WISDOM project XX -- Strong shear tearing molecular clouds apart in NGC 524

Early-type galaxies (ETGs) are known to harbour dense spheroids of stars but scarce star formation (SF). Approximately a quarter of these galaxies have rich molecular gas reservoirs yet do not form stars efficiently. We study here the ETG NGC~524, with strong shear suspected to result in a smooth molecular gas disc and low star-formation efficiency (SFE). We present new spatially-resolved observations of the \textsuperscript{12}CO(2-1)-emitting cold molecular gas from the Atacama Large Millimeter/sub-millimeter Array (ALMA) and of the warm ionised-gas emission lines from SITELLE at the Canada-France-Hawaii Telescope. Although constrained by the resolution of the ALMA observations ($\approx37$~pc), we identify only $52$ GMCs with radii ranging from $30$ to $140$~pc, a low mean molecular gas mass surface density $\langle\Sigma_{\rm gas}\rangle\approx125$~M$_\odot$~pc$^{-2}$ and a high mean virial parameter $\langle\alpha_{\rm obs,vir}\rangle\approx5.3$. We measure spatially-resolved molecular gas depletion times ($\tau_{\rm dep}\equiv1/{\rm SFE}$) with a spatial resolution of $\approx100$~pc within a galactocentric distance of $1.5$~kpc. The global depletion time is $\approx2.0$~Gyr but $\tau_{\rm dep}$ increases toward the galaxy centre, with a maximum $\tau_{\rm dep,max}\approx5.2$~Gyr. However, no pure \ion{H}{II} region is identified in NGC~524 using ionised-gas emission-line ratio diagnostics, so the $\tau_{\rm dep}$ inferred are in fact lower limits. Measuring the GMC properties and dynamical states, we conclude that shear is the dominant mechanism shaping the molecular gas properties and regulating SF in NGC~524. This is supported by analogous analyses of the GMCs in a simulated ETG similar to NGC~524.