Geometry Diagnostics of a Stellar Flare from Fluorescent X-rays

We present evidence of Fe fluorescent emission in the Chandra HETGS spectrum of the single G-type giant HR 9024 during a large flare. In analogy to solar X-ray observations, we interpret the observed Fe K$\alpha$ line as being produced by illumination of the photosphere by ionizing coronal X-rays, in which case, for a given Fe photospheric abundance, its intensity depends on the height of the X-ray source. The HETGS observations, together with 3D Monte Carlo calculations to model the fluorescence emission, are used to obtain a direct geometric constraint on the scale height of the flaring coronal plasma. We compute the Fe fluorescent emission induced by the emission of a single flaring coronal loop which well reproduces the observed X-ray temporal and spectral properties according to a detailed hydrodynamic modeling. The predicted Fe fluorescent emission is in good agreement with the observed value within observational uncertainties, pointing to a scale height $\lesssim 0.3$\rstar. Comparison of the HR 9024 flare with that recently observed on II Peg by Swift indicates the latter is consistent with excitation by X-ray photoionization.