Direct Measurements of Giant Star Effective Temperatures and Linear Radii: Calibration Against Spectral Types and V-K Color

Abstract

We calculate directly determined values for effective temperature ($T_{\rm EFF}$) and radius ($R$) for 191 giant stars based upon high resolution angular size measurements from optical interferometry at the Palomar Testbed Interferometer. Narrow- to wide-band photometry data for the giants are used to establish bolometric fluxes and luminosities through spectral energy distribution fitting, which allow for homogeneously establishing an assessment of spectral type and dereddened $V_{\rm 0}-K_{\rm 0}$ color; these two parameters are used as calibration indices for establishing trends in $T_{\rm EFF}$ and $R$. Spectral types range from G0III to M7.75III, $V_{\rm 0}-K_{\rm 0}$ from 1.9 to 8.5. For the $V_{\rm 0}-K_{\rm 0} = \{1.9,6.5\}$ range, median $T_{\rm EFF}$ uncertainties in the fit of effective temperature versus color are found to be less than 50K; over this range, $T_{\rm EFF}$ drops from 5050K to 3225K. Linear sizes are found to be largely constant at 11 $R_\odot$ from G0III to K0III, increasing linearly with subtype to 50 $R_\odot$ at K5III, and then further increasing linearly to 150 $R_\odot$ by M8III. Three examples of the utility of this data set are presented: first, a fully empirical Hertzsprung-Russell Diagram is constructed and examined against stellar evolution models; second, values for stellar mass are inferred based on measures of $R$ and literature values for $\log g$. Finally, an improved calibration of an angular size prediction tool, based upon $V$ and $K$ values for a star, is presented.