Radiative transfer in cylindrical threads with incident radiation
VI. A hydrogen plus helium system
P. Gouttebroze^{1}  N. Labrosse^{2}
1  Institut d'Astrophysique Spatiale, Univ. Paris XI/CNRS,
Bât. 121, 91405 Orsay cedex, France
2 
Department of Physics and Astronomy,
University of Glasgow, Glasgow G12 8QQ, Scotland
Received 8 December 2008 / Accepted 19 May 2009
Abstract
Context. Spectral lines of helium are commonly observed on the Sun. These observations contain important information about physical conditions and He/H abundance variations within solar outer structures.
Aims. The modeling of chromospheric and coronal looplike structures visible in hydrogen and helium lines requires the use of appropriate diagnostic tools based on NLTE radiative tranfer in cylindrical geometry.
Methods. We use iterative numerical methods to solve the equations of NLTE radiative transfer and statistical equilibrium of atomic level populations. These equations are solved alternatively for hydrogen and helium atoms, using cylindrical coordinates and prescribed solar incident radiation. Electron density is determined by the ionization equilibria of both atoms. Twodimensional effects are included.
Results. The mechanisms of formation of the principal helium lines are analyzed and the sources of emission inside the cylinder are located. The variations of spectral line intensities with temperature, pressure, and helium abundance, are studied.
Conclusions. The simultaneous computation of hydrogen and helium lines, performed by the new numerical code, allows the construction of loop models including an extended range of temperatures.
Key words: methods: numerical  radiative transfer  line: formation  line: profiles  Sun: chromosphere  Sun: corona
1 Introduction
Observation of the upper solar atmosphere with high angular resolution reveals a wealth of filamentary structures produced by magnetic fields. To model these objects, we developed a series of NLTE radiative transfer codes that are described in the present series of papers. Among the filamentary objects relevant to this kind of modeling, we can mention: cool coronal loops, chromospheric fine structure (cf. Patsourakos et al. 2007), prominence (or filament) threads (cf. Heinzel 2007), and spicules. Paper I (Gouttebroze 2004) dealt with 1D (i.e. radius dependent) cylindrical models, a case applicable to cylindrical structures with a vertical axis exposed to an incident radiation field independent of azimuth. Papers II and III (Gouttebroze 2005, 2006, respectively) treated the case of 2D (radius and azimuth dependent) cylinders. Paper II was restricted to a 2level atom, while Paper III used a multilevel hydrogen atom. Papers IV and V (Gouttebroze 2007, 2008) were dedicated to radiative equilibrium and velocity fields, respectively. All these papers dealt with the hydrogen atom. A certain amount of helium was included in the state equation, but it was assumed to be neutral and without any influence on the radiation field, as well as on the electron density.In the present paper, we assume that the cylinders are filled with a mixture of hydrogen and helium, and treat NLTE radiative transfer and statistical equilibrium of level populations for both atoms in two dimensions. The helium model atom includes the three stages of ionization, and the electron density is recomputed at each iteration in order to satisfy the equation of electric neutrality. In Sect. 2, we describe the computational methods used in the new numerical code. The results concerning hydrogen and helium ionization are detailed in Sect. 3. In Sect. 4, we study the formation of helium lines using a reference model defined in Sect. 2. Finally, in Sect. 5, we show how the helium line intensities react to changes in temperature, pressure and helium abundance.
2 Numerical methods
2.1 Formulation
The computation includes the numerical solution of the equations of NLTE radiative transfer for hydrogen and helium atoms, statistical equilibrium of level populations (for both atoms), pressure equilibrium, and electric neutrality. As in Papers II and III, the object under consideration is a cylinder of diameter D, whose axis makes an angle with the local vertical to the solar surface (this angle may vary between 0 and 90 ). The two active dimensions for radiative transfer are the distance to axis r and the azimuth . The method of resolution is of the MALI type (Rybicki and Hummer 1991). The special form of equations for twodimensional azimuth dependent (2DAD) cylindrical geometry and the method of solution, which are described in detail in Paper II, will not be repeated here. The equations of statistical equilibrium, independent of geometry, are treated in Paper I. In Paper II, we also described the method to compute the intensities incident on the cylinder, at different wavelengths, from the knowledge of the emission by the Sun, the inclination , and the altitude H. These incident intensities are also functions of azimuth, except in the special case . The condition for electric neutrality may be written(1) 
where is the electron density, the number density of ionized hydrogen (protons), and and the number densities of helium atoms in the second and third stages of ionization, respectively. If and are the total densities of hydrogen and helium, respectively, and and the corresponding densities of neutral atoms, the law of particle conservation yields
(2) 
and
(3) 
The gas pressure is
(4) 
where k is the Boltzmann constant and T the temperature. The parameter to check the convergence of iterations is the electrontohydrogen ratio . If is the (He/H) abundance ratio, Eq. (4) becomes
(5) 
The model atom for hydrogen includes 5 discrete levels plus 1 continuum. The equations of radiative transfer for the 10 discrete transitions and the 5 boundfree transitions are treated in detail, except in the case where the optical thicknesses are very low, which generally happens for continua from subordinate levels. The model atom for helium is the same as in Labrosse & Gouttebroze (2001, 2004). It contains 34 levels: 29 for He I, 4 for He II, and 1 for He III. The main part of this model comes from the neutral helium model of Benjamin et al. (1999). It is complemented with parameters of various origins, as described in Labrosse and Gouttebroze (2001). The number of permitted radiative transitions is 76, but most of them are optically thin under the usual conditions. All discrete transitions, for hydrogen as for helium, are treated under the assumption of complete frequency redistribution.
Table 1: Summary of cylindrical thread models.
2.2 Computational scheme
The computation is organized along two parallel series of routines, one for hydrogen, the other for helium. In each series of routines, the variables dependent on the atomic structures as atomic parameters, populations, intensities in different transitions are gathered into a specific Fortran ``common'', which is ignored by the main program. This main program only contains geometric (D, r, , etc.) and physical (, T, v_{T}, etc.) variables and the populations ( , , etc.) necessary to determine the ionization. The main phases of computations are:
 initialization: determination of geometrical, physical and atomic parameters. The incident intensities are also computed for each position at the surface of the cylinder and each direction, according to the method explained in Paper II;

