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The two point correlation function (2PCF) is a powerful statistical tool tomeasure galaxy clustering. Although 2PCF has also been used to study theclustering of stars on parsec and sub-parsec scales, its physical implicationis not clear on such non-linear scales. In this study, we use theIllustris-TNG50 simulation to study the connection between the 2PCF signals ofaccreted halo stars and the assembly histories of Milky Way-mass galaxies. Wefind, in general, the 2PCF signal increases with the increase in galactocentricradii, $r$, and with the decrease in the pair separations. Galaxies whichassemble 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, halfand three-fourths of their ex-situ stellar mass at today, we find all of themshow the strongest correlations with the 2PCF signals at $r\sim0.2R_{200}$.$z_{3/4}$ shows the strongest correlations at all radii than those of $z_{1/4}$or $z_{1/2}$, as later accreted stars preserve better clusterings. However, thecorrelations between the 2PCF signals at different radii and the galaxyformation times all have large scatters. The 2PCFs in velocity space showweaker correlations with the galaxy formation times within $0.38R_{200}$ thanreal space 2PCFs, and the scatter is considerably large. Both the real andvelocity space 2PCFs correlate with the assembly histories of the host darkmatter halos as well. Within $0.38R_{200}$, the real space 2PCF shows strongercorrelations with the galaxy formation histories than with the halo formationhistories, while the velocity space 2PCFs do not show large differences. Weconclude that it is difficult to use 2PCF alone to precisely predict theformation times or assembly histories of galaxies.

Using two point correlation functions to understand the assembly histories of Milky Way-like galaxies