Evidence of Radius Inflation Based on 50 Transiting Brown Dwarfs and Low-mass Stellar Companions

Technical Summary: Evidence of Radius Inflation Based on 50 Transiting Brown Dwarfs and Low-mass Stellar Companions

Problem Statement
Theoretical models of substellar evolution have historically struggled to accurately predict the radii of brown dwarfs and low-mass stars. While individual studies have suggested that measured radii in transiting systems can be significantly larger than model predictions, a systematic, population-level statistical assessment has been lacking. Previous work identified radius inflation in isolated late-M dwarfs and specific transiting brown dwarfs, but the degree of this discrepancy across a broad sample, and its dependence on physical parameters such as mass, orbital separation, equilibrium temperature, and metallicity, required a comprehensive re-evaluation using the latest observational data.

Methodology
The authors compiled a literature sample of 85 transiting brown dwarfs and low-mass stellar companions with masses ranging from $\sim13$ to $100\,M_{\text{Jup}}$. To ensure compatibility with the Baraffe et al. (2003) evolutionary models and to minimize uncertainties driven by age, the sample was rigorously filtered. The final analysis focused on 50 objects that satisfied the following criteria:

• Masses below $100\,M_{\text{Jup}}$.
• Ages less than 10 Gyr.
• Robust age uncertainties to ensure radius differences were attributable to model limitations rather than age errors.

The host stars in this sample spanned masses of $0.37–2.38\,M_{\odot}$, temperatures of $\sim3350–15900$ K, and metallicities of $-0.3$ to $+0.4$ dex. Companion separations ranged from $0.004$ to $0.317$ au, with 70% of the sample having separations $<0.1$ au.

To quantify radius inflation, the authors compared empirically measured radii against theoretical radii derived from the Baraffe et al. (2003) and Burrows et al. (2001) models. The comparison utilized a Monte Carlo approach with 1000 samplers to propagate errors, treating observed radii as Gaussian distributions, observed masses as Gaussian distributions, and host star ages as uniform distributions. The radius difference was defined as $(R_{\text{Empirical}} - R_{\text{Model}}) / R_{\text{Model}}$. Statistical significance was assessed using Jackknife sampling to determine median values and $1\sigma$ uncertainties.

Key Results

1. Population-Level Inflation: The analysis reveals a statistically significant radius inflation for the full sample of 50 objects. The median radius inflation is $8.7 \pm 1.9\%$, representing a $4.6\sigma$ discrepancy between observations and the Baraffe et al. (2003) models. A comparison with the Burrows et al. (2001) models yielded a slightly higher inflation of $10.4 \pm 2.0\%$ ($5.2\sigma$).
2. Mass Dependence: The majority of companions (34 out of 50) exhibit inflated radii, with 13 objects showing inflation greater than $3\sigma$. The inflation is more pronounced in the lower mass range ($0.01–0.04\,M_{\odot}$), where $\Delta R/R \approx 12.2 \pm 1.8\%$, compared to the higher mass range ($0.04–0.1\,M_{\odot}$), where $\Delta R/R \approx 7.9 \pm 2.5\%$.
3. Separation Dependence: A clear trend is observed where radius inflation decreases with increasing orbital separation. For companions at separations $\le 0.05$ au, the median inflation is $16 \pm 6\%$ ($2.7\sigma$). This inflation drops to $8.3 \pm 1.7\%$ ($5\sigma$) for separations of $0.05–0.1$ au, and further decreases to $6^{+7}_{-6}\%$ and $5^{+12}_{-5}\%$ for wider separations ($0.1–0.2$ au and $0.2–0.4$ au, respectively). The authors attribute this trend to reduced stellar irradiation at wider orbits.
4. Other Parameters: The study found no significant correlation between radius differences and equilibrium temperature or host star metallicity within the current sample.

Significance and Claims
The primary significance of this work lies in its validation of radius inflation as a population-level phenomenon in transiting brown dwarfs. By utilizing the largest literature compilation to date, the authors confirm that theoretical evolutionary models systematically underestimate the radii of these objects. The dependence of inflation on orbital separation suggests that stellar irradiation plays a critical role in the physical mechanisms driving this discrepancy, likely requiring modifications to current models to account for external heating effects.

The authors modestly note that while the trend with separation is clear, the sample size for wider orbits ($>0.1$ au) remains limited, necessitating larger datasets to fully validate these findings. The paper concludes by releasing the compiled dataset to the community to facilitate further characterization of substellar models, particularly for objects with larger sizes, younger ages, and lower metallicities.