Non-LTE Model Atmospheres for Late-Type Stars I. A Collection of Atomic Data for Light Neutral and Singly-Ionized Atoms

Abstract

With the goal of producing a reliable set of model atoms and singly-ionized ions for use in building NLTE model atmospheres, we have combined measured energy levels, critically-compiled line transition probabilities, and resonance-averaged calculations of photoionization cross-sections. A majority of the elements from Li to Ca are considered, covering most of the important species in late-type atmospheres. These include elements which contribute free electrons and/or continuous opacity in the ultraviolet (e.g., Mg, and Si), as well as trace elements whose abundance determinations rely on ultraviolet lines (e.g., B from B I lines). The new data complement and, for the species in common, supersede a previous collection of model atoms originally designed for use in studies of early-type stars. Comment: 6 pages, 4 figures, to appear in ApJS

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arXiv:astro-ph/0303559v1 25 Mar 2003
To Appear in ApJ
Preprint typeset using LATEX style emulateapj v. 04/03/99
NON-LTE MODEL ATMOSPHERES FOR LATE-TYPE STARS I. A COLLECTION OF ATOMIC
DATA FOR LIGHT NEUTRAL AND SINGLY-IONIZED ATOMS.
Carlos Allende Prieto and David L. Lambert
McDonald Observatory and Department of Astronomy,
The University of Texas at Austin, RLM 15.308, Austin, Texas 78712-1083
Ivan Hubeny1and Thierry Lanz2
Laboratory for Astronomy and Solar Physics,
NASA Goddard Space Flight Center, Greenbelt, Maryland 20771
To Appear in ApJ
ABSTRACT
With the goal of producing a reliable set of model atoms and singly-ionized ions for use in building
NLTE model atmospheres, we have combined measured energy levels, critically-compiled line transition
probabilities, and resonance-averaged calculations of photoionization cross-sections. A majority of the
elements from Li to Ca are considered, covering most of the important species in late-type atmospheres.
These include elements which contribute free electrons and/or continuous opacity in the ultraviolet (e.g.,
Mg, and Si), as well as trace elements whose abundance determinations rely on ultraviolet lines (e.g.,
B from B I lines). The new data complement and, for the species in common, supersede a previous
collection of model atoms originally designed for use in studies of early-type stars.
Subject headings: Atomic data — radiative transfer — stars: atmospheres
1. INTRODUCTION
Classical – Local Thermodynamical Equilibrium (LTE),
plane-parallel,horizontally homogeneous,
equilibrium – model stellar atmospheres have been provid-
ing a basic tool for stellar spectroscopy for several decades,
but are now known to suffer from various weaknesses when
applied to accurate observations of individual stars. Sev-
eral lines of research have been adopted to improve the
models. For example, in the context of late-type stars,
we mention here three-dimensional hydrodynamical simu-
lations of surface convection (e.g. Stein & Nordlund 1998,
Asplund et al. 2000); improvements in molecular opaci-
ties (e.g. Hauschildt et al. 1999a; Tsuji 2002); the adop-
tion of spherical geometry (e.g. Plez, Brett, & Nordlund
1992; Hauschildt et al. 1999b); and semi-empirical model-
ing (e.g. Allende Prieto et al. 2000).
LTE has been one of the strongest hypotheses invoked
extensively in solving the coupled problems of radiative
transfer and structure in stellar atmospheres.
sumption enormously simplifies the complexity of the cal-
culations, since the populations of all ions and molecules
involved follow from the Boltzmann and Saha formulae.
Yet, LTE has been recognized to be inappropriate in many
areas of the Hertzsprung-Russell diagram. Models that
take departures from LTE into account are traditionally
labeled non-LTE (or NLTE) models. The main area where
the NLTE models have been applied are hot stars (types O,
B, A, hot white dwarfs and subdwarfs, and other objects
with high-temperature atmospheres; see, e.g., Hubeny &
Lanz 1995). However, the advent of large telescopes with
high-dispersion spectrographs, and the subsequent refine-
ment of observations of late-type stars, call for an assess-
ment of the possible departures from LTE on the model
atmospheres for these stars.
