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 ${}^{12}\mathrm{C}{\mathrm{/}}^{13}\mathrm{C}=58_{-15}^{+18}$ in the atmosphere of the young super-Jupiter $\beta$ Pic b from 11 nights of CRIRES+ K-band spectroscopy ($\mathcal{R}\approx \mathrm{100,000}$) at the Very Large Telescope (VLT). We detect both ${}^{12}\mathrm{C}\mathrm{O}$ and ${}^{13}\mathrm{C}\mathrm{O}$ and constrain ${}^{12}\mathrm{C}{\mathrm{/}}^{13}\mathrm{C}$ with a Bayesian retrieval jointly fitted with near-infrared photometry. The inferred ${}^{12}\mathrm{C}{\mathrm{/}}^{13}\mathrm{C}$ 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 $T_{\mathrm{e}\mathrm{f}\mathrm{f}}=1629_{-28}^{+30}\mathrm{K}$, near-solar to mildly super-solar metallicity ([M/H]$=0.20_{-0.12}^{+0.16}$), 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.