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 \lesssim 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 .