It is found that the efficiency loss can be parameterized crudely with excess absorption. Although this is very crude, at least it allows us to represent the degradation with a single number for each SIS at a snapshot in time. This has already been demsonstrated for a few 2-CCD mode observations in Hwang et al 1999 (ApJ 516, 604). The effect on 2-CCD and 4-CCD mode data is much worse than 1-CCD mode. In this report we consider principally the 1-CCD mode data. The magnitude of the problem is illustrated in Figure 1 below with two observations of 3C 273. In each case a 4-instrument simultaneous fit was performed with a power law plus Galactic absorption; however an additional power-law was included for the first observation (1993/day 160) to model a soft-excess and there may be extra intrinsic absorption in the second observation (2000/day 10-11) which is not included. The main point, however, is to illustrate the divergence of the four instruments at low energies, which does not depend on the model.
Our strategy here will be the following.
For  we can use virtually any fairly bright source (more than a few tenths cts/s/SIS), observed at any time, even if it is highly variable.
For  , finding suitable sources is a very tall order. The SIS degradation we are investigating became noticable in observations made as early as the begininng of 1994 so we have to find sources which were observed in the PV phase (approxmately March 1993 to the end of 1993) AND then again at least once more at later date. There are several severe problems:
We painstakingly searched the entire ASCA public database for suitable sources for part  of the study. The enormous problems mentioned above resulted in only THREE suitable sources. These are NGC 4636 (an elliptical galaxy); NGC 1068 (a Seyfert 2 galaxy), and N103 (a supernova).
The ratios of SIS1 spectra to SIS0 spectra for some representative bright sources during the period 1994-2000 are shown below.
Figures 3a, 3b and 3c below show that the low-energy degradation is NOT strictly monotonic with time. Figure 3a shows the SIS1/SIS0 ratios for four observations of four different sources over the period 1996/day 180 to 1998/day 107. It can be seen that there is no clear trend of the SIS1/SIS0 discrepancy with time, and if anything, the discrepancy in NGC 5548 (1996/days 180-187) appears to be LARGER than that in 3C 273 (1996/day 201), which is opposite to the overall long-term trend. In fact, for the sources in Figure 2 we have parameterized the low-energy SIS1/SIS0 ratio as an effective absorbing column, using simple "eye-ball" fits and this effective excess column is shown below in Figure 3b. The overall trend is an SIS1/SIS0 ratio that is near unity up to about the begining of 1996 but then rises rapidly over the next year and then levels off and is possibly decreasing by the end of 1999. Superimposed upon the overall trend one can see local departures from the overall trend and in the opposite sense. This non-monotonic behavior CANNOT be due to a difference in the source spectra, as can be seen in Figure 3c which shows the SIS1/SIS0 ratios for four observations spanning four years, over the period 1995/day 362 to 2000/day 10. One observation is of NGC 4636 and the other three are of 3C 273. The latter source shows little spectral variability in these observations and the 3C 273 spectra are very different from the spectrum of NGC 4636. Yet all four of the SIS1/SIS0 ratios are fairly similar. Note that the ratios below 0.6 keV are more sensitive to any background subtraction systematics than at higher energies.
As mentioned above we found only THREE sources suitable for obtaining the absolute SIS degradation in the entire ASCA public database (NGC 4636, NGC 1068 and N103B). These are the only sources that satisfy the stringent but necessary requirements described above. (If the reader knows of a suitable source that we missed, please let us know). All three sources were of course observed in the PV phase (one of the necessary requirements) and all three have the added bonus that the second observation in each case had a relatively high exposure time. NGC 4636 is an elliptical galaxy so the soft spectrum, at least, is constant in time, as it should be for NGC 1068 which is a Seyfert 2 galaxy in which the soft X-ray emission is extended. N103B is a supernova remnant so the entire spectrum should be constant.
For NGC 1068 and N103B, Figures 4a to 4d below show two spectral ratios between the AO and PV observations (for SIS0 and SIS1). It can be seen that the ratios can be crudely modeled with an excess absorbing column. We do not show the corresponding ratios for NGC 4636 because they are not simple to interpret. This is because the source is extended and the PV observation was made in 4-CCD mode, with significant flux falling off the nominal chips. The effective excess NH values derived from spectral fitting the PV and AO spectra are fine, however. The six values of the effective NH derived from these data are plotted in Figure 5.
