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Context: When crossing the Hertzsprung gap, intermediate-mass stars develop aconvective envelope. Fast rotators on the main sequence, or Ap stardescendants, are expected to become magnetic active subgiants during thisevolutionary phase. Aims: We compare the surface magnetic fields and activityindicators of two active, fast rotating red giants with similar masses andspectral class but diferent rotation rates - OU And (Prot=24.2 d) and 31 Com(Prot=6.8 d) - to address the question of the origin of their magnetism andhigh activity.  Methods: Observations were carried out with the Narval spectropolarimeter in2008 and 2013.We used the least squares deconvolution technique to extractStokes V and I profiles to detect Zeeman signatures of the magnetic field ofthe stars. We provide Zeeman-Doppler imaging, activity indicator monitoring,and a precise estimation of stellar parameters. We use stellar evolutionarymodels to infer the evolutionary status and the initial rotation velocity onthe main sequence.  Results: The detected magnetic field of OU And is a strong one. Itslongitudinal component Bl reaches 40 G and presents an about sinusoidalvariation with reversal of the polarity. The magnetic topology of OU And isdominated by large scale elements and is mainly poloidal with an importantdipole component, and a significant toroidal component. The detected magneticfield of 31 Com is weaker, with a magnetic map showing a more complex fieldgeometry, and poloidal and toroidal components of equal contributions. Theevolutionary models show that the progenitors of OU And and 31 Com must havebeen rotat  Conclusions: OU And appears to be the probable descendant of a magnetic Apstar, and 31 Com the descendant of a relatively fast rotator on the mainsequence.

The different origins of magnetic fields and activity in the Hertzsprung gap stars, OU Andromedae and 31 Comae