Examining the Time Dependence of the O-K edge
The fits to many observations of several sources allowed NH to be free, as well as the C-K, N-K, O-K and F-K edges to be unconstrained and, perhaps, negative. As in my previous analysis, I scaled the uncertainties by sqrt(chi2) to account for unknown systematic errors in a dubious statistical manner.
Fig. 1: O-K edge measurements as a function of year compared to the model for the time dependence of the O-K optical depth. The model assumes that the O-K optical depth scales with the C-K edge and is forced to go through the best data point (Mk 421, in late 2002). In general, the trend given by the model is matched by the data: the O-K edge is detected only in the last year or so and is smaller in the first year. In particular, the possibility that the O-K edge is nearly constant after 2000.0 seems to be ruled out.
Fig. 1 shows that the measurements are mostly below the model. The three 3C 273 observations are nearly bang on the model but all except one of the PKS 2155 measurements are below the line. These deviations are not readily explained by O-K in the ISM. In all the PKS 2155 measurements, for example, the NH was free and varied between 1.0 and 1.7 x 1e20 cm-2. The "nominal" value is about 1.35e20 cm-2, for which two different ISM models give an O-K edge of 0.054 optical depths. If the NH were systematically decreased to 1.0e20 cm-2, say, the average O-K due to the contaminant would increase by 0.027. Another possiblity is that the NH from the Mk 421 fit is too low by ~0.5e20 cm-2, which would decrease it's O-K by 0.02 but this change wouldn't affect the low points from before 2001. One improvement in the analysis would be to tie the NH and the O/H values for the ISM of each source and then constrain these values to be the same for all observations of the same source. Then the chi2 could be minimized by allowing for more or less O in the ISM along each particular line of sight. Also, I haven't yet included constraints on the ISM O-K edge coming from LETG/HRC observations of three of these sources (3C 273, PKS 2155, & Mk 421). HRC calibration issues might make it difficult, however.
Last updated July 7, 2003