explanation blue bibcodes open ADS page with paths to full text
Author name code: hummer
ADS astronomy entries on 2022-09-14
author:"Hummer, David G."
---------------------------------------------------------
Title: The MHD Equation of State with Post-Holtsmark Microfield
Distributions
Authors: Nayfonov, Alan; Däppen, Werner; Hummer, David G.; Mihalas,
Dimitri
1999ApJ...526..451N Altcode: 1999astro.ph..1360N
The Mihalas-Hummer-Däppen (MHD) equation of state is a part of the
Opacity Project (OP), where it mainly provides ionization equilibria
and level populations of a large number of astrophysically relevant
species. Its basic concept is the idea of perturbed atomic and ionic
states. At high densities, when many-body effects become dominant,
the concept of perturbed atoms loses its sense. For that reason,
the MHD equation of state was originally restricted to the plasma of
stellar envelopes, that is, to relatively moderate densities, which
should not exceed ρ<10<SUP>-2</SUP> g cm<SUP>-3</SUP>. However,
helioseismological analysis has demonstrated that this restriction is
much too conservative. The principal feature of the original Hummer
& Mihalas paper is an expression for the destruction probability of
a bound state (ground state or excited) of a species (atomic or ionic),
linked to the mean electric microfield of the plasma. Hummer &
Mihalas assumed, for convenience, a simplified form of the Holtsmark
microfield for randomly distributed ions. An improved MHD equation
of state (Q-MHD) is introduced. It is based on a more realistic
microfield distribution that includes plasma correlations. Comparison
with an alternative post-Holtsmark formalism (APEX) is made, and good
agreement is shown. There is a clear signature of the choice of the
microfield distribution in the adiabatic index γ<SUB>1</SUB>, which
makes it accessible to present-day helioseismological analysis. However,
since these thermodynamic effects of the microfield distribution are
quite small, it also follows that the approximations chosen in the
original MHD equation of state were reasonable. A particular feature
of the original MHD papers was an explicit list of the adopted free
energy and its first- and second-order analytical derivatives. The
corresponding Q-MHD quantities are given in the Appendix.
---------------------------------------------------------
Title: Recombination of helium-like ions - I. Photoionization
cross-sections and total recombination and cooling coefficients for
atomic helium
Authors: Hummer, D. G.; Storey, P. J.
1998MNRAS.297.1073H Altcode:
A new calculation of photoionization cross-sections is described
for the ground and excited states of atomic helium up to principal
quantum number n=25 and angular momentum quantum number l=5. These
cross-sections are used to calculate total recombination and cooling
coefficients for atomic helium for electron temperatures given
by log(T)=1(0.2)4.4. A comparison of the threshold photoionization
cross-sections obtained here with extrapolations of the highly accurate
bound-bound oscillator strength calculations by Drake shows that the new
calculations are in error by no more than 1 per cent. The accuracy of
the photoionization cross-sections used by previous workers to derive
recombination coefficients is also discussed.
---------------------------------------------------------
Title: VizieR Online Data Catalog: Recombination line intensities
for hydrogenic ions (Storey+ 1995)
Authors: Storey, P. J.; Hummer, D. G.
1995yCat.6064....0S Altcode:
Line emissivities, effective recombination coefficients, opacity
factors, departure coefficients and total recombination coefficients are
calculated for hydrogenic ions with Z<=8. <P />There are 162 primary
files labelled rZCTTTT.d, where Z=1,2,..,8 is the ionic charge C=a or
b is the Case in the sense of Baker and Menzel (1938ApJ....88...52B),
i.e. -- A for a nebula transparent to Lyman line radiation, -- B for
an opaque nebula TTTT=0.01Te is a reduced temperature variable. <P
/>There are 9 values of electron densities (log(Ne)=2(1)10) for case A,
and 13 (log(Ne)=2(1)14) for case B. The structure of these files is
detailed in section 4 of the MNRAS paper. <P />There are 16 secondary
files labelled eZC.d, where Z=1,2,..,8 is the ionic charge C=a or b is
the Case in the sense of Baker and Menzel (1938ApJ....88...52B) which
contain emissivities and total recombination coefficients. <P />These
files are accompanied by an interactive data server intrat.f. Please
refer to section 5 of the MNRAS paper which details the usage of
the program. <P />CGS units are used, meaning that => densities
are expressed in cm<SUP>-3</SUP> => emissivities are expressed in
erg.s<SUP>-1</SUP>.cm<SUP>-3</SUP> (10<SUP>-7</SUP>W.cm<SUP>-3</SUP>)
=> effective recombination coefficients are expressed in
cm<SUP>3</SUP>.s<SUP>-1</SUP> <P />(1 data file).
---------------------------------------------------------
Title: Radiative Transfer
Authors: Hummer, D.
1995aelm.conf...35H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Recombination line intensities for hydrogenic ions-IV. Total
recombination coefficients and machine-readable tables for Z=1 to 8
Authors: Storey, P. J.; Hummer, D. G.
1995MNRAS.272...41S Altcode:
Line emissivities, effective recombination coefficients, opacity
factors, departure coefficients and total recombination coefficients
are calculated for hydrogenic ions with Z<=8. Results are
obtained for Cases A and B for n<=50. Collisional transitions
among individual n and l states are fully treated. Calculations were
made for log N_e=2(1)14 for Case B and logN_e=2(1)10 for Case A. The
electron temperature takes between nine and 12 values, lying within
the range 500 to 100 000 K, depending on the ion. All results are
available in the form of machine-readable files. Secondary files
containing only effective emissivities for transitions for n<=25
and total recombination coefficients are also available for use with
an interactive data server. The server produces tables of relative
intensities of any two specified transitions or emissivities for any
transition at all temperatures and densities in the data set. Extensive
facilities for two-dimensional interpolation of relative intensities,
emissivities and total recombination coefficients are provided.
---------------------------------------------------------
Title: An accelerated lambda iteration method for multilevel radiative
transfer. III. Noncoherent electron scattering
Authors: Rybicki, G. B.; Hummer, D. G.
1994A&A...290..553R Altcode: 1994astro.ph..4019R
Since the mass of the electron is very small relative to atomic masses,
Thomson scattering of low-energy photons (hν<<m_e_c^2^) produces
thermal Doppler frequency shifts that are much larger than atomic
Doppler widths. A method is developed here to evaluate the electron
scattering emissivity from a given radiation field which is considerably
faster than previous methods based on straightforward evaluation of the
scattering integral. This procedure is implemented in our multilevel
radiative code (MALI), which now takes full account of the effects of
noncoherent electron scattering on level populations, as well as on
the emergent spectrum. Calculations using model atmospheres of hot,
low-gravity stars display not only the expected broad wings of strong
emission lines but also effects arising from the scattering of photons
across continuum edges. In extreme cases this leads to significant
shifts of the ionization equilibrium of helium.
---------------------------------------------------------
Title: Total Recombination and Energy Loss Coefficients for Hydrogenic
Ions at Low Density for 10<T/E/Z/2<10/7K
Authors: Hummer, D. G.
1994MNRAS.268..109H Altcode:
Total recombination and energy-loss coefficients, including the
free-free component, are calculated for Cases A and B from extract
hydrogenic photoionization and free-free cross-sections, and are
tabulated for log( T<SUB>e</SUB>/Z<SUP>2</SUP>)=1(0.2)7.
---------------------------------------------------------
Title: Algorithms for rapid evaluation of band transfer functions
for linear molecules.
Authors: Hummer, D. G.; Kutepov, A. A.
1994JQSRT..51..729H Altcode:
Efficient algorithms are developed to compute transfer functions for
bands in linear molecules and their application to the determination
of non-LTE populations and cooling rates in planetary atmospheres
are discussed.
---------------------------------------------------------
Title: NLTE model stellar atmospheres with line blanketing near the
series limits.
Authors: Hubeny, I.; Hummer, D. G.; Lanz, T.
1994A&A...282..151H Altcode:
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</SUB> = 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.
---------------------------------------------------------
Title: Atomic data from the IRON project. I. Goals and methods.
Authors: Hummer, D. G.; Berrington, K. A.; Eissner, W.; Pradhan,
Anil K.; Saraph, H. E.; Tully, J. A.
1993A&A...279..298H Altcode:
The IRON Project has the goal of computing on a large scale
electron excitation cross sections and rates of astrophysical and
technological importance, using the most reliable procedures curently
available. Radiative transition probabilities and photoionization cross
sections not known from other sources e.g. from the Opacity Project,
will also be presented. Although the major effort will be for ions of
the iron-group elements, other ions of astrophysical interest will
also be included. In this introductory paper models and procedures
to be used are summarized and the approximations are discussed. As
an example of our computational procedures, typical results for fine
structure transitions involving electron collisions with Fe XVIII ions
and radiative data from Fe XVII are presented.
---------------------------------------------------------
Title: FOS Spectra of OB-type Stars in the LMC
Authors: Voels, S. A.; Butler, K.; Gabler, R.; Groth, H. G.; Lennon,
D. J.; Haser, S.; Hummer, D. G.; Husfeld, D.; Kudritzki, R. P.;
Pauldrach, A.; Puls, J.; Baade, D.; Walborn, N. R.; Heap, S. R.;
Garmay, C. D.; Conti, P. S.; Bohannan, B.
1992AAS...181.1908V Altcode: 1992BAAS...24.1151V
As part of continuing project to determine the intrinsic stellar
parameters (temperature, gravity, luminosity, chemical composition,
radius, mass-loss rate) of early OB-type stars, we are observing
several stars in the Large and Small Magellanic Clouds using the
HST/FOS high resolution gratings (G130H, G190H) in the UV (1200 to 2200
Angstroms). This part of the UV spectrum contains several line profiles
of C, N, O, and Si which when combined with ground based observations
in the optical and NLTE stellar atmosphere models allow us to accurately
determine the intrinsic stellar parameters of the star. In this poster,
we will present the FOS spectra and preliminary model fits for AV-232
(Sk-80) and AV-488 (Sk-159) which are to be obtained Fall 1992. We will
also present our latest work on the three stars (Sk-70D69, Sk-66D100,
and Sk-68D137) obtained last summer.
---------------------------------------------------------
Title: An accelerated lambda iteration method for multilevel radiative
transfer. II. Overlapping transitions with full continuum.
Authors: Rybicki, G. B.; Hummer, D. G.
1992A&A...262..209R Altcode:
The ALI method has been generalized to include treatment of overlapping,
active continuum transfer and overlapping lines. The linearity of
the iterative equations is maintained in this method by consistent
use of the psi operator rather than the lambda operator. The method
has been applied to a sample problem of pure helium, which includes 23
levels, 31 lines, 22 continua, three stages of ionization, and electron
scattering. Velocity fields of order of a few Doppler widths were also
included by means of an observer's frame formulation. The convergence
of the solutions was found to be comparable to that achieved in the
previous pure line method.
