Radiative equilibrium model

The plausibility of the results of Turco et al. (1983) can be demonstrated with simple radiative equilibrium models, in which we assume that all smoke is evenly distributed above the 750 mb level in the atmosphere, the remaining layer closest to the ground being smokefree (see Figure 3). 

Fig. 3. Assumed partition of atmosphere in layers for two radiative equilibrium models a) infrared transfer by atmospheric gases neglected b) infrared transfer by H2O and CO2 taken into account.

We have demonstrated our arguments on the basis of the Ambio (1982) war scenario, using much simplified rainout, aerosol physics and radiative equilibrium models. Our analysis of the amounts of burned materials and smoke production is likewise uncertain and no doubt can be much improved upon, but we have tried to avoid extreme assumptions. It is very hard to carry out sensitivity analyses in this new research field with so many uncertainties. It is quite possible to forward arguments for a much less severe impact of a nuclear war. For instance, one may propose... 

Samuelson, R. E. (1983). Radiative equilibrium model of Titan s atmosphere. Icarus, 53,... 

W. H. McCrea develops models of atmospheres of A-type stars in radiative equilibrium with opacity due to H I. 

Lopez-Puertas, M., G. Zaragoza, M. A. Lopez-Valverde, and F. W. Taylor, Nonlocal Thermodynamic Equilibrium (LTE) Atmospheric Limb Emission at 4.6 /urn. 1. An Update of the C02 Non-LTE Radiative Transfer Model, J. Geophys. Res., 103, 8499-8513 (1998a). 

For this purpose, a new type of "unified model atmospheres" has been developed at the Munich Observatory by R. Gabler (1986) and A. Wagner (1986) in cooperation with J. Puls, A. Pauldrach and R.P. Kudritzki. These NLTE model atmospheres are spherically extended, in radiative equilibrium, and include the density and velocity distribution of radiation driven winds. The spectra of H and He lines are then calcu-... 

We consider the non-LTE spectral formation in a spherically expanding atmosphere. The velocity field v(r) is specified in its supersonic part by the usual analytical law with the parameters y, (final velocity) and the exponent 8=1, The temperature structure is derived from the assumption of radiative equilibrium, but only approximately evaluated for the grey LTE case. The atmosphere is assumed to consist of pure helium. The model atom has a total of 28 energy levels, among these 17 levels of He I. The line radiation transfer is treated in the "comoving frame". 

We assume stationarity and radiative equilibrium for the energy balance because the radiative timescales are short in respect to the hydrodynamic timescales soon after the initial increase in luminosity. Spherical symmetry is assumed. According to detailed numerical models (Falk and Arnett, 1977 Muller, personal communication, 1987 Nompto, 1987 Nomoto et aL, 1987) and also analytical solutions for strong shock waves in spherical expanding enveloped (Sedov, 1959) density profiles are taken which are given by the self-similar expansion of an initial structure i.e. 

These models of expanding atmospheres, however, involve more parameters than the classical static atmospheres. The influences of each physical parameters on the observational quantities must be carefully investigated. The assumption of spherical symmetry and the radiative equilibrium may not be valid over all phases of the development of SN1987A whose speckle image was reported to be elongated. 

The first attempts to explain the observed abundances of molecules on the basis of non-therinodynamic equilibrium models were by Kramers and ter Haar (1946) and Bates and Spitzer (1951). These investigations considered in some detail the basic formation and destruction processes through radiative association, photodissociation, photoionization and dissociative recombination, but were unable to reproduce the observed abundances of the then known interstellar molecules CH and CH. Because of the difficulties encountered with the early gas-phase reaction schemes, subsequent models focussed on grain surface... 

The first law of climate is that the earth is in radiative equilibrium. The second is that the atmosphere and ocean transport heat from warmer to cooler regions. Combined with the fact that the albedo of the Arctic Ocean depends on whether its surface is frozen or free of ice, tiiese laws form a minimal model of climate. As Buinteraction between the arctic and die rest of the hemisphere— and to add one embellishment stochastic forcing. 

These two equations state that, in each cell, the surface radiates away as much heat (right hand side) as it receives (left hand side). The term involving F on the left hand side is the solar radiation absorbed at the surface. The downwelling longwave radiation from the atmosphere is a fraction p of die energy radiated upward by the surface plus half the meridional transport D. This result is taken from a toy model of the radiative equilibrium between the atmosphere and the surface, Thorndike 1992. P is a measure of die longwave emissivity of the atmosphere. In today s atmosphere P is... 

Our multi-level carbon model atom is adapted from D. Kiselman (private communication), with improved atomic data and better sampling of some absorption lines. The statistical equilibrium code MULTI (Carlsson 1986), together with ID MARCS stellar model atmospheres for a grid of 168 late-type stars with varying Tefj, log g, [Fe/H] and [C/Fe], were used in all Cl non-LTE spectral line formation calculations, to solve radiative-transfer and rate equations and to find the non-LTE solution for the multi-level atom. We put particular attention in the study of the permitted Cl lines around 9100 A, used by Akerman et al. (2004). 

Up to now, the sdB/sdOB stars, the classical sdOs and the extremely helium-rich luminous sdOs have been analyzed for the most important (and accessible) metal abundances. The analyses usually require extensive non-LTE line formation calculations to solve the statistical equilibrium in detailed model atoms simultaneously with the radiative transfer equations for all relevant frequencies. With the advent of computer codes based on modern powerful solution algorithms (Auer and Heasley, 1976 Werner and Husfeld, 1985) it has now become possible to test (and eventually remove) approximations necessary in older computations. This and the availability of improved atomic data make the non-LTE predictions more reliable, and obstacles in obtaining accurate abundance determinations come now mainly from the observational side where high-quality spectra are needed to identify and to measure weak... 

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