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Hummer, D. G.

Publications and source records attributed to Hummer, D. G..

At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

NLTE model stellar atmospheres with line blanketing near the series limits

In this paper we study the influence of line-merging regions at the intermediate long-wavelength side of a continuum threshold on the computed model atmosphere structure and predicted spectrum. In order to model these regions sufficiently accurately, we have developed two concepts. First, we have extended the occupation probability formalism of Hummer and Mihalas to non-local thermodynamic equilibrium (non-LTE) plasmas. Second, in order to treat the very complicated opacity in the line merging region, we have generalized the concept of opacity distribution functions to treat non-LTE situations. All Rydberg states are consistently included within this framework, so that no arbitrary cutoff of high (LTE) levels is made. We have calculated several pure hydrogen models atmospheres for two effective temperatures, T(sub eff) = 20000 and 35000 K, and discussed the differences between models calculated with various treatments of the line merging. In particular, we have shown that the error in the predicted profiles of Balmer lines resulting from the neglect of line merging is typically of the order of 3-4%, while the errors in the far-UV portion of the Balmer continuum reaches 15-35%. The errors generally decrease with increasing effective temperature. At the same time, the internal accuracy of the models is shown to be about or below 0.5% for all predicted spectral features. We conclude that for interpreting current high-accuracy spectrophotometric observations models including the line merging are necessary, and that the formalism developed in this paper is capable of providing a sufficiently accurate and robust modeling technique.

Hubeny, I.↗
NASA NTRS1992

The Sobolev approximation for line formation with partial frequency redistribution

Attention is given to the formation of a spectral line in a uniformly expanding infinite medium in the Sobolev approximation, with emphasis on the various mechanisms for frequency redistribution. Numerical and analytic solutions of the transfer equation are presented of a number of redistribution functions and their approximations, including type I and type II partial redistribution, coherent scattering and complete redistribution, and the Fokker-Planck and uncorrelated approximation to the R sub II function. The solutions for the mean intensity are shown to depend very much on the type of redistribution mechanism, while for the frequency-weighted mean intensity, which enters the rate equations, this dependence is weak. It is inferred that use of Sobolev escape probabilities based on complete redistribution can be an adequate approximation for many calculations for which only the radiative excitation rates are needed.

Hummer, D. G.↗
NASA NTRS1992

Recombination line intensities for hydrogenic ions. III - Effects of finite optical depth and dust

The effect on the recombination spectrum of hydrogen arising from: (1) finite optical thickness in the Lyman lines; (2) the overlapping of Lyman lines near the series limit; (3) the absorption of Lyman lines by dust or photoionization, and (4) the long-wave radiation emitted by dust is examined. Full account is taken of electron and heavy particle collisions in redistributing energy and angular momentum. It is seen that each of these deviations from the classical Case B leads to observable effects, and that dust influences the recombination spectrum in characteristic ways that may make possible new observational constraints on dust properties in nebulosities. On the basis of these calculations it is believed that the uncertainty in the determination of the helium-to-hydrogen abundance ratio in the universe may be larger than currently claimed.

Hummer, D. G.↗
NASA NTRS1991

The solution of radiative transfer problems in molecular bands without the LTE assumption by accelerated lambda iteration methods

An iterative method based on the use of approximate transfer operators, which was designed initially to solve multilevel NLTE line formation problems in stellar atmospheres, is adapted and applied to the solution of the NLTE molecular band radiative transfer in planetary atmospheres. The matrices to be constructed and inverted are much smaller than those used in the traditional Curtis matrix technique, which makes possible the treatment of more realistic problems using relatively small computers. This technique converges much more rapidly than straightforward iteration between the transfer equation and the equations of statistical equilibrium. A test application of this new technique to the solution of NLTE radiative transfer problems for optically thick and thin bands (the 4.3 micron CO2 band in the Venusian atmosphere and the 4.7 and 2.3 micron CO bands in the earth's atmosphere) is described.

