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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 over-estimated. 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 semi-analytic 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.

We study the growth of dark matter halos in the concordance LCDM cosmology using several N-body simulations of large cosmological volumes. We construct merger trees from the Millennium and Millennium-II Simulations, covering the ranges 109-1015 M in halo mass and 1-105 in merger mass ratio. Our algorithm takes special care of halo fragmentation and ensures that the mass contribution of each merger to halo growth is only counted once. This way the integrated merger rate converges and we can consistently determine the contribution of mergers of different mass ratios to halo growth. We find that all resolved mergers, up to mass ratios of 105:1, contribute only [?]60% of the total halo mass growth, while major mergers are subdominant, e.g., mergers with mass ratios smaller than 3:1 (10:1) contribute only [?]20% ([?]30%). This is verified with an analysis of two additional simulation boxes, where we follow all particles individually throughout cosmic time. Our results are also robust against using several halo definitions. Under the assumption that the power-law behavior of the merger rate at large mass ratios can be extrapolated to arbitrarily large mass ratios, it is found that, independent of halo mass, [?]40% of the mass in halos comes from genuinely smooth accretion of dark matter that was never bound in smaller halos. We discuss possible implications of our findings for galaxy formation. One implication, assuming as is standard that the pristine intergalactic medium is heated and photoionized by UV photons, is that all halos accrete >40% of their baryons in smooth "cold" T [?] 104 K gas, rather than as warm, enriched, or clumpy gas or as stars.

We have developed a new method to extract halo merger rates from the Millennium Simulation. First, by removing superfluous mergers that are artifacts of the standard friends-of-friends (FOF) halo identification algorithm, we find a lower merger rate compared to previous work. The reductions are more significant at lower redshifts and lower halo masses, and especially for minor mergers. Our new approach results in a better agreement with predictions from the extended Press-Schechter 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 particles that are gravitationally bound to their FOF groups. 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 merger rate per progenitor halo is the quantity that should be related to observed galaxy merger fractions when they are measured via pair counting. At low-mass/redshift, the merger rate increases moderately with mass and steeply with redshift. At high enough mass/redshift (for the rarest 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, in addition to the minor and major merger rates. We provide an analytic formula that converts any given merger rate per descendant halo into a merger rate per progenitor halo. Finally, we perform a direct comparison between observed merger fractions and the fraction of halos in the Millennium Simulation 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/.

High signal-to-noise, representative spectra of star-forming galaxies at z [?] 2, obtained via stacking, reveal a high-velocity component underneath the narrow Ha and [N II] emission lines. When modeled as a single Gaussian, this broad component has FWHM [?] 1500 km s-1; when modeled as broad wings on the Ha and [N II] features, it has FWHM [?] 500 km s-1. This feature is preferentially found in the more massive and more rapidly star-forming systems, which also tend to be older and larger galaxies. We interpret this emission as evidence of either powerful starburst-driven galactic winds or active supermassive black holes (SMBHs). If galactic winds are responsible for the broad emission, the observed luminosity and velocity of this gas imply mass outflow rates comparable to the star formation rate. On the other hand, if the broad-line regions of active black holes account for the broad feature, the corresponding black holes masses are estimated to be an order of magnitude lower than those predicted by local scaling relations, suggesting a delayed assembly of SMBHs with respect to their host bulges.

Recent observations of UV/optically selected, massive star-forming galaxies at z [?] 2 indicate that the baryonic mass assembly and star formation history is dominated by continuous rapid accretion of gas and internal secular evolution, rather than by major mergers. We use the Millennium Simulation to build new halo merger trees and extract halo merger fractions and mass accretion rates. We find that, even for halos not undergoing major mergers, the mass accretion rates are plausibly sufficient to account for the high star formation rates observed in z [?] 2 disks. On the other hand, the fraction of major mergers in the Millennium Simulation is sufficient to account for the number counts of submillimeter galaxies (SMGs), in support of observational evidence that these are major mergers. When following the fate of these two populations in the Millennium Simulation to z = 0, we find that subsequent mergers are not frequent enough to convert all z [?] 2 turbulent disks into elliptical galaxies at z = 0. Similarly, mergers cannot transform the compact SMGs/red sequence galaxies at z [?] 2 into observed massive cluster ellipticals at z = 0. We argue therefore, that secular and internal evolution must play an important role in the evolution of a significant fraction of z [?] 2 UV/optically and submillimeter-selected galaxy populations.