Transverse dissections of the fundamental planes of elliptical galaxies and clusters of galaxies

Seen edge-on, the fundamental plane (FP) of elliptical galaxies is very thin and tilted, which corresponds to a very small dispersion (≲12%) of the M/L ratio at each location on the FP, and to a trend by a factor ∼3 of M/L along the FP, respectively. In this Letter we investigate two possible origins of the tilt: a systematic change of the stellar initial mass function (IMF), and a trend in the relative distributions of the bright and dark matter. In both cases we find that major changes in either the IMF or the bright/dark matter relative distributions are required along the FP to account for its tilt, while its constant thickness requires an extremely small dispersion in the IMF or in the bright/dark matter distribution at every location on the FP. In both cases fine-tuning seems required to account for the tilt and yet preserve the small, constant thickness of the FP. We suggest observations that may distinguish between the two options. Also clusters of galaxies appear to define an equally thin but untilted FP (i.e., M/L = constant). We discuss some implication of the existence of such cluster FPs for galaxy formation and cluster evolution.