2010MNRAS.402.2609I

A number of substellar companions to evolved cool stars have now been reported. Cool giants are distinct from their progenitor main-sequence low-mass stars in a number of ways. First, the mass loss rates of cool giant stars are orders of magnitude greater than for the late-type main-sequence stars. Secondly, on the cool side of the Linsky-Haisch `dividing line', K and M giant stars are not X-ray sources, although they do show evidence for chromospheres. As a result, cool star winds are largely neutral for those spectral types, suggesting that planetary or brown dwarf magnetospheres will not be effective in standing off the stellar wind. In this case, one expects the formation of a bow shock morphology at the companion, deep inside its magnetosphere. We explore radio emissions from substellar companions to giant stars using (a) the radiometric Bode's law and (b) a model for a bow shock morphology. Stars that are X-ray emitters likely have fully ionized winds, and the radio emission can be at the milli-Jansky level in favourable conditions. Non-coronal giant stars produce only micro-Jansky level emissions when adjusted for low-level ionizations. If the largely neutral flow penetrates the magnetosphere, a bow shock results that can be strong enough to ionize hydrogen. The incoherent cyclotron emission is sub-micro-Jansky. However, the long wavelength radio emission of Solar system objects is dominated by the cyclotron maser instability (CMI) mechanism. Our study leads to the following two observational prospects. First, for coronal giant stars that have ionized winds, application of the radiometic Bode's law indicates that long wavelength emission from substellar companions to giant stars may be detectable or nearly detectable with existing facilities. Secondly, for the non-coronal giant stars that have neutral winds, the resultant bow shock may act as a `feeder' of electrons that is well embedded in the companion's magnetosphere. Incoherent cyclotron emissions are far too faint to be detectable, even with next generation facilities; however, much brighter flux densities may be achievable when CMI is considered.