data, which have large dark current, but we believe that the systematic error is not very large in most case.

RDD depends on the elapsed time since the launch of the satellite.
Because RDD results from the dark current, it is a strong function of the exposure time. But it is not proportional to the exposure time.
Because it takes about 4 sec to read an image data from the ccd, the last-read pixel stays on the ccd about 4 sec longer than the first-read pixel. This produce the position (V-address) dependence of the dark current, i.e. RDD.
Temperature of SIS ccds is usually controlled to -61.7°C, but sometimes increases up to about -58°C. Because the dark current depends on the ccd temperature, RDD also depends on the ccd temperature.
Light leak
Smoothly varying component (over the ccd position) of the light leak is subtracted as a part of the dark frame during the on-board processing and also by the DFE correction on ground. However, Poisson fluctuation of the number of electrons due to the light leak contributes to RDD.

3. Effects of RDD on the SIS Performance

RDD can affect the SIS performance in various way. Some effects are very complicated and are not fully investigated yet. I summarize below the effects briefly.

Shift of zero in energy scale
Definition of zero in energy scale (hereafter, zero level) is very simple and straightforward when the dark current is negligible. Readout noise has a gaussian distribution, and we can take the center of the gaussian distribution as zero. However, when the RDD becomes significant, the distribution shows a tail toward higher pulse height. This means that we need to define the zero level appropriately. We have introduced three definitions of zero level: (1) peak, (2) truncated mean, and (3) mean. "Peak" is for backward compatibility. "Truncated mean" is used for the analysis of the bright mode data, and "mean" is for the faint mode data. These definitions are shown in the above figure schematically.
Line profile
When the RDD effect is negligible (i.e. RDD is well approximated by a gaussian), a line for monochromatic X-ray has a profile approximated by two gaussians, i.e. main peak and sub peak. (There are several other features, such as constant component, escape, and fluorescence lines, which are not discussed here.) The line center energy is defined as the center of the main gaussian. When the RDD effect become significant, the two gaussians need to be replaced with the RDD profile. This is schematically explained in the right-hand-side figure. When the RDD effect is moderate, the line profile becomes almost symmetric. The line profile tends to have a hard tail, when the RDD effect become strong. "Mean" of the main RDD profile is taken as the center of the line.
Degradation of the energy resolution
As explained above, RDD makes the line profile broad. This causes the degradation of the energy resolution. Because this is equivalent to larger readout noise, the effect is most significant in the lower energy bands.
Loss of the detection efficiency
RDD can change the grade branching ratio, which results in the loss of the detection efficiency. ASCA SIS uses a grade to distinguish X-ray events from the particle events. Basically, single-pixel events and two-pixel events (grade 0234) are regarded as X-ray events, while others (3 or more pixel events) are discarded as particle events. RDD changes the grade branching ratio. RDD makes the zero distribution wider and asymmetric; zero distribution tends to have a tail toward higher pulse height. This makes the probability higher for a pixel to exceed the split threshold (40 adu in most cases). This means that a single-pixel event tends to become a two-pixel event, and a two-pixel event to a 3-pixel event, and so on, under the effect of RDD. Once the grade becomes larger than 4, it will be discarded as a particle event. This leads the reduction of the detection efficiency. As expected from the explanation above, loss of the detection efficiency due to RDD is basically energy independent.

Among these effects, loss of the detection efficiency may be reduced if we use higher split threshold. But we did not adopt this method, because, once the split threshold is changed, we need to re-calibrate the ccd almost completely. Split threshold affect the line profile, energy resolution, grade branching ratio, and quantum detection efficiency. Because it is practically impossible to redo all these calibration, we decided not to change the split threshold.

4. Decrease of the detection efficiency: Simulation based on 3C273 data

To estimate the decrease of the detection efficiency, we performed a Monte-Carlo simulation. The method of simulation is described below:

The RDD parameters we used are those expected on 1999/1/1 and have the following values:

RDD parameters used for the simulation
1 ccd 2 ccd 4 ccd 1 ccd 2 ccd 4 ccd
f 0.999999 1.0 1.0 1.0 1.0 1.0
Q 4.76428 15.7961 41.7353 7.46785 19.0230 59.1580

Results of the simulation are shown in the graphs below. Because of the degradation of the energy resolution due to RDD, the detection efficiency varies rapidly around 2 keV and 0.5 keV. Except for these energy ranges, the reduction of the detection efficiency is almost energy independent.

Detection efficiency obtained from the simulation may be tabulated as follows. Reduction of the efficiency is slightly energy dependent, which is ignored in the table below.

Relative detection efficiency as of 1999/1/1 compared to the 1 ccd mode data on 1993/12/20
1 ccd mode 2 ccd mode 4 ccd mode
SIS-0 1.0 0.75 0.4
SIS-1 1.0 0.7 0.3

5. Decrease of the detection efficiency: Observed data

To check the long-term change of the detection efficiency in the real ASCA data, we need to use observations of stable X-ray sources. Rotation powered pulsars and their synchrotron nebula, like the Crab, are the best. However, the Crab is too bright for SIS, and other sources, such as 3C58 and PSR0540-69, were not observed with enough intervals. Next best targets may be SNRs of small diameter (small enough to fit in the SIS fov). However, unfortunately, most of the SNRs are located on the galactic plane and suffer from large absorption. This is not good to see the long-term change of the lower energy part. In spite of this problem, we used SNRs to see the effects of RDD on the detection efficiencies, because there is no other choice.

Comparison of the energy spectra of the SNR observed twice with long interval is shown below.

So far, only 1 ccd mode data have been analyzed. The results are basically consistent with the simulation. No change of the detection efficiency is seen in 1 ccd mode data. Although there is a hint of the slight decrease of detection efficiency in SIS-1 data (especially lower energy part), we need more analysis to confirm whether or not this result is really due to the RDD.