We used high-spatial resolution (70 pc; 0.3) CO multi-transition (1-0, 2-1, 4-3, and 6-5) ALMA data to study the physical conditions and kinematics of the cold molecular outflow in the local LIRG ESO320-G030 (d=48 Mpc, log LIR/Lsun=11.3). ESO320-G030 is a double-barred isolated spiral, but its compact and obscured nuclear starburst (SFR~15 Msun/yr; Av~40 mag) resembles those of more luminous ULIRGs. In the outflow, the 1-0/2-1 ratio is enhanced with respect to the rest of the galaxy and the CO(4-3) transition is undetected. This indicates that the outflowing molecular gas is less excited than the gas in the nuclear starburst (launching site) and the galaxy disk. Non-LTE radiative transfer modeling reveals that the properties of the outflow molecular clouds differ from those of the nuclear and disk clouds: The kinetic temperature is lower (~9 K) in the outflow, and the outflowing clouds have lower column densities. Assuming a 10^-4 CO abundance, the large internal velocity gradients, 60^+250_-45 km/s/pc, imply that the outflowing molecular clouds are not bound by self-gravity. All this suggests that the life-cycle (formation, collapse, dissipation) of the disk clouds might differ from that of the outflowing clouds which might not be able to form stars. The low Tkin of the molecular outflow remains constant up to 1.7 kpc. This indicates that the heating by the hotter ionized outflow phase is not efficient and may favor the survival of the outflow molecular phase. The velocity structure of the outflow shows a 0.8 km/s/pc velocity gradient between 190-560 pc and then a constant maximum velocity (~750 km/s) up to 1.7 kpc. This is compatible with a pure gravitational evolution of the outflow under certain mass outflow rate and launching velocity variations. Alternatively, ram pressure acceleration and cloud evaporation could explain the observed kinematics and size of the molecular phase.
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