Resolved Schmidt–Kennicutt relation in a binary hyperluminous infrared galaxy at <i>z</i> = 2.41

Aims. Hyperluminous infrared galaxies (HyLIRGs; star-formation rates of up to ≈1000 M ⊙ yr −1 ) – while rare – provide crucial long-lever-arm constraints on galaxy evolution. H-ATLAS J084933.4+021443, a z = 2.41 binary HyLIRG (galaxies ‘W’ and ‘T’) with at least two additional luminous companion galaxies (‘C’ and ‘M’), is thus an optimal test ground for studies of star formation and galaxy evolution during ‘cosmic noon’. Methods. We have used ALMA to obtain resolved imaging and kinematics of atomic and molecular emission lines, and rest-frame 340 to 1160 GHz continuum emission, for the galaxies W, T, M, and C. Results. All four galaxies are spatially resolved in CO J:7–6, [C I ] 2–1, H 2 O, and the millimetre (mm) to sub-millimetre continuum, using circular apertures of ∼0.″3 (2.5 kpc) in radius. Rotation-dominated gas kinematics are confirmed in W and T. The gas and continuum emission of galaxy T are extended along its kinematic minor axis, attributable to spatial lensing magnification. Spatially resolved sub-millimetre spectral energy distributions (SEDs) reveal that galaxy W is well fitted with greybody emission from dust at a single temperature over its full extent, despite hosting a powerful active galactic nucleus, while galaxy T requires an additional component of hotter nuclear dust and additional sources of emission in the millimetre. We confirm that [C I ] J:2–1 can be used as a tracer of warm/dense molecular gas in extreme systems, though the [C I ] J:2–1/CO J:7–6 luminosity ratio increases sub-linearly. We obtain an exquisite resolved (2.5-kpc-scale) Schmidt-Kennicutt (SK) relationship for galaxies W and T, using both cold and warm/dense molecular gas. Gas exhaustion timescales for all apertures in W (T) are ∼50–100 Myr (∼100–500 Myr). Both W and T follow a resolved SK relationship with a power-law index of n ∼ 1.7, significantly steeper than the n ∼ 1 found previously via cold molecular gas in nearby ‘normal’ star-forming galaxies.