---------------------------------------------------------
Title: Radiation-driven winds of hot luminous stars. X. The
determination of stellar masses, radii and distances from terminal
velocities and mass-loss rates.
Authors: Kudritzki, R. -P.; Hummer, D. G.; Pauldrach, A. W. A.; Puls,
J.; Najarro, F.; Imhoff, J.
1992A&A...257..655K Altcode:
A new, purely spectroscopic method to determine masses, radii, and
distances of massive, luminous hot stars is presented. This method
is based on the theory of radiation-driven winds and uses terminal
velocity, mass-loss rate and effective temperature as observational
quantities determined from the spectrum. It is demonstrated that in
situations where the distance is already known from other methods,
masses can be determined from v<SUB>infinity</SUB> and T(eff)
with an accuracy of +/- 25 percent, which is a factor of two better
than the classical method using the information obtainable from the
quantitative analysis of photospheric absorption lines. These masses,
which agree with those obtained from the spectroscopic values of log g,
are systematically somewhat smaller than masses found from evolutionary
calculations. An independent determination of radii and distances is
possible, if good measurements of mass-loss rates can be carried out.
---------------------------------------------------------
Title: The Sobolev Approximation for Line Formation with Partial
Frequency Redistribution
Authors: Hummer, D. G.; Rybicki, G. B.
1992ApJ...387..248H Altcode:
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</SUB> 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.
---------------------------------------------------------
Title: Hot Stars and the Hubble Space Telescope
Authors: Kudritzki, R. P.; Lennon, D. J.; Becker, S. R.; Butler,
K.; Gabler, R.; Haser, S.; Hummer, D. G.; Husfeld, D.; Pauldrach,
A. W. A.; Puls, J.; Voels, S.; Walborn, N. R.; Heap, S. R.; Bohannan,
B.; Conti, P.; Garmany, C. D.; Baade, D.
1992ESOC...44..279K Altcode: 1992swhs.conf..279K
No abstract at ADS
---------------------------------------------------------
Title: Recombination line intensities for hydrogenic
ions. III. Effects of finite optical depth and dust.
Authors: Hummer, D. G.; Storey, P. J.
1992MNRAS.254..277H Altcode:
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.
---------------------------------------------------------
Title: Book-Review - Stellar Atmospheres Beyond Classical Models
Authors: Crivellari, L.; Hubeny, I.; Hummer, D. G.
1991JBAA..101..364C Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The solution of radiative transfer problems in molecular bands
without the LTE assumption by accelerated lambda iteration methods.
Authors: Kutepov, A. A.; Kunze, D.; Hummer, D. G.; Rybicki, G. B.
1991JQSRT..46..347K Altcode:
An iterative method based on the use of approximate transfer (or Λ)
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 (including
rotational NLTE, overlapping of lines in the bands and overlapping of
bands with continuua) using relatively small computers. This technique
converges much more rapidly than straightforward iteration between
the transfer equation and the equations of statistical equilibrium
(Λ-iteration). A test application of this new technique to the solution
of NLTE radiative transfer problems for optically-thick and thin bands
(the 4.3 μm CO<SUB>2</SUB> band in the Venusian atmosphere and the
4.7 and 2.3 μm CO bands in the Earth's atmosphere) is described.
---------------------------------------------------------
Title: An accelerated lambda iteration method for multilevel
radiative transfer.
Authors: Rybicki, G. B.; Hummer, D. G.
1991A&A...245..171R Altcode:
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.
---------------------------------------------------------
Title: Asymptotic expansions of the kernel functions for line
formation with continuous absorption.
Authors: Hummer, D. G.
1991JQSRT..45..211H Altcode:
Asymptotic expressions are obtained for the kernel functions
M∼<SUB>2</SUB>(τ,α,β) and K∼<SUB>2</SUB>(τ,α,β) appearing
in the theory of line formation with complete redistribution over
a Voigt profile with damping parameter α, in the presence of a
source of continuous opacity parameterized by β. For α > 0,
each coefficient in the asymptotic series is expressed as the product
of analytic functions of α and η ≡ βτ separately. For Doppler
broadening, only the leading term can be evaluated analytically.
---------------------------------------------------------
Title: Stellar atmospheres. Beyond classical models
Authors: Crivellari, Lucio; Hubeny, I.; Hummer, D. G.
1991ASIC..341.....C Altcode: 1991QB809.N38......; 1991sabc.conf.....C
No abstract at ADS
---------------------------------------------------------
Title: The Opacity Project and the Practical Utilization of Atomic
Data
Authors: Hummer, D. G.
1991ASIC..341..431H Altcode: 1991sabc.conf..431H
No abstract at ADS
---------------------------------------------------------
Title: Computer Codes for Stellar Atmospheric Modeling
Authors: Hummer, D. G.; Hubeny, I.
1991ASIC..341..119H Altcode: 1991sabc.conf..119H
No abstract at ADS
---------------------------------------------------------
Title: Photospheres of Hot Stars. IV. Spectral Type O4
Authors: Bohannan, Bruce; Voels, Stephen A.; Hummer, David G.; Abbott,
David C.
1990ApJ...365..729B Altcode:
The basic stellar parameters of a supergiant (Zeta Pup) and two
main-sequence stars, 9 Sgr and HD 46223, at spectral class O4 are
determined using line profile analysis. The stellar parameters are
determined by comparing high signal-to-noise hydrogen and helium
line profiles with those from stellar atmosphere models which include
the effect of radiation scattered back onto the photosphere from an
overlying stellar wind, an effect referred to as wind blanketing. At
spectral class O4, the inclusion of wind-blanketing in the model
atmosphere reduces the effective temperature by an average of 10
percent. This shift in effective temperature is also reflected by
shifts in several other stellar parameters relative to previous O4
spectral-type calibrations. It is also shown through the analysis
of the two O4 V stars that scatter in spectral type calibrations is
introduced by assuming that the observed line profile reflects the
photospheric stellar parameters.
---------------------------------------------------------
Title: The Equation of State for Stellar Envelopes. IV. Thermodynamic
Quantities and Selected Ionization Fractions for Six Elemental Mixes
Authors: Mihalas, Dimitri; Hummer, D. G.; Mihalas, Barbara Weibel;
Daeppen, Werner
1990ApJ...350..300M Altcode:
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.
---------------------------------------------------------
Title: Comparison of Stellar Parameters from Line Profile Analysis
with those from Stellar Evolution Calculations
Authors: Voels, S. A.; Bohannan, B.; Abbott, D. C.; Hummer, D. G.
1990BAAS...22..743V Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Quantitative spectroscopy of hot stars.
Authors: Kudritzki, R. P.; Hummer, D. G.
1990ARA&A..28..303K Altcode:
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.
---------------------------------------------------------
Title: Photospheres of Hot Stars. III. Luminosity Effects at Spectral
Type O9.5
Authors: Voels, Stephen A.; Bohannan, Bruce; Abbott, David C.; Hummer,
D. G.
1989ApJ...340.1073V Altcode:
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.
---------------------------------------------------------
Title: The Equation of State for Stellar Envelopes. III. Thermodynamic
Quantities
Authors: Daeppen, Werner; Mihalas, Dimitri; Hummer, D. G.; Mihalas,
Barbara Weibel
1988ApJ...332..261D Altcode:
The authors derive general formulae for the computation of the
thermodynamic properties of a partially ionized (and/or dissociated)
multicomponent gas in terms of second derivatives of the free energy
with respect to temperature, volume, and occupation numbers. For the
free energy used in previous work the authors give explicit analytical
expressions for all derivatives required to construct the thermodynamic
quantities. Representative results for several different thermodynamic
properties of a hydrogen-helium plasma with N(He)/N(H) = 0.10 are
presented as color plots.
---------------------------------------------------------
Title: The Equation of State for Stellar Envelopes. I. an Occupation
Probability Formalism for the Truncation of Internal Partition
Functions
Authors: Hummer, D. G.; Mihalas, Dimitri
1988ApJ...331..794H Altcode:
The authors have formulated a new equation of state for material in
stellar envelopes, subject to the limits T ⪉ 10<SUP>7</SUP>K and
ρ ⪉ 10<SUP>-2</SUP>g cm<SUP>-3</SUP>. Under these conditions,
the method of free energy minimization can be used to allow for
nonideal effects; this method ensures thermodynamic consistency
among the material properties. A chemical picture is used in which
atomic and molecular particles retain their identities. An occupation
probability formalism is used to represent the effects of the plasma
in establishing a finite partition function, and attention is paid
to representing these effects in a way that is consistent from the
point of view of statistical mechanics. The use of the static screened
Coulomb potential to calculate level shifts and to estimate the cutoff
of the internal partition function is shown by elementary arguments
to be 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 functions.
---------------------------------------------------------
Title: The Equation of State for Stellar Envelopes. II. Algorithm
and Selected Results
Authors: Mihalas, Dimitri; Dappen, Werner; Hummer, D. G.
1988ApJ...331..815M Altcode:
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.
---------------------------------------------------------
Title: Failure of Continuum Methods for Determining the Effective
Temperature of Hot Stars
Authors: Hummer, D. G.; Abbott, David C.; Voels, Stephen A.; Bohannan,
Bruce
1988ApJ...328..704H Altcode:
The authors demonstrate that for hot stars (T<SUB>eff</SUB> >
30,000K) methods based on the integrated continuum flux are completely
unreliable discriminators of the effective temperature. They show that
the observed continuum flux distribution of ζ Pup (O4f) can be fitted
to within the observational errors by photospheric models having a wide
range of effective temperatures and gravities. In contrast, absorption
line profiles provide much more accurate values of these parameters. As
an example, profiles of weak lines of H I, He I, and He II are computed
from standard non-LTE models at the effective temperature and surface
gravity inferred by Underhill from the continuous energy flux. These
profiles show a severe lack of agreement with observed profiles.
---------------------------------------------------------
Title: Recombination line intensities for hydrogenic ions. II. Case
B calculations for C VI, N VII and O VIII.
Authors: Storey, P. J.; Hummer, D. G.
1988MNRAS.231.1139S Altcode:
The intensities of recombination lines formed in extended, optically
thin, 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.
---------------------------------------------------------
Title: A Fast and Accurate Method for Evaluating the Nonrelativistic
Free-free Gaunt Factor for Hydrogenic Ions
Authors: Hummer, D. G.
