The ESO SupJup Survey. X. A carbon isotope contrast in the young ROXs 12 system

Technical Summary: The ESO SupJup Survey X: A carbon isotope contrast in the young ROXs 12 system

Problem and Context
The formation pathways of massive, wide-orbit super-Jupiters and substellar companions remain a subject of debate, with competing hypotheses suggesting formation via core accretion followed by scattering, or via gravitational collapse and fragmentation similar to stars. While elemental ratios (e.g., C/O) have long been proposed as formation tracers, emerging research suggests that isotopic ratios, specifically $^{12}\text{CO}/^{13}\text{CO}$, may offer distinct insights. Objects formed via gravitational collapse are expected to retain the isotopic signature of their parent molecular cloud, whereas those formed via core accretion may inherit the isotopic ratios of local disk solids, which can vary due to fractionation. The ESO SupJup Survey aims to test these hypotheses by characterizing the atmospheric compositions of substellar companions and isolated brown dwarfs. This work focuses on the ROXs 12 system, a young (~6 Myr) M0 star with a widely separated L0 brown dwarf companion (ROXs 12B), providing a unique opportunity to directly compare the atmospheric properties of a host and its companion.

Methodology
The authors obtained high-resolution K-band spectra (1.92–2.48 $\mu$m) of the ROXs 12 system using the CRIRES+ instrument on the Very Large Telescope (VLT). Observations were conducted in March 2023 with a 0.4" slit width, utilizing an ABBA nodding sequence to separate the companion from the host star. The data reduction was performed using the excalibuhr pipeline, which includes flat-fielding, sky subtraction, and optimal extraction. A critical step involved modeling the host star's Point Spread Function (PSF) with a Lorentzian profile to subtract the stellar light and isolate the faint companion signal.

Atmospheric retrieval analyses were conducted using the petitRADTRANS radiative transfer code coupled with the nested sampling algorithm PyMultiNest. The retrieval framework modeled the atmospheric properties as free parameters, including:

• Chemical abundances: Volume mixing ratios derived from thermo-chemical equilibrium tables (computed with FastChem), specifically retrieving C/O, metallicity ([Fe/H]), and isotope ratios ($^{12}\text{CO}/^{13}\text{CO}$ and $\text{H}_2^{16}\text{O}/\text{H}_2^{18}\text{O}$).
• Thermal structure: A parameterized pressure-temperature (P-T) profile defined by temperature gradients at specific pressure levels.
• Physical effects: Surface gravity ($\log g$) constrained by Gaussian priors based on evolutionary tracks, and veiling (continuum excess from circumstellar disks) modeled as a blackbody component.
• Broadening: Projected rotational velocity ($v \sin i$) and limb-darkening coefficients.

The likelihood function incorporated a Gaussian Process (GP) to account for correlated noise, and the robustness of the retrieval was validated through an injection-retrieval test using a synthetic spectrum with known parameters.

Key Results

1. Molecular Detections: The study confirms the presence of $\text{H}_2\text{O}$, $^{12}\text{CO}$, $^{13}\text{CO}$, and HF in both the host star (ROXs 12A) and the companion (ROXs 12B). A tentative detection of $\text{H}_2^{18}\text{O}$ is reported for ROXs 12B.
2. Isotopic Ratios:
   • $^{12}\text{CO}/^{13}\text{CO}$: The retrieved ratios are $77^{+10}_{-7}$ for ROXs 12A and $55^{+10}_{-7}$ for ROXs 12B. While both are consistent with the local interstellar medium (ISM) value ($68 \pm 15$), the companion exhibits a measurably lower ratio than the host, though the difference is not strongly significant (within $1\sigma$).
   • $\text{H}_2^{16}\text{O}/\text{H}_2^{18}\text{O}$: For ROXs 12B, a lower limit of $\gtrsim 300$ is derived, suggesting a potential slight enrichment of $\text{H}_2^{18}\text{O}$ compared to solar and ISM values, though large uncertainties prevent a definitive detection.
3. Elemental Composition:
   • C/O Ratio: ROXs 12B yields a C/O ratio of $0.54 \pm 0.01$, consistent with solar values and previous studies. For ROXs 12A, a higher ratio of $0.87 \pm 0.01$ is retrieved; however, the authors caution that this value is unreliable due to the absence of atomic oxygen lines in the K-band, which limits the ability to constrain the total oxygen budget at the host's photospheric temperatures.
   • Metallicity: ROXs 12A is found to have near-solar metallicity ($-0.06^{+0.02}_{-0.03}$), while ROXs 12B shows a subsolar metallicity ($-0.53 \pm 0.03$). The authors note that this subsolar value for the companion may be influenced by degeneracies with veiling and temperature structure, though injection tests suggest the isotopic ratios are robust against these effects.
4. Veiling and Thermal Structure:
   • Veiling: A moderate veiling coefficient of $r_k = 0.17^{+0.02}_{-0.03}$ is detected for the host star, consistent with a hot inner disk. No significant veiling is detected for the companion ($r_k < 0.03$), consistent with the non-detection of a massive accreting disk around ROXs 12B.
   • Thermal Profile: The retrieved P-T profile for ROXs 12B is more isothermal than predicted by standard models (e.g., Sonora Bobcat), exhibiting shallower temperature gradients.

Significance and Conclusions
The paper concludes that the ROXs 12 system provides a crucial case study for constraining formation mechanisms of wide-orbit super-Jupiters. The near-solar C/O ratio and the spin-orbit misalignment (previously reported) favor a formation via gravitational collapse. However, the slightly lower $^{12}\text{CO}/^{13}\text{CO}$ ratio in the companion compared to the host could be interpreted as a signature of core accretion involving local disk solids. The authors emphasize that this isotopic contrast, while only marginally significant, highlights the need for a broader sample to assess the frequency of such variations.

The study reinforces that $^{12}\text{CO}/^{13}\text{CO}$ ratios in young systems are generally consistent with the current ISM, serving as a potential age indicator. The work demonstrates the capability of high-resolution spectroscopy combined with atmospheric retrieval to disentangle complex atmospheric properties, including isotopic ratios, in young, widely separated systems. The authors maintain that while the current data offers insights, the formation history of ROXs 12B remains ambiguous, necessitating further observational and modeling efforts to definitively link isotopic variations to specific formation pathways.