Most present-day galaxies with stellar masses $\geq10^{11}$ solar masses show no ongoing star formation and are dense spheroids. Ten billion years ago, similarly massive galaxies were typically forming stars at rates of hundreds solar masses per year. It is debated how star formation ceased, on which timescales, and how this "quenching" relates to the emergence of dense spheroids. We measured stellar mass and star-formation rate surface density distributions in star-forming galaxies at redshift 2.2 with $\sim1$ kiloparsec resolution. We find that, in the most massive galaxies, star formation is quenched from the inside out, on timescales less than 1 billion years in the inner regions, up to a few billion years in the outer disks. These galaxies sustain high star-formation activity at large radii, while hosting fully grown and already quenched bulges in their cores.

Evidence for mature bulges and an inside-out quenching phase 3 billion years after the Big Bang