Examining the Time Dependence of the C-K edge

The fits to many observations of several sources allowed N
H 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. The new model of the C-K edge was used for consistency. Fig. 1 shows the results from the fits and the linear trend law that the optical depths follow.

Fig. 1. The C-K edge optical depth as a function of time for 11 observations of essentially featureless sources observed with the LETG and ACIS. The solid line is a linear regression that is not forced to go through zero, while the dashed line is a model with similar asymptotic behavior that is forced to zero at ACIS door opening.

The data are well fit by a linear model but a perhaps more physical model was adopted to allow the optical depth to be zero at the time of the opening of the ACIS door. The equation for the time dependence is

tau = a(t-y0) - a(t0-y0)exp( [t-t0]/q ),

where tau is the C-K optical depth, a is the asymptotic rate of increase (0.455 opt. depths per year), t0 is the date (1999.70) at which tau is forced to be zero, y0 is the year (1998.32) at which the linear regression gives tau=0, and q is the estimated timescale on which the optical depth approaches the asymptotic form: 0.15 yr.


Herman Marshall
Last updated July 7, 2003