hydrostatic
This as-
Non-LTE calculations require detailed radiative and col-
lisional rates of all involved transitions in order to solve the
statistical equilibrium equations. The role of photoioniza-
tion cross-sections should be emphasized, because changes
of the degree of ionization (with respect to the LTE ion-
ization equilibrium) are a major non-LTE effect in stellar
atmospheres. Not all of the required energies and cross-
sections for the atomic/molecular processes that play a
role in a stellar atmosphere are available. Nonetheless, the
available data has been expanded in recent years. Large
collaborative projects, such as the Opacity Project (see,
e.g., Cunto et al. 1993), the Iron Project (see, e.g. Butler
1998), and SAM (see, e.g. Brage, Judge, & Brekke 1996)
have been enormously helpful. Long-term efforts on com-
pilation of data, such as CHIANTI (e.g, Dere et al. 1997),
VALD (Kupka et al. 1999), and the Atomic Spectroscopic
Database (ASD) at the National Institute of Standards
and Technology (NIST), suplemented by numerous con-
tributions from individuals and small groups, are to be
noted.
The model atoms presented here are built for use in
the model stellar atmosphere code Tlusty (Hubeny 1988,
Hubeny & Lanz 1995). A family of model atoms and ions,
primarily in the context of hot stellar atmospheres, has
been made publicly available with the code3. These mod-
els are briefly described in §2. Section 3 is devoted to
the new set of model atoms, describing the numerical de-
tails of the smoothing process applied to the photoioniza-
tion cross-sections, and the construction of model atoms.
Some comments on the limitations and practicalities for
using these data, as well as a summary, are outlined in §4.
2. THE MODION MODEL ATOMS
In the context of hot stellar atmospheres, a collection
of model atoms for H I, He I, He II, C I–C IV, N I–N V,
1AURA/NOAO
2Department of Astronomy, University of Maryland, College Park, MD 20742
3http://tlusty.gsfc.nasa.gov/
1

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2
O II–O VI, Ne II–Ne IV, Mg I–Mg II, Si I–Si IV, and
S II–S VI was prepared, ranging from very simple to quite
complete structures. These models are essentially based
on data extracted from TOPBASE. To manipulate these
large sets of atomic data, an interactive, IDL-based tool,
was developed: modion (Varosi et al. 1995; see also Lanz
et al. 1996). This interface program works with three files
for each ion, containing the level energies, the line oscil-
lator strengths, and the photoionization cross-sections, as
extracted from TOPBASE. The energy files have been up-
dated with observed energies extracted from ASD/NIST
(Martin 1997; Wiese 1997), so that all transitions will be
calculated at their actual frequency.
Modion allows model atoms of various sophistication
to be built by displaying a Grotrian diagram from which
the explicit NLTE levels are interactively selected. Al-
though it might seem desirable to include as many levels
as possible, this is often impracticable due to computing
time and memory limitations. To overcome these limita-
tions, some individual levels are merged into superlevels
(see Hubeny & Lanz 1995). Low-excitation levels are gen-
erally considered as individual levels, while levels of higher
excitation are merged. The most excited levels are often
not treated explicitly, but are assumed to be in LTE with
respect to the ground state of the next ion. Model atoms
and ions have been built for different purposes: simple
model atoms (typically less than 15 explicit levels) are of-
ten quite appropriate for inclusion in photospheric struc-
ture calculations, while very detailed models (over 40 ex-
plicit levels) may be required for detailed line formation
studies.
After the level selection step, modion builds a list
of bound-bound and bound-free transitions.
strengths from TOPBASE are assigned to bound-bound
transitions between individual levels. Modion takes care
of the appropriate summing and averaging for transitions
between superlevels, supplementing TOPBASE data with
hydrogenic values when data are missing. The necessary
sums are similarly performed for photoionization cross-
sections. Tlusty is able to deal with detailed and com-
plex representations of the cross-sections, but in most cases
we use approximate, yet adequate, representations. Us-
ing modion, we display the cross-sections in a log−log
plot of the photoionization cross-section vs.
and hand-pick some points with a cursor. The approxi-
mate cross-sections are selected to be the lower envelopes
of the detailed cross-sections, thus the autoionization res-
onances are mostly neglected. Finally, when the selections
have been completed, modion writes out a data file in the
format required by Tlusty. Some limited upgrades have
been made in a later stage to incorporate Stark profiles
for strong resonance lines or to introduce fine-structure in
strong resonance doublets like C IV λ1550 or Si IV λ1496.
