We make use of four galaxy catalogs based on four different semi-analytical models (SAMs) implemented in the Millennium Simulation to study the environmental effects and the model dependence of the galaxy merger rate. We begin the analyses by finding that the galaxy merger rate in SAMs has a mild redshift evolution with luminosity-selected samples in the evolution-corrected B-band magnitude range,–21 ≤ Me B ≤ –19, consistent with the results of previous works. To study the environmental dependence of the galaxy merger rate, we adopt two estimators, the local overdensity (1 + δ n ), defined as the surface density from the nth nearest neighbor (n = 6 is chosen in this study), and the host halo mass Mh . We find that the galaxy merger rate F mg shows a strong dependence on the local overdensity (1 + δ n ) and the dependence is similar at all redshifts. For the overdensity estimator, the merger rate F mg is found to be about twenty times larger in the densest regions than in underdense ones in two of the four SAMs, while it is roughly four times higher in the other two. In other words, the discrepancies of the merger rate difference between the two extremes can differ by a factor of ~5 depending on the SAMs adopted. On the other hand, for the halo mass estimator, F mg does not monotonically increase with the host halo mass Mh but peaks in the Mh range between 1012 and 1013 h –1 M ☉, which corresponds to group environments. The high merger rate in high local density regions corresponds primarily to the high merger rate in group environments. In addition, we also study the merger probability of "close pairs" identified using the projected separation and the line-of-sight velocity difference C mg and the merger timescale T mg; these are two important quantities for observations to convert the pair fraction Nc into the galaxy merger rate. We discover that T mg has a weak dependence on environment and different SAMs, and is about 2?Gyr old at z ~ 1. In contrast, C mg depends on both environment (declining with density) and different SAMs; its environmental dependence is primarily due to the projection effect. At z ~ 1, it is found that only ~31% of projected close pairs will eventually merge by z = 0. We find that the projection effect is the dominant factor in accounting for the low merger probability of projected close pairs.
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