non-LTE Radiative Transfer Research Articles

Non-LTE line transfer with spatially correlated turbulence: Fluctuation against average emergent radiation field

The increasing interest in using turbulence to explain anomalies observed in stellar spectral lines is discussed. This turbulence occurs at a finite spatial scale, a key parameter. In our previous work on non-LTE radiation transfer in the presence of a turbulent velocity field (Loucif & Magnan 1982), we calculated individual profiles representing intensity fluctuations around the averaged line shape for photon diffusion with complete redistribution in frequency (CFR), a function well-adapted to media where collisional excitations dominate. We now generalize the problem by accounting for partial redistribution in frequency (PFR). To show the effect of the spatial correlation in the velocity field on the emergent line profiles as well as the importance of fluctuations in the medium's optical properties against the average, exhaustive calculations of emergent non-LTE line profiles are performed in the frame of a systematic comparison between the two processes of redistribution for the three following cases: static medium, averaged turbulent medium, and deviation from the average. In all cases, we confirm the differences and similarities in CFR and PFR descriptions previously derived for static media. These results seem reasonable since light scattering occurs at the atomic level–a scale well below the macroscopic size of the turbulence scale length. In addition, pronounced differences in the emergent radiation field are obtained between the average case and the so-called deviation from average for both frequency redistribution functions. These systematic differences rule out classical treatment of line formation in turbulent fields that assume averaged media to model observations obtained over an exposure time shorter than the turbulent field time scale (). Beyond the different assumptions made to describe the non-LTE line formation in a turbulent medium, our model provides a simple and coherent description of realistic media applicable to different astrophysical observational backgrounds. For this purpose, a unified picture is proposed for the radiation field formation, invoking mainly the medium opacity, the turbulence correlation length, and the velocity. Observations of variable objects, or along extended lines of sights, allowing a high probability for such deviations to occur (e.g., quasars), are suitable for application of our model.

Mass-loss rate determination for the massive binary V444 Cygni using 3-D Monte-Carlo simulations of line and polarization variability

A newly developed 3-D Monte Carlo model is used, in conjunction with a multi-line non-LTE radiative transfer model, to determine the mass-loss rate of the Wolf-Rayet (W-R) star in the massive binary \object{V444 Cyg} (WN5+O6). This independent estimate of mass-loss rate is attained by fitting the observed \HeI (5876) \AA and \HeII (5412) \AA line profiles, and the continuum light curves of three Stokes parameters ((I, Q, U)) in the (V) band simultaneously. The high accuracy of our determination arises from the use of many observational constraints, and the sensitivity of the continuum polarization to the mass-loss rate. Our best fit model suggests that the mass-loss rate of the system is (\dot{M}_{\WR}=0.6(\pm 0.2) \times 10^{-5} M_{\sun} \mathrm{yr}^{-1} ), and is independent of the assumed distance to \object{V444 Cyg}. The fits did not allow a unique value for the radius of the W-R star to be derived. The range of the volume filling factor for the W-R star atmosphere is estimated to be in the range of 0.050 (for $R_{\WR}=5.0 R_{\sun}$) to 0.075 (for $R_{\WR}=2.5 R_{\sun}$). We also found that the blue-side of \HeI (5876 ) \AA and \HeII (5412) \AA lines at phase 0.8 is relatively unaffected by the emission from the wind-wind interaction zone and the absorption by the O-star atmosphere; hence, the profiles at this phase are suitable for spectral line fittings using a spherical radiative transfer model.

