I've been playing around with Illustris TNG300-1 data and find for some halos center of mass given by Illustris does not look right. I attached one plot for the random subsample points of most massive halo and the center of mass point (red point) given by Illustris in TNG300-1 at redshift z=0.0.
I've read through the Illustris papers but did not find what algorithm you use to find center of halo. Could you tell me or point out where I can find more details about this?
I think the most likely explanation (particularly at high masses) is the "FoF bridging" issue. If you google ""fof bridging" cosmological simulation" you will find some papers that point out the issue.
Since we run Subfind, the GroupPos then comes actually from Subfind, i.e. is "Spatial position within the periodic box (of the particle with the minium gravitational potential energy)." as described in the docs. If you are particularly studying halo center issues (i.e. mis-centering between different components or observational tracers), you would want to calculate this carefully and newly. In these cases, it would be advisable to detect FoF-bridges and to separate them into two (or more) separate but close "halos".