1988ApJ...327..477H Altcode:
A two-dimensional Chebyshev expansion of the nonrelativistic hydrogenic
free-free Gaunt factor is presented which can be evaluated extremely
rapidly and which gives a maximum relative error of 0.7% over a very
wide range of temperatures and frequencies. This expansion is obtained
from numerical values computed primarily from the exact expressions
of Karzas and Latter, augmented by certain analytic approximations
that are valid in regions of the energy plane where the series given
by Karzas and Latter become computationally intractable. A brief table
of thermally averaged Gaunt factors is given.
---------------------------------------------------------
Title: Collisional-radiative switching - A powerful technique for
converging non-LTE calculations
Authors: Hummer, D. G.; Voels, S. A.
1988A&A...192..279H Altcode:
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.
---------------------------------------------------------
Title: C/He abundances in WC stars.
Authors: Smith, Lindsey F.; Hummer, David G.
1988MNRAS.230..511S Altcode:
Recombination theory has been used to determine the C/He abundances
in 17 southern WC stars from spectra in the H and K bands. An LTE
treatment of C II provides C/He values in the 0.04-0.3 range, by number,
and maximum allowance for possible non-LTE effects yields values in
the 0.1-0.7 range, by number. C/He is shown to decrease from WC4 to
WC7. The ionization balance is found to be lower than in previous
reports. He(+)/He(2+) values are between 2.6 and 3.0 for WC5-8 stars,
increasing to 7 for WC9 stars. Continuum slopes and corrections for
the emission line contributions to the H and K magnitudes are evaluated.
---------------------------------------------------------
Title: The Sobolev approximation for the line force and line source
function in a spherically-symmetrical stellar wind with continuum
opacity
Authors: Puls, J.; Hummer, D. G.
1988A&A...191...87P Altcode:
An expression for the force arising from diffuse line radiation is
derived in the context of the Sobolev approximation for spectral
line formation, as generalized by Hummer and Rybicki (1985) to
include the effects of continuous opacity and emissivity in a general
three-dimensional gas flow. This theory is then specialized to spherical
symmetry and used to calculate the line source function and radiative
pressure gradient in model stellar winds simulating essential aspects
of the outflows' characteristic of O-stars and Wolf-Rayet objects. These
models are compared both with models based on the Sobolev approximation
without continuum opacity, and with numerically exact solutions
obtained by using the co-moving frame method. The properties and
methods of evaluating the special functions, Z (τ, β) and U (τ,
β), arising in this work and in that of Hummer and Rybicki (1985)
are discussed in the appendices.
---------------------------------------------------------
Title: Effective Temperatures and Gravities for O-Type Stars
Determined from High Precision Line Profiles and Wind-Blanketed
Model Atmospheres
Authors: Bohannan, B.; Abbott, D. C.; Voels, S. A.; Hummer, D. G.
1988IAUS..132..127B Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Enhanced Helium Abundance in O Supergiants
Authors: Voels, S. A.; Bohannan, B.; Abbott, D. C.; Hummer, D. G.
1987BAAS...19.1025V Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Recombination-line intensities for hydrogenic ions - I. Case
B calculations for H I and He II.
Authors: Hummer, D. G.; Storey, P. J.
1987MNRAS.224..801H Altcode:
The relative intensities of H I and He II recombination lines are
calculated, including full collisional effects, for a considerably
larger range of temperature, density and principal quantum numbers than
before. Case B of Baker & Menzel (1938) is assumed, and tables of
line opacities are also presented to enable the assumption of negligible
optical depth in all but the Lyman series to be checked. Collisional
excitation of the n = 3 levels from both n = 1 and n = 2 states
is considered, and is found to invalidate Case B theory in some
conditions which depend on electron density and the Lyman-α escape
probability. The regimes of temperature and particle density for which
Case B is valid are discussed. Newly calculated collision strengths
for the n = 1, 2 and 3 states of He<SUP>+</SUP> are tabulated.
---------------------------------------------------------
Title: Luminosity Effects of Wind Blanketed Models for Late O-Type
Stars
Authors: Voels, S. A.; Bohannan, B.; Abbott, D. C.; Hummer, D. G.
1986BAAS...18..953V Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Photospheres of Hot Stars. II. an Analysis of Zeta Puppis
Authors: Bohannan, B.; Abbott, D. C.; Voels, S. A.; Hummer, D. G.
1986ApJ...308..728B Altcode:
High signal-to-noise ratio line profiles of ζ Puppis (O4f) obtained
with a CCD camera are compared with theoretical model atmospheres
that include radiation scattered back from the stellar wind onto
the photosphere, an effect referred to as wind blanketing. The
best-fit wind-blanketed model for the observed mass loss rate of
5×10<SUP>-6</SUP>M_sun;yr<SUP>-1</SUP> yields the following properties
of ζ Puppis: T<SUB>effective</SUB> = 42,000±1500K, log g = 3.5±0.1,
helium abundance by number, [Y] = 0.17±0.03. If one assumes a distance
modulus of 8.2±0.4 mag, ζ Puppis has a bolometric magnitude of
-10.1±0.4, a radius of 18±4 R_sun;, and current mass of 36 (+21,
-15) M_sun;.
---------------------------------------------------------
Title: Rational approximations for the Holtsmark distribution,
its cumulative and derivative.
Authors: Hummer, D. G.
1986JQSRT..36....1H Altcode:
The convergent series expansions of the Holtsmark distribution P(β),
its cumulative Q(β), its derivative R(β) and the semiconvergent
asymptotic series for these functions are used to calculate rational
approximations for P, Q and R, which are valid for all positive β and
have maximum errors of approximately 10<SUP>-8</SUP>, 10<SUP>-9</SUP>
and 10<SUP>-7</SUP>, respectively.
---------------------------------------------------------
Title: Non-Lte Analysis of Massive Stars in the Magellanic Clouds
Authors: Gehren, T.; Husfeld, D.; Kudritzki, R. P.; Conti, P. S.;
Hummer, D. G.
1986IAUS..116..413G Altcode:
The massive stars of the Magellanic Clouds are of considerable current
interest with regard to questions of initial mass function, star
formation mechanisms, stellar evolution with mass loss and the chemical
evolution of galaxies. The effective temperatures, surface gravities and
helium abundances of 6 main sequence O-type stars, obtained by fitting
non-LTE model atmospheres to high quality spectra, are presented.
---------------------------------------------------------
Title: Steps to a New Calibration of the Spectral Type - Effective
Temperature Relationship for Early-Type Stars
Authors: Bohannan, B.; Abbott, D. C.; Voels, S. A.; Hummer, D. G.
1986IAUS..116..111B Altcode:
The spectral type - effective temperature calibration is a cornerstone
of the understanding of massive stars and their environment. The
authors have begun a new determination of the basic stellar parameters
of massive stars with an analysis of ζ Pup (O4f).
---------------------------------------------------------
Title: Atoms in astrophysics.
Authors: Burke, P. G.; Eissner, W. B.; Hummer, D. G.; Percival, I. C.
1986atas.book.....B Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Intrinsic parameters of hot blue stars
Authors: Kudritzki, R. P.; Hummer, D. G.
1986IAUS..116....3K Altcode:
Problems involved in the determination of the intrinsic parameters
of hot blue stars are discussed. Discrepancies between effective
temperatures obtained by calibrating against spectral type and
temperatures obtained using measured angular diameters and flux
distributions are examined using Zeta Puppis as an example. The problems
posed by wind blanketing, metal opacity and non-LTE line blanketing,
and radiation-driven winds are addressed, and methods to handle these
problems are discussed. The results of applying some of these techniques
to a number of Galactic O3 stars in the Eta Car region are presented
and discussed.
---------------------------------------------------------
Title: Rotational relaxation of the 00<SUP>0</SUP>1 level of
CO<SUB>2</SUB> including radiative transfer in the 4.3-μm band of
planetary atmospheres.
Authors: Kutepov, A. A.; Hummer, D. G.; Moore, C. B.
1985JQSRT..34..101K Altcode:
The paper contains accurate numerical solutions of the problem of
rotational relaxation of the C<SUP>12</SUP>O<SUB>2</SUB><SUP>16</SUP>
molecules in the 00<SUP>0</SUP>1 level in conjunction with the transfer
of radiation in the lines of the 00<SUP>0</SUP>1-00<SUP>0</SUP>0
transition of the 4.3-μm band in a plane-parallel isothermal
atmosphere consisting of pure carbon dioxide. This model atmosphere
is illuminated by the sun, and has a pressure profile given by the
barometric formula. The band lines are assumed to be nonoverlapping,
with line shapes described by Voigt profiles depending on temperature
and pressure. The transfer problem has the form of a multiplet with a
large number of lines with a common lower level. The most recent data
on the rotational transition probabilities due to molecular collisions
have been used. This work may be viewed as the first attempt to model
the formation of the rotational populations of a vibrational level of
CO<SUB>2</SUB> in the upper atmospheres of Venus and Mars.
---------------------------------------------------------
Title: A radiation driven stellar wind model atmosphere for the
Wolf-Rayet binary V444 Cygni.
Authors: Pauldrach, A.; Puls, J.; Hummer, D. G.; Kudritzki, R. P.
1985A&A...148L...1P Altcode:
Using the stellar parameters of the WN5 component of the eclipsing
binary V 444 Cygni determined by Cherepashchuk et al. (1984)
from multi-color light curves, and employing an improved theory of
radiatively-driven stellar winds, models have been calculated which
yield an extended, supersonically expanding photosphere, with values
close to those observed for the photospheric radius, the mass-loss rate
and the terminal velocity. The radial distributions of velocity and
density are also in close agreement with those obtained by Cherepashchuk
et al. This is regarded as strong evidence that the basic observational
features of WR-stars can be reproduced by radiatively-driven wind
theory if some previous simplifications in the theory are dropped and
correctly determined stellar parameters are used.
---------------------------------------------------------
Title: Photospheres of hot stars. I. Wind-blanketed model atmospheres.
Authors: Abbott, D. C.; Hummer, D. G.
1985ApJ...294..286A Altcode:
Preliminary to an extensive and detailed comparison of improved non-LTE
photospheric models with observations of hot stars made with high
photometric accuracy, non-LTE stellar atmospheres are constructed
which account for the radiation reflected back onto the photosphere
by line and electron scattering from the wind. The effects of this
'wind blanketing' on the spectrum and internal structure of the
atmosphere are given for an example with an effective temperature
T(eff) of 42,000 K, and a wide range of wind density, gravity, and
model assumptions. Particular attention is given to the problem of
determining T(eff). Careful analysis of methods currently used to
determine T(eff) from continuous flux distributions, with and without
interferometric angular diameters, shows them to be unreliable in
practice. Line profiles continue to provide a legitimate means
of determining T(eff) but only when their dependence on gravity
and mass loss is included. For the more luminous OB stars spectral
classification is truly three-dimensional, with the mass loss rate,
gravity, and effective temperature all playing nearly equal roles in
specifying the observed spectrum.
