Spatially resolved kinematics have been used to determine the dynamical status of star-forming galaxies with ambiguous morphologies, and constrain the importance of galaxy interactions during the assembly of galaxies. However, measuring the importance of interactions or galaxy merger rates requires knowledge of the systematics in kinematic diagnostics and the visible time with merger indicators. We analyze the dynamics of star-forming gas in a set of binary merger hydrodynamic simulations with stellar mass ratios of 1:1 and 1:4. We find that the evolution of kinematic asymmetries traced by star-forming gas mirrors morphological asymmetries derived from mock optical images, in which both merger indicators show the largest deviation from isolated disks during strong interaction phases. Based on a series of simulations with various initial disk orientations, orbital parameters, gas fractions, and mass ratios, we find that the merger signatures are visible for ~0.2-0.4 Gyr with kinematic merger indicators but can be approximately twice as long for equal-mass mergers of massive gas-rich disk galaxies designed to be analogs of z~2-3 submillimeter galaxies. Merger signatures are most apparent after the second passage and before the black holes coalescence, but in some cases they persist up to several hundred Myr after coalescence. About 20-60% of the simulated galaxies are not identified as mergers during the strong interaction phase, implying that galaxies undergoing violent merging process do not necessarily exhibit highly asymmetric kinematics in their star-forming gas. The lack of identifiable merger signatures in this population can lead to an underestimation of merger abundances in star-forming galaxies, and including them in samples of star-forming disks may bias the measurements of disk properties such as intrinsic velocity dispersion.
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