Richard N. Thomas

The Source Function in a Non-Equilibrium Atmosphere. II. The Depth Dependence of the Source Function for Resonance and Strong Subordinate Lines.

ABSTRACT We obtain an algebraic solution for the depth variation of the source function SL (r) for resonance and strong subordinate lines by using the Eddington approximation plus the method of discrete ordinates. We show that if an observed line profile, produced in an atmosphere with the above Sl (r), is analyzed under the assumption of local thermodynamic equilibrium, an underestimate of T6(t) in the outer atmospheric layer results. The derived Sl(t) agrees in qualitative behavior with the source function found empirically by Athay and Thomas for the early Balmer lines of hydrogen.

The Temperature Control Bracket

Temperature control bracket energy equation as measure of temperature distribution in pure hydrogen stellar atmosphere, considering electron energy and radiation field

On the Dependence of T_{e} upon Quantity Versus Quality of the Radiation Field in a Stellar Atmosphere

Stellar atmosphere radiation field quantity vs quality, deriving electron temperature as function of tau

Sun-Hot Star Contrast in Chromospheric/Coronal Te(r). Nonradiative Heating vs. Outflow Enhanced Opacity

We present a condensed perspective on the contribution of studies of normal and peculiar hot stars to delineating facts/implications of chromosphere/coronae occurring throughout the HRD: (1) empirical evidence of nonradiative heating in hot stars atmospheres, with a strong continuum opacity dependence of the Te(r)-rise, like the Sun; (2) the observed existence of a multi-regional atmospheric structure, linked to nonradiative energy (Te-rise, grad ρ-fall) and mass (grad ρ-fall, Te-change) fluxes, like the Sun; (3) an observed long-term (decades) variability of all atmospheric regions and all energy and mass fluxes, in some well-observed stars, which implies that the character of atmospheric regions follows, not produces, the character of the stellar fluxes; (4) the strong suggestion by (2) and (4) of a stellar interior origin for the mass flux; (5) a representation/delineation of (1)-(2), and of the solar, hot star contrast, via the Temperature-Control-Bracket logic; (6) a clarification/modeling of the ensemble interior and atmosphere via an expanded Eddington, general, nonEquilibrium thermodynamics.

RADIATION TRANSFER PROBLEMS IN THE ROCKET ULTRA-VIOLET LINES

WE PRESENT here a summary of a current investigation of the radiative transfer problem in the solar corona, in its effect upon the excitation state of coronal ions. [Complete details of the investigation will be published elsewhere; C. PECKER and THOMAS”).] The investigation is one phase of a systematic treatment of the influence of ionic configuration and physical environment upon the excitation state of an ion. We have called this treatment the New Spectroscopy, to contrast it with the Local Thermodynamic Equilibrium treatment of a gas, where the excitation state of an ion depends only upon the local electron temperature, and is independent of ionic configuration or the physical environment. The situation usually assumed for the solar corona falls, conceptually, intermediate to the LTE situation and that of the chromososphere and photosphere. The coronal optical thickness is taken to be so small that any radiation field produced by the corona itself has negligible effect upon excitation of the ions. Consequently, the excitation state depends upon ionic configuration, but only locally upon physical environment. That is, the excitation state at a point depends only upon the values of electron density, electron temperature, and photospheric radiation field at the point. It does not depend upon the atmosphere as a whole-upon values of electron density and temperature at other points in the atmosphere-as it would were the optical thickness of the atmosphere large enough to produce significant self-emission. In the present work we have asked whether the assumption of negligible optical thickness for the corona is valid and, if not, what is the influence of coronal self-emission as a function of coronal optical thickness. We show that an upper limit on the effect of coronal self-emission in any transition comes from isolating the transition to solve the radiative transfer problem in it. That is, the actual atomic configuration is replaced by that of the 2-level-atom. Thus this upper limit does not depend upon ionic configuration, but only upon physical environment. An estimate of the largest optical depths likely to be encountered in resonance transitions of the most abundant ions falls below 104. At coronal densities, the ratio of collisional to radiative de-excitation, c, does not exceed 10-r. In this situation, the excitation effect due to coronal self-emission in some transition can be expressed as a function only of the coronal optical thickness in this transition, for an isothermal, constant-ns corona. Numerical results are given in the complete investigation cited. Here, we note only that a detection of the presence of a significant, optical depth in some line, by observing a self-reversed emission profile, appears to demand an optical thickness exceeding a value which lies between 10 and 100.

DEPARTURES FROM THE SAHA EQUATION FOR IONIZED HELIUM. I. CONDITION OF DETAILED BALANCE IN THE RESONANCE LINES

Conditions for the validity of the assumption of detailed balance in the Lyman lines of He/sub 11/ are investigated. An opacity of 10/sup 6/ in Lyman- alpha is required, which implies high opacity in the subordinate lines and resonance continuum. The b/sub n/-factors are computed, including the transfer problem in the subordinate lines and resonance continuum. (auth)