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We examine the thermal free-free millimetre fluxes expected from non-dusty and non-pulsating K through mid-M giant stars based on our limited understanding of their inhomogeneous chromospheres. We present a semi-analytic model that provides estimates of the radio fluxes for the mm wavelengths (e.g., CARMA, ALMA, JVLA Q-band) based on knowledge of the effective temperatures, angular diameters and chromospheric Mg II h & k emission fluxes. At 250 GHz, the chromospheric optical depths are expected to be significantly less than unity, which means that fluxes across the mm and sub-mm range will have a contribution from the chromospheric mate- rial that gives rise to the ultraviolet emission spectrum, as well as the cool molecular material known to exist above the photosphere. We predict a lower bound to the inferred brightness temperature of red giants based on heating at the basal-flux limit if the upper chromospheres have filling factor 1. Multi-frequency mm observations should provide important new information on the structuring of the inhomogeneous chromospheres, including the boundary layer, and allow tests of competing theoretical models for atmospheric heating. We comment on the suitability of these stars as mm flux calibrators.

Detailed models of the chromospheres of the «hybrid» bright giants α TrA (K4 II), ι Aur (K3 II), γ Aql (K3 II) and θ Her (K1 II) are presented. The models run from the base of the chromosphere and into the transition region. The chromospheric models are based on radiative transfer calculations for a range of atoms and emission lines, including : Mg II h and k; Al II] λ2669 A; C II λ1335 A; C II] λ2325 A; Si II λλ1808.0, 1816.9 and 1817.5 A. The transition region models are made using standard emission measure techniques. The presence of steep turbulent velocity gradients leads to profiles of optically thin chromospheric emission lines that are strongly dependent on the distribution of emitting material with temperature

The present study compares ratios of Si II UV emission lines in a variety of objects with computations based on recently published collisional data of Dufton and Kingston (1991). A high-quality spectrum of Alpha Tau (K5 III) obtained by Carpenter et al. (1991) is analyzed using the G270M mode of the GHRS on the HST, in addition to high-dispersion data from Skylab and IUE. Agreement between observation and theory is satisfactory for most lines. A blend with a line of Ni II accounts partially for the discrepancies and solves a problem with semiforbidden S II emission measures. Disagreement exists between certain observed flux ratios and computed values using recent atomic data for the intersystem lines. The discrepancy is most significant for Alpha Tau. The computed atomic collision strengths within the intersystem multiplet itself are argued as a possible cause of the discrepancy.