Testing star formation laws on spatially resolved regions in a z ≈ 4.3 starburst galaxy

We probe the star formation properties of the gas in AzTEC-1 in the COSMOS field, one of the best resolved and brightest starburst galaxies at z ≈ 4.3, forming stars at a rate > 1000 M_☉ yr⁻¹. Using recent ALMA observations, we study star formation in the galaxy nucleus and an off-centre star-forming clump and measure a median star formation rate (SFR) surface density of Σ^nucleus_SFR = 270 ± 54 and Σ^sfclump_SFR = 170 ± 38 M_☉ yr⁻¹ kpc⁻², respectively. Following the analysis by Sharda et al. (2018), we estimate the molecular gas mass, freefall time, and turbulent Mach number in these regions to predict Σ_SFR from three star formation relations in the literature. The Kennicutt–Schmidt (Kennicutt 1998; KS) relation, which is based on the gas surface density, underestimates the Σ_SFR in these regions by a factor 2–3. The Σ_SFR we calculate from the single-freefall model of Krumholz et al. (2012; KDM) is consistent with the measured Σ_SFR in the nucleus and the star-forming clump within the uncertainties. The turbulence-regulated star formation relation by Salim et al. (2015; SFK) agrees slightly better with the observations than the KDM relation. Our analysis reveals that an interplay between turbulence and gravity can help sustain high SFRs in high-redshift starbursts. It can also be extended to other high- and low-redshift galaxies thanks to the high-angular resolution and sensitivity of ALMA observations.