The carbon isotope ratio of \beta\ Pic b with high-resolution spectroscopy
Isotopic ratios trace the formation and evolution of planets and link their atmospheres to the chemistry of their natal protoplanetary discs. We measure $^{12}\mathrm{C}/^{13}\mathrm{C} = 58^{+18}_{-15}$ in the atmosphere of the young super-Jupiter $\beta$ Pic b from 11 nights of CRIRES+ K-band spectroscopy ($\mathcal{R} \approx 100{,}000$) at the Very Large Telescope (VLT). We detect both $^{12}\mathrm{CO}$ and $^{13}\mathrm{CO}$ and constrain $^{12}\mathrm{C}/^{13}\mathrm{C}$ with a Bayesian retrieval jointly fitted with near-infrared photometry. The inferred $^{12}\mathrm{C}/^{13}\mathrm{C}$ is consistent with the present-day interstellar medium (ISM), is below the solar value, and is comparable to measurements in other young super-Jupiters. We also retrieve $T_{\rm eff} = 1629^{+30}_{-28}\,\mathrm{K}$, near-solar to mildly super-solar metallicity ([M/H]$ = 0.20^{+0.16}_{-0.12}$), a solar-like carbon-to-oxygen ratio (C/O$ = 0.52 \pm 0.03$), and tentative evidence for thick clouds. We analyse each night independently and combine the results of the six epochs with the highest signal-to-noise ratio (S/N), propagating night-to-night scatter into the final uncertainties. This provides an isotopic benchmark for a directly imaged planet interior to the CO snow line.