The Universal Faber-Jackson Relation

TL;DR

This paper proposes that the Faber-Jackson relation, linking luminosity and velocity dispersion across various astronomical objects, is a universal scaling law under Modified Newtonian Dynamics, incorporating an additional fundamental constant.

Contribution

It demonstrates that the Faber-Jackson relation is a universal and fundamental scaling law across different astrophysical systems within the MOND framework, unlike the fundamental plane.

Findings

Faber-Jackson relation applies universally from globular clusters to galaxy clusters.

The relation incorporates the MOND acceleration as a fundamental constant.

High surface brightness objects follow the fundamental plane, low surface brightness objects deviate.

Abstract

In the context of modified Newtonian dynamics, the fundamental plane, as the observational signature of the Newtonian virial theorem, is defined by high surface brightness objects that deviate from being purely isothermal: the line-of-sight velocity dispersion should slowly decline with radius as observed in luminous elliptical galaxies. All high surface brightness objects (e.g. globular clusters, ultra-compact dwarfs) will lie, more or less, on the fundamental plane defined by elliptical galaxies, but low surface brightness objects (dwarf spheroidals) would be expected to deviate from this relation. This is borne out by observations. With MOND, the Faber-Jackson relation (the power-law relation between luminosity and velocity dispersion), ranging from globular clusters to clusters of galaxies and including both high and low surface brightness objects, is the more fundamental and universal scaling relation in spite of its larger scatter. Faber-Jackson reflects the presence of an additional dimensional constant (the MOND acceleration) in the structure equation.