Radiative Equilibrium Model Research Articles

One- and two-dimensional modeling of argon K-shell emission from gas-puff Z-pinch plasmas

In this paper, a theoretical model is described and demonstrated that serves as a useful tool for understanding K-shell radiating Z-pinch plasma behavior. Such understanding requires a self-consistent solution to the complete nonlocal thermodynamic equilibrium kinetics and radiation transport in order to realistically model opacity effects and the high-temperature state of the plasma. For this purpose, we have incorporated into the MACH2 two-dimensional magnetohydrodynamic (MHD) code [R. E. Peterkin et al., J. Comput. Phys. 140, 148 (1998)] an equation of state, called the tabular collisional radiative equilibrium (TCRE) model [J. W. Thornhill et al., Phys. Plasmas 8, 3480 (2001)], that provides reasonable approximations to the plasma’s opacity state. MACH2 with TCRE is applied toward analyzing the multidimensional implosion behavior that occurred in Decade Quad (DQ) [D. Price et al., Proceedings of the 12th IEEE Pulsed Power Conference, Monterey, CA, edited by C. Stallings and H. Kirbie (IEEE, New York, 1999), p. 489] argon gas puff experiments that employed a 12cm diameter nozzle with and without a central gas jet on axis. Typical peak drive currents and implosion times in these experiments were ∼6MA and ∼230ns. By using Planar Laser Induced Fluorescence measured initial density profiles as input to the calculations, the effect these profiles have on the ability of the pinch to efficiently produce K-shell emission can be analyzed with this combined radiation-MHD model. The calculated results are in agreement with the experimental result that the DQ central-jet configuration is superior to the no-central-jet experiment in terms of producing more K-shell emission. These theoretical results support the contention that the improved operation of the central-jet nozzle is due to the better suppression of instabilities and the higher-density K-shell radiating conditions that the central-jet configuration promotes. When we applied the model toward projecting argon K-shell yield behavior for Sandia National Laboratories’ ZR machine (∼25MA peak drive currents, ∼100ns implosion times) [D. McDaniel et al., Proceedings of the 5th International Conference on Dense Z-Pinches, Albuquerque, NM, 2002, edited by J. Davis, C. Deeney, and N. R. Pereira (American Institute of Physics, New York, 2002), Vol. 651, p. 23] for experiments that utilize the 12cm diameter central-jet nozzle configuration, it predicts over 1MJ of K-shell emission is attainable.

Non-symmetrical protoplanetary disks destroyed by UV photoevaporation

AbstractWe have developed geometric disk models to study the circumstellar geometries by fitting the spectral energy distribution (SED) of T Tauri and Herbig Ae/Be stars. The simulations provide means to recognize the signatures of different disk structures, including the effects due to external UV photoevaporation.Following Chiang & Goldreich (1997) and Dullemond et al. (2001), we used hydrostatic, radiative equilibrium models for passive, reprocessing flared disks. The grains in the surface of the disk are directly exposed to the radiation from the star and the interior of the disk is heated by diffusion from the surface. Adopting this two-layers disk structure, our disk model was improved in order to optimize the parameters estimated by using a calculation technique based on genetic algorithms presented by Bentley & Corne (2002).In the present work, we apply the code to model the SED of protoplanetary disks, which have being destroyed by photoevaporation due to the presence of ionizing OB stars, as the example of Trapezium region in the Orion Nebula. We compare geometric disk characteristics and physical conditions evaluated by our method to those obtained to the “proplyds” studied by Scally & Clarke (2001), Robberto et al. (2002) and Smith et al. (2005), among others. We also conclude that the parameter estimation by genetic algorithms assures accurate and efficient calculations.

Radiative equilibrium models of “hot Jupiters”

We present an extension of our equilibrium model, initially applied to 51 Peg b (Goukenleuque et al. 2000), to other irradiated extrasolar planets with different orbital distances (up to 1 AU). The model yields the mean atmospheric thermal structure and predicts the reflected spectral flux as well as the thermal flux emerging from such planets, in the visible and in the infrared wavelength ranges.

