Physics of ULIRGs with MUSE and ALMA: PUMA IV. No tight relation between cold molecular outflow rates and AGN luminosities

We study molecular outflows in a sample of 25 nearby (z< 0.17, d<750 Mpc) ULIRG systems (38 individual nuclei) as part of the "Physics of ULIRGs with MUSE and ALMA" (PUMA) survey, using ~400 pc (0.1-1.0" beam FWHM) resolution ALMA CO(2-1) observations. We used a spectro-astrometry analysis to identify high-velocity (> 300 km/s) molecular gas disconnected from the galaxy rotation, which we attribute to outflows. In 77% of the 26 nuclei with $\log L_{IR}/L_{\odot}>11.8$, we identifid molecular outflows with an average $v_{out}= 490$ km/s, outflow masses $1-35 \times 10^7$ $M_{\odot}$, mass outflow rates $\dot{M}_{out}=6-300$ $M_{\odot}$ yr$^{-1}$, mass-loading factors $\eta = \dot{M}_{out}/SFR = 0.1-1$, and an average outflow mass escape fraction of 45%. The majority of these outflows (18/20) are spatially resolved with radii of 0.2-0.9 kpc and have short dynamical times ($t_{dyn}=R_{out}/v_{out}$) in the range 0.5-2.8 Myr. The outflow detection rate is higher in nuclei dominated by starbursts (SBs, 14/15=93%) than in active galactic nuclei (AGN, 6/11=55%). Outflows perpendicular to the kinematic major axis are mainly found in interacting SBs. We also find that our sample does not follow the $\dot{M}_{out}$ versus AGN luminosity relation reported in previous works. In our analysis, we include a sample of nearby main-sequence galaxies (SFR = 0.3-17 $M_{\odot}$ yr$^{-1}$) with detected molecular outflows from the PHANGS-ALMA survey to increase the $L_{IR}$ dynamic range. Using these two samples, we find a correlation between the outflow velocity and the SFR, as traced by $L_{IR}$ ($v_{out} \propto SFR^{0.25\pm0.01})$, which is consistent with what was found for the atomic ionised and neutral phases. Using this correlation, and the relation between $M_{out}/R_{out}$ and $v_{out}$, we conclude that these outflows are likely momentum-driven.