Connection Between SDSS Galaxies and ELUCID Subhaloes in the Eye of Machine Learning

We explore the feasibility of learning the connection between SDSS galaxies and ELUCID subhaloes with random forest (RF). ELUCID is a constrained $N$-body simulation constructed using the matter density field of SDSS. Based on an SDSS-ELUCID matched catalogue, we build RF models that predict $M_r$ magnitude, colour, stellar mass $M_*$, and specific star formation rate (sSFR) with several subhalo properties. While the RF can predict $M_r$ and $M_*$ with reasonable accuracy, the prediction accuracy of colour and sSFR is low, which could be due to the mismatch between galaxies and subhaloes. To test this, we shuffle the galaxies in subhaloes of narrow mass bins in the local neighbourhood using galaxies of a semi-analytic model (SAM) and the TNG hydrodynamic simulation. We find that the shuffling only slightly reduces the colour prediction accuracy in SAM and TNG, which is still considerably higher than that of the SDSS. This suggests that the true connection between SDSS colour and subhalo properties could be weaker than that in the SAM and TNG without the mismatch effect. We also measure the Pearson correlation coefficient between galaxy properties and the subhalo properties in SDSS, SAM, and TNG. Similar to the RF results, we find that the colour-subhalo correlation in SDSS is lower than both the SAM and TNG. We also show that the galaxy-subhalo correlations depend on subhalo mass in the galaxy formation models. Advanced surveys with more fainter galaxies will provide new insights into the galaxy-subhalo relation in the real Universe.