Inhomogeneous model of an Ar–Hg direct current column discharge

The inhomogeneous electron Boltzmann equation is solved for an Ar–Hg positive column direct current glow discharge with properties similar to the standard fluorescent lamp. The inhomogeneity arises from the ambipolar potential and requires the inclusion of the spatial gradient term in the Boltzmann equation. The electron kinetics is coupled to a collisional–radiative equilibrium model for various states of Ar and Hg subject to a reaction set with electron and heavy particle collisions. The axial electric field and space-charge potential are solved self-consistently. The calculated electron distribution function satisfies neither the local nor nonlocal approaches, but rather is found to be a function of both the electron energy and radial position. The radial dependence produces an energy flow from one part of the discharge to another, which results in nonuniform ultraviolet radiative power. Results are given for global properties of the discharge such as power per unit length and axial electric field, as well as spatially averaged quantities (densities, electron and gas temperatures, and emission powers) as a function of the wall temperature and the current. Extensive comparisons are presented with experimental data and previous homogeneous Boltzmann models of the discharge. The optimum current and fill pressures are determined and the general trends of varying the input parameters are established. There is general agreement between the present model and data, except that the calculated average electron density is larger than the measured values.

Effects of the non-gray absorption in a simple radiative equilibrium model

Analytical solutions of the atmospheric vertical temperature profile are the first step in the analysis of planetary atmospheres. These types of studies usually make use of the gray assumption (i.e., absorption of radiation independent of wavelength). Since atmospheric gases absorb radiation at selective wavelengths, here we examine the implications of the non-gray absorption in a simple and analytically solvable planetary atmosphere. We find that in some cases the non-gray absorption by itself limits the maximum optical thickness that can be reached by the planetary atmosphere. The existence of a liquid phase at the surface in equilibrium with its vapor phase in the atmosphere also restricts the value of the optical thickness. For a constant value of absorbed sunlight, the non-gray atmosphere may produce two stable states, in comparison with the single one obtained in gray atmospheres. This result supports the existence of a warm ocean in an optically thick atmosphere with a low value of absorbed sunlight.

Surface Emission Properties of Strongly Magnetic Neutron Stars

We construct radiative equilibrium models for strongly magnetized (B 1013 G) neutron star atmospheres taking into account magnetic free-free absorption and scattering processes computed for two polarization modes. We include the effects of vacuum polarization in our calculations. We present temperature profiles and the angle-, photon energy-, and polarization-dependent emerging intensity for a range of magnetic field strengths and effective temperatures of the atmospheres. We find that for B 1014 G, the emerging spectra are bluer than the blackbody corresponding to the effective temperature Teff with modified Planckian shapes because of the photon energy dependence of the magnetic opacities. However, vacuum polarization resonance significantly modifies the spectra for B ~ 1015 G, giving rise to power-law tails at high photon energies. The angle dependence (beaming) of the emerging intensity has two maxima: a narrow (pencil) peak at small angles (5°) with respect to the normal and a broad maximum (fan beam) at intermediate angles (~20°-60°). The relative importance and the opening angle of the radial beam decreases strongly with increasing magnetic field strength and decreasing photon energy. We finally compute a Teff-Tc relation for our models, where Tc is the local color temperature of the spectrum emerging from the neutron star surface, and find that Tc/Teff ranges between 1.1 and 1.8. We discuss the implications of our results for various thermally emitting neutron star models.

A Radiative Equilibrium Model of 51 Peg b

We present a radiative equilibrium model for extrasolar giant planets applied to 51 Peg b. The atmospheric model extends from 10 −5 to ∼10 bar and is limited at the bottom by an optically thick cloud of silicate (Mg 2SiO 4 or MgSiO 3) or iron (Fe) particles. Rayleigh scattering at short wavelengths and absorption by the H 2–H 2 and H 2–He continuum and molecular bands of H 2O, CO, and CH 4 are included. Atmospheric heating and cooling result, respectively, from absorption of stellar flux and from infrared thermal emission. The solution temperature profiles do not show any temperature inversion, in contrast with the giant planets of the solar system. The lapse rate is subadiabatic at all levels above the cloudtop, justifying the use of radiative equilibrium. We find that, under thermochemical equilibrium, CO dominates over CH 4 at all levels. The effective temperature is in the range 1150–1270 K and the Bond albedo in the range 0.15–0.42, depending on the location and reflectivity of the lower cloud deck. Mg 2SiO 4 or Fe clouds are weakly reflective in contrast to a MgSiO 3 cloud. The thermal emission spectrum prevails over the stellar reflected component below 13,000–15,000 cm −1 (λ>0.7 μm); it shows various windows, between the H 2O and CO bands, with the brightest centered at 2550 cm −1 (3.9 μm). The most prominent CO and CH 4 bands occur around 2100 (4.7 μm) and 3030 cm −1 (3.3 μm. Assuming a jovian abundance for PH 3, the bands around 2300 (4.3 μm) and 2450 cm −1 (4.1 μm) are clearly visible in absorption at a resolving power of ∼100. We investigated the detectability of the minor species CO and CH 4 at a resolution of 4000–6000, adequate to separate the planet's absorption features from their stellar and telluric counterparts. Considering photon noise from the star as the only noise source, we find that S/ N ratios of about 8 are reached on the molecular features in the 4.7- and 3.3-μm regions after ∼10 h of integration on an 8-m telescope. On the other hand, the planet-to-star contrast is as low as (2–4)×10 −4.