Multidimensional Non‐LTE Radiative Transfer. I. A Universal Two‐dimensional Short‐Characteristics Scheme for Cartesian, Spherical, and Cylindrical Coordinate Systems

We have developed an efficient and robust two-dimensional non-LTE radiation transfer solver appropriate for line transfer in the equivalent two-level atom formalism. The numerical method applies the accelerated lambda iteration technique together with the short-characteristics scheme. The code presented in this paper incorporates all three standard geometries (Cartesian, cylindrical, and spherical) in a transparent way while allowing for arbitrary (three-dimensional) velocity fields. The geometry-specific parts of the radiative transfer solver are modularized so that the change of geometry is accomplished by simply setting the appropriate switch. We have also developed a parallel version of the code, in which we use a parallelization in spatial subdomains, and showed that such a scheme is sufficiently robust. We have performed a number of tests of the performance of the solver in all three geometries. Finally, we discuss the internal accuracy of the transfer solutions depending on the number of spatial, angular, and frequency grid points.

Hydrodynamic Simulations of Flares on Accretion Disks

We have constructed a hydrodynamic simulation of flares on the accretion disks of cataclysmic variable stars. In these flares the disk photosphere is heated by a beam of suprathermal electrons. The beam energy flux, beam duration, position in the accretion disk, and accretion disk temperature were varied in 20 flare simulations. All the flare simulations show that above a site of maximum heating the gas is blown upward from the disk. Below this point the gas is compressed and heated. A non-LTE radiative transfer program calculates the resulting continuous emission and Balmer line radiation from the flare. The temporal development of each flare model is followed by calculating the radiation at 15–20 time steps. The Hβ line flux from accretion disks is estimated for 20 dwarf novae and 12 nova and nova-like systems by using information gathered from the literature. We then use a simple approximation for the rate of flaring across an accretion disk to see whether flares can account for all the Hβ emission. The rate of flickering observed in cataclysmic variables is used as a constraint on this model. Using flickering rates from one study we find that if each observed flicker is one magnetic flare, then flares can account for only 1%–2% of the Hβ emission. A much higher flare rate can account for the observed Hβ emission if flickering studies underestimate the true rate of flaring. A flare avalanche model may account for both the observed Hβ flux and the observed flickering.

Cooling Rates of Molecular Clouds Based on Numerical Magnetohydrodynamic Turbulence and Non‐LTE Radiative Transfer

We have computed line-emission cooling rates for the main cooling species in models of interstellar molecular clouds. The models are based on numerical simulations of supersonic magnetohydrodynamic (MHD) turbulence. Non-LTE radiative transfer calculations have been performed to properly account for the complex density and velocity structures in the MHD simulations. Three models are used. Two of the models are based on MHD simulations with different magnetic field strength (one model is super-Alfvenic, while the other has equipartition of magnetic and kinetic energy). The third model includes the computation of self-gravity (in the super-Alfvenic regime of turbulence). The density and velocity fields in the simulations are determined self-consistently by the dynamics of supersonic turbulence. The models are intended to represent molecular clouds with linear size L ≈ 6 pc and mean density n ≈ 300 cm-3, with the density exceeding 104 cm-3 in the densest cores. We present 12CO, 13CO, C18O, O2, O I, C I, and H2O cooling rates in isothermal clouds with kinetic temperatures 10-80 K. Analytical approximations are derived for the cooling rates. The inhomogeneity of the models reduces photon trapping and enhances the cooling in the densest parts of the clouds. Compared with earlier models, the cooling rates are less affected by optical depth effects. The main effects come, however, from the density variation, since cooling efficiency increases with density. This is very important for the cooling of the clouds as a whole, since most cooling is provided by gas with density above the average.

Line mixing effect on the pure CO 2 absorption in the [formula omitted] region

The IR absorption of the pure CO 2 gas in the region of 15 μm was examined. A special attention was given to the line mixing effect that influences the spectral shape of the vibration–rotation absorption bands in the Q-branch regions. Two methods in shape description were analyzed. The first method uses the Rosenkranz line shapes with the line mixing parameters, which are found from an empirical rotational relaxation matrix. The second method is based on the strong collision model with adjusted branch coupling (ABC-model). The merits and the demerits of these two methods are discussed, and the results of the corresponding calculations are compared to the measured shapes. It is inferred that the ABC-model for the absorption coefficient calculations can be successfully applied for solving the non-LTE radiative transfer problem in CO 2 bands in the atmospheres of Earth-like planets.

