The Fundamental Plane Is Not a Plane: Warped Nature of the Fundamental Plane of Early-type Galaxies and Its Implication for Galaxy Formation

TL;DR

This study reveals that the fundamental plane of early-type galaxies is a warped, curved surface rather than a true plane, with its shape and coefficients varying systematically with galaxy velocity dispersion and surface brightness.

Contribution

It demonstrates the warped, non-planar nature of the fundamental plane in ETGs and links this to dry merger effects influencing galaxy formation.

Findings

The FP is a curved surface, not a plane.

FP coefficients vary with galaxy velocity dispersion.

Dry mergers may cause the warped shape of the FP.

Abstract

Based on $16,283$ early-type galaxies (ETGs) in $0.025\le z_\mathrm{spec}<0.055$ from Sloan Digital Sky Survey data, we show that the fundamental plane (FP) of ETGs is not a plane in the strict sense but is a curved surface with a twisted shape whose orthogonal direction to the surface is shifted as the central velocity dispersion ($\sigma_0$) or mean surface brightness within the half-light radius ($\mu_e$) changes. When ETGs are divided into subsamples according to $\sigma_0$, the coefficient of $\mu_e$ of the FP increases, whereas the zero-point of the FP decreases at higher $\sigma_0$. Taking the $z$ band as an example, the coefficient of $\mu_e$ rises from $0.28$ to $0.36$ as $\sigma_0$ increases from $\sim100$ to $\sim300$ km s$^{-1}$. At the same time, the zero-point of the FP falls from $-7.5$ to $-9.0$ in the same $\sigma_0$ range. The consistent picture on the curved nature of the FP is also reached by inspecting changes in the FP coefficients for ETG subsamples with different $\mu_e$. By examining scaling relations that are projections of the FP, we suggest that the warped nature of the FP may originate from dry merger effects that are imprinted more prominently in ETGs with higher masses.