On the Limited Sizes of Dusty Starbursting Regions at High Redshifts

TL;DR

This study uses Herschel far-infrared data to show that the limited sizes of dusty starbursting regions at high redshifts explain the observed infrared luminosity and dust temperature relation, highlighting the compactness of these regions.

Contribution

It introduces a new interpretation of the L_IR-T relation based on a maximum effective radius of dusty starbursting regions, reconciling previous size discrepancies.

Findings

R_eff is a good measure of DSBR size and is consistent with direct measurements.

The L_IR-T relation is due to R_eff being limited to about 2 kpc.

Interferometric size measurements may be affected by blending effects.

Abstract

Using the far-infrared data obtained by the Herschel Space Observatory, we study the relation between the infrared luminosity (L_IR) and the dust temperature (T) of dusty starbursting galaxies at high redshifts (high-z). We focus on the total infrared luminosity from the cold-dust component (L_IR^(cd)), whose emission can be described by a modified black body (MBB) of a single temperature (T_mbb). An object on the (L_IR^(cd), T_mbb) plane can be explained by the equivalent of the Stefan-Boltzmann law for a MBB with an effective radius of R_eff. We show that R_eff is a good measure of the combined size of the dusty starbursting regions (DSBRs) of the host galaxy. In at least one case where the individual DSBRs are well resolved through strong gravitational lensing, R_eff is consistent with the direct size measurement. We show that the observed L_IR-T relation is simply due to the limited R_eff (<~ 2 kpc). The small R_eff values also agree with the compact sizes of the DSBRs seen in the local universe. However, previous interferometric observations to resolve high-z dusty starbursting galaxies often quote much larger sizes. This inconsistency can be reconciled by the blending effect when considering that the current interferometry might still not be of sufficient resolution. From R_eff we infer the lower limits to the volume densities of the star formation rate ("minSFR3D") in the DSBRs, and find that the $L_{IR}$-$T$ relation outlines a boundary on the (L_IR^(cd), T) plane, below which is the "zone of avoidance" in terms of minSFR3D.