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

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Table 6

Comparison of estimated temperature (T) and column density (N) values for blue and red clump species using two methods: the traditional RD method and the χ² fitting method.

Species	Source	Estimated temperature T (K)	Estimated column density N (cm⁻²)	Method
Blue clump
C₂H₂ (even, Para)	Nickerson et al. (2023)	145 ± 9	(1.23 ± 0.15) × 10¹⁶	RD
	This work	$161_{- 3}^{+ 3}$ $161^{+3}_{-3}$	(0.984 ± 0.019) × 10¹⁶	χ²
C₂H₂ (odd, Ortho)	Nickerson et al. (2023)	175 ± 12	(1.50 ± 0.15) × 10¹⁶	RD
	This work	$192_{- 3}^{+ 3}$ $192^{+3}_{-3}$	(1.31 ± 0.015) × 10¹⁶	χ²
¹³CCH₂	Nickerson et al. (2023)	91 ± 9	(2.56 ± 0.18) × 10¹⁵	RD
	This work	${87.2}_{- 10.5}^{+ 12.2}$ $87.2^{+12.2}_{-10.5}$	$({2.45}_{- 0.19}^{+ 0.20}) \times 10^{15}$ $(2.45^{+0.20}_{-0.19}) \times 10^{15}$	χ²
Red clump
C₂H₂ (even, Para)	Nickerson et al. (2023)	158 ± 16	(3.09 ± 0.57) × 10¹⁵	RD
	This work	$170_{- 10}^{+ 11}$ $170^{+11}_{-10}$	$({2.43}_{- 0.18}^{+ 0.18}) \times 10^{15}$ $(2.43^{+0.18}_{-0.18}) \times 10^{15}$	χ²
C₂H₂ (odd, Ortho)	Nickerson et al. (2023)	229 ± 27	(3.58 ± 0.71) × 10¹⁵	RD
	This work	$270_{- 19}^{+ 21}$ $270^{+21}_{-19}$	$({2.65}_{- 0.16}^{+ 0.17}) \times 10^{15}$ $(2.65^{+0.17}_{-0.16}) \times 10^{15}$	χ²
¹³CCH₂	Nickerson et al. (2023)	64 ± 6	(6.74 ± 0.64) × 10¹⁴	RD
	This work	${64.4}_{- 23.4}^{+ 70.7}$ $64.4^{+70.7}_{-23.4}$	$({6.69}_{- 1.66}^{+ 1.98}) \times 10^{14}$ $(6.69^{+1.98}_{-1.66}) \times 10^{14}$	χ²

Notes. The χ² method significantly reduces error bars for C₂H₂ in the blue clump, while revealing larger uncertainties for ¹³CCH₂ in the red clump due to sparse observational data. References: Nickerson et al. (2023).

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