A machine learning approach to infer the accreted stellar mass fractions
  of galaxies
  We propose a random forest (RF) machine learning approach to determine the
accreted stellar mass fractions ($f_\mathrm{acc}$) of central galaxies, based
on various dark matter halo and galaxy features. The RF is trained and tested
using 2,710 galaxies with stellar mass $\log_{10}M_\ast/M_\odot>10.16$ from the
TNG100 simulation. For galaxies with $\log_{10}M_\ast/M_\odot>10.6$, global
features such as halo mass, size and stellar mass are more important in
determining $f_\mathrm{acc}$, whereas for galaxies with
$\log_{10}M_\ast/M_\odot \leqslant 10.6$, features related to merger histories
have higher predictive power. Galaxy size is the most important when calculated
in 3-dimensions, which becomes less important after accounting for
observational effects. In contrast, the stellar age, galaxy colour and star
formation rate carry very limited information about $f_\mathrm{acc}$. When an
entire set of halo and galaxy features are used, the prediction is almost
unbiased, with root-mean-square error (RMSE) of $\sim$0.068. If only using
observable features, the RMSE increases to $\sim$0.104. Nevertheless, compared
with the case when only stellar mass is used, the inclusion of other observable
features does help to decrease the RMSE by $\sim$20%. Lastly, when using galaxy
density, velocity and velocity dispersion profiles as features, which represent
approximately the maximum amount of information one can extract from galaxy
images and velocity maps, the prediction is only slightly improved. Hence, with
observable features, the limiting precision of predicting $f_\mathrm{acc}$ is
$\sim$0.1, and the multi-component decomposition of galaxy images should have
similar or larger uncertainties. If the central black hole mass and the spin
parameter of galaxies can be accurately measured in future observations, the
RMSE is promising to be further decreased by $\sim$20%.
