Energy balance in the solar transition region. IV. Hydrogen and helium mass flows with diffusion

In this paper we extend our previous modeling of energy balance in the chromosphere-corona transition region to cases with particle and mass flows. The cases considered here are quasi-steady and satisfy the momentum and energy balance equations in the transition region. We assume one-dimensional geometry and include the flow velocity terms in all equations, but we neglect the partial derivatives with respect to time. We present a complete and physically consistent formulation and method for solving the non-LTE and energy balance equations in these situations, including both particle diffusion and flows of Hand He. Our calculations include partial frequency redistribution in the Lyalpha and Lybeta lines. Our results show quantitatively how mass flows affect the ionization and radiative losses of H and He, thereby affecting the structure and extent of the transition region. Furthermore, our computations show that the H and He line profiles are greatly affected by flows. We find that line shifts are much less important than the changes in line intensity and central reversal as a result of the influence of flows on the excitation and ionization. In this paper we use fixed conditions at the base of the transition region and in the underlying chromosphere. Our intent is to show the physical effects of flows on the transition region, not to match any particular observations. However, our computed Lyalpha profiles can account for the range of observed high spectral and spatial resolution from the quiet Sun. We suggest that dedicated modeling of specific sequences of observations based on physically consistent methods like those presented here will substantially improve our understanding of the energy balance in the chromosphere and corona.