ASCA/RXTE and BeppoSAX observed 3C 273 simultaneously on three occassions. We can use the LECS on BeppoSAX to compare with the ASCA SIS. Of course, this does not necessarily mean that the absolute calibration of the LECS is perfect but such an excercise will add more data points to the investigation. We spectral fit the LECS, SIS0 and SIS1 data simultaneously with a power-law plus Galactic absorption, allowing independent, extra column densities for each SIS. The results are plotted in Figure 5. Currently we only have measurements for the June 1998 observation; work is in progress for the other two.
Finally, we can compare the SIS data with the GIS data. This method suffers the most from systematic effects. The GIS response diminishes below 0.7 keV and the accuracy of the low-energy calibration is limiting. Also, if the source spectrum is already (intrinsically) absorbed then we cannot get a handle on the "excess NH" from spectral fitting data from the detectors simultaneously. The method works best for sources which are bright and which do not appear to be intrinsically absorbed. The latter condition effectively means that it only works well when the CCD degradation is small, because otherwise we cannot tell whether there is significant intrinsic absorption, unless there is an independent way of knowing (e.g. ROSAT data). Since methods 1-3 above leave a gap during the period between 1994 and 1996 when the degradation was small, we searched for suitable ASCA observations from this period and found three. Values of the excess NH derived are plotted in Figure 5.
All the measurements derived from methods 1-4 above are plotted together in Figure 5.
It can be seen that the SIS0 data fit very well with a straight line but the SIS1 data do not. It seems that both SIS0 and SIS1 underwent a dramatic degradation during 1995--1996 and that the gap between SIS0 and SIS1 diverged dramaticaly at the same time, and this was also indicated by the SIS1/SIS0 ratios (see Figure 3b). If we draw a straight line going through the 16 Decemeber 1993 point (3C 273 anchor) and the 24 June 1998 SIS0 point (3C 273 simultaneous ASCA/BeppoSAX), it agrees with all the other SIS0 calibration points extremely well. The equation of the straight line going through the SIS0 data is
NH(SIS0) = 3.635857508e-8(T-3.0174828e7) e20 cm^-2
where T is ASCATIME (take the average of the start and stop times of your observation). The SIS1 degradation with time cannot be modeled by a straight line. However, one can measure the SIS1/SIS0 ratio for the observation we are trying to correct, providied the signal-to-noise is sufficient. One measures the NH excess from the SIS1/SIS0 ratio and simply add this to the SIS0 correction to correct the SIS1 data. If the signal-to-noise is insufficient to measure the SIS1/SIS0 ratio, then attempting to correct either the SIS0 or SIS1 data is not useful anyway.
An observation of the Blazar PKS 2155 was made in 1-CCD mode in 1996/day 319-320 and then in 2-CCD mode in 1996/day 143-147. Figure 6 compares the SIS1/SIS0 ratios for these two observations. Remarkably it shows that the ratios are virtually identical! Moreover, the PKS 2155 ratios are compared with the SIS1/SIS0 ratio for 3C 273 from the 1996/day 201 observation. Figure 6 shows that the 3C 273 SIS1/SIS0 ratios are also virtually identical to both PKS 2155 SIS1/SIS0 ratios! This means that the relative degradation between SIS1 and SIS0 does not depend on CCD mode.
We have crudely parameterized the low-energy degradation of the ASCA SIS0 and SIS1 versus time, with the primary purpose that the form of the relationship may provide important clues about the physical origin of the problem. The relationship is summarized in Figure 5.
The spectral characteristics of the low-energy problem appear to be complex but we simply characterized it by a simple number (an effective "excess absorption column density" for each SIS).
We derived a straight line fit to estimate this excess NH parameter for a given observation time for SIS0 (a linear approximation is not good for SIS1). The corresponding number for SIS1 can be derived from the data itself by examining the model-independent SIS1/SIS0 ratio. If the signal-to-noise of the data is insufficient, then one need not worry abut correcting the data anyway since the statistics are then worse than the systematics.
Until a physical model of the CCD degradation is available one should only use this parameterization to estimate the magnitude of the effect. One cannot apply an "excess NH correction" and derive meaningful parameters from models soft X-ray features below 2 keV, especially from 1996 onwards when the degradation became very significant.
Note that no RDD correction was applied to the data in all of this analysis (the current tools have little effect on 1-CCD mode data).