Precision analysis of ¹²C/¹³C ratios in Orion IRc2 acetylene isotopologs via χ² fitting

Department of Physics and Origin of Matter and Evolution of Galaxies (OMEG) Institute, Soongsil University, Seoul 06978, Republic of Korea

^★ Corresponding author.

Received: 28 February 2025
Accepted: 30 June 2025

Abstract

We present a detailed analysis of acetylene (C₂H₂) and its isotopologs in the Orion IRc2, focusing on the determination of ¹²C/¹³C isotopic ratios using high-resolution infrared spectra from SOFIA. By employing a robust χ² fitting method, we simultaneously determined the temperature and column density, achieving a ¹²C/¹³C ratio of 18.73_−1.47^+1.54 for the blue clump and 15.07_−1.60^+1.61 for the red clump. These results revealed significant discrepancies with the traditional rotational diagram method, which overestimated the ratios by 12.1% and 23.9%, respectively. Our χ² approach also reduced uncertainties by up to 75% , providing more precise and reliable isotopic ratios. Additionally, we extended the analysis to isotopologs not covered in HITRAN, calculating vibrational and rotational constants through quantum chemical calculations. This allowed us to model subtle isotopic shifts induced by ¹³C and deuterium substitution, enabling accurate isotopolog detection in astrophysical environments. The Python package (TOPSEGI) developed in this study facilitates efficient χ² fitting and isotopic ratio analysis, making it a valuable tool for future high-resolution observations. This work highlights the critical role of advanced spectral models and fitting techniques in understanding isotopic fractionation and the chemical evolution of interstellar matter.