A fitting formula for the merger timescale of galaxies in hierarchical clustering

TL;DR

This paper introduces a new fitting formula for galaxy merger timescales based on high-resolution simulations, improving accuracy over previous models by better accounting for mass dependence and orbital parameters.

Contribution

The study provides a revised, more accurate fitting formula for galaxy merger timescales that corrects limitations of earlier models, incorporating improved Coulomb logarithm expressions and weaker dependence on circularity.

Findings

The new formula better matches simulation data for both minor and major mergers.

The Coulomb logarithm expression (1+m_pri/m_sat) improves mass dependence modeling.

Merger timescale dependence on circularity is weaker than previously thought.

Abstract

We study galaxy mergers using a high-resolution cosmological hydro/N-body simulation with star formation, and compare the measured merger timescales with theoretical predictions based on the Chandrasekhar formula. In contrast to Navarro et al., our numerical results indicate, that the commonly used equation for the merger timescale given by Lacey and Cole, systematically underestimates the merger timescales for minor mergers and overestimates those for major mergers. This behavior is partly explained by the poor performance of their expression for the Coulomb logarithm, \ln (m_pri/m_sat). The two alternative forms \ln (1+m_pri/m_sat) and 1/2\ln [1+(m_pri/m_sat)^2] for the Coulomb logarithm can account for the mass dependence of merger timescale successfully, but both of them underestimate the merger time scale by a factor 2. Since \ln (1+m_pri/m_sat) represents the mass dependence slightly better we adopt this expression for the Coulomb logarithm. Furthermore, we find that the dependence of the merger timescale on the circularity parameter \epsilon is much weaker than the widely adopted power-law \epsilon^{0.78}, whereas 0.94*{\epsilon}^{0.60}+0.60 provides a good match to the data. Based on these findings, we present an accurate and convenient fitting formula for the merger timescale of galaxies in cold dark matter models.