Simulations for the evolution of the chemical clock HC₃N/N₂H⁺ in high-mass star-forming regions

¹ Purple Mountain Observatory, Chinese Academy of Sciences, 10 Yuanhua Road, 210023 Nanjing, PR China
² University of Science and Technology of China, 96 Jinzhai Road, 230026 Hefei, PR China
³ Max-Planck-Institut für Radioastronomie, Auf dem Hügel 69, 53121 Bonn, Germany
⁴ Center for Astrophysics, Guangzhou University, 230 Wai Huan Xi Road, 510006 Guangzhou, PR China

^★ Corresponding author; wangyao@pmo.ac.cn

Received: 1 April 2024
Accepted: 10 February 2025

Abstract

Context. From observations, column density ratios or integrated intensity ratios between some species exhibit monotonic increase or decrease along with the evolution of high-mass star-forming regions (HMSFRs). Such ratios are defined as chemical clocks, which can be used to constrain the evolutionary stage.

Aims. We performed chemical simulations to reproduce the observed column density ratio of HC₃N/N₂H⁺ and the abundances of these two species across various evolutionary stages in HMSFRs. Simultaneously, we identified the chemical processes responsible for the observed time-dependent trends in these stages.

Methods. Our simulations utilized the astrochemical code Nautilus and the existing 1D models of HMSFRs that cover four evolutionary stages, accompanied by variations in density and temperature throughout the entire evolution. In addition, to maintain a steady increase in density and temperature over time as predictions of the global hierarchical collapse scenario, we adjusted parameters such as density, temperature, and time spent in each evolutionary stage.

Results. When averaging over large spatial scales, the best model produced successfully matches the observed column density ratio of HC₃N/N₂H⁺ and the abundances of the species involved at specific times for each evolutionary stage; that is, the late high-mass starless core stage, the early high-mass protostellar object stage, and the early ultracompact H II stage. HC₃N is mainly affected by the warm carbon-chain chemistry (WCCC) and its own thermal desorption, while N₂H⁺ is primarily influenced by the thermal desorption of N₂, CO, CH₄, NH₃, and H₂O followed by dissociative recombination and ion-molecule reactions.

Conclusions. The results obtained from the best-fitting model timescales broadly agree with statistical estimates. However, a continuous increasing ratio of HC₃N/N₂H⁺ throughout the entire evolution of HMSFRs is not acquired. Some observed ratios between adjacent stages overlap, which could be induced by observational uncertainties (such as those in deriving column densities and abundances, clump classification, and systematic effects), or indicate that the evolution of HC₃N/N₂H⁺ may not strictly monotonically increase throughout the entire evolution. Based on our best-fit model, we further examined other 350 ratios involving 27 species, and 178 ratios exhibit an increasing or decreasing evolutionary trend around the best-fit timescales of HC₃N/N₂H⁺. Among them, 157 ratios are observable and could be considered as candidate chemical clocks. Our results indicate that 1D models with abrupt jumps in physical parameters have reached their limits in terms of the insights they can provide, and more sophisticated models need to be adopted.