Dynamical Friction and Galaxy Merging Timescales

TL;DR

This study uses N-body simulations to evaluate galaxy merging timescales, revealing that standard models underestimate these timescales and proposing a new fitting formula for more accurate predictions.

Contribution

The paper introduces a new fitting formula for galaxy merging timescales based on extended dark matter halo simulations, correcting systematic underestimations in standard models.

Findings

Standard predictions are shorter than simulation results by a factor of ~1.7 for certain mass ratios.

Discrepancies increase to a factor of ~3.3 for smaller satellite-to-host mass ratios.

Using the new formula, stellar mass growth estimates from satellite mergers are reduced by about 40%.

Abstract

The timescale for galaxies within merging dark matter halos to merge with each other is an important ingredient in galaxy formation models. Accurate estimates of merging timescales are required for predictions of astrophysical quantities such as black hole binary merger rates, the build-up of stellar mass in central galaxies, and the statistical properties of satellite galaxies within dark matter halos. In this paper, we study the merging timescales of extended dark matter halos using N-body simulations. We compare these results to standard estimates based on the Chandrasekhar theory of dynamical friction. We find that these standard predictions for merging timescales, which are often used in semi-analytic galaxy formation models, are systematically shorter than those found in simulations. The discrepancy is approximately a factor of 1.7 for $M_sat/M_host \approx 0.1$ and becomes larger for more disparate satellite-to-host mass ratios, reaching a factor of $\sim 3.3$ for $M_sat/M_host\approx 0.01$. Based on our simulations, we propose a new, easily implementable fitting formula that accurately predicts the timescale for an extended satellite to sink from the virial radius of a host halo down to the halo's center for a wide range of $M_sat/M_host$ and orbits. Including a central bulge in each galaxy changes the merging timescale by $\la 10%$. To highlight one concrete application of our results, we show that merging timescales often used in the literature overestimate the growth of stellar mass by satellite accretion by $\approx 40 %$, with the extra mass gained in low mass ratio mergers.