The relationship between dust and [C i] at z = 1 and beyond

Measuring molecular gas mass is vital for understanding the evolution of galaxies at high redshifts (z$\geq$1). Most measurements rely on CO as a tracer, but dependences on metallicity, dynamics and surface density lead to systematic uncertainties in high-z galaxies, where these physical properties are difficult to observe, and where the physical environments can differ systematically from those at z=0. Dust continuum emission provides a potential alternative assuming a known dust/gas ratio, but this must be calibrated on a direct gas tracer at z$\geq$1. In this paper we consider the [CI] 492-GHz emission line, which has been shown to trace molecular gas closely throughout Galactic clouds and has the advantages of being optically thin in typical conditions (unlike CO), and being observable at accessible frequencies at high redshifts (in contrast to the low-excitation lines of CO). We use the Atacama Large Millimetre/submillimetre Array (ALMA) to measure [CI], CO(4-3) and dust emission in a representative sample of star-forming galaxies at z=1, and combine these data with multi-wavelength spectral energy distributions to study relationships between dust and gas components of galaxies. We uncover a strong [CI]-dust correlation, suggesting that both trace similar phases of the gas. By incorporating other samples from the literature, we show that this correlation persists over a wide range of luminosities and redshifts up to z$\sim$4. Finally we explore the implications of our results as an independent test of literature calibrations for dust as a tracer of gas mass, and for predicting the CI abundance.