High dense gas fraction in intensely star-forming dusty galaxies

We present ALMA $J=3\mbox{--}2$ and VLA $J=1\mbox{--}0$ observations of the dense molecular gas tracers HCN, HCO+, and HNC in two lensed, high-redshift starbursts selected from the Herschel-ATLAS survey: H-ATLAS J090740.0−004200 (SDP.9, ${z}_{\mathrm{spec}}=1.575$) and H-ATLAS J091043.1−000321 (SDP.11, ${z}_{\mathrm{spec}}=1.786$). In SDP.9 we have detected all $J=3\mbox{--}2$ transitions and also HCN(1–0) and HCO+(1–0). In SDP.11 we have detected HCN(3–2) and HCO+(3–2). The amplification factors for both galaxies have been determined from subarcsecond-resolution CO and dust emission observations carried out with NOEMA and the SMA. The HNC(1–0)/HCN(1–0) line ratio in SDP.9 suggests the presence of photon-dominated regions, as happens in most local (U)LIRGs. The CO, HCN, and HCO+ spectral line energy distribution (SLEDs) of SDP.9 are compatible to those found for many local, IR-bright galaxies, indicating that the molecular gas in local and high-redshift dusty starbursts can have similar excitation conditions. We obtain that the correlation between total IR (${L}_{\mathrm{IR}}$) and dense line (${L}_{\mathrm{dense}}$) luminosity in SDP.9 and SDP.11 and local star-forming galaxies can be represented by a single relation. We argue that the scatter of the ${L}_{\mathrm{IR}}\mbox{--}{L}_{\mathrm{dense}}$ correlation, together with the lack of sensitive dense molecular gas tracer observations for a homogeneous sample of high-redshift galaxies, prevents us from distinguishing differential trends with redshift. Our results suggest that the intense star formation found in some high-redshift, dusty, luminous starbursts is associated with more massive dense molecular gas reservoirs and higher dense molecular gas fractions