Theoretical uncertainties on the radius of low- and very-low-mass stars

We performed an analysis of the main theoretical uncertainties that affect the radius of low- and very-low-mass stars predicted by current stellar models. We focused on stars in the mass range 0.1-1M⊙, on both the zero-age main sequence (ZAMS) and on 1, 2, and 5 Gyr isochrones. First, we quantified the impact on the radius of the uncertainty of several quantities, namely the equation of state, radiative opacity, atmospheric models, convection efficiency, and initial chemical composition. Then, we computed the cumulative radius error stripe obtained by adding the radius variation due to all the analysed quantities. As a general trend, the radius uncertainty increases with the stellar mass. For ZAMS structures the cumulative error stripe of very-low-mass stars is about ±2 and ±3 per cent, while at larger masses it increases up to ±4 and ±5 per cent. The radius uncertainty gets larger and age dependent if isochrones are considered, reaching for M ~ 1M⊙ about +12(-15) per cent at an age of 5Gyr. We also investigated the radius uncertainty at a fixed luminosity. In this case, the cumulative error stripe is the same for both ZAMS and isochrone models and it ranges from about ±4 to +7 and +9(-5) per cent. We also showed that the sole uncertainty on the chemical composition plays an important role in determining the radius error stripe, producing a radius variation that ranges between about ±1 and ±2 per cent on ZAMS models with fixed mass and about ±3 and ±5 per cent at a fixed luminosity.