A Physically Motivated Framework to Compare Merger Timescales of Isolated Low- and High-Mass Galaxy Pairs Across Cosmic Time

The merger timescales of isolated low-mass pairs ($\rm 10^8<M_*<5\times10^9\,M_{\odot}$) on cosmologically motivated orbits have not yet been studied in detail, though isolated high-mass pairs ($\rm 5\times10^9<M_*<10^{11}\,M_{\odot}$) have been studied extensively. It is common to apply the same separation criteria and expected merger timescales of high-mass pairs to low-mass systems, however, it is unclear if their merger timescales are similar, or if they evolve similarly with redshift. We use the Illustris TNG100 simulation to quantify the merger timescales of isolated low-mass and high-mass major pairs as a function of cosmic time, and explore how different selection criteria impact the mass and redshift dependence of merger timescales. In particular, we present a physically-motivated framework for selecting pairs via a scaled separation criteria, wherein pair separations are scaled by the virial radius of the primary's FoF group halo ($r_{\mathrm{sep}}< 1 R_{vir}$). Applying these scaled separation criteria yields equivalent merger timescales for both mass scales at all redshifts. Alternatively, static physical separation selections applied equivalently to all galaxy pairs at all redshifts leads to a difference in merger rates of up to $\rm \sim 1\, Gyr$ between low- and high-mass pairs, particularly for $\rm r_{sep}<150\, kpc$. As a result, applying the same merger timescales to physical separation-selected pairs will lead to a bias that systematically over-predicts low-mass galaxy merger rates.