Kutepov, A. A.↗
NASA NTRS1991

An accelerated lambda iteration method for multilevel radiative transfer. I - Non-overlapping lines with background continuum

A method is presented for solving multilevel transfer problems when nonoverlapping lines and background continuum are present and active continuum transfer is absent. An approximate lambda operator is employed to derive linear, 'preconditioned', statistical-equilibrium equations. A method is described for finding the diagonal elements of the 'true' numerical lambda operator, and therefore for obtaining the coefficients of the equations. Iterations of the preconditioned equations, in conjunction with the transfer equation's formal solution, are used to solve linear equations. Some multilevel problems are considered, including an eleven-level neutral helium atom. Diagonal and tridiagonal approximate lambda operators are utilized in the problems to examine the convergence properties of the method, and it is found to be effective for the line transfer problems.

Rybicki, G. B.↗
NASA NTRS1991

Asymptotic expansions of the kernel functions for line formation with continuous absorption

Asymptotic expressions are obtained for the kernel functions M2(tau, alpha, beta) and K2(tau, alpha, beta) appearing in the theory of line formation with complete redistribution over a Voigt profile with damping parameter a, in the presence of a source of continuous opacity parameterized by beta. For a greater than 0, each coefficient in the asymptotic series is expressed as the product of analytic functions of a and eta. For Doppler broadening, only the leading term can be evaluated analytically.

Hummer, D. G.↗
NASA NTRS1990

The equation of state for stellar envelopes. IV - Thermodynamic quantities and selected ionization fractions for six elemental mixes

The free-energy minimization technique in the form developed in the preceding papers in this series is employed to evaluate thermodynamic quantities and ionization fractions on a fine temperature and density grid for six astrophysical mixtures of 15 elements. The mixtures range from that appropriate to super-metal-rich stars, through solar abundance, to that for extreme Population II objects. In this paper, the results for solar abundances are summarized in a form that is illustrative and which facilitates comparison with the results from other equation of state calculations.

Mihalas, Dimitri↗
NASA NTRS1990

Quantitative spectroscopy of hot stars

A review on the quantitative spectroscopy (QS) of hot stars is presented, with particular attention given to the study of photospheres, optically thin winds, unified model atmospheres, and stars with optically thick winds. It is concluded that the results presented here demonstrate the reliability of Qs as a unique source of accurate values of the global parameters (effective temperature, surface gravity, and elemental abundances) of hot stars.

Kudritzki, R. P.↗
NASA NTRS1989

Photospheres of hot stars. III - Luminosity effects at spectral type 09.5

Hydrogen and helium line profiles with high signal-to-noise ratios were obtained for four stars of spectral type 09.5 (Alpha Cam, Xi Ori A, Delta Ori A,AE Aur) that form a sequence in luminosity: Ia, Ib, II, V. The basic stellar parameters of these stars are determined by fitting the observed line profiles of weak photospheric absorption lines with profiles from models which include the effect of radiation scattered back onto the photosphere from their stellar winds, an effect referred to as wind blanketing. For these stars, the inclusion of wind blanketing is significant only for the most luminous star, Alpha Cam, for which the effective temperature was shifted about -2000 K relative to an unblanketed model.

Voels, Stephen A.↗
NASA NTRS1988

The equation of state for stellar envelopes. III - Thermodynamic quantities

A method is described for deriving general expressions for all thermodynamic quantities of interest of a partially ionized multicomponent gas in terms of derivatives of the free energy. Explicit analytical formulas for all derivatives required in the evaluation of these quantities are given. Representative results for a hydrogen-helium mixture are shown.

Daeppen, Werner↗
NASA NTRS1988

The equation of state for stellar envelopes. I - An occupation probability formalism for the truncation of internal partition functions

An equation of state for material in stellar envelopes, subject to the limits of temperature less than about 10 to the 7th K and density less than about .01 g/cu cm is presented. The equation makes it possible to express free energy as the sum of several terms representing effects such as partial degeneracy of the electron, Coulomb interactions among charged particles, finite-volume, hard sphere repulsion, and van der Waals attraction. An occupation probability formalism is used to represent the effects of the plasma in establishing a finite partition function. It is shown that the use of the static screened Coulomb potential to calculate level shifts and to estimate the cutoff of the internal partition function is invalid. For most of the parameter space relevant to stellar envelopes, perturbations arising from the plasma ions are shown to be dominant in establishing the internal partition function.

