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Different theoretical methodologies lead to order-of-magnitude variations in predicted galaxy-galaxy merger rates. We examine how this arises and quantify the dominant uncertainties. Modeling of dark matter and galaxy inspiral/merger times contribute factor of ∼2 uncertainties. Different estimates of the halo-halo merger rate, the subhalo "destruction" rate, and the halo merger rate with some dynamical friction time delay for galaxy-galaxy mergers, agree to within this factor of ∼2, provided proper care is taken to define mergers consistently. There are some caveats: if halo/subhalo masses are not appropriately defined the major-merger rate can be dramatically suppressed, and in models with "orphan" galaxies and under-resolved subhalos the merger timescale can be severely overestimated. The dominant differences in galaxy-galaxy merger rates between models owe to the treatment of the baryonic physics. Cosmological hydrodynamic simulations without strong feedback and some older semianalytic models (SAMs), with known discrepancies in mass functions, can be biased by large factors (∼5) in predicted merger rates. However, provided that models yield a reasonable match to the total galaxy mass function, the differences in properties of central galaxies are sufficiently small to alone contribute small (factor of ∼1.5) additional systematics to merger rate predictions. But variations in the baryonic physics of satellite galaxies in models can also have a dramatic effect on merger rates. The well-known problem of satellite "over-quenching" in most current SAMs-whereby SAM satellite populations are too efficiently stripped of their gas-could lead to order-of-magnitude under-estimates of merger rates for low-mass, gas-rich galaxies. Models in which the masses of satellites are fixed by observations (or SAMs adjusted to resolve this "over-quenching") tend to predict higher merger rates, but with factor of ∼2 uncertainties stemming from the uncertainty in those observations. The choice of mass used to define "major" and "minor" mergers also matters: stellar-stellar major mergers can be more or less abundant than halo-halo major mergers by an order of magnitude. At low masses, most true major mergers (mass ratio defined in terms of their baryonic or dynamical mass) will appear to be minor mergers in their stellar mass ratio-observations and models using just stellar criteria could underestimate major-merger rates by factors of ∼3-5. We discuss the uncertainties in relating any merger rate to spheroid formation (in observations or theory): in order to achieve better than factor of ∼3 accuracy, it is necessary to account for the distribution of merger orbital parameters, gas fractions, and the full efficiency of merger-induced effects as a function of mass ratio. © 2010. The American Astronomical Society. All rights reserved. Printed in the U.S.A.

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