Discrete populations, better distribution over frequency

[lzkelley]

We can generally get a (semi-analytic) expression for df/dt in the frequency band of interest, so we can use that expression to distribute binaries over frequency instead of using the KDE based on bin-center values which gives lumpy results. This addresses the issues that Bence and Sarah Burke-Spolaor have had.

[xiggystardust]

Wanted to give a quick update here to detail the issue. The "lumpiness" in f_gw is shown in the two plots below - first as a straight histogram of f_gw from one universe, and secondly as a plot of h_0 vs f_gw. To be clear the h_0 here is calculated as in the NANOGrav CW papers (Sarah's 11yr and Caitlin's 3C66b/targeted).

Here is h_0 vs f_gw for a subset of one of the universes:

BUT, this lumpiness disappears when plotting the characteristic strain, which we're calculating as h_0 * f/df for each source:

I thought this might be a relevant piece of information, as it indicates that if we tinker with the frequency distribution of CWs it might mess with GWB calculations elsewhere in the code. Just putting this in here for posterity's sake!

edit to add: these plots were made by my great REU student Sydney Jetton! Accept her to grad school if she applies!!