first evaluation of level populations, in the optically thin
approximation. By averaging the incident intensities, we obtain mean
intensities in the different transitions of hydrogen and helium.
From these intensities and physical parameters, we compute the
radiative and collisional transition rates. Then, we solve
statistical equilibrium equations to obtain atomic level populations
at each point of the ()
mesh. Since the transition rates depend
on electron density, it is necessary to iterate.
We start from an arbitrary value of
(e.g.
)
and,
using Eqs. (3) and (5), successively deduce:
(6)
(7)
and
(8)
After computation of transition rates and solution of statistical equilibrium equations, we compute , , and by adding the populations of individual levels together, and deduce a new value of by
(9)
These operations are repeated until convergence.  full iterations with radiative transfer. This is the main part of the computation. The external scheme is similar to that of the preceding step, with a variable controlling the convergence of iterations but, in the meantime, the internal intensities for all transitions of hydrogen and helium are recomputed according to the principles of NLTE radiative transfer: absorption coefficients are derived from atomic level populations (determined in the preceding iteration). Then, intensities are computed by solving the transfer equation along each ray and integrating with respect to direction and frequency. At the same time, the diagonal terms of the operator are calculated by the method of Rybicki & Hummer (1991). The formulae appropriate to the cylindrical geometry are given in Paper II. The new intensities and the diagonal coefficients are used to form preconditioned statistical equilibrium equations, similar to those of Werner & Husfeld (1985). These equations are solved to obtain new level populations. Generally, one radiative transfer iteration for hydrogen and one for helium, between two iterations on , are sufficient to obtain a good convergence. In a few cases, it was necessary to perform two radiative transfer iterations for one iteration. These cases are indicated by an asterisk in the last column of Table 1.
2.3 Models
The model cylinders are defined by a series of geometric and physical parameters. The geometrical ones, diameter D, altitude Hand inclination , have been defined above. Physical parameters include: gas pressure , temperature T, microturbulent velocity v_{T}, and relative helium abundance . The code allows the definition of each of these parameters as a function of r and , but this possibility is not used in practice, except for the temperature. A summary of models used in the present paper is displayed in Table 1. First, there is a series of isothermal models (``t1'' to ``t11'') with temperature ranging from 6000 to 10^{5} K. Their diameter is fixed to 1000 km, their pressure to 0.1 dyn cm^{2}, helium abundance to 0.1, and microturbulent velocity to 5 km s^{1}. Other models have a prescribed temperature variation T(r), which comes from Paper III, and is represented in the upper part of Fig. 1 (models using this temperature distribution are indicated by ``var.'' in the third column of Table 1). The mean model ``p4'' (or ``a4'') is similar to that of Paper III. In the series ``p1'' to ``p7'', we change the pressure while keeping the other parameters constant. In the series ``a1'' to ``a7'', we investigate the effects of helium abundance. The last column of Table 1 indicates the number of iterations necessary to achieve the convergence on , the criterion being fixed to 10^{6} and the minimum iteration number to 5.3 Ionization
The introduction of helium ionization in models allows the electron density to be greater than the hydrogen density. Let be the ionization ratio for hydrogen, and similarly and be the corresponding ratios for the two stages of helium ionization. Equation (9) becomes(10) 
The ionization ratios , and are principally controlled by temperature. However, near the surface of the structure, the influence of incident radiation becomes more important and tends to moderate the effects of temperature.
3.1 Model with temperature gradient
Figure 1: Variations of temperature T and population ratios with the distance to the axis (r), for the model ``p4'' at the foot of the loop (). Abscissae: distance to axis relative to the total radius R. Top: temperature. Middle: ionization ratios for hydrogen (: dotdashed line) and helium (: dashed line; : continuous line). Bottom: electrontohydrogen ratio (dashed line: model assuming neutral helium; continuous line: model with both hydrogen and helium ionization). 