The Origin of M[CLC]n[/CLC] [CSC]ii[/CSC] Emission in the Spectra of Chemically Peculiar Stars

Emission from Mn II multiplet 13 (λλ6122-6132) in the spectrum of the 3He star 3 Centauri A and the hot, mild, HgMn star 46 Aquilae can be naturally explained by interlocked non-LTE effects. However, reproduction of the strength of the Mn II emission in both stars requires vertical stratification of the manganese abundance, with manganese concentrated high in the photosphere (column mass 10-2 g cm-2). If this formation picture is correct, several additional transitions of Mn II with λ > 8000 A should also be present in emission in the spectrum of 3 Cen A. The wide range in the strength of Mn II multiplet 13 among upper main-sequence stars (ranging from absorption to emission) is made possible by the interplay in the non-LTE radiative transfer solution of the stellar Teff, manganese abundance, and manganese stratification profile. In particular, emission is strongly suppressed by a large manganese overabundance in the photosphere. This explains why the hot, mild, HgMn star 46 Aql, which has only a modest manganese enhancement, is detected in emission in Mn II multiplet 13 while other HgMn stars of similar Teff but with large photospheric manganese overabundances, such as κ Cancri, present Mn II multiplet 13 in absorption.

Photospheric fine structure: An observational challenge

The requirement on spatial resolution of a large solar telescope is frequently based on the assumption that the smallest observable features in the solar photosphere could not be much dierent from a photon mean free path due to smoothing by radiative transfer. Although hydrodynamic simulations show that much smaller structures should exist, a resolution of the order of 100 km is typically considered sucient for observations in the photosphere. We performed 2D non-LTE radiative transfer computations for thin flux sheets with widths ranging from 10 to 160 km in the solar photosphere. We demonstrate that such small structures { should they exist { could be observed as small scale variations of intensity and polarization. We conclude that the size limit below which photospheric structure cannot be observed due to smoothing radiative transfer eects must lie well below 10 km. A spatial resolution limit for telescopes based on photon mean free path arguments should therefore be abandoned.

Modeling the Variable Chromosphere of α Orionis

A spectral analysis of the prototypical red supergiant star a Ori that is based on near-UV, optical, and near-IR high-dispersion spectra obtained between 1992 September and 1999 July with the Space Tele- scope Imaging Spectrograph and the Goddard High Resolution Spectrograph on the Hubble Space Telescope, the Utrecht Echelle Spectrograph, and the SoFin Echelle Spectrograph is presented. With detailed non-LTE radiative transfer calculations in spherical geometry, we model the mean conditions in the stellar chromosphere from Ha and the Mg II resonance doublet. The Ha absorption line emerges from an extended chromosphere. Temporal changes of its velocity structure are determined from detailed —ts to near-UV Si I lines, and chromospheric expansion velocities around 4 km s ~1 are found in 1992, whereas the chromosphere was collapsing onto the photosphere with a velocity of 5 km s ~1 in 1998¨ 1999. The Ha core depth is correlated over time with weaker depression changes seen in prominent TiO band heads that dominate the optical spectrum. From elaborate spectral synthesis calculations, we isolate unblended metal absorption lines in the near-IR and determine K and log (g) \( 0.5 T eff 3500 for solar metallicity and 12 ^ 0.5 km s ~1 for macrobroadening and v sin i. Semiempirical —ts yield chromospheric temperatures not in excess of 5500 K, but with long-term changes by D400 K. The model extends over 5000 and requires supersonic microturbulence values ranging to 19 km s ~1 ,i n R _ strong contrast with the photospheric value of only 2 km s ~1. We observe Doppler shifts of 4¨ 8k m s~1 in the scattering cores of many double-peaked near-UV emission lines which correlate with changes in the intensity ratio of their emission components. The red emission components were much stronger in 1992, indicating a phase of enhanced chromospheric out—ow, for which we determine a spherical mass- loss rate of 6 ) 10~7 yr ~1. We present a discussion of chromospheric pulsation in this massive star. M _ Detailed modeling of the observed Mg II h and k line asymmetry is also presented. We demonstrate that a chromospheric Mn I blend strongly contributes to this puzzling asymmetry. Subject headings: line: identi—cationstars: chromospheresstars: individual (a Orionis) ¨ stars: late-typestars: mass losssupergiants

