A 2-3 mm high-resolution molecular line survey towards the centre of the nearby spiral galaxy NGC 6946

The complex physical, kinematic, and chemical properties of galaxy centres make them interesting environments to examine with molecular line emission. We present new $2-4$" (${\sim}75{-}150$ pc at $7.7$ Mpc) observations at 2 and 3 mm covering the central $50$" (${\sim}1.9$ kpc) of the nearby double-barred spiral galaxy NGC 6946 obtained with the IRAM Plateau de Bure Interferometer. We detect spectral lines from ten molecules: CO, HCN, HCO$^+$, HNC, CS, HC$_3$N, N$_2$H$^+$, C$_2$H, CH$_3$OH, and H$_2$CO. We complemented these with published 1mm CO observations and 33 GHz continuum observations to explore the star formation rate surface density ${\Sigma_{\mathrm{SFR}}}$ on 150 pc scales. In this paper, we analyse regions associated with the inner bar of NGC 6946 $-$ the nuclear region (NUC), the northern (NBE), and southern inner bar end (SBE) and we focus on short-spacing corrected bulk (CO) and dense gas tracers (HCN, HCO$^+$, and HNC). We find that HCO$^+$ correlates best with ${\Sigma_{\mathrm{SFR}}}$, but the dense gas fraction ($f_{\mathrm{dense}}$) and star formation efficiency of the dense gas (${\mathrm{SFE_{dense}}}$) fits show different behaviours than expected from large-scale disc observations.The SBE has a higher ${\Sigma_{\mathrm{SFR}}}$, $f_{\mathrm{dense}}$, and shocked gas fraction than the NBE. We examine line ratio diagnostics and find a higher CO(2-1)/CO(1-0) ratio towards NBE than for the NUC. Moreover, comparison with existing extragalactic datasets suggests that using the HCN/HNC ratio to probe kinetic temperatures is not suitable on kiloparsec and sub-kiloparsec scales in extragalactic regions. Lastly, our study shows that the HCO$^+$/HCN ratio might not be a unique indicator to diagnose AGN activity in galaxies.