NLTE ionization and energy balance in high- Z laser-plasmas including two-electron transitions

We describe a new non-LTE statistical atomic kinetics model of plasmas in which the two-electron transitions of auto-ionization and its inverse, resonant-capture, play a dominant role in establishing ionization and energy balance. We show that, compared with a familiar collisional–radiative-equilibrium model which includes only the one-electron bound–bound and bound–free transitions: (1) the two-electron transitions force recombination of the plasma with decreasing density, (2) the two-electron transitions nevertheless further act to greatly increase the radiative emissivity of the plasma, and (3) the relaxation of the two-electron transition driven sysems proceeds much faster.

Radiative characteristics of pulsed power driven Z-pinch aluminum plasmas

In this paper, we study the dynamics of a massive aluminum Z-pinch plasma load and evaluate its performance as a soft X-ray radiator. A radiation hydrodynamic model self-consistently driven by a circuit describes the dynamics. Comparisons are made for the K- and L-shell soft X-ray emission as a function of the ionization dynamic model. The ionization dynamic models are represented by: 1) a time-dependent nonequilibrium (NEQ) model, 2) a collisional radiative equilibrium (CRE) model, and 3) a local thermodynamic equilibrium (LTE) model. For all three scenarios the radiation is treated 1) in the free streaming optically thin approximation where the plasma is treated as a volume emitter and 2) in the optically thick regime where the opacity for the lines and continuum is self-consistently calculated online and the radiation is transported through the plasma. Each simulation is carried out independently to determine the sensitivity of the implosion dynamics to the ionization and radiation model, i.e., how the ionization dynamic model affects the radiative yield and emission spectra. Results are presented for the L- and K-shell radiation yields and emission spectra as a function of photon energy from 10 eV to 10 keV. Also, departure coefficients from LTE are presented for selected levels and ionization stages.

Spectral Energy Distributions of T Tauri Stars with Passive Circumstellar Disks

We derive hydrostatic, radiative equilibrium models for passive disks surrounding T Tauri stars. Each disk is encased by an optically thin layer of superheated dust grains. This layer reemits directly to space about half the stellar energy it absorbs. The other half is emitted inward and regulates the interior temperature of the disk. The heated disk flares. As a consequence, it absorbs more stellar radiation, especially at large radii, than a flat disk would. The portion of the spectral energy distribution contributed by the disk is fairly flat throughout the thermal infrared. At fixed frequency, the contribution from the surface layer exceeds that from the interior by about a factor 3 and is emitted at more than an order of magnitude greater radius. Spectral features from dust grains in the superheated layer appear in emission if the disk is viewed nearly face-on.

Atmospheric radiative equilibria in a simple column model

An analytic radiative-equilibrium model is for- mulated where both short- and longwave radiation are treated as two-stream (down- and upward) fluxes. An equilibrium state is defined in the model by the vertical temperature profile. The sensitivity of any such state to the model atmosphere's optical properties is formulated analytically. As an example, this general formulation is applied to a single-column 11-layer model, and the model's optical parameters are obtained from a detailed radiative parametrization of a general circulation model. The resulting simple column model is then used to study changes in the Earth-atmosphere system's radiative equi- librium and, in particular, to infer the role of greenhouse trace gases, water vapor and aerosols in modifying the vertical temperature profile. Multiple equilibria appear when a positive surface-albedo feedback is introduced, and their stability is studied. The vertical structure of the radiative fluxes (both short- and longwave) is substan- tially modified as the temperature profile changes from one equilibrium to another. These equilibria and their stability are compared to those that appear in energy- balance models, which heretofore have ignored the details of the vertical temperature and radiation profiles.

Design and Characterization of a UHV Arcjet Nitrogen Source

AbstractA UHV-compatible nitrogen arcjet suitable for the growth of III-nitrides by molecular beam epitaxy is described and characterized. The arcjet operates at powers between 10W and 300W (the highest power used for these studies); typical nitrogen flows range between 5sccm and 100sccm. Optical emission spectra show the presence of activated atomic (N*) and molecular (N2*) nitrogen. A collisional radiative equilibrium model has been employed to provide insight into the excitation state of the active nitrogen. These results indicate that the arcjet is capable of supplying atomic nitrogen fluxes consistent with growth rates on the order of several monolayers per second. Langmuir probe measurements conducted near the position of the sample holder in the MBE chamber show the charged particle flux density is very low. The arcjet operates over a large powerpressure parameter space, and properties of the arc can be systematically “tuned” to provide a source suitable for selected-energy-epitaxy.

