A census of star-formation and gas mass tracers in two lensed $z \sim 4$ dusty star-forming galaxies

TL;DR

This study investigates how to reliably infer gas masses and star formation rates in two strongly lensed DSFGs at high redshift using multiple millimeter tracers. Through beam-matched, pixel-resolved ALMA analyses of CO(7-6), CI(2-1), CII, and, in one source, p-H2O, coupled with lens modeling, it assesses the spatial distribution of gas and dust and tests the resolved Kennicutt-Schmidt relation. A key result is that the SFR–gas surface density slopes are broadly consistent across tracers, while dust is more compact and CII is more extended; the authors also propose the CI(2-1)/CO(7-6) flux-density ratio as a practical proxy for the gas depletion timescale, τ_dep. These findings inform tracer selection for high-z galaxies and highlight cautions when using [C II] as a universal gas/mass or SFR tracer in extended regions.

Abstract

We present new and archival Atacama Large Millimeter/submillimeter Array (ALMA) observations of two strongly lensed dusty star-forming galaxies (DSFGs) selected from the South Pole Telescope survey, SPT0418-47 $(z = 4.225)$ and SPT2147-50 $(z = 3.760)$. We study the [C II], CO(7-6), [C I](2-1), and, in SPT0418-47, $p$-H$_2$O emission, which along with the underlying continuum (rest-frame 160 $μ$m and 380 $μ$m) are routinely used as tracers of gas mass and/or star-formation rate (SFR). We perform a pixel-by-pixel analysis of both sources in the image plane to study the resolved Kennicutt-Schmidt relation, finding generally good agreement between the slopes of the SFR versus gas mass surface density using the different tracers. Using lens modeling methods, we find that the dust emission is more compact than the line emission in both sources, with CO(7-6) and [C I](2-1) similar in extent and [C II] the most extended, reminiscent of recent findings of extended [C II] spatial distributions in galaxies at similar cosmic epochs. We develop the [C I](2-1) / CO(7-6) flux density ratio as an observable proxy for gas depletion timescale ($τ_{\rm dep}$), which can be applied to large samples of DSFGs, in lieu of more detailed inferences of this timescale which require analysis of observations at multiple wavelengths. Furthermore, the extended [C II] emission in both sources, compared to the total continuum and line emission, suggests that [C II], used in recent years as a molecular gas mass and SFR tracer in high-$z$ galaxies, may not always be a suitable tracer of these physical quantities.

Figures (2)

• Figure 1: From left to right: CO(7--6), [C i](2--1), $p$-H$_2$O, and [C II] emission lines (top) with associated moment-0 maps (bottom). The spectra have a resolution of 50 km s$^{-1}$ and are generated from data cubes of SPT0418-47 within a circular aperture whose radius is 2.5$"$ (as shown by the white circle). The cubes are re-imaged via CASA with a fixed circular restoring beam size of 0.5$"$ and a pixel scale of 0.1$"$. All four lines are robustly detected and have similar line widths. Moment-0 maps are generated by integrating the channels highlighted in the spectra above, all encompassing 1000 km s$^{-1}$ in channel width.
• Figure 2: As in Figure 1, but for SPT2147-50. The aperture radius here, shown by the white circle, is 2$"$. We indicate, via the red contours, the location of the tentative AGN in birkin2023. These pixels are removed for the fits in Figure \ref{['fig:ks_law']}.