Submillimetre compactness as a critical dimension to understand the main sequence of star-forming galaxies

We study the interstellar medium (ISM) properties as a function of molecular gas size for 77 infrared-selected galaxies at $z \sim 1.3$. Molecular sizes are measured on ALMA images that combine CO(2-1), CO(5-4) and underlying continuum observations, include CO(4-3), CO(7-6)+[CI]($^3 P_2-^3P_1$), [CI]($^3 P_1-^3P_0$) observations subset sample. The $\gtrsim 46 \%$ our have compact reservoir, lie below optical disks mass-size relation. Compact above main sequence higher CO excitation star formation efficiency than with extended reservoirs, traced by CO(5-4)/CO(2-1) CO(2-1)/$L_{\rm IR, SF}$ ratios. Average CO+[CI] spectral line energy distributions indicate in compacts relative to sources. Using CO(2-1) dust masses mass tracers, conversion factors tailored their ISM conditions, we measure lower fractions main-sequence compared suggest sub-millimetre compactness, defined ratio between stellar size, is an unavoidable information be used offset describe galaxies, least $M_{\star} \geqslant 10^{10.6}$ M$_{\odot}$, where fully probe scatter. Our results consistent mergers driving nuclear regions, enhancing efficiency. being early post-starburst population following merger-driven starburst episode, stressing important role evolution massive galaxies.