Deductions from a simple climate model: Factors governing surface temperature and atmospheric thermal structure

Radiative equilibrium solutions are the starting point in our attempt to understand how the atmospheric composition governs the surface and atmospheric temperatures, and the greenhouse effect. The Schwarzschild analytical grey gas model (SGM) was the workhorse of such attempts. However, the solutions suffered from serious deficiencies when applied to Earth's atmosphere and were abandoned about 3 decades ago in favor of more sophisticated computer models. Here we show that simple heuristic modifications to the SGM resolve these deficiencies, at least the catastrophic ones. The modifications include the addition of a spectral window, as well as allowing the scale height of optical depth to be different from that of the atmospheric pressure. The modified SGM reveals the fundamental factors that govern the radiative equilibrium thermal structure. (1) The presence of a spectral window allows the temperature jump between the surface and the immediately overlying atmosphere to become small, irrespective of the magnitude of the surface temperature. (2) In an optically thick atmosphere (such as Earth and Venus), the surface temperature and the runaway greenhouse effect depend inversely (as the one‐fourth power) on the Planck function‐weighted width of the window and are independent of the optical depth and other atmospheric parameters. The vertical variation of temperature within the atmosphere, however, is determined by the vertical variation of optical depth. (3) The degree of convective instability of the radiative equilibrium thermal structure γ is proportional to the ratio H/Hτ, where H is the atmospheric scale height and Hτ is the scale height of the vertical variation of optical depth. Here, γ is the ratio of the radiative equilibrium lapse rate and the neutral lapse rate for dry convection; γ > 1 indicates that the profile is unstable to free convection. Thus Hτ < H emerges as one of the fundamental criteria for convective instability. These factors lead to several corollaries regarding the specific details of atmospheric thermal structure on Earth and Venus. For example, according to the modified SGM, the radiative equilibrium temperature profile is strongly superadiabatic in Earth's lower atmosphere because Hτ is dominated by the water vapor's scale height being much less (2 compared with 8 km) than the atmospheric scale height. In the case of Venus, the pressure broadening of the CO2 rotational lines makes Hτ a factor of 2 smaller than H. Some of these results have been obtained using more detailed, multispectral radiative equilibrium models.

Carbon Monoxide Fundamental Bands in Late-Type Stars. III. Chromosphere or CO-mosphere?

view Abstract Citations (56) References (35) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Carbon Monoxide Fundamental Bands in Late-Type Stars. III. Chromosphere or CO-mosphere? Wiedemann, G. ; Ayres, T. R. ; Jennings, D. E. ; Saar, S. H. Abstract The strong vibration-rotation lines of CO at 4.6 microns (Δυ = 1) are unique diagnostics for the thermal conditions in the atmospheric altitude range of late-type stars near and above the temperature minimum in chromospheric models. Exploiting recent improvements in IR instrumentation, we observed a number of cool stars with high spectral resolution (R ≍ 100,000). The analysis of the spectra was based on an earlier theoretical study which had established CO Δυ = 1 non-LTE spectra as useful probes for stars of spectral type F, G, and K with log g ≥ 1. No direct chromospheric indicators were detected in the CO spectra. Stellar boundary (CO) temperatures were determined for the program stars and temperature profiles were constructed for α Tau, α Boo, β Gem and β Dra. The CO-based models feature a steady decrease in temperature at the height where the temperature increases in chromospheric models. Further comparison with chromospheric indicators shows an increasing discrepancy between the temperatures determined from CO measurements and those predicted from radiative equilibrium models, respectively, with increasing chromospheric activity. Thermal bifurcation of the stellar surfaces is proposed to reconcile the contradicting scenarios derived based on different spectral diagnostics. Publication: The Astrophysical Journal Pub Date: March 1994 DOI: 10.1086/173859 Bibcode: 1994ApJ...423..806W Keywords: INFRARED: STARS; LINE: FORMATION; STARS: CHROMOSPHERES; STARS: LATE-TYPE full text sources ADS | data products SIMBAD (9)

Near IR Observations of the 11 July 1991 Total Solar Eclipse from Mauna Kea, Hawaii

Near IR total eclipse measurements have provided clear evidence during both 2nd and 3rd contacts for a limb extension of about 125 km for wavelengths in the range containing the CO fundamental vibration-rotation bands between 4.3 and 5.5 μm, when compared to the limb at nearby shorter wavelengths. This is interpreted as a “flash” spectrum in the CO lines, with the above extension representing the outer level of the CO emission layer. This height can be compared to the τCO = 1.0 level incorporated into recent representative atmospheric models (Ayres and Wiedemann, 1989) which is 90 km above the visible limb for a semi-empirical “hot chromosphere” model (Avrett, 1985) and 220 km for a “cool” radiative equilibrium model based upon work by Anderson (1989).