Hummer, D. G.↗
NASA NTRS1988

The equation of state for stellar envelopes. II - Algorithm and selected results

A free-energy-minimization method for computing the dissociation and ionization equilibrium of a multicomponent gas is discussed. The adopted free energy includes terms representing the translational free energy of atoms, ions, and molecules; the internal free energy of particles with excited states; the free energy of a partially degenerate electron gas; and the configurational free energy from shielded Coulomb interactions among charged particles. Internal partition functions are truncated using an occupation probability formalism that accounts for perturbations of bound states by both neutral and charged perturbers. The entire theory is analytical and differentiable to all orders, so it is possible to write explicit analytical formulas for all derivatives required in a Newton-Raphson iteration; these are presented to facilitate future work. Some representative results for both Saha and free-energy-minimization equilibria are presented for a hydrogen-helium plasma with N(He)/N(H) = 0.10. These illustrate nicely the phenomena of pressure dissociation and ionization, and also demonstrate vividly the importance of choosing a reliable cutoff procedure for internal partition functions.

Mihalas, Dimitri↗
NASA NTRS1988

Failure of continuum methods for determining the effective temperature of hot stars

It is demonstrated here that, for hot stars, methods based on the integrated continuum flux are completely unreliable discriminators of the effective temperature. Absorption line profiles provide much more accurate values of these parameters. It is not necessary to invoke nonradiative energy and momentum effects to explain the spectroscopic appearance of O-type stars of very different spectral type; rather, the observed spectra can be well modeled and fully interpreted by normal interaction of gas and radiation in stellar atmospheres of differing effective temperature and gravity.

Hummer, D. G.↗
NASA NTRS1988

Recombination line intensities for hydrogenic ions. II - Case B calculations for C VI, N VII and O VIII

The intensities of recombination lines formed in extended, optically thim, photoionized plasmas such as those found in PN, H II regions, and winds of certain hot stars are an important source of information on chemical abundances and can sometimes provide estimates of electron temperature. In this paper, the intensities of the recombination lines of C VI, N VII, and O VIII are calculated, accounting for both electron and heavy particle collisions and assuming case B of Baker and Menzel. The computational procedure is explained. The intensities of lines formed by transitions n(u) - n(l) are tabulated for n(u) of 50 or less, n(l) of 29 or less, at log N(e) = 4(1)13 and 10 values of electron temperature in the interval 10,000 K to 500,000 K.

Storey, P. J.↗
NASA NTRS1988

A fast and accurate method for evaluating the nonrelativistic free-free Gaunt factor for hydrogenic ions

A fast method for obtaining a two-dimensional Chebyshev expansion of the nonrelativistic hydrogenic free-free Gaunt factor is presented which gives a maximum relative error of 0.7 percent over a wide range of temperatures and frequencies. The expansion derived by Karzas and Latter (1961) is used to derive primary values of the free-free Gaunt factor as a function of the initial and final electron energies. Thermal averages have been numerically computed and are presented in tabular form in intervals of 0.25 dex.

Hummer, D. G.↗
NASA NTRS1988

Collisional-radiative switching - A powerful technique for converging non-LTE calculations

A very simple technique has been developed to converge statistical equilibrium and model atmospheric calculations in extreme non-LTE conditions when the usual iterative methods fail to converge from an LTE starting model. The proposed technique is based on a smooth transition from a collision-dominated LTE situation to the desired non-LTE conditions in which radiation dominates, at least in the most important transitions. The proposed approach was used to successfully compute stellar models with He abundances of 0.20, 0.30, and 0.50; Teff = 30,000 K, and log g = 2.9.

Hummer, D. G.↗
NASA NTRS1987

Recombination-line intensities for hydrogenic ions. I - Case B calculations for H I and He II

Assuming Case B of Baker and Menzel (1938), the relative intensities of H I and He II recombination lines are determined for a larger range of temperature and density than previously considered and with the upper principle quantum number up to 50 and the lower number up to 29. Full collisional effects are included, and new collision strengths for the n = 1, 2, and 3 states of He(+) are presented. Case B theory is found to be invalidated for collisional excitation of the n = 3 levels from both n = 1 and n = 2 states under certain conditions which depend upon electron density and the Lyman-alpha escape probability, and the regimes of temperature and density for which Case B is valid are also considered.

Hummer, D. G.↗