---------------------------------------------------------
Title: The Sobolev approximation for line formation with continuous
opacity
Authors: Hummer, D. G.; Rybicki, G. B.
1985ApJ...293..258H Altcode:
The Sobolev approximation for line-formation problems in atmospheres
with high-speed flows is generalized to include the effects of
continuum absorption and emission in the region of the line. The
result is very simple, being expressed entirely in terms of known
functions with the exception of one quantity of order unity, which
is tabulated. Comparison with accurate numerical solutions for simple
problems in plane-parallel geometry shows the approximation to be quite
accurate in those regions of the atmosphere where the conditions for
the validity of the approximation are satisfied. A three-dimensional
version of the theory is given that applies to general geometries.
---------------------------------------------------------
Title: The Line Spectrum of Zeta Puppis With High Photometric Accuracy
Authors: Hummer, D. G.; Abbott, D. C.; Bohannan, B.
1984BAAS...16..509H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: A family of angle-moments proportional to r<SUP>-n</SUP>,
n = 1,2,..., in free space.
Authors: Hummer, D. G.
1984JQSRT..31..283H Altcode:
The moments M<SUB>n</SUB>(r) of the intensity I(r, θ) in free space
surrounding a spherical object emitting radiation with an arbitrary
directional dependence are shown to be exactly proportional to
r<SUP>-(n+1)</SUP>, n = 0, 1,....
---------------------------------------------------------
Title: Book-Review - Atoms in Astrophysics
Authors: Burke, P. G.; Eissner, W. B.; Hummer, D. G.; Percival, I. C.;
Domke, H.
1984AN....305...58B Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The specific luminosity of a three-dimensional medium in
terms of the escape probability
Authors: Rybicki, G. B.; Hummer, D. G.
1983ApJ...274..380R Altcode:
Radiation emitted by a three-dimensional medium and received by a
distant observer is expressed in terms of the specific luminosity,
which can be evaluated in terms of escape probability functions for
the medium. This approach is simpler in many cases than an integration
over the plane of the sky, because it allows any symmetries of the
problem to be more fully exploited. Integral theorems are derived
involving averaged escape probabilities that generalize a theorem
of Irons. Analogous results are presented for a three-dimensional
line-emitting region in the Sobolev (or large velocity gradient)
limit. To illustrate the theory, results for expanding spherical media
and differently rotating thin disks are discussed. Computationally
useful results for several related escape probability functions
are given.
---------------------------------------------------------
Title: Erratum - Second-Order Escape Probability Approximations in
Radiative Transfer
Authors: Hummer, D. G.; Rybicki, G. B.
1983ApJ...271..888H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The generalized exponential-integral V(x,y) = ∫<SUB>1</SUB>
exp(-xt)ln(t+y)dt/t and computer algorithms for y = 0 and y = 1.
Authors: Hummer, D. G.
1983JQSRT..30..281H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Radiative transfer problems in planetary nebulae
Authors: Hummer, D. G.
1983IAUS..103..211H Altcode:
Models of radiative transfer in planetary nebulae (PN) based on UV
observations such as those obtained with the IUE are surveyed. The
formation of resonance lines is considered, taking the effects of
frequency redistribution, dust absorption, the expansion velocity
of the PN shell, and the inhomogeneous distribution of the PN gas
into account. The casee of the He II Lyman-alpha resonance line,
which is involved in the Bowen fluorescent mechanism, is explored in
detail. The treatment of continuum transfer in PN models is discussed,
and the significance of a quasi-diffusion (or variable-Eddington-factor)
analysis of PN dust as (Petrosian and Dana, 1980) a bridge between UV
spectra and IR features is indicated.
---------------------------------------------------------
Title: Atoms in Astrophysics, 1983
Authors: Burke, P. G.; Eissner, W. B.; Hummer, D. G.; Percival, I. C.
1983aia..conf.....B Altcode: 1983atas.book.....B
Selected topics in the atomic and nuclear physics of astronomical
objects are examined in reviews contributed in honor of
M. J. Seaton. Topics explored include low-energy electron collisions
with complex atoms and ions, numerical methods for asymptotic
solutions of scattering equations, collisions between charged
particles and highly excited atoms, proton-impact excitation of
positive ions, long-range interactions in atoms and diatomic molecules,
applications of quantum defect theory, and electron-ion processes in
hot plasmas. Consideration is given to the development and application
of the atomic-data-calculation computer system at University College,
London, planetary nebulae, and forbidden atomic lines in auroral
spectra.
---------------------------------------------------------
Title: Wind-Blanketed Stellar Atmospheres
Authors: Abbott, D. C.; Hummer, D. G.
1983IAUS..103..546A Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Book-Review - Atoms in Astrophysics
Authors: Burke, P. C.; Eissner, W. B.; Hummer, D. G.; Percival, I. C.
1983Sci...221..946B Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Atoms in Astrophysics
Authors: Burke, P. G.; Eissner, W. B.; Hummer, D. G.; Percival, I. C.;
Osterbrock, Donald E.
1983PhT....36h..67B Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Second-order escape probability approximations in radiative
transfer
Authors: Hummer, D. G.; Rybicki, G. B.
1982ApJ...263..925H Altcode:
Second-order escape probability approximations make some allowance
for the transfer of radiation between the point where a photon is
created and that where it escapes or is absorbed. An approximation of
this kind has recently been formulated by Puetter et al. (1982) for
planar atmospheres of finite thickness, in the form of a first-order
differential equation relating the integrated mean intensity to the
source function. Two alternative normalizations to the one proposed by
these authors are given, the first of these enforces global conservation
of photons in each transition, and the second gives reasonably accurate
results with much less computational effort than the first. These
results, along with the first-order approximation and a second-order
result of Ivanov (1972), are compared with accurate numerical results
for static isothermal planar atmospheres. The maximum error for the
photon-conserving approximation is less than 25 percent for Doppler
and 7 percent for Lorentz broadening.
---------------------------------------------------------
Title: On redistribution and the equations for radiative transfer
Authors: Cooper, J.; Ballagh, R. J.; Burnett, K.; Hummer, D. G.
1982ApJ...260..299C Altcode:
The derivation of the equations of statistical equilibrium are
outlined, starting from the quantum density-matrix equations,
drawing particular attention to the approximations and assumptions
used in the development of tractable expressions. Then, using the
quantum-fluctuation-regression theorem, emission and absorption
coefficients are obtained for multilevel atomic systems which are
nondegenerate except for m-substates. These coefficients are valid to
first order in the incident intensity. Possible extensions to higher
intensity broadband incoherent fields are suggested.
---------------------------------------------------------
Title: Wind-Blanketed Stellar Atmosphere
Authors: Hummer, D. G.; Abbott, D. C.
1982BAAS...14..914H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The effect of reflected and external radiation on stellar
flux distributions
Authors: Hummer, D. G.
1982ApJ...257..724H Altcode:
The effect of radiation emitted or scattered by circumstellar material,
such as a stellar wind, into the stellar photosphere is investigated
on the basis of a gray model atmosphere generalized to include the
effects of an external radiation field and a surface boundary condition
describing the reflection of a specified fraction, depending on the
frequency, of the outgoing radiation. Substantial modifications both
to the temperature and flux distributions are found.
---------------------------------------------------------
Title: A unified treatment of escape probabilities in static and
moving media. I - Plane geometry.
Authors: Hummer, D. G.; Rybicki, G. B.
1982ApJ...254..767H Altcode:
An expression giving the escape probability for photons in a spectral
line formed in a planar atmosphere with an arbitrary monotonic velocity
law is derived and evaluated. For a small velocity gradient, the usual
static result is recovered; for large velocity gradients the Sobolev
result is obtained, but only at optical depths sufficiently large that
the static part of the escape probability is negligible. Extensive
numerical results for the escape-probability function for a constant
velocity gradient are given for Doppler, Voigt (a = 0.001, 0.01) and
Lorentz profiles. The use of these results for flows with nonconstant
gradients is discussed.
---------------------------------------------------------
Title: The WO Wolf-rayet stars.
Authors: Barlow, M. J.; Hummer, D. G.
1982IAUS...99..387B Altcode:
The intensities of all the recombination lines in the dereddened
spectrum of Sand 3 are measured and compared with theoretical
recombination line predictions for the relevant ions as calculated by
Hummer and Storey (1982). The results for the case where the electron
temperature is 200,000 K and the density is 10 to the 11th/cu cm are
found to have given an excellent fit to the observed relative line
intensities of transitions within He II, C IV, C V, O VI, O VII,
and O VIII, covering upper levels as low as 3 and as high as 15 over
the wavelength range 1170-7100 A. The derived relative abundances
(by number), normalized to He(2+) = 100, are presented. The surface
chemical composition of Sand 3 (by mass) is therefore H:He:C:O =
0:38:54:8. Since the mass fraction of oxygen in a ZAMS star is only 1%,
these results suggest enhancement of oxygen through a alpha-particle
capture by carbon in addition to the expected enhancement of carbon
by the triple-alpha process.
---------------------------------------------------------
Title: The infrared recombination-line spectra of Wolf-Rayet stars
Authors: Hummer, D. G.; Barlow, M. J.; Storey, P. J.
1982IAUS...99...79H Altcode:
Effective recombination coefficients have recently been calculated
for recombination lines of He I, He II and C IV (among other ions with
up to three electrons) for densities and temperatures appropriate for
Wolf-Rayet atmospheres. These have been applied to recently obtained
infrared spectra of Gamma Vel in order to derive the He(+)/He(+2)
and C(+4)/He(+) + He(+2) ratios.
---------------------------------------------------------
Title: High order asymptotic expansions of the four kernel functions
for line formation with the Voigt profile.
Authors: Hummer, D. G.
1982JQSRT..27..569H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Rate coefficients for electron impact excitation of helium-like
ions
Authors: Pradhan, A. K.; Norcross, D. W.; Hummer, D. G.
1981ApJ...246.1031P Altcode:
The distorted wave (DW) approximation is used to solve the e(+)
ion scattering problem. It is found that for He-like ions the DW
approximation, which neglects coupling between states other than the
initial and the final, compares extremely well with the more elaborate
close-coupling approximation. Rate parameters gamma(T) are presented
for all 10 transitions involving the ground state and the n=2 states,
for He-like Be, C, O, Ne, Si, Ca, and Fe. The rate parameters were
obtained from collision strengths calculated and fitted to expressions
in energy, separately in a number of different energy intervals. In
terms of the variation with temperature T, the results gamma(T),
may be divided into three categories corresponding to forbidden,
intercombination, and allowed transitions.
