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In this paper we have extended 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 include in all equations the flow velocity terms and 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 H and He. 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. Also, 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 due to the effects of flows. In this paper we use fixed conditions at the base of the transition region and in the chromosphere because our intent is to show the physical effects of flows and not to match any particular observations. However, we note that the profiles we compute can explain the range of observed high spectral and spatial resolution Lyman alpha profiles 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., Comment: 50 pages + 20 figures; submitted to ApJ 9/10/01; a version with higher resolution figures is available at http://cfa-www.harvard.edu/~avrett/

In our previous papers we described the mathematical formalism and the computed results for energy-balance hydrostatic models of the solar transition region. In this paper we discuss in some detail the limitations of the hydrostatic and one-dimensional assumptions used. Then we analyze the determination of helium emission when diffusion is included. We use transport coefficients estimated from kinetic theory to determine the helium departures from local ionization balance. We calculate the helium spectra for each of our models and evaluate the role of helium in the energy transport. Also, we investigate the effects of coronal illumination on the structure of the transition region and upper chromosphere, and show how coronal illumination affects various EUV lines and the He I 10830 A line. Comparing with both absolute intensities and detailed line profiles, we show that our models are consistent not only with the observed hydrogen spectra but also with the available helium spectra.

A non-LTE radiative transfer investigation of the emission lines is conducted at 7 and 12 microns using a realistic atomic model for neutral magnesium. An average quiet sun atmospheric model is used to calculate emission-line profiles that resemble the observed ones, i.e., broad absorption troughs with narrow central emission, and significant limb brightening. The charge exchange rates are found to be significant, but the effects of high-n coupling between Mg and Mg(+) together with radiative low-n transitions are of greater importance. It is confirmed that the emission cores are formed no higher than the temperature minimum region, and that the emission is caused by non-LTE effects rather than by the chromospheric temperature rise. It is inferred from the model calculations that the line core is sensitive to magnetic fields located almost 400 km above those measured in ordinary magnetograms; the gas pressure decreases 20-fold between these two heights.

The radiation of energy by hydrogen lines and continua in hydrostatic energy-balance models of the transition region between the solar chromosphere and corona is studied using models which assume that mechanical or magnetic energy is dissipated in the hot corona and is then transported toward the chromosphere down the steep temperature gradient of the transition region. These models explain the average quiet sun and also the entire range of variability of the Ly-alpha lines. The relations between the downward energy flux, the pressure of the transition region, and the different hydrogen emission are described.

The energy balance in the lower transition region is analyzed by constructing theoretical models which satisfy the energy balance constraint. The energy balance is achieved by balancing the radiative losses and the energy flowing downward from the corona. This energy flow is mainly in two forms: conductive heat flow and hydrogen ionization energy flow due to ambipolar diffusion. Hydrostatic equilibrium is assumed, and, in a first calculation, local mechanical heating and Joule heating are ignored. In a second model, some mechanical heating compatible with chromospheric energy-balance calculations is introduced. The models are computed for a partial non-LTE approach in which radiation departs strongly from LTE but particles depart from Maxwellian distributions only to first order. The results, which apply to cases where the magnetic field is either absent, or uniform and vertical, are compared with the observed Lyman lines and continuum from the average quiet sun. The approximate agreement suggests that this type of model can roughly explain the observed intensities in a physically meaningful way, assuming only a few free parameters specified as chromospheric boundary conditions.

The integral-operator method is extended to line and continuum transfer calculations for static and expanding spherical radiating atmospheres. A relationship is defined between radiative transfer and the source function at particular optical depths. Linearized equations are developed for the mean intensity, monochromatic scattering, line transfer, and line transfer with absorption. Numerical solutions are obtained for each equation, as well as for background absorption and scattering, partial redistribution when the line source is frequency dependent, and line transfer in connection with the expansion velocity. Finally, a solution is found for spherical expansion in concert with partial redistribution and Doppler line broadening.