A fading radius valley towards M-dwarfs, a persistent density valley across stellar types

The radius valley separating super-Earths from mini-Neptunes is a fundamental benchmark for theories of planet formation and evolution. Observations show that the location of the radius valley decreases with decreasing stellar mass and with increasing orbital period. Here, we build from our previous pebble-based formation model, which, combined with photoevaporation after disc dispersal, unveiled the radius valley as a separator between rocky- and water-worlds. We expand our models for a range of stellar masses spanning from 0.1 to 1.5 $M_\odot$. We find that the location of the radius valley is well described by a power-law in stellar mass as $R_{\rm valley} = 1.8197 \, M_{\star}^{\!0.14({+0.02}/{-0.01})}$, which is in excellent agreement with observations. We also find very good agreement with the dependence of the radius valley on orbital period, both for FGK- and M-dwarfs. Additionally, we note that the radius valley gets filled towards low stellar masses, particularly at 0.1-0.4 $M_\odot$, yielding a rather flat slope in $R_{\rm valley} - P_{\rm orb}$. This is the result of orbital migration occurring at lower planet mass for less massive stars, which allows for low-mass water-worlds to reach the inner regions of the system, blurring the separation in mass (and size) between rocky- and water-worlds. Furthermore, we find that for planetary equilibrium temperatures above 400 K, the water in the volatile layer exists fully in the form of steam, puffing the planet radius up compared to condensed-water worlds. This produces an increase in planet radii of $\sim 30\%$ at 1 $M_\oplus$, and of $\sim 15\%$ at 5 $M_\oplus$, compared to condensed-water-worlds. As with Sun-like stars, pebble accretion leaves its imprint on the overall exoplanet population as a depletion of planets with intermediate compositions, carving a valley in planet density for all spectral types (abridged).