Redshift evolution of the fundamental plane up to z ∼6

Context. The fundamental plane (FP) is an empirical scaling relation linking the structure and dynamics of early-type galaxies. However, the traditionally used luminosity-based FP is sensitive to variations in stellar populations and dust, limiting its reliability at high redshifts. Aims. We investigate the redshift evolution of the stellar mass fundamental plane (SM-FP) as a more physically motivated alternative, using a sample of spheroidal galaxies selected from the Horizon Run 5 (HR5) cosmological hydrodynamical simulation. Methods. We selected spheroidal galaxies mainly based on morphological criteria, using structural parameters such as the asymmetry parameter (A) and the Sérsic index (nSérsic), and constructed the SM-FP by replacing surface brightness with stellar mass surface density. We then studied the evolution of the FP parameters and its scatter over the redshift range from z = 0.625 to z = 6. Results. Our analysis reveals a well-defined SM-FP existing as early as z ∼ 6, exhibiting a low intrinsic scatter (∼0.07 dex). The FP slope parameters evolve systematically, with the velocity dispersion coefficient decreasing and the surface density coefficient also decreasing in magnitude towards higher redshifts. The FP tightness improves when selecting slow rotators with Vrot/σe < 0.55. Additionally, we observe systematic dependencies of FP residuals on the stellar age, specific star formation rate (sSFR), and Vrot/σe, highlighting the importance of internal kinematics over age or sSFR in defining the FP. Conclusions. Our results demonstrate that the structural and dynamical scaling relations of spheroidal galaxies were established early in cosmic history, with the SM-FP established robustly by z ≈ 6. The systematic evolution of FP parameters with redshift can provide crucial insights into the processes governing galaxy assembly and morphological evolution.