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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.

We use a suite of semi-empirical models to predict the galaxy-galaxy merger rate and relative contributions to bulge growth as a function of mass (both halo and stellar), redshift, and mass ratio. The models use empirical constraints on the halo occupation distribution, evolved forward in time, to robustly identify where and when galaxy mergers occur. Together with the results of high-resolution merger simulations, this allows us to quantify the relative contributions of mergers with different properties (e.g., mass ratios, gas fractions, redshifts) to the bulge population. We compare with observational constraints, and find good agreement. We also provide useful fitting functions and make public a code to reproduce the predicted merger rates and contributions to bulge mass growth. We identify several robust conclusions. (1) Major mergers dominate the formation and assembly of L * bulges and the total spheroid mass density, but minor mergers contribute a non-negligible 30%. (2) This is mass dependent: bulge formation and assembly is dominated by more minor mergers in lower-mass systems. In higher-mass systems, most bulges originally form in major mergers near L *, but assemble in increasingly minor mergers. (3) The minor/major contribution is also morphology dependent: higher B/T systems preferentially form in more major mergers, with B/T roughly tracing the mass ratio of the largest recent merger; lower B/T systems preferentially form in situ from minor mergers. (4) Low-mass galaxies, being gas-rich, require more mergers to reach the same B/T as high-mass systems. Gas-richness dramatically suppresses the absolute efficiency of bulge formation, but does not strongly influence the relative contribution of major versus minor mergers. (5) Absolute merger rates at fixed mass ratio increase with galaxy mass. (6) Predicted merger rates agree well with those observed in pair and morphology-selected samples, but there is evidence that some morphology-selected samples include contamination from minor mergers. (7) Predicted rates also agree with the integrated growth in bulge mass density with cosmic time, but with a factor 2 uncertainty in both - up to half the bulge mass density could come from non-merger processes. We systematically vary the model assumptions, totaling 103 model permutations, and quantify the resulting uncertainties. Our conclusions regarding the importance of different mergers for bulge formation are very robust to these changes. The absolute predicted merger rates are systematically uncertain at the factor 2 level; uncertainties grow at the lowest masses and high redshifts. © 2010. The American Astronomical Society. All rights reserved.