Planetary formation tracks on the Hertzsprung–Russell diagram

Context. The Hertzsprung-Russell diagram (HRD) has long served as a cornerstone of astrophysics, illustrating the relationship between stellar luminosity and effective temperature. Although HRDs have been instrumental in understanding stellar evolution, they have rarely been applied to planet formation. Aims. We extended the HRD framework to visualise planet formation and provide a new perspective on the physical processes involved. Specifically, we investigated how gas and solid accretion, cooling and contraction, and orbital migration shape these tracks under different formation scenarios. Methods. We used the Bern model to calculate the interior structure of planets throughout their entire formation and evolution. We also coupled this, for the first time, with radiation-hydrodynamical simulations to dynamically calculate the accretion shock heating efficiency, providing insight into the cold-start and hot-start ambiguity. Results. The planetary HRDs exhibit three branches, each corresponding to a distinct phase of planet formation. The first phase, the ascending branch, is heavily influenced by the size of the smallest accreted bodies, the associated solid accretion rate, and orbital migration. During this phase, the HR tracks rise steeply. For in situ planetesimal accretion, we analytically derive L ∝ T 8 . The second phase, the planetary horizontal branch, begins when the gas accretion rate becomes disc-limited, and the planet detaches from the disc before contracting rapidly. Planets move nearly horizontally to the left, with hot accretion, more massive planets, and pebble accretion leading to upward bending. Planetary interiors are close to an ideal gas at detachment, but increasing electron degeneracy causes the central temperature to decrease, stabilising the radius and halting the rapid movement to the left. The third phase, the descending branch, begins when the effective temperature begins to decrease. Gas accretion ceases during this phase, and planets join classical constant-mass cooling tracks. Because the radius changes only weakly, the tracks descend diagonally with L ~ T 4 . We also find substantial agreement between our analysed tracks, synthetic-population data, and observational data. Conclusions. Planetary HRDs provide a unique way to link the luminosities and effective temperatures of young planets to their formation physics, with pebble and planetesimal accretion producing distinct early-time tracks. Comparisons with currently directly imaged planets are broadly consistent with our tracks because these objects are mostly non-accreting or near the end of their formation and are expected to follow standard post-formation cooling evolution. However, observationally populating the short-lived early horizontal or ascending branch will be challenging, and interpreting embedded, actively accreting planets will require models that include accretion-shock emission and circumplanetary-disc reprocessing.