On the Possibility of an Upper Limit on Magnetically Induced Radius Inflation in Low-mass Stars

Abstract

The radii of low-mass stars are observed to be inflated above standard model predictions, especially in magnetically active stars. Typically, the empirical relative radius inflations Δ R / R are ≤10% but in (rare) cases may be ≥20%. Our magneto-convective stellar models have already replicated many empirical Δ R / R values. Here, we ask: is there any theoretical upper limit on the amount of such inflation? We use our magneto-convective model to compute Δ R / R using empirically plausible values of the surface field strength parameter δ . Inside each model, the maximum internal field is set to a particular value: B _ceil = 10, or 100 kG, or 1 MG. When B _ceil = 10 kG, peak inflation with Δ R / R ≈ 90% occurs in stars with masses of 0.7 M _⊙ . With B _ceil = 100 kG, peak inflation with Δ R / R ≈ 140% occurs in stars with M ≈ 0.5 M _⊙ . But with B _ceil = 1 MG, we find no peak in Δ R / R as a function of δ ; instead, the larger δ is, the larger Δ R / R becomes, reaching 300%–350% in the case of the largest δ considered. Thus, magneto-convective modeling can accommodate Δ R / R values which are considerably larger than any reported empirical inflations. We find that a maximum occurs in Δ R / R as a function of δ only in model stars where the field reaches its maximum strength B _ceil inside the convective envelope. Moreover, our models of completely convective stars undergo smaller amounts of relative radius inflation than models with radiative cores, a result consistent with some previous reports.

Keywords

• Late-type dwarf stars
• M dwarf stars
• Magnetic stars
• Stellar interiors