We present and discuss the 2D kinematic properties of the ionized gas (Halpha) in a sample of 38 local (ultra) luminous infrared galaxies [(U)LIRGs] (31 LIRGs and 7 ULIRGs) observed with VIMOS at the VLT using integral field spectroscopy. This sample covers well the less studied LIRG luminosity range and includes isolated disks, interacting systems, and mergers. The majority of the galaxies have two main kinematically distinct components. One component (i.e., narrow or systemic) extends over the whole line-emitting region and is characterized by small to intermediate velocity dispersions (i.e., sigma from 30 to 160 km s^-1). It traces the overall velocity field. The second component (broad) has in general a larger velocity dispersion (up to 320 km s^-1), mainly found in the inner regions and generally blueshifted with respect to the systemic component. Most of the objects (76%) are dominated by rotation, more relevant in LIRGs than in ULIRGs. Isolated disks, interacting galaxies, and merging systems define a sequence of increasing mean velocity dispersion, and decreasing velocity field amplitude.The LIRGs classified as isolated disks have similar velocity amplitudes but larger mean velocity dispersions (44 vs. 24 km s^-1) than local spirals, implying a larger turbulence and thicker disks. Interacting systems and mergers have values closer to those of low velocity dispersion ellipticals/lenticular galaxies (E/SOs). The (U)LIRGs classified as mergers have kinematic properties similar to those shown by the Lyman break analogs (LBAs). The dynamical masses range from \sim 0.04 m* to 1.4 m* (i.e., m* = 1.4x10^{11} Msun), with ULIRGs (M{dyn} sim 0.5 +/- 0.2 m*) being more massive than LIRGs by, on average, a factor of about 2. The mass ratio of individual pre-coalescence galaxies is <2.5 for most of the systems, confirming that most (U)LIRG mergers involve sub-m* galaxies of similar mass.
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