The MALATANG survey: star formation, dense gas, and AGN feedback in NGC 1068

We aim to investigate the interplay between dense molecular gas, star formation, and active galactic nucleus (AGN) feedback in the luminous infrared galaxy (LIRG) NGC 1068 at sub-kiloparsec scales. We present the HCN (4-3) and HCO$^+$ (4-3) maps of NGC 1068, obtained with JCMT as part of the Mapping the dense molecular gas in the strongest star-forming galaxies (MALATANG) project, and perform spatially resolved analyses of their correlations with infrared luminosity and soft X-ray emission. Spatially resolved relations between the luminosities of infrared dust emission and dense molecular gas tracers ($L_{\rm IR}-L'_{\rm dense}$) are found to be nearly linear, without clear evidence of excess contributions from AGN activity. The spatially resolved X-ray emission ($L^{\rm gas}_{0.5-2\,\mathrm{keV}}$) displays a radially-dependent twofold correlation with the star formation rate (SFR), suggesting distinct gas-heating mechanisms between the galaxy center and the outer regions. A super-linear scaling is obtained in galactic center regions with SFR surface density ($Σ_{\rm SFR}$) $>$ 8.2 $\times$ 10$^{-6}$ $M_\odot$ yr$^{-1}$ kpc$^{-2}$: log($L^{\rm gas}_{0.5-2\,\mathrm{keV}}$/erg s$^{-1}$) = 2.2 log(SFR/$M_\odot$ yr$^{-1}$) + 39.1. We further found a statistically significant super-linear correlation ($β= 1.34$ $\pm$ 0.86) between $L^{\rm gas}_{0.5-2\,\mathrm{keV}}$/SFR and HCN(4-3)/CO(1-0) intensity ratio, whereas no such trend is seen for HCO$^+$(4-3)/CO(1-0) or CO(3-2)/CO(1-0). These findings indicate that AGN feedback does not dominate star formation regulation on sub-kiloparsec scales, and that the excitation of dense gas traced by HCN (4-3) may be more directly influenced by high-energy feedback processes compared to HCO$^+$ (4-3) and CO (3-2).