---------------------------------------------------------
Title: Radiative Recombination Coefficients at Stellar Densities
Authors: Hummer, D. G.; Storey, P. J.
1981BAAS...13..793H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Line Formation in Accretion Disks
Authors: Carroll, D.; Hummer, D. G.; Rybicki, G. B.
1981BAAS...13Q.818C Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Cross sections and excitation rates for electron collisions
with heliumlike ions
Authors: Pradhan, A. K.; Norcross, D. W.; Hummer, D. G.
1981PhRvA..23..619P Altcode:
We describe the techniques and the approximations used in extensive
calculations for cross sections and reaction-rate parameters for
electron-impact excitation of a number of heliumlike ions. All
transitions involving the ground state and the n=2 states are
considered. Calculations are made in the distorted-wave approximation
using configuration-interaction wave functions to represent the target
states. Autoionizing resonances in the scattering cross sections are
included through bound-channel correlation-type functions and through
quantum-defect-theory analysis of the reactance matrices. The resonances
are shown to make considerable contributions to the cross sections and
thereby, in many cases, to enhance the excitation-rate coefficients
by a significant factor. This should have important consequences for
practical applications in the analysis of laboratory and astrophysical
plasmas. The accuracy of our approximations is also discussed.
---------------------------------------------------------
Title: Expressions for the computer-evaluation of the four kernel
functions for line formation with Doppler and Lorentz profiles.
Authors: Hummer, D. G.
1981JQSRT..26..187H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Optical observations of the ultrahigh-excitation Wolf-Rayet
star Sanduleak 3.
Authors: Barlow, M. J.; Blades, J. C.; Hummer, D. G.
1980ApJ...241L..27B Altcode:
Recombination lines of O VII, O VIII, and C V have been identified
in the optical spectrum of an O VI Wolf-Rayet star, representing the
first non-X-ray detection of these ions in astronomical spectra and
implying excitation energies in excess of 800 eV. Rapid variations on
a time scale of about 150 s have been observed in the profile of one
of the O VII lines.
---------------------------------------------------------
Title: Escape-Probability Method for Flows of Arbitrary Velocity
Amplitude
Authors: Hummer, D. G.; Rybicki, G. B.
1980BAAS...12..798H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Energy loss by resonance line photons in an absorbing medium
Authors: Hummer, D. G.; Kunasz, P. B.
1980ApJ...236..609H Altcode:
The mean path length of photons undergoing repeated scatterings
in media of large optical thickness is calculated from accurate
numerical solutions of the transfer equation including the effect
of frequency redistribution characteristic of combined Doppler and
natural broadening. Energy loss by continuous absorption processes,
such as ionization or dust absorption, is discussed, and asymptotic
scaling laws for the energy loss, the mean path length, and the mean
number of scatterings are inferred from the numerical data.
---------------------------------------------------------
Title: A generalization of the Sobolev method for flows with nonlocal
radiative coupling.
Authors: Rybicki, G. B.; Hummer, D. G.
1978ApJ...219..654R Altcode:
The escape-probability technique of Sobolev for solving radiative
transfer problems in moving atmospheres is extended to treat flows
in which the line-of-sight component of the flow velocity is not
monotonic. A completely general geometrical configuration and flow
velocity field are considered; an integral equation is derived for
configurations in which a surface is intersected an arbitrary number
of times. For the case of just two intersections, it is shown that an
iterative solution always converges rapidly. Numerical results for
inverse power-law velocity fields demonstrate the magnitude of the
radiative coupling between distant parts of the atmosphere.
---------------------------------------------------------
Title: Atmospheres of central stars.
Authors: Hummer, D. G.
1978IAUS...76..171H Altcode:
Atmospheric models that are of relevance to the central stars of
planetary nebulae are summarized. The extent to which these models
accord with the observations of both nebulae and central stars is
examined. Particular attention is given to the significance of the very
high Zanstra temperature implied by the nebular He II line at 4686 A,
and to the discrepancy between the Zanstra He II temperature and the
considerably lower temperatures suggested by the appearance of the
visual stellar spectrum for some of these objects.
---------------------------------------------------------
Title: Erratum and Addendum: "Solution of the comoving-frame equation
of transfer in spherically symmetric flows. IV. Frequency-dependent
source functions for scattering by atoms and electrons [Astrophys. J.,
Vol. 210, p. 419 - 433 (1976)].
Authors: Mihalas, D.; Kunasz, P. B.; Hummer, D. G.
1977ApJ...214..337M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Solution of the comoving-frame equation of transfer in
spherically symmetric flows. IV. Frequency-dependent source functions
for scattering by atoms and electrons.
Authors: Mihalas, D.; Kunasz, P. B.; Hummer, D. G.
1976ApJ...210..419M Altcode:
A numerical method is presented of solving the radiative transfer
equation in the comoving frame of a spherically symmetric expanding
atmosphere in which both the line and the electron-scattering source
function can depend on frequency (i.e., when there is partial frequency
redistribution in the scattering process). This method is used to assess
the adequacy of various assumptions regarding frequency redistribution
in the comoving frame and to discuss the effects of electron scattering
more accurately than previously possible. The methods developed here
can be used in realistic model atmospheres to account for the (major)
effects of electron scattering upon emergent flux profiles.
---------------------------------------------------------
Title: Escape Probability Method for Line Transfer in Accelerating
Inflows and Decelerating Outflows.
Authors: Hummer, D. G.; Rybicki, G. B.
1976BAAS....8R.546H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Solution of the Comoving-Frame Equation of Transfer in
Spherically Symmetric Flows. III. Effect of Aberration and Advection
Terms
Authors: Mihalas, Dimitri; Kunasz, P. B.; Hummer, D. G.
1976ApJ...206..515M Altcode:
We investigate the importance of the advection and aberration terms,
which are of order V/c, in the comoving-frame transfer equation in
spherical geometry. Characteristic trajectories are found which reduce
the spatial derivatives to a perfect differential, and a generalization
of the numerical procedure developed in the earlier papers of this
series that permits the integration of the transfer equation on these
characteristics is presented. For cases in which V/c 1, a perturbation
solution is developed which reduces the problem to that solved in the
first paper in this series. For velocities of the form V(r) r (n = 0,
1, 2), it is shown that the magnitude of the effects arising from the
advection and aberration terms is about 5 V/c relative to the solution
with these terms omitted. In stellar winds V/c <% 0.01; hence we
conclude that aberration and advection terms may safely be ignored,
and that consideration of the Doppler-shift term alone is adequate in
the computation of spectra from such expanding atmospheres. Subject
headings: radiative transfer - stars: atmospheres
---------------------------------------------------------
Title: Resonance-line transfer with partial
redistribution. VIII. Solution in the comoving frame for moving
atmospheres.
Authors: Mihalas, D.; Shine, R. A.; Kunasz, P. B.; Hummer, D. G.
1976ApJ...205..492M Altcode:
The effects of partial frequency redistribution in the scattering
process for lines formed in moving atmospheres are analyzed using a
general method that allows the transfer equation to be solved in the
comoving frame of the gas. The same chromospheric and atomic model
studied by Cannon and Vardavas (1974) is employed in the calculations,
but a depth scale with logarithmically spaced points is adopted. It is
found that in both static and moving atmospheres, the profiles obtained
with complete and partial frequency redistribution are virtually
identical. The large differences in profiles obtained by Cannon and
Vardavas when they used complete and partial redistribution are shown
to be spurious (and physically unreal) effects resulting from angle
averaging in the observer's frame instead of the comoving frame.
---------------------------------------------------------
Title: Solution of the comoving-frame equation of transfer in
spherically symmetric flows. II. Picket-fence models.
Authors: Mihalas, D.; Kunasz, P. B.; Hummer, D. G.
1976ApJ...203..647M Altcode:
To examine the effect of the radial flow of atmospheric material on
the temperature distribution in a stellar atmosphere, a picket-fence
model with Gaussian lines is formulated and solved numerically
in the comoving frame of the gas, which is assumed to move with a
prescribed velocity law. Extensive results have been obtained for
both static and dynamical models, with planar and moderately extended
spherical geometries. For static models, the effect of lines on the
temperature distribution is virtually independent of extension. When
a large-scale velocity field is imposed, significant surface heating
and additional back-warming are found; the magnitude of these effects
increases with the extension of the atmosphere. If a significant flow
velocity persists to sufficient depth, the enhanced escape probability
can lead to a cooling in the deeper layers, which competes with the
back-warming. The results obtained here suggest that the deposition of
energy arising from the intrusion of line opacity into the continuum,
caused by velocity gradients, could influence the dynamics of the flow.-
---------------------------------------------------------
Title: Line Formation in Expanding Atmospheres (review Paper)
Authors: Hummer, D. G.
1976IAUS...70..281H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Migration of excitation in transfer of spectral-line radiation.
Authors: Hummer, D. G.; Kunasz, P. B.
1976JQSRT..16...77H Altcode:
A simple mathematical model is developed for the transfer of energy
through a gas by the combined effect of radiative transfer and migration
of excitation. The excitation is carried through the gas by a succession
of atoms which experience resonant excitation exchange; it thus appears
to random walk through the medium. The theory developed here is valid
when the distance traveled by an atom while excited is much larger
than the typical distance at which two atoms can exchange excitation
(roughly one millionth cm). The model is expressed in terms of a pair
of coupled transport equations for the intensity of radiation and the
density of excited atoms, which are solved by means of a generalized
discrete-ordinate technique. Extensive numerical results are obtained
and discussed in terms of characteristic lengths for the various
transfer processes. Substantial effects of migration are seen in both
the distribution of excited atoms near the cell windows and the line
profile of the emergent radiation for typical laboratory conditions.
---------------------------------------------------------
Title: Solution of the comoving-frame equation of transfer
in spherically symmetric flows. I. Computational method for
equivalent-two-level-atom source functions.
Authors: Mihalas, D.; Kunasz, P. B.; Hummer, D. G.
1975ApJ...202..465M Altcode:
A method for solving the line-formation problem using the full
comoving-frame formulation of the radiative-transfer equation is
presented for the case of spherically symmetric atmospheres expanding
with arbitrarily large velocities. A stable differencing scheme and a
frequency-by-frequency elimination procedure are developed to solve the
partial differential equations that describe the radiation field in the
comoving frame. It is noted that this method allows computation of the
radiation field from a given model atmosphere which must specify the
depth dependence of all the relevant physical variables. Numerical
results obtained for several models involving line formation by
two-level atoms, electron scattering, and continuous absorption are
discussed which simulate situations in the stellar winds of hot stars
and similar objects. The force exerted by radiation on the gas is
examined in a number of situations, and flux profiles are described
for very high-velocity flows with very weak or nonexistent continuum
and electron-scattering opacities. It is concluded that the mechanism
proposed by Noerdlinger and Rybicki (1974) for the destruction of
radially driven envelopes in planar geometries becomes inoperative
even in the case of slightly extended spherical configurations.