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3.2 Isothermal models
Figure 2: Variations of the ionization ratios ( top) and ( bottom) with r for different isothermal models (for clarity, not all models are represented). Number densities are averaged with respect to the azimuth . Symbols for hydrogen: open circles: T = 6000 K; full circles: 8000 K; open squares: 10 000 K; full squares: 15 000 K; crosses: 20 000 K; continuous line: 50 000 K. Same symbols for helium, plus: dotted line: 30 000 K; dashed line: 65 000 K; dotdashed line: 80 000 K. 

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4 Formation of helium lines
The computations described in Sect. 2 provide us with absorption coefficients and source functions in the different lines of hydrogen and helium, which may be subsequently used to calculate the intensities emerging from the cylinder. The introduction of helium ionization has little influence on hydrogen lines, which are formed in regions where helium is essentially neutral. Since hydrogen lines have been treated in preceding papers, we concentrate here on helium lines, and use the standard model ``p4'' to study their formation.Figure 3: Emission of the loop model ``p4'' in several lines of helium: He I 10 830 Å ( top, left); He I 584 Å ( top, right); He I 5876 Å ( bottom, left); He II 304 Å ( bottom, right). Frequencyintegrated intensities are normalized to the maximum value of each image. Horizontal and vertical coordinates indicate distances in megameters. 

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Figure 4: Ray path through the cylinder. 

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Figure 5: Total emergent intensities computed from model ``p4'', for different helium lines vs. position across the cylinder. Abscissae are in megameters and grow as the distance from the Sun. Ordinates are intensities in erg cm^{2} s^{1} sr^{1}. Dashed line: He I 10 830 Å; dotted line: He I 5876 Å; dotdashed line: He I 584 Å; continuous line: He II 304 Å. 

