Star formation timescale in the molecular filament WB 673

We present observations of ammonia emission lines toward the interstellar filament WB~673 hosting the dense clumps WB~673, WB~668, S233-IR and G173.57+2.43. LTE analysis of the lines allows us to estimate gas kinetic temperature ($\lesssim$ 30~K in all the clumps), number density ($7-17\times10^3$~cm$^{-3}$), and ammonia column density ($\approx 1-1.5\times 10^{15}$~cm$^{-2}$) in the dense clumps. We find signatures of collapse in WB 673 and presence of compact spatially unresolved dense clumps in S233-IR. We reconstruct 1D density and temperature distributions in the clumps and estimate their ages using astrochemical modelling. Considering CO, CS, NH$_3$ and N$_2$H$^+$ molecules (plus HCN and HNC for WB~673), we find a chemical age of $t_{\rm chem}=1-3\times 10^5$~yrs providing the best agreement between the simulated and observed column densities in all the clumps. Therefore, we consider $t_{\rm chem}$ as the chemical age of the entire filament. A long preceding low-density stage of gas accumulation in the astrochemical model would break the agreement between the simulated and observed column densities. We suggest that rapid star formation over a $\sim 10^5$~yrs timescale take place in the filament.