NR investigation to set default number of orbits to exclude before merger
We provide an option to exclude a certain number of orbits before the merger for locating the pericenters and the apocenters in the data using the argument num_orbits_to_exclude_before_merger.
- The interpolant through the pericenters and apocenters becomes non-monotonic and hence the measured eccentricity becomes non-monotonic and show nonphysical feature very close to the merger.
- For the methods that use envelope fits, the fit has singularity at the merger and there we don't want to use data all the way to the merger. Using data close to merger makes the residual data diverge at the end which might result in non detection of extrema.
To decide the default value for num_orbits_to_exclude_before_merger, we look at the measured eccentricity vs time plot using different values of num_orbits_to_exclude_before_merger for a set of eccentric NR simulations. The attached pdf shows these results.
num_orbits_to_exclude_before_merger=1 has the most nonphysical feature in the measured eccentricity. num_orbits_to_exclude_before_merger=2 removes this nonphysical feature by some amount. As we increase the value num_orbits_to_exclude_before_merger, the nonphysical feature goes away. But with increasing num_orbits_to_exclude_before_merger, we also lose data in many cases without much improvement. Thus we need to balance these two factors. Looking at the results in the above plots, it seems that num_orbits_to_exclude_before_merger=2 is the best choice. It improves the measure eccentricity plot in many cases without losing too much data.