Evidence for a Low Surface Temperature on Pluto from Millimeter-Wave Thermal Emission Measurements

Thermal continuum emission from the Pluto-Charon system has been detected at wavelents of 800 and 1300 micrometers, and significant upper limits have been obtained at 450 and 1100 micrometers. After the subtraction of emission from Charon, the deduced surface temperature of much of Pluto is between 30 and 44 kein, probably near 35 to 37 kelvin. This range is significantly cooler than what radiative equilibrium models have suged and cooler than the surface temperature derived by the Infrared Astronomy Satellite. The low temperature indicates that methane cannot be present at the microbar pressure levels indicated by the 1988 stellar occultation measurements and that the methane features in Pluto's spectrum are from solid, not gas-phase, absorptions. This result is evidence that Pluto's atmosphere is dominated by nitrogen or carbon monoxide rather than methane.

The embedded young stars in the Taurus-Auriga molecular cloud. II - Models for scattered light images

We describe NIR imaging observations of embedded young stars in the Taurus-Auriga molecular cloud. We find a large range in J-K and H-K colors for these class I sources. The bluest objects have colors similar to the reddest T Tauri stars in the cloud; redder objects lie slightly above the reddening line for standard ISM dust and have apparent K extinctions of up to 5 mag. Most of these sources also show extended NIR emission on scales of 10-20 arcsec which corresponds to linear sizes of 1500-3000 AU. The NIR colors and nebular morphologies for this sample and the magnitude of linear polarization in several sources suggest scattered light produces most of the NIR emission in these objects. We present modeling results that suggest mass infall rates that agree with predictions for cold clouds and are generally consistent with rates estimated from radiative equilibrium models. For reasonable dust grain parameters, the range of colors and extinctions require flattened density distributions with polar cavities evacuated by bipolar outflows. These results support the idea that infall and outflow occur simultaneously in deeply embedded bipolar outflow sources. The data also indicate fairly large centrifugal radii and large inclinations to the rotational axis for a typical source.

Line profile modeling for non-LTE partially ionized plasmas based on average atom model with l–splitting

We have developed a new opacity modeling of partially ionized high-Z plasma to solve radiation transport in fluid codes. The average atom model is used to describe the electronic state of the plasma. The electronic state of the plasma is determined by solving the collisional radiative equilibrium model. We have taken into account the electron energy level splitting owing to the difference in the azimuthal quantum number. To model the line groups made of the same electronic transitions from ions indifferent charge states, we used a statistical method and calculated the distribution of the charge states from the averaged electron population in each bound state. By using the new opacity model, we can well reproduce the X-ray spectra from the plasmas. It is found that the Δn = 0 transition can explain the peaked spectra near hv = 300 eV and l–splitted emission of the n = 5–4 transition can explain the flat spectra in the region of hv = 400–800 eV seen in the experiments.

Comparisons of observed ozone and temperature trends in the lower stratosphere

One result of the Ozone Assessment [WMO, 1989] is that there is a significant negative ozone trend in the lower stratosphere and upper troposphere from 1970 through 1986. In this paper we examine the relationship of this trend in ozone to that of temperature in the same altitude region utilizing a 62 station set of rawinsonde data, and compare the results to the changes in temperature determined from a radiative equilibrium model calculation. The calculated and observed trends in lower stratospheric temperature indicate substantive agreement in shape and magnitude of the vertical profiles.

Ionization and excitation in cool giant stars. I - Hydrogen and helium

The influence that non-LTE radiative transfer has on the electron density, ionization equilibrium, and excitation equilibrium in model atmospheres representative of both oxygen-rich and carbon-rich red giant stars is demonstrated. The radiative transfer and statistical equilibrium equations are solved self-consistently for H, H(-), H2, He I, C I, C II, Na I, Mg I, Mg II, Ca I, and Ca II in a plane-parallel static medium. Calculations are made for both radiative-equilibrium model photospheres alone and model photospheres with attached chromospheric models as determined semiempirically with IUE spectra of g Her (M6 III) and TX Psc (C6, 2). The excitation and ionization results for hydrogen and helium are reported.