---------------------------------------------------------
Title: Theory of extended stellar atmospheres. II. A grid of static
spherical models for O stars and planetary nebula nuclei.
Authors: Kunasz, P. B.; Hummer, D. G.; Mihalas, D.
1975ApJ...202...92K Altcode:
Spherical static non-LTE model atmospheres are presented for stars
from 30 to 60 solar masses at various points on their evolutionary
tracks, and for some nuclei of planetary nebulae at two points of
a modified Harman-Seaton sequence. The method of Mihalas and Hummer
was employed, which uses a parametrized radiation force multiplier
to simulate the force of radiation arising from the entire line
spectrum. However, in the present work the density structure
computed in the LTE models was held fixed in the calculation of
the corresponding non-LTE models; in addition, the opacity of an
average light ion was taken into account. The effects of sphericity,
as distinct from those arising from a density structure modified by
a large radiation force, were investigated by computing a few planar
models using the same parametrized radiation force multiplier as for
the spherical models. Extensive tables are given of monochromatic
magnitudes, continuum jumps and gradients, Stroemgren-system colors,
monochromatic extensions, and the profiles and equivalent widths of
the hydrogen lines for all models.
---------------------------------------------------------
Title: Solution of the Co-Moving Frame Equation of Transfer in
Spherically Symmetric Flows. II. Picket-Fence Models.
Authors: Mihalas, D.; Kunasz, P. B.; Hummer, D. G.
1975BAAS....7..449M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Solution of the Co-moving Frame Equation of Transfer in
Spherically Symmetric Flows.
Authors: Mihalas, D.; Kunasz, P. B.; Hummer, D. G.
1975BAAS....7R.256M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Solution of the co-moving frame equation of transfer in
spherically symmetric flows.
Authors: Mihalas, D.; Kunasz, P. B.; Hummer, D. G.
1975BAAS....7..256M Altcode:
No abstract at ADS
---------------------------------------------------------
Title: A note on the ' peaking effect ' in spherical-geometry
transfer problems
Authors: Rybicki, G. B.; Hummer, D. G.
1975MNRAS.170..423R Altcode:
This note presents evidence that the claims advanced by Wilson, Tung
& Sen regarding the adequacy of Wilson & Sen's half-range
moment method for treating the outward peaking of the radiation field
in a spherical system are unjustified. In particular, the emergent
intensity obtained by Wilson et al. is shown to be negative for 0 <
<0.5 and greatly in error for larger values of . A discussion is
presented of the essential indeterminacy of the Wilson-Sen half-range
method. It is suggested that the good values obtained by Wilson et
al. for the mean intensity and the Eddington factor arise from their
choice of the arbitrary function A(r) to include the known asymptotic
forms of the source function.
---------------------------------------------------------
Title: Theory of extended stellar atmospheres. I. Computational
method and first results for static spherical models.
Authors: Mihalas, D.; Hummer, D. G.
1974ApJS...28..343M Altcode:
A method is presented that makes possible, for the first time, the
calculation of extended spherical non-LTE model stellar atmospheres in
hydrostatic and radiative equilibrium. This method is a generalization
of the complete-linearization technique of Auer and Mihalas. Models
have been obtained for a star with 60 solar masses, 1,000,000 solar
luminosities, and 24 solar radii, whose atmosphere is characterized by
an effective temperature of 39,500 K and a surface gravity log g = 3.45,
i.e., with a spectral type near O6. These models are differentiated by
the magnitude and radial dependence of a radiation force multiplier that
is inserted into the equation of hydrostatic equilibrium to simulate
the effect of radiation force on opacity sources which have not been
included explicitly in the calculation. Models have been obtained very
close to the limit at which the radiation force and gravity balance;
as this condition is approached, the atmospheres become more and
more extended.
---------------------------------------------------------
Title: Rate Coefficients for Electron Excitation of the First
Resonance Transition in h, Li, Na, Ca, Ca', and Ba' Calculated from
Experimental Data
Authors: Crandall, D. H.; Dunn, G. H.; Gallagher, A.; Hummer, D. G.;
Kunasz, C. V.; Leep, D.; Taylor, P. O.
1974ApJ...191..789C Altcode:
By fitting cubic splines augmented with special functional forms for
low and high energies to cross-section data determined experimentally
at discrete values of the electron energy, we obtain an interpolation
that can be visually inspected and adjusted to prevent the appearance of
spurious features. The familiar integral expressing the rate coefficient
in terms of the cross-sections can then be evaluated with no further
approximation. This procedure is applied here to cross-section data for
the first resonance transition of H, Li, Na, Ca, Ca +, and Ba +. The
resulting collisional de-excitation rate coefficient, from which the
excitation-rate coefficient can be determined by the detailed balance
relation, is tabulated in each case for electron temperatures in the
interval from 1O to 1O K and is expressed in terms of a Chebyshev
expansion valid for this range of temperature. Subject heading:
transition probabilities
---------------------------------------------------------
Title: Light ions of astrophysical interest-radiative transition
probabilities for C m, N iv, 0 V and NE VII
Authors: Hummer, D. G.; Norcross, D. W.
1974MNRAS.168..263H Altcode:
Multiconfiguration calculations of energy levels and bound-bound
radiative transition probabilities for four astrophysically important
ions of the Be isoelectronic sequence are presented. Convergence of the
results with respect to the number of configurations included in the
expansion is discussed. Results are presented for all ions from models
with I I and 16 configurations including transition probabilities for
24 allowed electric dipole transitions. Some significant differences
with previous calculations are obtained. The theoretical lifetimes are
generally in good accord with those obtained by the beam-foil technique,
and the results of other ab initio calculations.
---------------------------------------------------------
Title: Some Observational Implications of Extended Static O-Star
Model Atmospheres
Authors: Mihalas, Dimitri; Hummer, David G.
1974ApJ...189L..39M Altcode:
Some results and observational implications are presented for the
first extended spherical non-LTE model atmospheres in hydrostatic and
radiative equilibrium. These models all correspond to a star with =
60 , L = 1.25 X 106 Lo and R = 24 , with an effective temperature
Te 39,500 K and surface gravity log g 3.45 (spectral type near
06). They are differentiated by the magnitude and radial dependence
of a radiation-force multiplier , inserted into the equation of
hydrostatic equilibrium, to simulate the effect of radiation force
on opacity sources (e.g., lines) that have not been included in the
calculations. It has been possible to obtain models very close to the
limit at which the radiation force balances the gravity. Hydrogen and
helium (`7= 0.1) constitute the gas; siz hydrogen lines are treated
explicitly. These models show La in emission, the lower Balmer lines
in absorption, the Balmer jump in absorption, and both infrared and
ultraviolet excesses relative to the visual. Continuum jumps and
gradients, -system colors, and equlvalent widths of Ha, Hp, and H
are tabulated and discussed briefly. Subject headings: atmospheres,
stellar - radiative transfer
---------------------------------------------------------
Title: Radiative transfer in spherically symmetric
systems-III. Fundamentals of line formation
Authors: Kunasz, P. B.; Hummer, D. G.
1974MNRAS.166...19K Altcode:
A generalization of the variable Eddington factor method is presented
hat makes possible the solution of line formation problems in extended
spherical atmospheres whose constitutive properties depend on radius in
an arbitrary way. Extensive numerical results for Doppler broadening
in models with power law opacities (n = 0, 2, 3) are presented and
interpreted. Very substantial deviations are found from the solutions of
sanalogous plane-parallel models. The single-flight escape probability
is sderived for a general opacity law and is shown to exceed that
for an sanalogous plane-parallel slab by no more than a factor of
approximately stwo for Doppler broadening, or three- halves for Lorentz
broadening. sHowever, it is shown that each time a photon is scattered,
it has a sprobability greater than one-half of ending its flight at
a radius slarger than that at which it was emitted. This effect is
peculiar to sspherical geometries and may be important in aiding the
escape of sphotons from optically thick systems. Finally the effects of
dilution sare considered and some properties of the infinite radius,
finite soptical depth models are inferred. An appendix contains the
solution of sthe line transfer problem for a homogeneous sphere by
the kernel-approximation method.
---------------------------------------------------------
Title: Radiative transfer in spherically symmetric
systems-IV. Solution of the line transfer problem with radial
velocity fields
Authors: Kunasz, P. B.; Hummer, D. G.
1974MNRAS.166...57K Altcode:
A numerical procedure is presented for solving the line transfer problem
with complete redistribution in spherically symlnetric atmospheres in
which the radial velocity is an arbitrary function of radius, limited
by spractical considerations to maximum velocities a few times the mean
thermal velocity. In this procedure the transfer equation, written in
the observer's frame, is differenced along rays and the resulting very
large set of coupled linear equations is cast into the novel form,
proposed by Rybicki, that allows for extremely rapid solution of the
system. Numerical results are discussed for three sequences of models,
two with linear velocity laws and one with constant velocities, in which
sthe effect of the transverse velocity gradient is demonstrated. It
is sshown that velocities as small as of the mean thermal velocity
produce sobservable asymmetries in the flux profile.
---------------------------------------------------------
Title: Informal remarks on a problem in astrophysics
Authors: Hummer, D.
1973NucIM.110..421H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Analyses of light-ion spectra in stellar atmospheres.
Authors: Mihalas, D.; Hummer, D. G.
1973ApJ...179..827M Altcode:
An analysis of the N iii emission lines in 0 stars has been
carried out on the basis of a detailed solution of the coupled
statistical-equilibrium and transfer equations for a multiline,
multilevel, multi-ion ensemble. Our calculations, using static,
plane-parallel models reproduce successfully the observed emission
at AA4634, 4640, 4641 (3p 2P -3d 2D) and absorption at AA4097,
4103 (3s 2S-3p 2P ). The multiplet is found to come into emission
at the observed temperature for both main-sequence and low-gravity
objects. The equivalent widths of the emission lines agree very well
with those measured for the class of Of stars thought to have compact
atmospheres, i.e., those classified as O((f)) by Walborn. In these stars
the basic physical mechanism responsible for this phenomenon is the
overpopulation of 3d by means of dielectronic recombinations from the
low-lying 2s2p(1P )3d autoionizing states with cascades 3d 3p. The 3p
state is drained by the "two-electron jumps" coupling 3p to the 2s2p2
(25, 2p, 2D) states, thus preventing emission in the 3s-3p lines. The
possible importance of the Swings mechanism to the fully developed
Of stars (in Walborn's sense) is pointed out, and the irrelevance of
the Bowen mechanism to all Of stars is firmly demonstrated. The fact
that the N iii emission lines can be produced in static nonextended
atmospheres in radiative equilibrium has the far-reaching significance
that the presence of emission lines in a spectrum is not in itself
sufficient evidence for the existence of a stellar chromosphere
(i.e., an extended, nonradiatively heated region). Subject headings:
atmospheres, stellar - emission-line stars line formation Of-type stars
---------------------------------------------------------
Title: Interpretation of the spectra of planetary nebulae.