Oscillator
frequency,
3. THE RAP MODEL ATOMS
This new set of model atoms is, like the modion mod-
els, based on data from TOPBASE and NIST. They
treat, however, the photoionization cross-sections differ-
ently, and in more detail. As they are new and have never
been used in calculations of radiative transfer and model
atmospheres before, we describe them in depth. These
models are, at the time of this writing, available for neu-
tral Na and S, singly ionized Ne, and neutral and singly-
ionized Li, Be, B, C, N, O, F, Mg, Al, Si and Ca.
3.1. Resonance-Averaged Photoionization Cross-Sections
It has been acknowledged that errors in the computed
energies of the atomic levels may result in spurious shifts
of the frequencies at which strong photoionization reso-
nances are predicted by theoretical calculations. Conse-
quently, several authors have suggested different proce-
dures to smooth the Opacity Project data (see, e.g., Verner
et al. 1996; Bautista, Romano, & Pradhan 1998). In addi-
tion, smoothing the cross-sections reduces sometimes the
number of data points to a more manageable level.
Bautista et al (1998) suggest a recipe for a convenient
Gaussian smoothing. They recommend a value for the
width of the Gaussian of σ = 0.03E, where E is the en-
ergy of the ionizing photon. They apply such a smooth-
ing to the photoionization cross-sections of ground levels
of all atoms and ions included in TOPBASE and to new
data on Fe I−Fe V provided by the Iron Project, pro-
ducing Resonance-Averaged Photoionization (RAP) cross-
sections. While in low-density environments, such as
gaseous nebulae, virtually all atoms and ions are in ground
states, this is not the case for stellar atmospheres. Ex-
tending the calculations of RAP cross-sections to the rest
of the levels is therefore desirable.
tral and singly-ionized species of the elements included
in TOPBASE that have been described by LS coupling
in ASD/NIST, excluding H and Fe. In fact, the list cov-
ers most of the atomic species of relevance for studying
late-type stellar atmospheres.
We have closely followed the procedure described by
Bautista et al. (1998). The RAP cross-section at a given
energy, σA(E), is computed from the TOPBASE photoion-
ization cross-section, σ(E), through the integral
We deal with neu-
σA(E) =
?∞
E0
σ(x)exp
?−(x − E)2
?−(x − E)2
2(δE)2
?
dx
?∞
E0
exp
2(δE)2
?
dx
(1)
where E0 is the ionization threshold energy, and δE =
0.03E. E0is slightly lower than the energy difference be-
tween the level and the continuum, due to line merging
near the series limit.
To speed up the calculations, without losing accuracy,
we restricted the limits of the integral (1) to E ± 5δE. In
order to avoid unwanted systematic effects at the min-
imum (threshold) and maximum energies in the TOP-
BASE calculations, we performed a linear interpolation
over the energies for which less than five points were
available within ±5δE. The RAP cross-sections were de-
rived at energies separated by the smallest steps allowed
by the sampling theorem, using the recurrence formula
E(i + 1) = E(i)(1 + δE/E) from E = E0to E ≤ EMAX.
Figure 1 shows two examples corresponding to the ground
levels of Na I, and Ca I: the thin solid line corresponds
to the original cross-sections, and the filled dots represent
the RAP cross-sections.
3.2. Assembling the RAP Model Atoms
The following sections describe how radiative and colli-
sional processes are accounted for in the the RAP model

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Fig. 1.— Detailed (solid line) and resonance-averaged (filled circles) cross-section for the ground states of Na I and Ca I. These two cases
exemplify a smooth cross-section and a complex resonance structure.
atoms. Only collisions with electrons are included. Colli-
sions with neutral H atoms may be important in late-type
stars, but lacking term-dependent or species-dependent
data, they are not considered in these models. The phe-
nomenological approximations usually found in the liter-
ature are best implemented directly in the NLTE codes,
rather than in the input data files.
3.2.1. Radiative processes
The Opacity Project provides energies and oscillator
strengths for atomic levels and radiative transitions among
them. However, even though this database provides a large
amount of atomic data of sufficient quality for many pur-
poses, theoretical calculations cannot, with few exceptions,
predict the energies of the levels with accuracy. As a result,
the wavelengths of the lines cannot be predicted to the pre-
cision available to laboratory spectroscopists. There are
also measurements of transition probabilities that may be
more accurate than those in the OP database.
