r**-1/2 recovered

Walter's e-mail set me onto the right track, the r^-1/2 behavior is farther to the interior of the halo than where I was plotting in my previous studies. I changed the binning to have logarithmic spacing and what I find is (indeed) over several decades there is a powerlaw behavior r^-1/2.

My first attempt to plot looked like this:

Indicating that there does seem to be power law behavior, but as Walter pointed out, the center has drifted from x=0 (there are two separate density curves, for particles with positive and negative position coordinates). My crude fast way of correcting this was to find the x position of the density maximum, and shift all the coordinates by this amount, and re-make the histograms. When I did this, I got this plot:


Which as you can see is still not perfect, but improved. Anyhow, I think this probably now agrees with what Walter's students were finding.

Regarding the question: Btw, I havn't yet got an anwser to my question of how you obtain the density. Sorry, the method is pretty simple, I make a histogram of the particle positions, normalize it (because each particle has mass 1/N) and also divide by the bin width to get mass per unit length.