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Number and Luminosity Evolution of Interacting Galaxies as a Natural explanation for the Galaxy Counts

A newly developed isochrone synthesis algorithm for the photometric evolution of galaxies is described. Two initial mass functions, IMFs, in particular, the recent IMF determined by Kroupa, Tout, and Gilmore, three photometric transformations, and a 1-Gyr-burst star formation rate, SFR, are used to compute the $B-V$ and $V-K$ color index evolution. Non-negligible differences are observed among model results. In the framework of the galaxy count model by Colín, Schramm, and Peimbert a simple merging scenario is considered to account for the excess of galaxies observed in the blue band counts. The excess is explained by the number and luminosity evolution of a group of galaxies called interacting, I. It is assumed that the number of I galaxies increases as $(1+z)^η$ due to mergers. Moreover, it is proposed that their characteristic luminosity increases as $(1+z)^3$ due to starbursts driven by galaxy-galaxy collision and decreases as $(1+z)^{-η}$ due to the change in the size of the galaxies. Not much number evolution is needed to account for the excess; for example, a model with $η= 4.0$ predicts that about 17 \% of the galaxies at $z = 0.4$ are interacting. Number evolution models with a rather high value of $η$ fit better the data; in particular, the model with $η= 4.0$ predicts that about 13 \% of the galaxies have $z > 0.7$ in the $21.0 < m_{b_J} < 22.5$ interval, this contrasts with the upper bound of 5 \% obtained with the sample of 78 galaxies by Colless et al. The excess of high redshift galaxies can not be simply explained by changing reasonably the parameters of the luminosity function of I galaxies. This result could indicate that mergers are not the whole story. Our best-fit model produces the following values for the