ON THE INTERPRETATION OF CHROMOSPHERIC EMISSION-LINES

There exist in the literature important differences in the interpretation of ultraviolet emission lines formed below ∼104 K, temperatures characteristic of stellar chromospheres. This paper reexamines emission-line formation using detailed radiative transfer calculations and simpler methods based on approximate line cooling rates, including escape probabilities. Cooling integrals yield frequency-integrated line fluxes which can be estimated without a full solution of the statistical equilibrium and radiative transfer equations. In the effectively thin limit the approximations reduce to the "coronal" approximation. Approximations for the cooling integrals are examined and are demonstrated to work well for "effectively thin" chromospheric lines. Two cases have been identified, whose behavior can be understood using Ayres's chromospheric scaling laws relating global chromospheric structure to stellar properties: 1. For inactive stars (e.g., cool giants; the case of α Tau (K5 III) is studied in detail) lines such as Mg II k thermalize in the upper photosphere, and they are effectively thin in the entire chromosphere. Chromospheric integrated line fluxes and cooling rates can be reliably calculated using complete redistribution, escape probability, and even optically thin approximations. Emission measure and similar techniques can be applied to such lines. 2. For more active stars like the Sun the lines thermalize in the chromosphere (a well-established result). Partial redistribution calculations are required to obtain reliable line-integrated fluxes and cooling rates: other approximations yield gross overestimates owing to transfer-dependent thermalization properties. Great care must be taken when applying emission measure techniques to these lines. Analyses based on the "coronal approximation" (effectively thin lines) should be used with great care because chromospheric line fluxes are generated over regions spanning several gas pressure scale heights where hv/kTe ≫ 1. Line fluxes are the result of a convolution of the atomic excitation physics and the thermal atmospheric structure, hence model atmosphere techniques are generally required to derive information on the chromospheric emitting regions. The implications of this study for past and future studies of the outer atmospheres of cool stars are discussed. Unfortunately, some authors have oversimplified the analyses of chromospheric line fluxes leading to incorrect and misleading conclusions. The arguments presented also apply in principle to emission lines formed below 104 K in other astrophysical situations (e.g., broad-line emitting regions of active galactic nuclei).