Non-LTE Infrared Emissions of CO 2 in the Atmosphere of Venus

A non-local thermodynamic equilibrium (non-LTE) radiative transfer model previously developed for the martian atmosphere has been applied to the venusian atmosphere to study the CO 2 infrared emissions and its radiative equilibrium temperature profile. The model computes the populations of more than 60 vibrational levels of the four major isotopes of CO 2, and the cooling and heating rates by more than 90 radiative transitions. The departure from LTE of all the CO 2(0,ν 2,0) levels is found to occur around 115 km (or 0.2 μb) during both night and daytime conditions, while it takes place around 105 and 90 km for the (0,0,1) level at night and day, respectively. The daytime populations of the (ν 1,ν 2,1) and high combination levels are very large. The cooling rate due to the 15-μm bands peaks around 125 km (10 nb) and amounts to 130 K/day for the reference nighttime model, being very dependent on the thermal structure. The 15-μm fundamental bands (FB) of the minor isotopes and the first hot bands of the major isotope produce much greater cooling than the FB of the main isotope between 110 and 125 km. The solar heating rate presents a double peak maximum between 120 and 135 km, with a very strong component from the 2.7-μm FB around 130 km. This component is much more important than its martian counterpart, due to the larger relative abundance of atomic oxygen in the thermosphere of Venus. The rate coefficient for collisional activation of CO 2(ν 2) by atomic oxygen used in this work, 3×10 −12cm 3 s −1, coincides with the value currently recommended for the Mars' and Earth's upper atmospheres, although a definitive measurement of this important rate remains to be carried out in the laboratory. Radiative relaxation times have been computed with focus on the 80–130 km region. The relaxation at 15 μm varies from more than an Earth's week around 80 km to a minimum of 6 min around 130 km during daytime. It increases above this altitude, in clear contrast to LTE calculations. Sensitivity studies to evaluate the effects of the current uncertainties in the major rate coefficients and comparisons with previous non-LTE models and data, as well as with similar situations in the atmosphere of Mars, are presented.

A Comparison of13CO Local Thermodynamic Equilibrium and True Column Densities in Molecular Cloud Models

In this work we use models of molecular clouds and non-LTE radiative transfer calculations to compare the column densities of molecular clouds with their LTE 13CO column densities. The cloud models consist of three-dimensional grids of density and velocity fields obtained as solutions of the compressible magnetohydrodynamic equations in a 1283 periodic grid in both the supersonic and super-Alfvenic regimes. Because of the random nature of the velocity field and the presence of shocks, the densities span a continuous range of values covering about 6 orders of magnitude (from ~0.1 to ~105 cm-3). As a result, the LTE column densities can be calculated over 3 orders of magnitude. We find that LTE column densities of molecular clouds typically underestimate the mean 13CO true column densities by factors ranging from 1.3 to 7. These results imply that the standard LTE methods for the derivation of column densities from CO data systematically underestimate the true values independent of other major sources of uncertainty such as the relative abundance of CO.

He I Line Profiles Obtained From a Be Wind Model

AbstractWe undertook a non-LTE radiative transfer calculation to find out the possible conditions under which observed H and He I line profiles arise from some Be stars.

