Modelling the hidden magnetic field of low-mass stars

Abstract

Zeeman-Doppler imaging is a spectropolarimetric technique that is used to map\nthe large-scale surface magnetic fields of stars. These maps in turn are used\nto study the structure of the stars' coronae and winds. This method, however,\nmisses any small-scale magnetic flux whose polarisation signatures cancel out.\nMeasurements of Zeeman broadening show that a large percentage of the surface\nmagnetic flux may be neglected in this way. In this paper we assess the impact\nof this 'missing flux' on the predicted coronal structure and the possible\nrates of spin down due to the stellar wind. To do this we create a model for\nthe small-scale field and add this to the Zeeman-Doppler maps of the magnetic\nfields of a sample of 12 M dwarfs. We extrapolate this combined field and\ndetermine the structure of a hydrostatic, isothermal corona. The addition of\nsmall-scale surface field produces a carpet of low-lying magnetic loops that\ncovers most of the surface, including the stellar equivalent of solar 'coronal\nholes' where the large-scale field is opened up by the stellar wind and hence\nwould be X-ray dark. We show that the trend of the X-ray emission measure with\nrotation rate (the so-called 'activity-rotation relation') is unaffected by the\naddition of small-scale field, when scaled with respect to the large-scale\nfield of each star. The addition of small-scale field increases the surface\nflux; however, the large-scale open flux that governs the loss of mass and\nangular momentum in the wind remains unaffected. We conclude that spin-down\ntimes and mass loss rates calculated from surface magnetograms are unlikely to\nbe significantly influenced by the neglect of small-scale field.\n