New Nov 2010! A new version of the ACIS CTI/Background anti-correlation correction which fits the CTI/Background relation to a quadratic rather than linear function and makes no assumptions about the shape of the CTI increase with time. The older linear correction is discussed here.
Now that we have many years worth of CTI and background data, we can better determine the anti-correlation between ACIS CTI and background rate directly from the data. Only front-illuminated CCDs show this strong correlation; back-illuminated CCDs show much less background related variance. By sorting the CTI data into groups with equal background rate (± 2 cts/frame), we can remove any background variance. Any remaining change in the CTI must then be due to real changes.
The figure below shows the background rate (as measured by the S3 high energy reject counter) and the measured CTI as a function of time. This data has been filtered to include only cold data. The colors and symbols identify the equal-background groups that were used to determine the real CTI increase. If the CTI increase is assumed to be linear over the entire eleven year time period, the CTI increase is (3.29 ± 0.07) x 10-6 / year.
The figure below uses the same color/symbol combinations but shows the background rate as a function of CTI.
Previously, the assumption of a linear CTI increase appeared to match the data well and a linear background correction to the CTI data did a good job of removing sharp features due to jumps in the background rates. As the mission has continued and ACIS background rates have doubled, this simple linear assumption breaks down. Features that are clearly seen in the background rates are not being completely removed from the corrected CTI data. The background corrected CTI data shown below uses the linear assumptions and demonstrates the current problem.
I now examine both these assumptions of linearity further.
The figure below shows the linear CTI increase as a function of time. Each point represents a fit to data with the same background rate (± 2 cts/frame). The time assigned to the data points is the mean time of the individual observations in the group. Independent of background level, the rate of CTI increase appears to have been roughly 3 x 10-6 / year before 2004 and then drops to about 2 x 10-6 / year. This change could be due to solar activity which peaked in 2001-2003 and was minimal 2007-2010. The assumption that the rate of increase in CTI has remained constant for the entire mission seems to be incorrect.
As a first test of a solution, we remove the assumption of a fixed linear CTI increase. Then we step through a grid of possible linear correction coefficients and minimize the residuals of the corrected CTI fit to a polynomial. The polynomial fit to the corrected CTI as a function of time removes the larger scale structures, which may be real, and leaves the sharp background related structures, which we want to remove. The best linear correction is shown below. The CTI increase appears something like the above plot, with a higher rate of increase at earlier times. The features associated with background changes are smaller than before, but they are still noticable, particularly around 2004.
The dependence of CTI on the background rate is due to the sacrificial charge provided by the particle events. Higher particle background rates will fill more of the electron traps that cause CTI and thus the measured CTI will be decreased. While this relation is linear over some range of background rates, it must, at some point saturate as particle events shield each other and not the X-ray events. A quadratic background correction could account for this deviation from linearity and provide a better overall fit. The best quadratic background correction is shown below. The primary difference between the linear and quadratic correction is that the background features are better supressed by the quadratic correction.
The quadratic CTI/background correction seems to do a much better job at removing background features from the CTI data and will be adopted for regular CTI monitoring. The coefficients of the correction are:
Corrected CTI = Measured CTI + 4.71 x 10-7 x Bkg rate - 1.79 x 10-9 x (Bkg rate)2
where the background rate is measured in counts per frame.
I-array (FI) CCDs: Corrected CTI = Measured CTI + 4.72 x 10-7 x Bkg rate - 1.74 x 10-9 x (Bkg rate)2
S3 (BI) CCD: No sacrificial charge correction