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We derive the velocity and mass-loss rate of a steady state Wolf-Rayet (WR) wind, using a nonisotropic diffusion approximation applied to the transfer between strongly overlapping spectral lines. Following the approach of Friend & Castor (1983), the line list is assumed to approximate a statistically parameterized Poisson distribution in frequency, so that photon transport is controlled by an angle-dependent, effectively gray opacity. We show the nonisotropic diffusion approximation yields good agreement with more accurate numerical treatments of the radiative transfer, while providing analytic insight into wind driving by multiple scattering. We illustrate, in particular, that multiple radiative momentum deposition does not require that potons be repeatedly reflected across substantial distances within the spherical envelope, but indeed is greatest when photons undergo a nearly local diffusion, e.g., through scattering by many lines closely spaced in frequency. Our results reiterate the view that the so-called 'momentum problem' of Wolf-Rayet winds is better characterized as an 'opacity problem' of simply identfying enough lines. One way of increasing the number of thick lines in Wolf-Rayet winds is to transfer opacity from saturated to unsaturated lines, yielding a steeper opacity distribution than that found in OB winds. We discuss the implications of this perspective for extending our approach to W-R wind models that incorporate a more fundamental treatment of the ionization and excitation processes that determine the line opacity. In particular, we argue that developing statistical descriptions of the lines to allow an improved effective opacity for the line ensemble would offer several advantages for deriving such more fundamental W-R wind models.

We reexamine the physics of flow driving by line scattering of a continuum radiation source to determine the degree to which such line scattering can heat as well as accelerate the flow. Within the framework of the Sobolev theory for line transfer, we argue that the finite thermal width of the line scattering profile can lead to a significant 'Doppler heating' via photon frequency redistribution within a Sobolev resonance layer. Quantitative computation of this heating shows, however, that it is largely canceled by a corresponding cooling by the diffuse radiation. The resulting reduction in net Doppler heating or cooling means that the overall effect is only of limited importance in the energy balance of line-driven stellar winds. Through simple scaling relations, we compare the effect to other competing heating or cooling terms, including the ion-drag frictional heating recently discussed by Springmann and Pauldrach. We also provide a physical explanation of the unexpected cooling effect, and comment that its near cancellation of the anticipated heating provides another example of the tendency for ideal Sobolev theory to apply to a higher order than expected.

The conditions necessary for partially coherent scattering to influence the thermalization depth are investigated, and the effects of partial redistribution in homogeneous slab atmospheres are approximated using several common resonance lines as examples. For electron densities above 10 exp 10/cu cm, it is concluded that even when coherent scattering dominates the escape process, the thermalization depths of the strongest resonance lines of H, Ca II, and Mg II agree roughly with the Doppler diffusion in frequency. No elastic scattering effects on the thermalization of Mg II h and k and Ca II H and K are found. At lower densities, such as for giant star chromospheres and QSO models, the results deviate strongly from the Doppler complete redistribution case.

Using transition region fluxes and high resolution spectra of the Ly-alpha and Mg II h and k lines observed by the GHRS spectrograph, I determine the total flux radiated from each temperature regime in the Capella upper chromosphere and transition region. This contains essentially the same information as the emission measure distribution, but to better suggest physical interpretations of the heating mechanisms it is expressed instead in terms of the efficiency for extracting convection zone energy flux and depositing it over the temperature ranges considered.

Time-dependent H-alpha profiles were computed for the dynamic model atmospheres of Fisher, Canfield, and McClymont (1985) simulating the effects of an intense impulsively initiated power-law beam of electrons incident on the chromosphere. The temporal response of H-alpha arises from three separate physical mechanisms, whose relative importance varies over the line profile. The fastest variations (typically less than 0.1 s for the explosive heating discussed here) arise from energy imbalance; these are apparent on chromospheric heating and cooling time scales and have their greatest amplitude at line center. Slower variations arise from ionization imbalance and are most apparent in the blue wing. The slowest variations arise from hydrodynamic effects and are related to the formation of a chromospheric condensation; these are most apparent in the red wing. These results provide a basis for the design and analysis of observations of H-alpha, in coordination with hard X-rays or microwaves, to test mechanisms of energy transport in solar flares.

In order to understand the temporal relationship between H alpha and hard X-ray emission predicted by the nonthermal electron thick target model of impulsive-phase energy transport the time-dependent theoretical H alpha profiles were computed for the dynamic model atmospheres of Fisher, Canfield, and McClymont, which simulate the effects of an impulsively initiated power-law beam of electrons. On the basis of the physical analysis it was expected that a very rapid H alpha response to an instantaneous increase in the flux of a nonthermal deka-keV electron beam, as compared to the timescale associated with the propagation of these electrons over characteristic flare coronal loop spatial scales. It was concluded that observational efforts to test the thick target nonthermal electron model through detection of impulsive H alpha brightenings associated with impulsive hard X-ray or microwave bursts should initially focus attention on the H alpha line center. Additional simultaneous blue-wing measurements will have substantial diagnostic potential.