Sub-kpc star-formation law in the local luminous infrared galaxy IC 4687 as seen by ALMA

We analyze the spatially resolved (250 pc scales) and integrated star-formation (SF) law in the local luminous infrared galaxy (LIRG) IC4687. This is one of the first studies of the SF law on a starburst LIRG at these small spatial scales. We combined new interferometric ALMA CO(2-1) data with existing HST/NICMOS Pa$\alpha$ narrow-band imaging and VLT/SINFONI near-IR integral field spectroscopy to obtain accurate extinction corrected SF rate (SFR) and cold molecular gas surface densities ($\Sigma_{gas}$ and $\Sigma_{SFR}$). We find that IC4687 forms stars very efficiently with an average depletion time ($t_{dep}$) of 160 Myr for the individual 250 pc regions. This is approximately one order of magnitude shorter than the $t_{dep}$ of local normal spirals and also shorter than that of main-sequence high-z objects, even when we use a Galactic $\alpha_{CO}$ conversion factor. This result suggests a bimodal SF law in the $\Sigma_{SFR} \propto \Sigma_{gas}^{N}$ representation. A universal SF law is recovered if we normalize the $\Sigma_{gas}$ by the global dynamical time. However, at the spatial scales studied here, we find that the SF efficiency (or $t_{dep}$) does not depend on the local dynamical time for this object. Therefore, an alternative normalization (e.g., free-fall time) should be found if a universal SF law exists at these scales.