We have chosen to use the atomic energy levels and
the spectral lines included in ASD/NIST, version 2.0, to
build models for the same atoms and singly-ionized ions
for which the have derived RAP cross-sections from TOP-
BASE data. The photoionization cross-sections are given
as a function of the energy from the threshold, and there-
fore they are simply shifted to the observed energy lev-
els. TOPBASE ignores fine structure, and so have we, by
grouping the split levels into a single one with an averaged
energy, using (2J+1) as weights (where J is the quantum
number that represents the total angular momentum), ac-
cording to the relative populations of the levels expected
in thermodynamic equilibrium. Transitions between fine-
structure states of a given level are ignored.
A scaled hydrogenic photoionization cross-section has
been assigned to the levels whose photoionization cross-
sections were not listed in TOPBASE, assuming that the
ionization takes place to the ground state of the next ion:
σ(ν) =2.815× 1029(Z + 1)4
ν3n5
gII
?
n,
ν
(Z + 1)2
?
cm2
(ν ≥ ν0≡ E0/h),
(2)
where h is Planck’s constant, n is the quantum principal
number of the last electron in the configuration, ν the fre-
quency, Z the charge of the ion (i.e., Z = 0 for neutrals,
Z = 1 for once ionized, etc.), and gII the Gaunt factor
expressed as
gII(n,ν) =
7
?
i=1
Cn
iνi−4
(3)
with the coefficients Cn
(1975). C.g.s. units are used throughout the paper.
The radiative transitions between fine-structure states
(i, j) of two levels (l and u) have been summed to a single
one with a gf-value:
igiven by Mihalas, Heasley, & Auer
glflu=
?
i
gi
?
j
fij
(4)
where gi= 2J+1 represents the statistical weight of a fine
structure level.
Allowed and forbidden radiative transitions whose f-
values are listed in the NIST database have been included
in the models4.Also, allowed radiative transitions not
listed in NIST have been included, assuming a scaled hy-
drogenic transition probability
fij= fH
ij
gi
2n2
i
.(5)
When more than one level in TOPBASE – with separate
photoionization cross-sections – was listed with identical
energies in the NIST lists, they were included in the models
with their respective RAP cross-sections. The states de-
scribed in the NIST database with a coupling other than
LS have not been included, but states with configurations,
terms, or energies listed as uncertain are included when
4We note that, in some particular cases, NIST may list theoretical calculations less accurate than OP.

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4
Fig. 2.— Energy levels for Na I and Si I.
matched by the TOPBASE states within 0.08 Ryd. Only
levels with energies lower than the series limit are kept.
As an example, Figure 2 displays the Grotrian diagrams
for Na I and Si I. Table 1 lists the number of levels and
radiative transitions considered for each model.
We have formatted the described data to be read by the
program Tlusty. The code is designed to build non-LTE
model atmospheres, and it will be the tool we shall employ
in future analyses of stellar spectra. There are several doc-
uments explaining the data format in detail (Hubeny 1988;
Hubeny & Lanz 1997), hence we shall not describe it here.
In the files, a series of options that apply to the solution
of the statistical equilibrium equations have been chosen.
These options set several input parameters (e.g. collisional
ionization and excitation, depth-dependency of the line ab-
sorption profiles, etc.), which are briefly described below,
but they can be changed at ease by the user (see Hubeny
1988).Free-free absorption for metals is accounted for
by a hydrogenic cross-section with the Gaunt factor set
to one, while the exact Gaunt factors are used for H and
He II. The line absorption profiles are assumed Gaussian
and depth-independent. All levels are connected with each
other and with the continuum by collisions with electrons.
How these collisional processes are treated is described in
more detail below. Mostly, but not all, applies as well to
the modion models.
3.2.2. Collisional processes involving electrons
The collisional rate for the transition i → j is given by
neqij, where neis the number density of electrons and qij
is the excitation rate coefficient. Excitations induced by
electron collisions between states connected by radiatively
permitted transitions are accounted for using Van Rege-
morter’s formula (Van Regemorter 1962, Mihalas 1972),
with the excitation rate coefficient as:
qij
= πa2
0
?
8k
meπ8π
√3
√Tfij
?
IH
Eij
?2
U0e−U0Γ(U0)
≃
19.7
fij
T3/2U0
e−U0Γ(U0) cm3s−1,
(6)
where a0 is the Bohr radius, k is Boltzmann’s constant,
meis the mass of the electron, IHis the threshold ioniza-
tion energy for hydrogen, T is the electron temperature,
U0= Eij/kT, and for ions
Γ(U0) = max
?
g,
√3
2πeU0E1(U0)
?
