Estimating magnetic filling factors from Zeeman–Doppler magnetograms

V.S., S.P.M., and A.J.F.acknowledge funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreement No. 682393 AWESoMeStars). S.B.S. acknowledges funding via the Austrian Space Application Programme (ASAP) of the Austrian Research Promotion Agency (FFG) within ASAP11, the FWF NFN project S11601-N16 and the sub-project S11604-N16. A. A.V. acknowledges funding received from the Irish Research Council Laureate Awards 2017/2018.Low-mass stars are known to have magnetic fields that are believed to be of dynamo origin. Two complementary techniques are principally used to characterize them. Zeeman–Doppler imaging (ZDI) can determine the geometry of the large-scale magnetic field while Zeeman broadening can assess the total unsigned flux including that associated with small-scale structures such as spots. In this work, we study a sample of stars that have been previously mapped with ZDI. We show that the average unsigned magnetic flux follows an activity-rotation relation separating into saturated and unsaturated regimes. We also compare the average photospheric magnetic flux recovered by ZDI, BV, with that recovered by Zeeman broadening studies, BI. In line with previous studies, BV ranges from a few % to ~20% of BI. We show that a power-law relationship between BV and BI exists and that ZDI recovers a larger fraction of the magnetic flux in more active stars. Using this relation, we improve on previous attempts to estimate filling factors, i.e., the fraction of the stellar surface covered with magnetic field, for stars mapped only with ZDI. Our estimated filling factors follow the well-known activity-rotation relation, which is in agreement with filling factors obtained directly from Zeeman broadening studies. We discuss the possible implications of these results for flux tube expansion above the stellar surface and stellar wind models.Publisher PDFPeer reviewe