Authors: Hummer, D. G.; Seaton, M. J.
1973LIACo..18..225H Altcode: 1973MSRSL...5..225H
No abstract at ADS
---------------------------------------------------------
Title: Formation of Spectral Lines in Spherical Stellar Atmospheres.
Authors: Kunasz, P.; Hummer, D. G.
1973BAAS....5...11K Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Numerical evaluation of the formal solution of radiative
transfer problems in spherical geometries.
Authors: Hummer, D. G.; Kunasz, C. V.; Kunasz, P. B.
1973CoPhC...6...38H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: ON THE N III λλ4640, 4097 LINES IN Of STARS
Authors: Mihalas, Dimitri; Hummer, D. G.; Conti, Peter S.
1972ApJ...175L..99M Altcode:
Detailed calculations based on non-LTE plane-parallel model atmospheres
show that the N iii emission lines at XX4634, 4640, 4641 observed
in Of stars are produced primarliy by dielectronic recombination to
3d 3D followed by the 3d-3p transition in a compact atmosphere. The
3P state in turn is drained by two-electron transitions to the 2p2
levels. We find that X4640 is in emission for Teff < 37,0000
K for main-sequence objects (55,0000 K for giants), while X4097
remains strongly in absorption, in accordance with observations. The
calculated equivalent widths are in substantial agreement with the
observed values for those Of stars with He II X4686 in absorption,
i.e., for those objects designated by Walborn as O((f)).
---------------------------------------------------------
Title: The Transfer of Linearly Polarized Radiation in Extended
Atmospheres.
Authors: Cassinelli, J. P.; Hummer, D. G.
1971BAAS....3Q.378C Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Numerical evaluation of the redistribution function
R<SUB>II-A</SUB>(x, xÿ) and of the associated scattering integral.
Authors: Adams, T. F.; Hummer, D. G.; Rybicki, G. B.
1971JQSRT..11.1365A Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Radiative transfer in spherically symmetricsystems-II. The
non-conservative case and linearly polarized radiation
Authors: Cassinelli, J. P.; Hummer, D. G.
1971MNRAS.154....9C Altcode:
The method for the solution of transfer problems in spherically
symmetric systems developed recently by Hummer and Rybicki is
here generalized to the nonconservative case. This procedure,
which depends on the iterative determination of the Eddington
factor J = K/J, handles in a natural way the outward peaking of the
radiation field which occurs in extended atmospheres. To illustrate
the present extension of this method, solutions are obtained for
the problem of scattering of linearly polarized radiation by an
extended electron-scattering atmosphere. Although the transfer of
radiation through such an atmosphere is conservative, each of the
component equations is not. For opacity laws of the form K = r -
,o <r <R, n = a and 3' very large values of the polarization
are found as a general feature arising from the strong peaking of the
radiation field. It is found that the temperature distribution in such
extended electron-scattering atmospheres differs negligibly from that
computed on the assumption of isotropic scattering, with the neglect
of polarization. The procedure used for the polarization problem can
also be applied directly to problems with a non-grey opacity involving
many frequencies simultaneously.
---------------------------------------------------------
Title: The Formation of Spectral Lines
Authors: Hummer, D. G.; Rybicki, G.
1971ARA&A...9..237H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Radiative transfer in spherically symmetric systems. The
conservative grey case
Authors: Hummer, D. G.; Rybicki, G. B.
1971MNRAS.152....1H Altcode:
A practical computational method is presented for the solution of
radiative transfer problems in spherically symmetric systems. This
procedure involves iteration on the `Eddington factor ` f = K/J and
is designed to handle the outward peaking of the radiation field in
extended spherical systems. Extensive numerical results are obtained
and discussed for systems in which `cp = o< , for n = 3/2, 2 and 3.
---------------------------------------------------------
Title: Electron Impact Excitation of Positive Ions
Authors: Burgess, A.; Hummer, D. G.; Tully, J. A.
1970RSPTA.266..225B Altcode:
Non-relativistic Coulomb-Born-Oppenheimer reactance matrices and
cross-sections are given for all transitions between the 1s, 2s and 2p
states in He<SUP>+</SUP> and in hydrogen-like ions of large nuclear
charge. From these results some cross-sections for intercombination
transitions in highly charged non-hydrogenic ions are estimated.
---------------------------------------------------------
Title: Joint Institute for Laboratory Astrophysics of the National
Bureau of Standards and the University of Colorado, Boulder,
Colorado. Report 1968-1969.
Authors: Hummer, D. G.
1970BAAS....2...59H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Non-coherent scattering - VII. Frequencydependent
thermalization lengths and scattering with continuous absorption
Authors: Hummer, D. G.; Rybicki, G. B.
1970MNRAS.150..419H Altcode:
Our previous definition of the thermalization length is generalized to
cases in which the initial photon frequency is prescribed. This permits
treatment of cases in which the emissivity does not have a unique
frequency dependence. This definition is then applied to the case of
a line formed by scattering in the presence of continuous opacity. In
this case the emissivity in the line has a unique frequency dependence
but the total emissivity does not. Equations for the distribution of
thermalization distances are derived both by a diagrammatic technique
and by use of resolvents. Median thermalization lengths are defined in
terms of these distributions. Extensive numerical results are reported
and the utility of this approach is discussed.
---------------------------------------------------------
Title: Model atmospheres for the central stars of planetary nebulae.
Authors: Hummer, D. G.; Mihalas, D.
1970MNRAS.147..339H Altcode:
Approximately 70 model atmospheres for the central stars of
planetary nebulae have been computed under the assumptions of
hydrostatic, radiative and local thermodynamic equilibrium and of
stratification. These models have effective temperatures and surface
gravities in the range and log . The atmospheres have been taken to
consist of hydrogen, helium, oxygen, nitrogen, carbon and neon, and the
opacity included contributions from both ground and excited states of
each ion. The transfer equation is solved using Feautrier's method and
the temperature corrections are calculated by means of the Krook-Avrett
procedure. Particular attention is given to the effects of gravity
and chemical composition on the surface fluxes. The photon fluxes in
the H I, He I and He ii continua and the stellar flux at H have been
tabulated for use in the determination of Zanstra temperatures.
---------------------------------------------------------
Title: Spectral Line Formation by Noncoherent Scattering with a
Dipole Phase Function
Authors: Hummer, D. G.
1970ApL.....5....1H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Part C Chromospheres and Coronae of Stars
Authors: Pecker, J. C.; Hummer, D. G.
1970sfss.coll..239P Altcode: 1970IAUCo...2..239P
No abstract at ADS
---------------------------------------------------------
Title: Non-coherent scattering-VI. Solutions of the transfer problem
with a frequency-dependent source function
Authors: Hummer, D. G.
1969MNRAS.145...95H Altcode:
A generalized discrete-ordinate method is used to obtain accurate
numerical solutions of the line transfer problem in which the scattering
is described by a redistribution function. Extensive results are
obtained and discussed for the cases of pure Doppler broadening and
of Doppler and natural broadening combined. It is shown that, in the
latter case, the intensity of radiation emerging from a semi-infinite
isothermal atmosphere approaches that for coherent scattering in the
line wings instead of approaching the value of the Planck function.
---------------------------------------------------------
Title: The normalized on-the-spot approximation for line transfer
problems.
Authors: van Blerkom, D.; Hummer, D. G.
1969JQSRT...9.1567V Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Non-coherent scattering-V. Thermalization distances and their
distribution function
Authors: Rybicki, G. B.; Hummer, D. G.
1969MNRAS.144..313R Altcode:
The distribution function for thermalization distances is derived
for an infinite atmosphere with a plane source. Precise definitions
of the thermalization length are discussed from the point of view of
representing the distribution by a single characteristic length; of
these a definition in terms of the median of the distribution seems
to be most useful. The distribution of longest flights is derived
and shown to provide a good approximation to the distribution of
thermalization lengths at large distances from the source. Extensive
numerical illustrations are provided.
---------------------------------------------------------
Title: Line Formation in Differentially Moving Media with Temperature
Gradients
Authors: Hummer, D. G.; Rybicki, G. B.
1968rla..conf..213H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: A Non-Lte Theory of Overlapping Lines Near the Series Limit
Authors: van Blerkom, D.; Hummer, D. G.
1968ApJ...154..741V Altcode:
The effects of overlapping on the formation of spectral lines near
the series limit are investigated through the introduction of a band
model Numerical solutions are obtained which show that the source
function can be increased by a factor of 2 for e = 0 1 and by much
larger amounts for smaller A cri- terion is presented to check when
overlapping is likely to be important
---------------------------------------------------------
Title: Redshifted Line Profiles from Differentially Expanding
Atmospheres
Authors: Hummer, D. G.; Rybicki, G. B.
1968ApJ...153L.107H Altcode:
Accurate numerical solutions of the non-LTE radiative-transfer problem
with non-coherent scatter- ing have been obtained using a generalization
of the Riccati method of Rybicki and Hummer (1967). Differential
expansion in the direction of the observer is found to produce
significantly redshifted line profiles
---------------------------------------------------------
Title: Radiative Transfer Processes in Planetary Nebulae
Authors: Hummer, D. G.
1968IAUS...34..166H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Summary-introduction to radiative transfer problems in
stellar atmospheres
Authors: Hummer, D. G.
