Calculations of the far-wing line profiles of sodium and potassium in the atmospheres of substellar-mass objects

At the low temperatures achieved in cool brown dwarf and hot giant planet atmospheres, the less refractory neutral alkali metals assume an uncharacteristically prominent role in spectrum formation. In particular, the wings of the Na-D (5890 Å) and K I (7700 Å) resonance lines come to define the continuum and dominate the spectrum of T dwarfs from 0.4 to 1.0 μm. Whereas in standard stellar atmospheres the strengths and shapes of the wings of atomic spectral lines are rarely needed beyond 25 Å from a line center, in brown dwarfs the far wings of the Na and K resonance lines out to thousands of angstroms detunings are important. Using standard quantum chemical codes and the unified Franck-Condon model for line profiles in the quasi-static limit, we calculate the interaction potentials and the wing line shapes for the dominant Na and K resonance lines in H₂- and helium-rich atmospheres. Our theory has natural absorption profile cutoffs, has no free parameters, and is readily adapted to spectral synthesis calculations for stars, brown dwarfs, and planets with effective temperatures below 2000 K.