Mass plots reveal to us the evolution of halos through time. On the y axis, we usually have the mass of the object or equivalently the number of particles it contains (because the mass of all particles is the same in N-body simulations). On the x axis, we have time. In our case, the y axis is shown in logarithmic units (i.e. 10, 100, 1000, 10000, etc. instead of 1, 2, 3, 4, etc.). We do this because in astronomy we work with very big numbers which are incomprehensible if shown linearly. The x axis in the plots below shows which snapshot the simulation is at. We are working with only the last 10 snapshots, so Time = 0 corresponds to snapshot = 90 in the original TNG simulation data (as the total number of snapshots is 100). Usually, one expects to find the mass of a given halo nearly constant with a slight increase in time as the halo grows and accretes mass into itself through mergers. For this reason, any rapid fluctuations up and down in the mass plot are unphysical and are most likely indicative of an issue with the halo finder. Below we isolate the cases for both FoF and ROCKSTAR where the halos lost a significant percentage of their mass (40%) within one snapshot and then rapidly gained it back. The fewer these cases, the more robust the halo finder and the more reliable the final halo properties one extracts from the simulation will be.
In the figure above, we show the case for the FoF finder. Wee see that there are quite many examples in the TNG300 simulation we are working with. There are 23 unphysical cases out of 1000 halos and 425 out of 16000 halos.
ROCKSTAR exhibits far fewer unphysical examples -- only 2 out of 1000. In the full sample, there are 18 out of 16000 halos. This is a significantly smaller number than the FoF result, i.e. ROCKSTAR does about 22 times better.
Conclusion: We believe that this finding suggests that using FoF for more sophisticated analysis can result in substantial errors in the final result. Great accuracy is extraordinarily important in the current age of precision cosmology where the most state-of-the-art science is done at the subpercentage level (i.e. < 1%).