ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Dataset O O B-Formula I-Formula I-Formula O B-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula I-Formula O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: along their main branch progenitor history (according to a given radius definition). In practice, applying this definition to merger trees created by almost any halo finder leads to erratic results due to spurious, temporary subhalo periods. In major mergers, for example, the host–subhalo relation can be ambiguous and switch between two halos, after which point the eventual host halo would be classified as a flyby halo. We follow the strategy of Mansfield Kravtsov ( 2020 ) to eliminate such cases: we do not count a halo as a flyby if its former host is no longer alive, if the former host is a subhalo of the halo in question, or if the former host’s mass is now smaller than that of the halo in question (all defined given the same radius and mass definition). In some cases, particularly for subhalo epochs at high redshift, the host may not be part of the merger trees because it never exceeded the necessary mass threshold. We also discard such events because the peak host mass was clearly smaller than the current mass of the halo in question. We emphasize that this definition of what constitutes a flyby halo is not unique. For example, we could consider future epochs to establish whether a flyby halo will eventually fall into its former host. Similarly, omitting any one of our exclusion criteria causes noticeable changes in the flyby fraction, raising the suspicion that f flyby is not a particularly well-defined quantity. Nevertheless, the relative differences in flyby fractions according to different radius definitions do remain similar, which is the focus of our work. Figure 4 shows the flyby fraction in the WMAP7 cosmology at z ≈ 0 and z = 2; the meaning of the lines is very similar to Figure 3 (see the Appendix for details). Regardless of the radius definition, mass variable, or redshift, f flyby asymptotes to zero at the highest masses and increases toward low masses. At the smallest masses we can probe, f flyby is still increasing so that we cannot put an upper bound on it. At fixed M 200m,bnd , f flyby varies between about 7% and 12% at the low-mass end. While this range sounds relatively modest, the relative fractions differ substantially between mass definitions, especially at intermediate masses. For instance, at M ≈ 10 12 h −1 M ⊙ , using R sp,90% leads to only 15% of the flyby halos found when using R 500c . When plotted as a function of peak mass, the fractions are shifted to higher values (middle column of Figure 4 ). In reverse, the shift means that flyby halos are more likely to have a high ratio of peak to current mass, meaning that they have lost mass at some point along their trajectory, which makes sense given that they had an encounter with a larger halo. Finally, the right column of Figure 4 shows the same results as a function of . In all cases, the relative differences between the radius definitions are similar. At higher redshift (bottom row), all curves are shifted to lower masses. Figure 4. Same as Figure 3 but for