Abstract

Context. The nature and evolution of high-redshift dusty star-forming galaxies (high-z DSFGs) remain open questions. Their massive gas reservoirs play an important role in driving the intense star formation rates hosted in these galaxies.Aims. Our aim is to estimate the molecular gas content of high-z DSFGs by using various gas mass tracers, such as the [CI], CO, [CII] emission lines and the dust content. These tracers need to be well calibrated as they are all limited by uncertainties on factors such as & alpha;(CO), X-CI, & alpha;([CII]), and & delta;(GDR), thereby affecting the accurate determination of the gas mass. The main goal of our work is to check the consistency between the gas mass tracers and to cross-calibrate the uncertain factors.Methods. We observed the two [CI] line transitions for 29 South Pole telescope Submillimeter Galaxies (SPT-SMGs) with the Atacama Large Millimeter/submillimeter Array-Atacama Compact Array (ALMA-ACA). Additionally, we also present new Atacama Pathfinder EXperiment (APEX) observations of [CII] line for nine of these galaxies. We combined our observations with the rich ancillary data of low- and mid-J CO lines, ancillary [CII] line, and dust mass estimations for these galaxies.Results. We find a nearly linear relation between the infrared luminosity and [CI] luminosity if we fit the starbursts and main-sequence galaxies separately. We measure a median [CI]-derived excitation temperature of 34.5 & PLUSMN; 2.1 K. We probed the properties of the interstellar medium (ISM), such as density and radiation field intensity, using [CI] to mid- or high-J CO lines and the [CI]-to-infrared luminosity ratio, and find similar values to the SMG populations in the literature. Finally, the gas masses estimated from [CI], CO, dust, and [CII] do not exhibit any significant trend with the infrared luminosity or the dust temperature. We provide the various cross-calibrations between these tracers.Conclusions. Our study confirms that [CI] is a suitable tracer of the molecular gas content, and shows an overall agreement between all the classical gas tracers used at high redshift. However, their absolute calibration, and thus the gas depletion timescale measurements, remain uncertain.