Robust machine learning model of inferring the ex situ stellar fraction of galaxies from photometric data

We searched for the parameters defined from photometric images to quantify the ex situ stellar mass fraction of galaxies. We created mock images using galaxies in the cosmological hydrodynamical simulations TNG100, EAGLE, and TNG50 at redshift z = 0. We defined a series of parameters describing their structures, including the absolute magnitude in r and g bands ( M r , M g ), the half-light and 90% light radius ( r 50 , r 90 ), the concentration ( C ), the luminosity fractions of inner and outer halos ( f innerhalo , f outerhalo ), and the inner and outer surface brightness gradients (∇ ρ inner ,∇ ρ outer ) and g − r colour gradients (∇( g − r ) inner ,∇( g − r ) outer ). In particular, the inner and outer halo of a galaxy are defined by sectors ranging from 45 to 135 degrees from the disk major axis, and with radii ranging from 3.5 to 10 kpc and 10 to 30 kpc, respectively, to avoid the contamination of disk and bulge. The surface brightness and colour gradients are defined by the same sectors along the minor axis and with similar radii ranges. We used the random forest method to create a model that predicts f exsitu from morphological parameters. The model predicts f exsitu well with a scatter smaller than 0.1 compared to the ground truth in all mass ranges. The models trained from TNG100 and EAGLE work similarly well and are cross-validated; they also work well in making predictions for TNG50 galaxies. The analysis using random forest reveals that ∇ ρ outer , ∇( g − r ) outer , f outerhalo , and f innerhalo are the most influential parameters in predicting f exsitu , underscoring their significance in uncovering the merging history of galaxies. We further analysed how the quality of images will affect the results by using SDSS-like and HSC-like mock images for galaxies at different distances. Our results can be used to infer the ex situ stellar mass fractions for a large sample of galaxies from photometric surveys.