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We present position-position-velocity (PPV) cubes of the physical andchemical properties of the molecular medium in the central 1.2 kpc region ofthe active galaxy NGC 613 at a PPV resolution of0.$^{\prime\prime}$8$\times$0.$^{\prime\prime}$8$\times$10 km s$^{-1}$(0.$^{\prime\prime}$8 = $\sim$68 pc). We used eight molecular lines obtainedwith ALMA. Non-LTE calculation with hierarchical Bayesian inference was used toconstruct PPV cubes of the gas kinetic temperature ($T_\mathrm{kin}$),molecular hydrogen volume density ($n_\mathrm{H_2}$), column densities($N_\mathrm{H_2}$), and fractional abundances of four molecules($^{12}$C$^{18}$O, HCN, HCO$^+$, and CS). The derived $n_\mathrm{H_2}$,$N_\mathrm{H_2}$, and $T_\mathrm{kin}$ ranged 10$^{3.21-3.85}$ cm$^{-3}$,10$^{20.8-22.1}$ cm$^{-2}$, and 10$^{2.33-2.64}$ K, respectively. Our firstapplication of the non-LTE method with the hierarchical Bayesian inference toexternal galaxies yielded compatible results compared with the previous studiesof this galaxy, demonstrating the efficacy of this method for application toother galaxies. We examined the correlation between gas surface density$\Sigma_\mathrm{H_2}$ (converted from $N_\mathrm{H_2}$) and the star formationrate $\Sigma_\mathrm{SFR}$ obtained from the 110 GHz continuum flux map andfound two distinct sequences in the $\Sigma_\mathrm{H_2}$-$\Sigma_\mathrm{SFR}$diagram; the southwestern subregion of the star-forming ring exhibited a$\sim$0.5 dex higher star formation efficiency (SFE;$\Sigma_\mathrm{SFR}/\Sigma_\mathrm{H_2}$) than the eastern subregion. However,they exhibited no systematic difference in $n_\mathrm{H_2}$, which is oftenargued as a driver of SFE variation. We suggest that the deficiency ofmolecular gas in the southwestern subregion, where no significant gas supply isevident along the offset ridges in the bar, is responsible for the elevatedSFE.

Distributions of the Density and Kinetic Temperature of the Molecular Gas in the Central Region of NGC 613 using Hierarchical Bayesian Inference