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(11) 
Let and be the absorption coefficient and the source function, respectively, at frequency . From the transfer equation
(12) 
and the boundary condition
(13) 
we deduce the emergent intensity
(14) 
with the optical thickness between the running point M (abscissa s) and B
(15) 
The total emergent intensity for the line under consideration is then
(16) 
These frequencyintegrated intensities have been computed as functions of r and for different helium lines. They are shown in Fig. 5. For all these lines, we observe a global decrease of intensities from the lower to the upper edge, which is due to the decrease of incident radiation. However, several differences may be noticed. Concerning ultraviolet optically thick lines, the cylinder appears broader in the He II resonance line at 304 Å than in the corresponding line for He I at 584 Å. The two triplet lines of He I under consideration have in common a transversal variation with three smooth peaks.
To locate the origin of emission inside the cylinder, we rewrite
Eq. (14) as
(17) 
with
(18) 
Thus, Eq. (16) becomes
(19) 
with
(20) 
C(s) is the contribution function appropriate for the frequencyintegrated emergent intensity. This function is plotted as shades of gray in Fig. 6 for the three lines at 10 830, 584 and 304 Å. The figure for the 5876 Å line is very similar to that of the 10 830 Å line. The existence of three maxima of emission for the intensity at 10 830 Å is due to the existence of two zones in the contribution function: a central patch and a ring. The patch corresponds to radiative processes of emission by low temperature matter, while the ring corresponds to a range of temperature where the maximum excitation of He I is occuring. The radiative processes of emission that occur in the central patch include direct scattering of incident radiation and the photoionizationrecombination process (Hirayama 1971; Zirin 1975). Since these two processes are dependent on incident radiation, the contribution functions in the central zone decrease with height. In contrast, the ring is produced by collisional excitation, so that it is practically independent of . The contribution function for the 584 Å line is concentrated in a single ring, without a central part: since the line is optically thick, the front part of the ring only contributes to intensity. The same is true for the 304 Å line but, in this case, the emitting layer is located at high temperature, very close to the surface. For this reason, the loop looks broader in this transition than in the He I lines.
Figure 6: Contribution functions corresponding to the standard model with a horizontal axis, for three lines of helium. Top: He I 10 830 Å; Middle: He I 584 Å; Bottom: He II 304 Å. Bright zones correspond to the maximum of the function. Directions are the same as in Fig. 4 (observer at right, Sun below). 

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5 Influence of physical parameters
5.1 Temperature
Figure 7: Frequencyintegrated intensities, averaged over position, emitted by isothermal models ``t1'' to ``t11''. Intensities (erg cm^{2} s^{1} sr^{1}) are plotted as functions of the temperature (K) of the model, in 4 transitions: He I 10 830 Å (open circles); He I 584 Å (full circles); He I 5876 Å (open squares); He II 304 Å (full squares). 

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Figure 8: Helium line halfprofiles emitted by five isothermal models: continuous line: ``t1'' (6000 K); dashed line: ``t4'' (15 000 K); dotted line: ``t6'' (30 000 K); dotdashed line: ``t8'' (50 000 K); longdashed line: ``t11'' (100 000 K). Each frame corresponds to a specific line, as indicated. 

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5.2 Pressure
The effects of gas pressure on emitted intensities are studied by means of a series of models ``p1'' to ``p7''. These models have the same variation of temperature as the standard model, but differ from each other by pressures ranging from 0.02 to 0.5 dyn cm^{2}. Frequencyintegrated intensities for the principal helium lines emitted by these models are displayed in Fig. 9. It appears that all intensities increase with pressure, but the slopes of the curves differ from one line to another. For neutral helium lines, the variation may be understood by considering the two main processes of emission: scattering of incident radiation and collisional excitation. In the optically thin case, the first process yields intensities proportional to atom populations. The second emission process, collisional excitation, which is proportional not only to the emitting atom density, but also to the electron density, tends to produce a quadratic variation of emission as a function of pressure. These considerations apply to the two He I lines at 10 830 and 5876 Å. It is visible in Fig. 9 that the emitted intensities for these two lines are proportional to pressure from 0.02 to about 0.2 dyn cm^{2}, and that the slope slightly increases at higher pressures, when collisions cease to be negligible. The same considerations apply to the 584 Å line, but the change of slope begins at lower pressures, around 0.1 dyn cm^{2}. The case of the He II 304 Å line is more complicated, since the slope of I(P) is less than linear below 0.1 dyn cm^{2} and greater than linear at higher pressures. It is visible on profiles (Fig. 8) that this line is optically thick and formed in the outermost part of the cylinder (Fig. 6). Whatever the pressure, the incident ultraviolet radiation from the Sun ionizes helium near the surface of the cylinder and creates a zone which scatters the 304 Å radiation. This part of emission due to scattering is nearly constant and constitutes the main contribution at low pressures (0.02 to 0.05 dyn cm^{2}). In contrast, at high pressures (0.2 to 0.5 dyn cm^{2}), collisional excitation becomes dominant and results in a quasiquadratic variation of I(P).
Figure 9: Frequencyintegrated intensities, averaged over position, emitted by models ``p1'' to ``p7''. Abscissae: gas pressure inside the cylinder (dyn cm^{2}). Ordinates: intensities in erg cm^{2} s^{1} sr^{1}. Spectral lines: He I 10 830 Å (open circles); He I 584 Å (full circles); He I 5876 Å (open squares); He II 304 Å (full squares). 

