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 ΔR/R are ≤10% but in (rare) cases may be ≥20%. Our magneto-convective stellar models have already replicated many empirical ΔR/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 ΔR/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 ΔR/R ≈ 90% occurs in stars with masses of 0.7 M ⊙. With B ceil = 100 kG, peak inflation with ΔR/R ≈ 140% occurs in stars with M ≈ 0.5 M ⊙. But with B ceil = 1 MG, we find no peak in ΔR/R as a function of δ; instead, the larger δ is, the larger ΔR/R becomes, reaching 300%–350% in the case of the largest δ considered. Thus, magneto-convective modeling can accommodate ΔR/R values which are considerably larger than any reported empirical inflations. We find that a maximum occurs in ΔR/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.