I’ve been working on better error estimates in the Np(T) calculations, and I needed a way to quickly calculate the transmission fraction produced by the windtabs model. The point of windtabs is to have a big table full of data (hence “tabs”) to use for model fitting, but I didn’t have access to that table (it’s in a weird XSPEC file format).
The answer is pretty straightforward–make my own table, and interpolate over it. The windtabs transmissions are pretty smooth, so I didn’t need that many points. Using a 30 by 30 grid evenly spaced across for and for , we get a pretty good fit. The plot below is for , with an exponential absorption model plotted for comparison in red, the full double integral in blue, and the interpolation function in gold. Note the deviation because I only used .
If we explore this parameter space a bit, we find that it was indeed pretty smooth (below is ).
The end result is that I can really quickly generate values for a particular and combination, for use in a Monte Carlo error estimate. Below is a histogram for normally distributed and .
Unfortunately, I’m now stuck! I need an input probability distribution to model the asymmetric error on , but I have no idea what it is! Some talking with David suggests that the base distribution (and upper/lower errors) comes from fitting, so some exploration of what XSPEC is doing might be fruitful.
You can get the (rather messy) Mathematica notebook here.