A search for radius inflation among active M-dwarfs in Praesepe

Rotation periods from Kepler K2 are combined with projected rotation velocities from the WIYN 3.5-m telescope, to determine projected radii for fast-rotating, low-mass ($0.15 \leq M/M_{\odot} \leq 0.6$) members of the Praesepe cluster. A maximum likelihood analysis that accounts for observational uncertainties, binarity and censored data, yields marginal evidence for radius inflation -- the average radius of these stars is $6\pm4$ per cent larger at a given luminosity than predicted by commonly-used evolutionary models. This over-radius is smaller (at 2-sigma confidence) than was found for similar stars in the younger Pleiades using a similar analysis; any decline appears due to changes occurring in higher mass ($>0.25 M_{\odot}$) stars. Models incorporating magnetic inhibition of convection predict an over-radius, but do not reproduce this mass dependence unless super-equipartition surface magnetic fields are present at lower masses. Models incorporating flux-blocking by starspots can explain the mass dependence but there is no evidence that spot coverage diminishes between the Pleiades and Praesepe samples to accompany the decline in over-radius. The fastest rotating stars in both Praesepe and the Pleiades are significantly smaller than the slowest rotators for which a projected radius can be measured. This may be a selection effect caused by more efficient angular momentum loss in larger stars leading to their progressive exclusion from the analysed samples. Our analyses assume random spin-axis orientations; any alignment in Praesepe, as suggested by Kovacs (2018), is strongly disfavoured by the broad distribution of projected radii.