1968JQSRT...8..193H Altcode:
A central problem in the theory of stellar atmospheres is the
determination of the radiation field and distribution of atomic states
throughout the atmosphere, given the temperature-pressure structure of
the atmosphere, and the chemical composition and the dynamical state of
the gas. This problem has a diagnostic aspect, since it can be used to
obtain the external radiation field for the purpose of comparing stellar
models with observations. There is also a constructive aspect, since the
computation of a self-consistent model, without the LTE assumptions,
must necessarily involve the problem, usually as one step in an
iterative process. Here attention is limited to the radiation field
in resonance lines, in which the problem is especially simple. From
the considerable body of numerical solutions now available, it is
possible to discern some rather general features of these problems,
which can be conveniently discussed in terms of processes coupling the
radiation field to the electron gas. A concept which has proven useful
in understanding these solutions is that of the so-called thermalization
length, defined as the optical distance between the point where a
photon is created at the expense of electron kinetic energy and the
point where it is converted back into kinetic energy. For example,
it is seen that a rather severe limit is placed on the resolution
with which any observation of the radiation field can determine
the temperature-pressure structures of an atmosphere. One technical
difficulty encountered in this work is that of solving the combined
transfer and statistical equilibrium equations for an atmosphere with
optical properties depending on depth. Mathematically, the problem is
the numerical solution of a set of coupled linear differential equations
with non-constant coefficient, with two-point boundary conditions. Some
recent work on this problem by Dr. G. B. Rybicki and the author will
be discussed, in which the linear equations are converted into a set
of coupled non-linear equations with a one-point boundary condition
by means of a transformation due to Rybicki and Usher.
---------------------------------------------------------
Title: Non-coherent scattering-III. The effect of continuous
absorption on the formation of spectral lines
Authors: Hummer, D. G.
1968MNRAS.138...73H Altcode:
The formation of spectral lines by completely redistributed non-coherent
scattering is systematically investigated for situations in which
photo-ionization or extinction by dust grains occurs at the line
frequencies. Particular attention is given to cases for which the
source function associated with the continuous opadty differs from the
Planck function at the local electron temp eratare. Very large effects
are found to occur, even when the ratio of continuous opacity to line
opacity is very small. Extensive numerical results are presented, and
the relevant scaling laws and the generalized thermalization length
are discussed.
---------------------------------------------------------
Title: Non-coherent scattering-IV. Doppler redistribution functions
in moving atmospheres
Authors: Hummer, D. G.
1968MNRAS.141..479H Altcode:
Redistribution functions and their directional averages are derived
for scattering by an assembly of atoms possessing a Maxwellian
distribution in a frame moving with respect to the observer. Various
assumptions concerning the form of the absorption coefficient and the
coherence properties in the atom's rest frame are considered. The
exact redistribution function for pure Doppler broadening is
expanded in Legendre polynomials to facilitate evaluation of the
source function. From the expansion it is clear that the use of
directionaveraged redistribution functions will be significantly less
accurate for moving than for static media.
---------------------------------------------------------
Title: Spectral Line Formation in Variable-Property Media: the
Riccati Method
Authors: Rybicki, G. B.; Hummer, D. G.
1967ApJ...150..607R Altcode:
A numerical method, based on a generalized Riccati transformation of
Rybicki and Usher, is presented for the integration of the radiative
transfer equation for spectral line formation by non-coherent scattering
in inbomogeneous plane-parallel media. A model atom with two discrete
levels is assumed. An asymptotic theory is developed which permits
the application of this method to problems involving semi-infinite
media. Numerical results obtained by the Riccati method are used to
discuss the effects of spatial variations in the Doppler width on
lines formed by pure Doppler broadening.
---------------------------------------------------------
Title: Line Formation with Non-Coherent Electron Scattering in O
and B Stars
Authors: Hummer, D. G.; Mihalas, D.
1967ApJ...150L..57H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The ionization structure of planetary nebulae-VI. The Lyman
continuum problem
Authors: van Blerkom, D.; Hummer, D. G.
1967MNRAS.137..353V Altcode:
Because of the recent evidence that a planetary nebula does not
completely absorb Lyman continuum radiation for a substantial part
of its life, we have used a generalized discrete-ordinate method
to obtain accurate numerical solutions to the ionization balance
problem in pure hydrogen, plane-parallel model nebulae of various
optical thicknesses. The effects of incomplete absorption, interior
boundary conditions and non-Plancidan stellar fluxes are examined. We
find that the density of neutral hydrogen in the nebula increases
by less than a factor of two as the optical thickness varies from to
Co, and is insensitive to large deviations in the stellar flux from
the Planckian distribution, if the total number of Lyman photons is
constant. The radius of the Strbmgren sphere differs by about 5 per
cent for the two boundary conditions considered. The accuracies of two
simple approximations are assessed, and conditions for their validity
are obtained.
---------------------------------------------------------
Title: Computational Methods for Non-LTE Line_transfer Problems
Authors: Hummer, D. G.; Rybicki, G.
1967MComP...7...53H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Thermalization Lengths and the Homogeneous Transfer Equation
in Line Formation
Authors: Hummer, D. G.; Stewart, J. C.
1966ApJ...146..290H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: General Noncoherent Scattering
Authors: Hummer, D. G.
1965SAOSR.174..143H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Emission Coefficient
Authors: Hummer, D. G.
1965SAOSR.174...13H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: Non-coherent scattering, II: Line formation with a frequency
independent source function
Authors: Avrett, E. H.; Hummer, D. G.
1965MNRAS.130..295A Altcode:
The frequency-independent source function for a two-level atom in a
self-excited atmosphere with no continuous absorption is encountered,
for example, in theories of line formation in the solar corona
and outer chromosphere. We present accurate numerical solutions to
this transfer problem in finite and semi-infinite atmospheres for
physically interesting values of the relevant parameters and discuss the
mathematical and physical features of the source functions we obtain. We
do not here apply our results to any particular astrophysical problem,
but rather concentrate on understanding the physics of the transfer
problem. Particular attention is given to the effects of collision
broadening. Finally, the assumption of a frequency-independent source
function for Doppler broadening is examined for self-consistency.
---------------------------------------------------------
Title: The Voigt function: An eight-significant-figure table and
generating procedure
Authors: Hummer, D. G.
1965MmRAS..70....1H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The Mean Number of Scatterings by a Resonance-Line Photon.
Authors: Hummer, D. G.
1964ApJ...140..276H Altcode:
A rigorous upper bound to the mean number of scatterings (N) experienced
by a resonance-line photon is obtained very simply. For completely
non-coherent scattering this bound provides a good estimate of (N)
and explicit expressions are obtained for the cases of Doppler, Voigt,
and Lorentz absorption coefficients. These results are contrasted with
those of Osterbrock (1962) and are interpreted in terms of the concept
of effective band width.
---------------------------------------------------------
Title: The ionization structure of planetary nebulae, III
Authors: Hummer, D. G.; Seaton, M. J.
1964MNRAS.127..217H Altcode:
In planetary nebulae the helium to hydrogen abundance ratio, by numbers
of atoms, is Y=o I to C 2 the abundance of heavier elements, by numbers
of atoms relative to hydrogen, is Z IC- . The heavier elements may be
neglected when considering the ionization of hydrogen and helium, but
are of importance in considering the thermal balance. Three main regions
are considered In region (i), that is, the innermost region, the most
abundant ions are He+2 and H+. The He+2 - He+ ionization equilibrium
is calculated by the method of Paper I. Recombinations of He+2 to He+
produce sufficient quanta to keep the hydrogen ionized. With Z =0,
the electron temperature in region (i) would be very high (T8 >7.5
x io4 K with no collisional excitation), but with Z io an efficient
cooling process is shown to be excitation of allowed transitions in
lithium-like ions such as C+3, giving Te 2 X i04 K. In region (ii)
the most abundant ions are He+ and H+. The He+-He0 and H+-H0 ionization
equilibria are calculated on solving coupled equations. At lower star
temperatures (Ts <5 X I0 K for Y= ), the inner part of region (ii)
contains He+ and H+ and the outer part contains He0 and H+. At higher
star temperatures the transitions from He + to He0 and from H+ to H0
occur at approximately the same point. In region (iii) none of the
gas is ionized. This region exists only if the total amount of gas is
sufficient to produce absorption of all ionizing stellar quanta.
---------------------------------------------------------
Title: The ionization structure of planetary nebulae, II. Collisional
cooling of pure hydrogen nebulae
Authors: Hummer, D. G.
1963MNRAS.125..461H Altcode:
Collisional excitation and ionization of hydrogen are mechanisms which
lead to the removal of energy from planetary nebulae. The ionization
and thermal balance equations including these effects are solved
for a pure hydrogen nebula to determine the electron temperature
in the nebula for a wide range of star temperatures. For reasonable
stellar fluxes the electron temperature considered as a function of
star temperature assumes a maximum value of 2>c I0 0K. Collisional
excitation greatly enhances the line emission from low-lying states of
hydrogen; in particular, it may be important to allow for collisional
excitation of Ly o' when one obtains star temperatures from estimates
of the total energy radiated by the nebula. The role of hydrogen
collisional cooling in real nebulae is discussed briefly. Accurate
and convenient expressions are obtained for the collisional excitation
and ionization rates for hydrogen.
---------------------------------------------------------
Title: Atomic collision and radiative transfer phenomena in planetary
nebulae
Authors: Hummer, David Graybill
1963PhDT........65H Altcode:
No abstract at ADS
---------------------------------------------------------
Title: The ionization structure of planetary nebulae, I. Pure
hydrogen nebulae
Authors: Hummer, D. G.; Seaton, M. J.
1963MNRAS.125..437H Altcode:
The problem is formulated in terms of the equations of radiative
transfer, of ionization equilibrium and of the thermal balance. The
intensity of ionizing radiation is I = lyS + 1yd where lyS is the
attenuated intensity of stellar radiation and lyd the intensity of
diffuse radiation produced in the nebula. In Approximation I it is
assumed that there is no transfer problem for the diffuse radiation,
emission and absorption occurning at the same place. The problem is
then solved using a method due to Zanstra and de Jong. Assuming the
star to radiate as a black body, numerical results are obtained for
a wide range of star temperatures. In Approximation II the transfer
equation for 1yd is solved using the source function from Approximation
I. For an isothermal plane parallel model it is found that the mean
intensities Jy as given by Approximations I and II, never differ by
more than a few per cent.
---------------------------------------------------------
Title: Non-coherent scattering: I. The redistribution function with
Doppler broadening
Authors: Hummer, D. G.
1962MNRAS.125...21H Altcode:
The redistribution in frequency of radiation scattered from moving
atoms is examined in some generality, allowing for the different types
of scattering which occur in the atom's rest frame under different
circumstances. Some general formulae are obtained and a number of
explicit results are given. Finally some attention is devoted to the
properties of the redistribution functions and to the methods which
may be used for computing them.
---------------------------------------------------------
Title: The Ultra-Violet Radiation of the Central Stars of Planetary
Nebulae
Authors: Hummer, D. G.; Seaton, M. J.
1961LIACo..10..539H Altcode: 1961MSRSL...4..538H; 1961LIACo..10..538H
No abstract at ADS
