# Carbon Isotope Ratios in M10 Giants

## TL;DR

This study measures carbon isotope ratios in M10 giant stars, compares them with previous data, and models surface abundance evolution, revealing the need for increased thermohaline mixing efficiency in stellar models.

## Contribution

It provides new IR spectroscopic measurements of $^{12} ext{C}/^{13} ext{C}$ ratios in M10 giants and evaluates stellar mixing models against these observations.

## Key findings

- No significant difference in isotope ratios between star populations.
- IR-derived carbon abundances agree with previous measurements.
- Models require substantially increased thermohaline mixing efficiency.

## Abstract

We measured carbon abundances and the $^{12}\mathrm{C}/^{13}\mathrm{C}$ ratio in 31 giant branch stars with previous CN and CH band measurements that span -2.33 $<$ M$_{\rm V}$ $<$ 0.18 in the globular cluster M10 (NGC 6254). Abundances were determined by comparing CO features at $\sim 2.3\, \mu \mathrm{m}$ and specifically the $^{13}$CO bandhead at $2.37\, \mu \mathrm{m}$, to synthetic spectra generated with MOOG. The observed spectra were obtained with GNIRS on Gemini North with a resolution of R $\approx 3500$. The carbon abundances derived from the IR spectra agree with previous [C/Fe] measurements found using CN and CH features at the near-UV/blue wavelength range. We found an average carbon isotope ratio of $^{12}\mathrm{C}/^{13}\mathrm{C}$ = 5.10$_{-0.17}^{+0.18}$ for first generation stars (CN-normal; 13 stars total) and $^{12}\mathrm{C}/^{13}\mathrm{C}$ = 4.84$_{-0.22}^{+0.27}$ for second generation stars (CN-enhanced; 15 stars). We therefore find no statistically significant difference in $^{12}\mathrm{C}/^{13}\mathrm{C}$ ratio between stars in either population for the observed magnitude range. Finally, we created models of the expected carbon, nitrogen, and $^{12}\mathrm{C}/^{13}\mathrm{C}$ surface abundance evolution on the red giant branch due to thermohaline mixing using the MESA stellar evolution code. The efficiency of the thermohaline mixing must be increased to a factor of $\approx 60$ to match [C/Fe] abundances, and by a factor of $\approx 666$ to match $^{12}\mathrm{C}/^{13}\mathrm{C}$ ratios. We could not simultaneously fit the evolution of both carbon and the $^{12}\mathrm{C}/^{13}\mathrm{C}$ ratio with models using the same thermohaline efficiency parameter.