A polytropic model is used to investigate the effects of dark photospheric spots on the evolution and radii of magnetically active , low-mass ( M < 0.5 M _ { \odot } ) , pre-main sequence ( PMS ) stars .
Spots slow the contraction along Hayashi tracks and inflate the radii of PMS stars by a factor of ( 1 - \beta ) ^ { - N } compared to unspotted stars of the same luminosity , where \beta is the equivalent covering fraction of dark starspots and N \simeq 0.45 \pm 0.05 .
This is a much stronger inflation than predicted by the models of Spruit & Weiss ( 1986 ) for main sequence stars with the same \beta , where N \sim 0.2 –0.3 .
These models have been compared to radii determined for very magnetically active K- and M-dwarfs in the young Pleiades and NGC 2516 clusters , and the radii of tidally-locked , low-mass eclipsing binary components .
The binary components and ZAMS K-dwarfs have radii inflated by \sim 10 per cent compared to an empirical radius-luminosity relation that is defined by magnetically inactive field dwarfs with interferometrically measured radii ; low-mass M-type PMS stars , that are still on their Hayashi tracks , are inflated by up to \sim 40 per cent .
If this were attributable to starspots alone , we estimate that an effective spot coverage of 0.35 < \beta < 0.51 is required .
Alternatively , global inhibition of convective flux transport by dynamo-generated fields may play a role .
However , we find greater consistency with the starspot models when comparing the loci of active young stars and inactive field stars in colour-magnitude diagrams , particularly for the highly inflated PMS stars , where the large , uniform temperature reduction required in globally inhibited convection models would cause the stars to be much redder than observed .