The role of dark matter in the galaxy mass-size relationship

TL;DR

This paper explores how dark matter influences the galaxy mass-size relationship within a cosmological framework, using virial theorem models and density profiles to explain observed correlations and their connection to galaxy formation.

Contribution

It introduces a theoretical model linking dark matter distribution and baryonic mass to galaxy size, fitting observational data within a LambdaCDM context and discussing implications for galaxy formation theories.

Findings

Theoretical mass-size relation aligns with observed galaxy data.

Dark matter distribution steepness affects baryonic virialization.

Intrinsic dispersion impacts the mass ratio and galaxy structure.

Abstract

The observed relationship between stellar mass and effective radius for early type galaxies, pointed out by many authors, is interpreted in the context of Clausius' virial maximum theory. In this view, it is strongly underlined that the key of the above mentioned correlation is owing to the presence of a deep link between cosmology and the existence of the galaxy Fundamental Plane. Then the ultimate meaning is: understanding visible mass - size correlation and/or Fundamental Plane means understanding how galaxies form. The mass - size relationship involves baryon (mainly stellar) mass and its typical dimension related to the light, but it gets memory of the cosmological mass variance at the equivalence epoch. The reason is that the baryonic component virializes by sharing virial energy in about equal amount between baryons and dark matter, this sharing depending, in turn, on the steepness of the dark matter distribution. The general strategy consists in using the two-component tensor virial theorem for determining the virialized baryonic configurations. A King and a Zhao density profile are assumed for the inner baryonic and the outer dark matter component, respectively, at the end of the relaxation phase. All the considerations are restricted to spherical symmetry for simplicity. The effect of changing the dark-to-baryon mass ratio, m, is investigated inside a LambdaCDM scenario. A theoretical mass - size relation is expressed for the baryonic component, which fits fairly well to the data from a recently studied galaxy sample. Finally, the play of intrinsic dispersion on the mass ratio, m, is discussed in the light of the cusp/core problem and some consequences are speculated about the existence of a limit, m_l, expected by the theory.