Supersonic Turbulence in the Perseus Molecular Cloud

We compare the statistical properties of J=1-0 13CO spectra observed in the Perseus Molecular Cloud with synthetic J=1-0 13CO spectra, computed solving the non-LTE radiative transfer problem for a model cloud obtained as solutions of the three dimensional magneto-hydrodynamic (MHD) equations. The model cloud is a randomly forced super-Alfvenic and highly super-sonic turbulent isothermal flow. The purpose of the present work is to test if idealized turbulent flows, without self-gravity, stellar radiation, stellar outflows, or any other effect of star formation, are inconsistent or not with statistical properties of star forming molecular clouds. We present several statistical results that demonstrate remarkable similarity between real data and the synthetic cloud. Statistical properties of molecular clouds like Perseus are appropriately described by random super-sonic and super-Alfvenic MHD flows. Although the description of gravity and stellar radiation are essential to understand the formation of single protostars and the effects of star formation in the cloud dynamics, the overall description of the cloud and of the initial conditions for star formation can apparently be provided on intermediate scales without accounting for gravity, stellar radiation, and a detailed modeling of stellar outflows. We also show that the relation between equivalent line width and integrated antenna temperature indicates the presence of a relatively strong magnetic field in the core B1, in agreement with Zeeman splitting measurements.

Constraints on the Evolution of Massive Stars through Spectral Analysis. I. The WC5 Star HD 165763

Using a significantly revised non-LTE radiative transfer code that allows for the effects of line blanketing by He, C, O, Si, and Fe, we have performed a detailed analysis of the Galactic Wolf-Rayet (W-R) star HD 165763 (WR 111, WC5). Standard W-R models consistently overestimate the strength of the electron scattering wings, especially on strong lines, so we have considered models where the wind is both homogeneous and clumped. The deduced stellar parameters for HD 165763 are as follows: The stellar parameters deduced for HD 165763 are significantly different from earlier analyses. The deduced luminosity is a factor of 2 larger, and a smaller core radius is found. The smaller radius is in better agreement with expectations from stellar evolution calculations. Both of these changes can be attributed to the effects of line blanketing. The deduced C/He abundance is similar to earlier calculations, and the O/He abundance had not previously been determined. The observed iron spectrum, principally due to Fe V and Fe VI, is well reproduced using a solar iron mass fraction, although a variation of at least a factor of 2 about this value cannot be precluded. In particular, the models naturally produce the Fe V emission feature centered on 1470 A and the complex Fe emission/absorption spectrum at shorter wavelengths. Also, Fe strongly modifies the line strengths and profile shapes shortward of 1800 A and must be taken into account if we are to successfully model this region. The reddening toward HD 165763 does not follow the mean Galactic extinction law. We determine the reddening law toward HD 165763 by comparing our model continuum levels to observations. In order to simultaneously match the UV, optical, and particularly the infrared fluxes, we used the parameterized reddening law of Cardelli, Clayton, and Mathis with EB-V = 0.3 and R = 4.5, where R = AV/EB-V. Based on both observational and theoretical suggestions we have considered models in which the wind is still accelerating at large radii. In particular, we discuss models in which the velocity law can be characterized by β = 1 for r < 10R* but that undergo a substantial velocity increase (~600 km s-1) beyond 10R*. These models appear to give slightly better fits to the line profiles, but the improvements are small, and it is difficult to gauge whether observational data require such a velocity law. We cannot yet determine whether the winds of W-R stars are driven by radiation pressure, because we neglect many higher levels of iron in our model ions, and we do not include important elements such as cobalt and nickel. However, the wind problem in W-R stars is less severe than previously assumed if clumping occurs. For our clumped model, the single scattering limit is only exceeded by a factor of 10 compared to 3 times this value for a homogeneous wind. Clumping appears to be the key to explaining the apparent high mass-loss rates determined for W-R stars and is extremely important in understanding how or even whether W-R winds are driven by radiation pressure. A reduction in W-R mass-loss rates has important implications for stellar evolution calculations.

3D non-LTE radiative transfer: a new code and its application to γ2 Velorum

A new approach to 3D optically thick non-LTE radiative transfer for moving media is presented. As a first application, we look at the ionization state of the colliding winds interaction zone between two stars.

