  We developed a new method to extract halo merger rates from the Millennium
Simulation. First, by removing superfluous mergers that are artifacts of the
FOF halo finder, we find a lower merger rate compared to previous work. The
reductions are more significant at lower redshifts, lower halo masses, and
minor mergers. Our approach agrees better with predictions from the EPS model.
Second, we find that the FOF halo finder overestimates the halo mass by up to
50% for halos that are about to merge, which leads to an additional ~20%
overestimate of the merger rate. Therefore, we define halo masses by including
only gravitationally bound particles. We provide new best-fitting parameters
for a global formula to account for these improvements. In addition, we extract
the merger rate per progenitor halo, as well as per descendant halo. The former
is the quantity that is related to observed galaxy merger fractions when they
are measured via pair counting. At low mass/redshift the merger rate increases
with mass and redshift. At high mass/redshift (for halos with masses a few
times the "knee" of the mass function) these trends break down, and the merger
rate per progenitor halo decreases with mass and increases only moderately with
redshift. Defining the merger rate per progenitor halo also allows us to
quantify the rate at which halos are being accreted onto larger halos. We
provide an analytic formula to convert given merger rates per descendant halo
into merger rates per progenitor halo. Finally, we perform a comparison between
observed merger fractions and the fraction of halos that have undergone a major
merger during the recent dynamical friction time, and find a fair agreement,
within the large uncertainties of the observations. Our new halo merger trees
are available at http://www.mpe.mpg.de/ir/MillenniumMergerTrees/.
