  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.