Synthetic Molecular Clouds from Supersonic MHD and Non‐LTE Radiative Transfer Calculations

The dynamics of molecular clouds is characterized by supersonic random motions in the presence of a magnetic field. We study this situation using numerical solutions of the three-dimensional compressible magneto-hydrodynamic (MHD) equations in a regime of highly supersonic random motions. The non-LTE radiative transfer calculations are performed through the complex density and velocity fields obtained as solutions of the MHD equations, and more than 5x10^5 synthetic molecular spectra are obtained. We use a numerical flow without gravity or external forcing. The flow is super-Alfvenic and corresponds to model A of Padoan and Nordlund (1997). Synthetic data consist of sets of 90x90 synthetic spectra with 60 velocity channels, in five molecular transitions: J=1-0 and J=2-1 for 12CO and 13CO, and J=1-0 for CS. Though we do not consider the effects of stellar radiation, gravity, or mechanical energy input from discrete sources, our models do contain the basic physics of magneto-fluid dynamics and non-LTE radiation transfer and are therefore more realistic than previous calculations. As a result, these synthetic maps and spectra bear a remarkable resemblance to the corresponding observations of real clouds.

The Effect of Photospheric Granulation on the Determination of the Lithium Abundance in Solar‐type Stars

I investigate non-local thermodynamic equilibrium (non-LTE) formation of the 670.6 nm Li I resonance doublet in the presence of convective surface inhomogeneities in solar-type stars. This doublet is widely used for lithium abundance determination in stars. It has been suggested that the presence of hot and cool elements in a stellar atmosphere due to convective heat transport might lead to an underestimate of lithium abundance by as much as a factor of 10 when the equivalent width of the doublet is analyzed in terms of a one-dimensional plane-parallel model atmosphere. To explore this possibility, I solved the two-dimensional non-LTE radiative transfer equations for a sufficiently large lithium model atom in a hydrodynamic simulation snapshot of the solar granulation. This was done for different values of the lithium abundance ranging from ALi = 0.0 to 3.3. In all cases the effects of the inhomogeneities in the atmosphere on lithium line strength are small, never amounting to more than 0.1 dex in the derived abundance. This occurs mainly for three reasons. First, because of the exponential decrease of density with height in the gravitationally stratified stellar atmosphere, radiation escapes mostly vertically with little horizontal exchange. Some lateral transfer does occur at the boundaries between hot and cold elements, but the effect of this exchange on the spatially averaged line strength cancels out. It leads to a smoothing over the surface rather than to a diminishing overall strength of the doublet. Second, the sharp drop in temperature over hot upwelling material, in contrast to the much shallower gradient over the dark intergranular lanes, causes the 670.6 nm doublet to be deeper and narrower in the former and broader in the latter. Consequently, the contrast of equivalent line width between profiles emerging over hot upflows and cold downflows is small. Finally, because of its small abundance the opacity scale in lithium ionizing continua is mostly set by H- bound-free processes. Optical depth unity at the photoionization edges, therefore, follows the contours of electron temperature, moderating contrast in the ionizing radiation field.

Probing the structure of molecular cloud cores: observations and modelling of C I and C18O in HH24-26

We describe observations of the (CO)-O-18 J = 2 --> 1, 3 --> 2 and C I P-3(1) --> P-3(0) lines towards the HH24-26 molecular cloud core. The (CO)-O-18 traces the north-south molecular ridge, but the dense clumps identified by previous high-resolution HCO+ and dust continuum data do not stand out. Using H-2 column densities estimated from dust continuum measurements, we find that the CO abundance may be reduced by factors of at least 10 towards three positions (two of which are Class O protostars). Depending on the assumptions employed, the reduction may be as high as similar to 50 towards the clump positions. The magnitude of the reduced abundances is in good agreement with chemical models of collapsing clouds in which molecules accrete on to dust grains. Alternative interpretations, retaining normal abundances. and relying on subtle optical depth and beam filling effects, are considered, but shown to be less likely. The contrast in C I line intensity is low across the source. The greater part of the emission probably arises from the outer surface of the cloud, but it is impossible to determine the exact contribution from C atoms deeper into the core as their emission cannot be separated from that arising at the surface. Non-LTE radiative transfer modelling of the (CO)-O-18 emission towards the two Class O sources HH24MMS and HH25MMS confirms a widespread reduction of the CO abundance by a factor of greater than 10 within a radius of 0.3 pc and not just close to the clumps. In HH24MMS, the abundance is required to rise again towards the centre of the model clouds in accordance with the rise in temperature near to the central embedded object where CO is desorbed from grains. Application of the same radiative transfer model to the C I emission provides little constraint on the carbon abundance profile, although fits can be obtained for reasonable forms. The depletion of CO in the core, coupled with the lack of an infrared cluster, suggests that HH24-26 may be in the process of forming its first generation of stars.

