Using the Two-point Correlation Function to Understand the Assembly Histories of Milky Way-like Galaxies

The two-point correlation function (2PCF) is a powerful statistical tool to measure galaxy clustering. Although 2PCF has also been used to study the clustering of stars on subparsec to kiloparsec scales, its physical implication is not clear. In this study, we use the Illustris-TNG50 simulation to study the connection between the 2PCF of accreted halo stars and the assembly histories of Milky Way-mass galaxies. We find, in general, that the 2PCF signal increases with the increase in galactocentric radii, r, and with the decrease in the pair separations. Galaxies that assemble late on average have stronger 2PCF signals. With z(1/4), z(1/2), and z(3/4) defined as the redshifts when galaxies accreted one-fourth, half, and three-fourths of their ex situ stellar mass today, we find they all show the strongest correlations with the 2PCF signals at r < similar to 0.2R(200). z(3/4) shows the strongest correlations than those of z(1/4) or z(1/2). However, the correlations have large scatters. The 2PCFs in the velocity space show weaker correlations with the galaxy formation times within similar to 0.35R(200) than real-space 2PCFs, and the scatter is considerably large. Both the real- and velocity-space 2PCFs correlate with the assembly histories of the host dark matter halos as well. Within 0.3R(200), the real-space 2PCF shows stronger correlations with the galaxy formation histories than with the halo formation histories. We conclude that it is difficult to use 2PCF alone to precisely predict the formation times or assembly histories of galaxies.