Implications of a spatially resolved main sequence for the size evolution of star forming galaxies

TL;DR

This paper explores how the local or global nature of the star formation main sequence influences the size evolution of star-forming galaxies, linking local star formation properties to galaxy growth and structural changes.

Contribution

It introduces a growth function relating galaxy size change to star formation rates and demonstrates the implications of a local main sequence on galaxy size evolution and mass-size relation.

Findings

A growth function g is derived relating size change to sSFR differences.

Galaxies with a local main sequence follow a stationary mass-size relation.

The results challenge the idea that the main sequence is fundamentally local at z=0.

Abstract

Two currently debated problems in galaxy evolution, the fundamentally local or global nature of the main sequence of star formation and the evolution of the mass-size relation of star forming galaxies (SFGs), are shown to be intimately related to each other. As a preliminary step, a growth function $g$ is defined, which quantifies the differential change in half-mass radius per unit increase in stellar mass ($g = d \log R_{1/2}/d \log M_\star$) due to star formation. A general derivation shows that $g = K \Delta(sSFR)/sSFR$, meaning that $g$ is proportional to the relative difference in specific star formation rate between the outer and inner half of a galaxy, with $K$ a dimensionless structural factor for which handy expressions are provided. As an application, it is shown that galaxies obeying a fundamentally local main sequence also obey, to a good approximation, $g \simeq \gamma n$, where $\gamma$ is the slope of the normalized local main sequence ($sSFR \propto \Sigma_\star^{-\gamma}$) and $n$ the Sersic index. An exact expression is also provided. Quantitatively, a fundamentally local main sequence is consistent with SFGs growing along a stationary mass-size relation, but inconsistent with the continuation at $z=0$ of evolutionary laws derived at higher $z$. This demonstrates that either the main sequence is not fundamentally local, or the mass-size relation of SFGs has converged to an equilibrium state some finite time in the past, or both.