JOYS+ study of solid state $^{12}$C/$^{13}$C isotope ratios in protostellar envelopes: Observations of CO and CO$_2$ ice with JWST

The carbon isotope ratio is a powerful tool for studying the evolution of stellar systems. Recent detections of CO isotopologues in disks and exoplanet atmospheres pointed towards significant fractionation in these systems. In order to understand the evolution of this quantity, it is crucial to trace the isotope abundance from stellar nurseries to planetary systems. During the protostellar stage the multiple vibrational modes of CO$_2$ and CO ice provide a unique opportunity to examine the carbon isotope ratio in the solid state. Now with the sensitivity of the \textit{James Webb Space Telescope}, these absorption features have become accessible at high S/N in Solar-mass systems. We quantify the $^{12}$CO$_2$/$^{13}$CO$_2$ and the $^{12}$CO/$^{13}$CO isotope ratios in 17 class 0/I low mass protostars from the $^{12}$CO$_2$ combination modes (2.70 ${\mu}$m and 2.77 ${\mu}$m), the $^{12}$CO$_2$ stretching mode (4.27 ${\mu}$m), the $^{13}$CO$_2$ stretching mode (4.39 ${\mu}$m), the $^{12}$CO$_2$ bending mode (15.2 ${\mu}$m), the $^{12}$CO stretching mode (4.67 ${\mu}$m) and the $^{13}$CO stretching mode (4.78 ${\mu}$m) using JWST observations. We also report a detection of the $^{12}$CO overtone mode at 2.35 ${\mu}$m. The $^{12}$CO$_2$/$^{13}$CO$_2$ ratios are in agreement and we find mean ratios of 85 $\pm$ 23, 76 $\pm$ 12 and 97 $\pm$ 17 for the 2.70 ${\mu}$m, 4.27 ${\mu}$m and the 15.2 ${\mu}$m bands, respectively. The main source of uncertainty stem from the error on the band strengths. The $^{12}$CO/$^{13}$CO ratios derived from the 4.67 ${\mu}$m bands are consistent, albeit elevated with respect to the $^{12}$CO$_2$/$^{13}$CO$_2$ ratios and we find a mean ratio of 165 $\pm$ 52. These findings indicate that ices leave the pre-stellar stage with elevated carbon isotope ratios relative to the interstellar medium and that fractionation becomes significant during the later stages.