Spatially Resolved Water Emission from Gravitationally Lensed Dusty Star Forming Galaxies at z $\sim$ 3

Abstract

Water (${\mathrm{H}}_2\mathrm{O}$), one of the most ubiquitous molecules in the universe, has bright millimeter-wave emission lines easily observed at high-redshift with the current generation of instruments. The low excitation transition of ${\mathrm{H}}_2\mathrm{O}$, p$-$${\mathrm{H}}_2\mathrm{O}$(202 $-$ 111) (${\nu }_{rest}$ = 987.927 GHz) is known to trace the far-infrared (FIR) radiation field independent of the presence of active galactic nuclei (AGN) over many orders-of-magnitude in FIR luminosity (L${}_{\mathrm{FIR}}$). This indicates that this transition arises mainly due to star formation. In this paper, we present spatially ($\sim$0.5 arcsec corresponding to $\sim$1 kiloparsec) and spectrally resolved ($\sim$100 kms${}^{-1}$) observations of p$-$${\mathrm{H}}_2\mathrm{O}$(202 $-$ 111) in a sample of four strong gravitationally lensed high-redshift galaxies with the Atacama Large Millimeter/submillimeter Array (ALMA). In addition to increasing the sample of luminous ($>$ $10^{12}$L${}_{\odot }$) galaxies observed with ${\mathrm{H}}_2\mathrm{O}$, this paper examines the L${}_{{\mathrm{H}}_2\mathrm{O}}$/L${}_{\mathrm{FIR}}$ relation on resolved scales for the first time at high-redshift. We find that L${}_{{\mathrm{H}}_2\mathrm{O}}$ is correlated with L${}_{\mathrm{FIR}}$ on both global and resolved kiloparsec scales within the galaxy in starbursts and AGN with average L${}_{{\mathrm{H}}_2\mathrm{O}}$/L${}_{\mathrm{FIR}}$ =$2.76_{-1.21}^{+2.15}\times 10^{-5}$. We find that the scatter in the observed L${}_{{\mathrm{H}}_2\mathrm{O}}$/L${}_{\mathrm{FIR}}$ relation does not obviously correlate with the effective temperature of the dust spectral energy distribution (SED) or the molecular gas surface density. This is a first step in developing p$-$${\mathrm{H}}_2\mathrm{O}$(202 $-$ 111) as a resolved star formation rate (SFR) calibrator.