Mining the information content of member galaxies in the halo mass
  modelling
  Motivated by previous findings that the magnitude gap between certain
satellite galaxy and the central galaxy can be used to improve the estimation
of halo mass, we carry out a systematic study of the information content of
different member galaxies in the modelling of the host halo mass using a
machine learning approach. We employ data from the hydrodynamical simulation
IllustrisTNG and train a Random Forest (RF) algorithm to predict a halo mass
from the stellar masses of its member galaxies. Exhaustive feature selection is
adopted to disentangle the importances of different galaxy members. We confirm
that an additional satellite does improve the halo mass estimation compared to
that estimated by the central alone. However, the magnitude of this improvement
does not differ significantly using different satellite galaxies. When three
galaxies are used in the halo mass prediction, the best combination is always
that of the central galaxy with the most massive satellite and the smallest
satellite. Furthermore, among the top 7 galaxies, the combination of a central
galaxy and two or three satellite galaxies gives a near-optimal estimation of
halo mass, and further addition of galaxies does not raise the precision of the
prediction. We demonstrate that these dependences can be understood from the
shape variation of the conditional satellite distribution, with different
member galaxies accounting for distinct halo-dependent features in different
parts of the cumulative stellar mass function.