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5.3 Helium abundance
The abundance of helium is one of the most important parameters when analysing helium lines (see for instance Andretta et al. 2008, and references therein). Some observations, like that of filaments by Gilbert et al. (2007) suggest that very important changes of helium abundance may occur between the top, and the base of these objects. To evaluate the importance of this parameter to the emission of cylinder threads, we use a series of models (``a1'' to ``a7''), with the same pressure and temperature variation as the standard model, but helium to hydrogen ratios varying from 0.01 to 0.3. The variations of intensities as functions of are displayed in Fig. 10. The interpretation of these curves is relatively easy. As long as the cylinder is optically thin in the considered transition, the intensity is proportional to . This is the case for the 10 830 and 5876 lines until . For higher abundances, the slopes of the curves slightly decrease as the line centers begin to saturate. For optically thick lines at 584 and 304 Å, the intensity is still a growing function of abundance, but the slope is significantly lower than that corresponding to proportionality.
Figure 10: Frequencyintegrated intensities, averaged over position, emitted by models ``a1'' to ``a7''. Abscissae: log (abundance ratio ). Ordinates: intensities in erg cm^{2} s^{1} sr^{1}. Spectral lines: He I 10 830 Å (open circles); He I 584 Å (full circles); He I 5876 Å (open squares); He II 304 Å (full squares). 

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6 Conclusion
At this stage of our project, it is possible to perform a modeling of solar coronal loops including the following ingredients: NLTE radiative transfer in cylindrical geometry;
 2 dimensions (radius and azimuth);
 statistical equilibrium of atomic level populations;
 selfconsistent treatment of the two principal chemical elements: hydrogen and helium, including ionization;
 pressure equilibrium.
Acknowledgements
We wish to thank Petr Heinzel for useful suggestions concerning this manuscript.
References
 Andretta, V., & Jones, H. P. 1997, ApJ, 489, 375 [NASA ADS] [CrossRef] (In the text)
 Andretta, V., Mauas, P. J. D., Falchi, A., & Teriaca, L. 2008, ApJ, 681, 650 [NASA ADS] [CrossRef] (In the text)
 Benjamin, R. A., Skillman, E. D., & Smits, D. P. 1999, ApJ, 514, 307 [NASA ADS] [CrossRef] (In the text)
 Gilbert, H. R., Kilper, G., & Alexander, D. 2007, ApJ, 671, 978 [NASA ADS] [CrossRef] (In the text)
 Gouttebroze, P. 2004, A&A, 413, 733 [NASA ADS] [CrossRef] [EDP Sciences] (Paper I) (In the text)
 Gouttebroze, P. 2005, A&A, 434, 1165 [NASA ADS] [CrossRef] [EDP Sciences] (Paper II) (In the text)
 Gouttebroze, P. 2006, A&A, 448, 367 [NASA ADS] [CrossRef] [EDP Sciences] (Paper III) (In the text)
 Gouttebroze, P. 2007, A&A, 465, 1041 [NASA ADS] [CrossRef] [EDP Sciences] (Paper IV) (In the text)
 Gouttebroze, P. 2008, A&A, 487, 805 [NASA ADS] [CrossRef] [EDP Sciences] (Paper V) (In the text)
 Heinzel, P. 2007, in The Physics of Chromospheric Plasmas, ed. P. Heinzel, I. Dorotovic, & R. J. Rutten, ASP Conf. Ser., 368, 271 (In the text)
 Hirayama, T. 1971, Sol. Phys., 17, 50 [NASA ADS] [CrossRef] (In the text)
 Labrosse, N., & Gouttebroze, P. 2001, A&A, 380, 323 [NASA ADS] [CrossRef] [EDP Sciences] (In the text)
 Labrosse, N., & Gouttebroze, P. 2004, ApJ, 617, 614 [NASA ADS] [CrossRef] (In the text)
 Laming, J. M., & Feldman, U. 1993, ApJ, 403, 434 [NASA ADS] [CrossRef] (In the text)
 Patsourakos, S., Gouttebroze, P., & Vourlidas, A. 2007, ApJ, 664, 1214 [NASA ADS] [CrossRef] (In the text)
 Rybicki, G. B., & Hummer, D. G. 1991, A&A, 245, 171 [NASA ADS] (In the text)
 Werner, K., & Husfeld, D. 1985, A&A, 148, 417 [NASA ADS] (In the text)
 Zirin, H. 1975, ApJ, 199, L63 [NASA ADS] [CrossRef] (In the text)
All Tables
Table 1: Summary of cylindrical thread models.
All Figures
Figure 1: Variations of temperature T and population ratios with the distance to the axis (r), for the model ``p4'' at the foot of the loop (). Abscissae: distance to axis relative to the total radius R. Top: temperature. Middle: ionization ratios for hydrogen (: dotdashed line) and helium (: dashed line; : continuous line). Bottom: electrontohydrogen ratio (dashed line: model assuming neutral helium; continuous line: model with both hydrogen and helium ionization). 

