On the Frequency of Multiple Galaxy Mergers in $Λ$CDM Cosmological Simulations

TL;DR

This study extends galaxy merger statistics to the regime of multiple mergers using Illustris and IllustrisTNG simulations. It introduces a probability-based merger fraction that accounts for finite merger durations, enabling robust measurements of $f_t$ and $f_m$ and their relationship $f_m \,\approx\,0.5\,f_t^{5/3}$ (with potential up to $0.7\,f_t^{5/3}$). The results show mergers are temporally clustered, with the time to the second-closest merger typically within ~1 Gyr of the closest, and that a Poisson process underestimates the prevalence of multiple mergers. Across parameter space, $f_m/f_t \approx 0.5 f_t^{2/3}$, implying multiple mergers are subdominant but non-negligible and more common at higher $f_t$. These findings inform interpretations of observational merger fractions and the role of hierarchical structure formation, with implications for modeling mergers in halos and galaxies alike.

Abstract

Mergers are believed to play a pivotal role in galaxy evolution, and measuring the galaxy merger fraction is a longstanding goal of both observational and theoretical studies. In this work, we extend the consideration of the merger fraction from the standard measure of binary mergers, namely those comprising two merging galaxies, to multiple mergers, namely mergers involving three or more galaxies. We use the Illustris and IllustrisTNG cosmological hydrodynamical simulations to provide a theoretical prediction for the fraction of galaxy systems that are involved in a multiple merger as a function of various parameters, with a focus on the relationship between the multiple merger fraction $f_m$ and the total merger fraction $f_t$. We generally find that binary mergers dominate the total fraction and that $f_m\approx (0.5-0.7)f_t^{5/3}$, a prediction that can be tested observationally. We further compare the empirical simulation results with toy models where mergers occur, on the evolution timeline of a galaxy, either at constant intervals or as a Poisson process at a constant rate. From these comparisons, where the toy models typically produce lower multiple merger fractions, we conclude that in cosmological simulations, mergers are more strongly clustered in time than in these toy scenarios, likely reflecting the hierarchical nature of cosmological structure formation.

Figures (17)

• Figure 1: A demonstration of the dependence on the snapshot separation in a naïve approach to determining whether a merger is a multiple merger, i.e. between more than two galaxies at once. On the left, case (a) shows how small snapshot separations delineates the mergers in time into a sequence of two binary mergers, with one descendant at snapshot $t_{m,e-1}$ and the final descendant in snapshot $t_{m,e}$, implying this case would not be counted as a multiple merger. In case (b) on the right, however, a larger difference in time between adjacent snapshots $t_{m,e}$ and $t_{m,e-2}$ implies that the three galaxies in snapshot $t_{m,e-2}$ appear to be merging all together into one descendant at $t_{m,e}$, naïvely appearing as a multiple merger. This demonstrates that relying on the connectivity of the merger tree for identifying multiple mergers is fraught, since that connectivity significantly depends on the snapshot separation.
• Figure 2: An illustration of the role of the concept of the merger duration in our methodology. By identifying a descendant at snapshot $t_{m,e}$ (the post-merger time) and its pair of progenitors at snapshot $t_{m,s}$ (the pre-merger time), we consider the merger to have occurred at some indeterminate time in between (marked by thin black arrows). Since we assume the merger is observable for a time duration $T$ that is centered around the actual merger occurrence time, namely as early as around $t_{m, s}$ (green) or as late as around $t_{m, e}$ (blue), any analysis time point $t_a$ in the range $t_{m, s} - T/2 \le t_a \le t_{m, e} + T/2$ (red) could potentially be a time at which the merger is observable. The probability $p$ that the analysis time $t_a$ is an instant that is actually covered by the $T$-long duration window equals the ratio of two particular time segments, as described by Equation \ref{['eq:p']} and illustrated here (dashed) for an arbitrarily chosen $t_a$.
• Figure 3: Illustration of descendant and progenitor skips. On the left is a descendant skip, where the mass of the descendant (at time $t_{m,e}$) is less than the total mass of its progenitors. Since galaxy masses typically increase over time, this is likely a skip, so we set the mass of the descendant to be equal to that of its progenitors at time $t_{m,e-1}$. On the right, the mass of the progenitors at time $t_{m,e-1}$ is much less than that of its descendant at time $t_{m,e}$. This is a case of a likely progenitor skip, which we remedy by creating at time $t_{m,e-1}$ a 'virtual progenitor' galaxy with mass equal to the mass of the descendant that is in excess of the sum of the masses of its progenitors. Since there is some ambiguity with regards to when such a remedy is appropriate (since some mass growth can truly occur via unresolved objects), we generate and compare results both with and without these virtual progenitors.
• Figure 4: An illustration of the maximum past mass algorithm for determining the mass ratio of a merger, following RG15. The smaller progenitor ('next progenitor', here NP) is followed backwards along its first progenitor branch and the time of its maximum past mass is determined (depicted here at $t_{m,e-2}$ with the largest circle along the left branch). Its mass at that time is then compared to the mass of the primary galaxy ('first progenitor', here FP) at that same time, and their ratio is recorded as the merger's mass ratio.
• Figure 5: Illustration of the toy scenario where mergers occur at constant intervals on a galaxy's timeline. Here $t_{n+1} - t_n = t_{n} - t_{n-1}$ for any $n$ and the merger rate is therefore $R=1/(t_{n+1} - t_n)$. An analysis time $t_a$ is marked at an arbitrary location, representing the independence between the arbitrary times at which simulation snapshots are written and the merger occurrence sequence.