The Kormendy Relation in the First Billion Years: Evidence from $JWST$

Abstract

Galaxy scaling relations encode key information about the structural, dynamical, and mass assembly histories of galaxies, and provide constraints on galaxy formation models as well as the onset of galaxy assembly. While these relations are well characterized out to intermediate redshifts, their existence during the first billion years of cosmic history remains largely unconstrained due to observational limitations. In this work, we investigate the Kormendy relation (KR) for spheroidal systems at $z~\ge~6$ using rest-frame $B$-band structural parameters derived from publicly available deep \textit{JWST} imaging of the GOODS, CEERS, PRIMER-UDS, and PRIMER-COSMOS fields. We find that spheroidal galaxies at these epochs already occupy a well-defined locus in the mean effective surface brightness $(\langle~μ_{\rm e}~\rangle)$ and effective radius ($\rm~R_{\rm e}$) plane, demonstrating that a KR is already in place when the universe was less a gigayear old. The best-fit relation has a slope of $β~=~4.25^{+0.40}_{-0.39}$ and a zero-point of $α~=~15.89^{+0.17}_{-0.17}$, indicating a steeper relation and systematically higher surface brightness compared to the local relation. This steepness reflects the compact sizes and high central stellar-mass densities of these systems, consistent with rapid, dissipative assembly in environments with high gas fractions, likely driven by efficient gas inflows, and gas-rich mergers. The presence of dense bulges embedded in some of these galaxies at similar redshifts further supports a common formation pathway for both bulges and spheroids. Altogether, these findings indicate a predominantly dissipative mode of assembly for the first spheroidal systems which may evolve into the compact quiescent galaxies observed at later cosmic epochs.

Figures (2)

• Figure 1: (a) False-colour images of a few $z \ge 6$ galaxies from our sample that are best fit with a single Sersic model. For each galaxy, we present the JWST image sampling the rest-frame optical $B$-band, the best-fit model, and the residual image in the first, second, and third column, respectively. The black dotted ellipse represents the effective radius ($R_{\mathrm{e}}$) of the model. (b) The 1D surface-brightness profiles of the galaxies. We present the best-fit surface brightness model profiles (and intrinsic profiles) using solid (dotted) curves. We show the corresponding residual profiles in the bottom panel of each plot. The green inverted arrow marks the 80% light-enclosing radius of the corresponding JWST PSF (shown by the brown dashed curve). We show the PSF of the repective JWST filter in the inset, with the 80% enclosed-flux aperture indicated by a green circle.
• Figure 2: (a) Modelling of the KR for Sample 1 ($n>1.5$). Top: The marginalized posterior distributions for the KR slope, $\beta$, zero-point, $\alpha$ and intrinsic scatter, $\sigma_{int}$. The off-diagonal panels show the 2D joint distributions for the KR parameters, with the contours representing the 1$\sigma$, 2$\sigma$, and 3$\sigma$ probability regions. The diagonal panels show the corresponding 1D histograms, with the vertical lines marking the 16$^{\rm{th}}$ and 84$^{\rm{th}}$ percentiles around the median values quoted at the top. Bottom: The black solid curve with gray shaded region represent the best-fit relation with 3$\sigma$ boundaries for spheroidal systems at $z\ge$ 6 in this work. Here, galaxies from other deep fields are also taken into account from the morphological catalog of Dawn JWST Archive genin_etal2025. As the bulges in this work have $n<$ 1.5 (BS25), we exclude them from the KR-modelling but place them onto the plot for comparison. The local ellipticals (Es) and early-type galaxies (ETGs) are taken from graham2002reda_etal2005khanday_etal2022. The $z\sim$ 1.3 ellipticals are taken from saracco_etal2017 and their best-fit relation is given by the red dashed curve. The gray hatched region represent local KR from khanday_etal2022 with 3$\sigma$ boundaries. (b) Same as panel a, but for Sample 2.