(7)
with g = 0.7 (transitions between levels with the same
principal quantum number) or g = 0.2 (otherwise) (Miha-
las 1978), E1is the first-order exponential integral, but for
neutral atoms
Γ(U0)=
√3
2πeU0E1(U0),U0≤ 14
Γ(U0)=
0.066
?
U0
?
1 +
3
2U0
?
,U0> 14
(8)
(Auer & Mihalas 1973). Collisional excitation between lev-
els linked by forbidden radiative transitions is considered
by means of the Eissner-Seaton formula (Seaton 1962):
qij=8.631 × 10−6
gi
√T
e−U0Υij cm3s−1, (9)
adopting, Υij = 0.05 for all cases.
(1995) and Pradhan & Zhang (2000) review some of the
detailed calculations and scaling laws of effective collisional
strengths that are available for particular ions. Those data
should update the approximate values adopted here.
We also used an approximate formula (Seaton 1962) to
evaluate collisional ionizations:
Pradhan & Peng
qij=1.55 × 1013
U0
√T
e−U0σ0 cm3s−1,(10)
with the photo-ionization cross-section at the threshold
(σ0) from TOPBASE cross-sections (when available), or
the hydrogenic approximation (with the Gaunt factor
equal to one)
σ0= 7.91 × 10−18
n
(Z + 1)2
cm2
(11)

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5
Fig. 3.— Relative difference between the bound-free continuum flux from H and H−, and the same plus the contribution from C, N, O,
Mg, Al, or Si, for Kurucz’s model atmospheres with the stellar parameters of the Sun (G2V) and Procyon (F2 IV-V).
where n is again the principal quantum number of the
last electron and Z the charge of the ion. Collisional re-
combinations and de-excitations follow from the principle
of detailed balance. Detailed calculations should replace
these approximate values where available (see, e.g., Nahar
& Pradhan 1997 and Nahar 1999).
4. SUMMARY
We have smoothed the photoionization cross-sections
of the Opacity Project for neutral Na and S, singly ion-
ized Ne, and neutral and singly-ionized Li, Be, B, C, N,
O, F, Mg, Al, Si and Ca, using a Gaussian profile with
σ ≡ δE = 0.03E, where E is the energy of the ionizing
photon. This procedure follows Bautista et al. (1998).
The smoothed cross-sections have been merged with the
energy levels and line transition probabilities listed in the
Atomic and Spectroscopic Database at NIST to derive
model atoms and ions suitable for non-LTE calculations
of model atmospheres and line formation. This new col-
lection of model atoms complements and, for the species
in common, supersedes a previous dataset, the modion
model atoms, developed for early-type stellar atmospheres.
As an example, we show the results of two calcula-
tions involving the RAP models. Figure 3 shows the rel-
ative importance of neutral C, N, O, and Mg on the con-
tinuum absorption in the near-UV spectrum of the Sun
(Teff = 5777 K; logg = 4.44 dex; [Fe/H]=0.0 dex) and
Procyon (Teff= 6530 K; logg = 4.0 dex; [Fe/H]=0.0 dex).
The spectral synthesis assumes LTE and makes use of Ku-
rucz’s atmospheric structures (Kurucz 1993).
Although the models are based on observed energy lev-
els and lines, together with detailed calculations of pho-
toionization cross-sections, judging their appropriateness
for non-LTE calculations in stellar atmospheres is beyond
the scope of this paper. Several approximations and sim-
plifications are implicit in the models and, therefore, cau-
tion is required. Only detailed comparison with high qual-
ity observed spectra will determine the models’ usefulness.
More complex ions not yet included in TOPBASE are
of interest. Iron is at the head of this group, and new
calculations of photoionization cross-sections are available
(Bautista 1997) – but not as part of TOPBASE at the
time of this writing. Many other sources of data, although
with a significant heterogeneity, exist and should be used
to complement, check, and improve these models. Such
tasks and a detailed comparison with high-quality obser-
vations for a series of standard stars are in progress and
will be reported in the future.
Both, the modion models5and the RAP models6(and,
independently, the RAP photoionization cross-sections)
are publicly available.
We thank the people and institutions involved in cre-
ating and maintaining the ASD/NIST and TOPBASE
databases, which have been extensively used in this work.
This research has been supported by NSF through grant
AST-0086321 and by the Robert A. Welch Foundation of
Houston, Texas.
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