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We present a sub-kpc resolved study of the interstellar medium properties inSDP.81, a z=3.042 strongly gravitationally lensed dusty star-forming galaxy,based on high-resolution, multi-band ALMA observations of the FIR continuum, COladder and the [CII] line. Using a visibility-plane lens modelling code, weachieve a median source-plane resolution of ~200 pc. We use photon-dominatedregion (PDR) models to infer the physical conditions - far-UV field strength,density, and PDR surface temperature - of the star-forming gas on 200-pcscales, finding a FUV field strength of ~10^3-10^4 G0, gas density of ~10^5cm^-3 and cloud surface temperatures up to 1500 K, similar to those in theOrion Trapezium region. The [CII] emission is significantly more extended thanthat FIR continuum: ~50 per cent of [CII] emission arises outside theFIR-bright region. The resolved [CII]/FIR ratio varies by almost 2 dex acrossthe source, down to ~2x10^-4 in the star-forming clumps. The observed [CII]/FIRdeficit trend is consistent with thermal saturation of the C+ fine-structurelevel occupancy at high gas temperatures. We make the source-planereconstructions of all emission lines and continuum data publicly available.

Full of Orions: a 200-pc mapping of the interstellar medium in the redshift-3 lensed dusty star-forming galaxy SDP.81