The ionised interstellar medium of DSFGs revealed by JWST/NIRSpec and ALMA: Super-solar metallicity, low ionisation parameters, and typical electron densities

We present a detailed study of the observed-frame near-infrared (2,--,4,̆m) JWST/NIRSpec spectra of 48 high-redshift +1.32 _ -0.70 $) galaxies detected with ALMA at $>3σ$. Through a multi-wavelength spectral energy distribution (SED) analysis, we establish the sample has a median stellar mass of ),=,10.8,±,0.1 and a dust mass of * M_⊙ d M_⊙ ),=,8.7,±,0.1, covering a broad range of far-infrared luminosity ( ),=,10.9,--,12.7). Analysing the rest-frame optical emission-line properties, we discern the majority of the sources show no indication of AGN activity with 40% having either X-ray counterparts (L_̊m Xc,>,1042,erg/s), elevated optical ( (n_ FIR L_⊙ emission-line ratios, or broad (FWHM,$>$,800,km/s) ̋a emission line profiles, although we note this is a lower limit given the stochastic placement of NIRSpec slits. We establish the sample has a median gas-phase metallicity of as derived from the ratio, with the more far-infrared luminous ( ),$>12.0) galaxies exhibiting a 0.15,±$,0.03,dex higher metallicity at their epoch than predicted by the fundamental metallicity relation. From the FIR L_⊙ emission-line doublet ratio, we measured a median electron density for the sample of log_ 10 ̊m e cm $ -3 ),=,2.53,±,0.07, which is consistent with less-massive, star-forming galaxies at the same epoch. Finally, for a subsample of nine sources with and ̋b detections (median FIR L_⊙ ),=,11.81,±,0.15), we derived a median observed (dust-uncorrected) ionisation parameter of log_ 10 (U),=,-2.84,±,0.06, suggesting our sample falls below the ionisation parameter ̋a star-formation rate surface density ($Σ_ ̊m Hα,SFR ) relation of typical star-forming galaxies. Our results indicate that luminous far-infrared galaxies are massive, chemically evolved systems that appear to deviate from the standard dust and metal production equilibrium observed in less obscured galaxies. This study demonstrates the powerful synergy of JWST and ALMA in unveiling the nature of dusty star-forming galaxies, and it highlights the need for a NIRSpec survey of uniformly selected, massive, dust-obscured galaxies to fully characterise their interstellar medium.