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Recent observations revealed a bimodal radius distribution of small,short-period exoplanets with a paucity in their occurrence, a radius `valley',around $1.5-2.0$ $R_\oplus$. In this work, we investigate the effect of aplanet's own cooling luminosity on its thermal evolution and atmosphericmass-loss (core-powered mass-loss) and determine its observational consequencesfor the radius distribution of small, close-in exoplanets. Using simpleanalytical descriptions and numerical simulations, we demonstrate thatplanetary evolution based on the core-powered mass-loss mechanism alone (i.e.,without any photoevaporation) can produce the observed valley in the radiusdistribution. Our results match the valley's location, shape and slope inplanet radius-orbital period parameter space, and the relative magnitudes ofthe planet occurrence rate above and below the valley. We find that the slopeof the valley is, to first order, dictated by the atmospheric mass-losstimescale at the Bondi radius and given by $\text{d log} R_p/ \text{d log} P\simeq 1/(3(1-\beta))$ which evaluates to $ -0.11$ for $ \beta \simeq 4$, where$M_c/M_\oplus = (R_c/R_{\oplus})^{\beta} (\rho_{c*}/\rho_{\oplus})^{\beta/3}$is the mass-radius relation of the core. This choice for $\beta$ yields goodagreement with observations and attests to the significance of internalcompression for massive planetary cores. We further find that the location ofthe valley scales as $\rho_{c*}^{-4/9}$ and that the observed planet populationmust have predominantly rocky cores with typical water-ice fractions of lessthan $\sim 20\%$. Furthermore, we show that the relative magnitude of theplanet occurrence rate above and below the valley is sensitive to the detailsof the planet-mass distribution but that the location of the valley is not.

Sculpting the Valley in the Radius Distribution of Small Exoplanets as a by-product of Planet Formation: The Core-Powered Mass-Loss Mechanism