Abstract
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 ($0.15 M/M_ødot 0.6$) 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 ($>0.25 M_ødot$) 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.
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