Mergers in Galaxy Groups. II. The Fundamental Plane of Elliptical Galaxies

Observations consistently show that elliptical galaxies follow a tight "fundamental plane" scaling relation between size, mean surface brightness and velocity dispersion, with the form $R \propto \sigma^{a}\mu^{b}$. This relation not only has very small (<0.05 dex) intrinsic scatter, but also has significantly different coefficients from the expected virial scaling (a "tilt"). We analyze hundreds of simulations of elliptical galaxies formed from mergers of spiral galaxies in groups to determine if the fundamental plane can emerge from multiple, mostly minor and hierarchical collisionless mergers. We find that these simulated ellipticals lie on a similar fundamental plane with $a \approx 1.7$ and $b \approx 0.3$. The scatter about this plane is not larger than observed, while the tilt is in the correct sense, although $a$ is larger than for typical observations. This supports the idea that collisionless mergers can contribute significantly to the tilt of the fundamental plane. The tilt is mainly driven by a mass-dependent dark matter fraction, such that more massive galaxies have larger dark matter fractions within $R_{e}$. We further discuss the origin of this mass-dependent dark matter fraction and its compatibility with strong lensing observations, as well as the links between the fundamental plane, dynamical masses and the virial theorem.