I've been trying to find a way to select field galaxies in order to compare their population in color magnitude plots with galaxies within 1 Mpc of a cluster/halo center (this is to try and define red and blue galaxy populations in clusters so if you have any insight on that, that would be extremely helpful too!). I read through your previous suggestions on field galaxies (defining field galaxies as subhalos outside a certain radius around the halo or as subhalos that have no higher mass object nearby). You also seem to suggest using central galaxies since you say satellites are by definition not alone. Since I am interested in field galaxies as not just isolated but as galaxies that have not "fallen" into clusters and gone through cluster processes etc, would using central galaxies (even if it is the only galaxy/subhalo in the cluster) or galaxies outside a certain range still make any sense?
Some related clarifying questions: it seems like all subhalos "belong" to a halo, at least they have a halo ID under SubhaloGrNr, is that correct? For subhalos that are the only ones belonging to their halo, they are still in a larger collapsed region of gas, dark matter, etc, right? And have gone through cluster processes? So they couldn't really be viably defined as field galaxies?
Sorry for the many related questions, any insight would be great!
Is your goal to compare to observational data, or is this a theoretical study? If the former, I would consider a definition of field which is similar to the working definition used in the data, e.g. you should move into 2D projected distances and some line-of-sight/redshift cut. If this is a theoretical study, I would use centrals as you say. If you want more and more isolated (or pure) field samples, you could define them as more and more distant from any massive neighboring galaxies/halos. If you are particularly looking around clusters, you should be careful of contamination by splashback galaxies (which would usually extend out to ~2 rvir). I.e. you may want to define field as centrals which have always been centrals, and never were satellites (or "near to") of other hosts in their past history.
All subhalos live in a halo. The first (most massive) is the "central", and if it is the only subhalo in that halo, then the halo has no satellites.
I'm not sure what you mean "gone through cluster processes". To me, I would say that no central galaxies have gone through cluster processes, except those which are splashbacks or had strong tidal interactions with clusters in the past (e.g. fly-bys).