The Treatment of Non‐LTE Line Blanketing in Spherically Expanding Outflows

Extensive modifications to the non-LTE radiative transfer code of Hillier have been made in order to improve the spectroscopic analysis of stars with stellar winds. The main improvement to the code is the inclusion of blanketing due to thousands of overlapping lines. To implement this effect, we have used the idea of super levels first pioneered by Anderson. In our approach, levels with similar excitation energies and levels are grouped together. Within this group, we assume that the departure coefficients are identical. Only the population (or equivalently, the departure coefficient) of the super level need be solved in order to fully specify the populations of the levels within a super level. Our approach is a natural extension of the single-level LTE assumption, and thus LTE is recovered exactly at depth. In addition to the line blanketing modifications, the code has been improved significantly in other regards. In particular, the new code incorporates the effect of level dissolution, the influence of resonances in the photoionization cross sections, and the effect of Auger ionization. Electron scattering with a thermal redistribution can be considered, although it is normally treated coherently in the comoving frame (which still leads to redistribution in the observer's frame). Several example calculations are described to demonstrate the importance of line blanketing on spectroscopic analysis. We find that the inclusion of blanketing modifies the strengths of some optical CNO lines in Wolf-Rayet (W-R) stars by factors of 2-5. In particular, the strengths of the WC classification lines C III λ5696 and C IV λ5805 are both increased because of iron blanketing. This should help alleviate problems found with nonblanketed models, which were incapable of matching the strengths of these lines. We also find that, in the UV (1100-1800 A), the influence of Fe is readily seen in both emission and absorption. The emission is sensitive to the iron abundance and should allow, for the first time, Fe abundances to be deduced in W-R stars. The improvements made to our code should greatly facilitate the spectroscopic analysis of stars with stellar winds. We will be able to determine the importance and influence of line blanketing, as well as of several other effects that have been included in the new code. It will also allow us to better determine W-R star parameters, such as luminosity, elemental abundances, wind velocity, and mass-loss rate. With future application to related objects, such as novae and supernovae, our new code should also improve our understanding of these objects with extended outflowing atmospheres.

The non-LTE correction to the vibrational component of the internal partition sum for atmospheric calculations

In this paper, we develop the theoretical basis for the non-local thermodynamic equilibrium (non-LTE) correction to the vibrational component of the internal partition sum Q v , and we show how this correction enters into the radiative transfer calculation for a limb-viewing radiometer. The importance of the non-LTE correction to Q v depends, for the most part, on the degree to which the lowest vibrational state of the molecule is in non-LTE for a given altitude, since it is this vibration that contributes most to the partition sum. The affect on high-altitude emission depends on the principle excitation mechanism of the radiating molecule, and we compare CO 2 and O 3. In the case of CO 2, to first order, the high-altitude radiance measured by a limb-viewing radiometer is dependent on the value of the inverse of the partition sum in the region just above the tangent point. We have shown that in the case of the high-altitude temperature sounding channel of the High Resolution Dynamics Limb Sounder (HIRDLS) the non-LTE correction can result in a difference in calculated radiance of some 30% at 130 km. This suggests that the non-LTE correction to Q v is an important consideration for high-altitude non-LTE radiative transfer models.