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In the text 
Figure 2: Variations of the ionization ratios ( top) and ( bottom) with r for different isothermal models (for clarity, not all models are represented). Number densities are averaged with respect to the azimuth . Symbols for hydrogen: open circles: T = 6000 K; full circles: 8000 K; open squares: 10 000 K; full squares: 15 000 K; crosses: 20 000 K; continuous line: 50 000 K. Same symbols for helium, plus: dotted line: 30 000 K; dashed line: 65 000 K; dotdashed line: 80 000 K. 

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In the text 
Figure 3: Emission of the loop model ``p4'' in several lines of helium: He I 10 830 Å ( top, left); He I 584 Å ( top, right); He I 5876 Å ( bottom, left); He II 304 Å ( bottom, right). Frequencyintegrated intensities are normalized to the maximum value of each image. Horizontal and vertical coordinates indicate distances in megameters. 

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In the text 
Figure 4: Ray path through the cylinder. 

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In the text 
Figure 5: Total emergent intensities computed from model ``p4'', for different helium lines vs. position across the cylinder. Abscissae are in megameters and grow as the distance from the Sun. Ordinates are intensities in erg cm^{2} s^{1} sr^{1}. Dashed line: He I 10 830 Å; dotted line: He I 5876 Å; dotdashed line: He I 584 Å; continuous line: He II 304 Å. 

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In the text 
Figure 6: Contribution functions corresponding to the standard model with a horizontal axis, for three lines of helium. Top: He I 10 830 Å; Middle: He I 584 Å; Bottom: He II 304 Å. Bright zones correspond to the maximum of the function. Directions are the same as in Fig. 4 (observer at right, Sun below). 

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In the text 
Figure 7: Frequencyintegrated intensities, averaged over position, emitted by isothermal models ``t1'' to ``t11''. Intensities (erg cm^{2} s^{1} sr^{1}) are plotted as functions of the temperature (K) of the model, in 4 transitions: He I 10 830 Å (open circles); He I 584 Å (full circles); He I 5876 Å (open squares); He II 304 Å (full squares). 

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In the text 
Figure 8: Helium line halfprofiles emitted by five isothermal models: continuous line: ``t1'' (6000 K); dashed line: ``t4'' (15 000 K); dotted line: ``t6'' (30 000 K); dotdashed line: ``t8'' (50 000 K); longdashed line: ``t11'' (100 000 K). Each frame corresponds to a specific line, as indicated. 

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In the text 
Figure 9: Frequencyintegrated intensities, averaged over position, emitted by models ``p1'' to ``p7''. Abscissae: gas pressure inside the cylinder (dyn cm^{2}). Ordinates: intensities in erg cm^{2} s^{1} sr^{1}. Spectral lines: He I 10 830 Å (open circles); He I 584 Å (full circles); He I 5876 Å (open squares); He II 304 Å (full squares). 

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In the text 
Figure 10: Frequencyintegrated intensities, averaged over position, emitted by models ``a1'' to ``a7''. Abscissae: log (abundance ratio ). Ordinates: intensities in erg cm^{2} s^{1} sr^{1}. Spectral lines: He I 10 830 Å (open circles); He I 584 Å (full circles); He I 5876 Å (open squares); He II 304 Å (full squares). 

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In the text 
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