Dust temperature in ALMA $\hbox{[C $\scriptstyle\rm II $]}$-detected high-$z$ galaxies

TL;DR

This paper introduces a new method combining dust continuum and [C II] line emission to accurately determine dust temperature in high-redshift galaxies, reducing uncertainties in key galaxy properties.

Contribution

The novel method breaks the degeneracy between dust mass and temperature using a single [C II] observation, applicable to ALMA and NOEMA data, enhancing high-z galaxy analysis.

Findings

The method reliably constrains dust temperature with one observation.

Derived a relation between total gas surface density and [C II] surface brightness.

Predicted the cosmic evolution of the molecular to total gas surface density ratio.

Abstract

At redshift $z>5$ the far-infrared (FIR) continuum spectra of main-sequence galaxies are sparsely sampled, often with a single data point. The dust temperature $T_{\rm d, SED}$ thus has to be assumed in the FIR continuum fitting. This introduces large uncertainties regarding the derived dust mass ($M_{\rm d}$), FIR luminosity, and obscured fraction of the star formation rate. These are crucial quantities to quantify the effect of dust obscuration in high-$z$ galaxies. To overcome observations limitations, we introduce a new method that combines dust continuum information with the overlying $\hbox{[C $\scriptstyle\rm II $]} 158\mu$m line emission. By breaking the $M_{\rm d} - T_{\rm d, SED}$ degeneracy, with our method, we can reliably constrain the dust temperature with a single observation at $158\mu$m. This method can be applied to all ALMA and NOEMA $\hbox{[C $\scriptstyle\rm II $]}$ observations and exploited in ALMA Large Programs such as ALPINE and REBELS targeting $\hbox{[C $\scriptstyle\rm II $]}$ emitters at high-$z$. We also provide a physical interpretation of the empirical relation recently found between $molecular$ gas mass and $\hbox{[C $\scriptstyle\rm II $]}$ luminosity. We derive an analogous relation linking the $total$ gas surface density and $\hbox{[C $\scriptstyle\rm II $]}$ surface brightness. By combining the two, we predict the cosmic evolution of the surface density ratio $\Sigma_{\rm H_2} / \Sigma_{\rm gas}$. We find that $\Sigma_{\rm H_2} / \Sigma_{\rm gas}$ slowly increases with redshift, which is compatible with current observations at $0 < z < 4$.