Optically thick sources

Astrophysical objects that do not contribute to UHECR spectrum are not constrained by the WB limit. In optically thick sources (for which the optical depth is r/r. = Rgource (vp 11 ) 1) nucleons interact while neutrinos... 

We shall now apply the concepts developed in Chapter 9 to a discussion of the emission and absorption of radiation by an excited gas. We start by deriving the equation of radiative transfer in terms of the volume emission and absorption coefficients for line radiation and consider simple solutions for the case of uniformly excited sources. The terms source function and optical thickness are defined and the effect of self absorption and self reversal in optically thick sources is outlined. 

Optically thick sources, t (L) > 1. In the case of spectral lines which terminate on the ground, metastable, or resonance levels of an atom the assumption that r (L) 1... 

Tegen, I., and I. Fung, Modeling of Mineral Dust in the Atmosphere Sources, Transport, and Optical Thickness, J. Geophys. Res., 99, 22897-22914 (1994). 

Line reversal temperatures can be obtained if the hot gas is optically thick in the wavelength of some particular line (P2, P3). With a light source of known temperature (i.e., a calibrated tungsten lamp) placed behind the gas emitting this line, if the gas is hotter than the source it will appear brighter. At the same temperature both blend. 

Photolysis of CO occurs by absorption of stellar UV radiation in the wavelength range 90-100 nm. The reaction proceeds by a predissociation mechanism, in which the excited electronic state lives long enough to have well-defined vibrational and rotational energy levels. As a consequence, the three isotopic species—C O, C O, and C O—absorb at different wavelengths, corresponding to the isotope shift in vibrational frequencies. Because of their different number densities, the abundant C O becomes optically thick in the outermost part of the cloud (nearest to the external source of UV radiation), while the... 

Aerosol particle optical thickness (AOT) Sun photometry Beer s law using sun as light source -h... 

Schulz M., Balkanski Y. J., Guelle W., and Dulac F. (1998) Role of aerosol size distribution and source location in a three-dimensional simulation of a Saharan dust episode test against satellite-derived optical thickness. J. Geophys. Res. 103, 10579-10592. 

The thermal conductivity values for polycrystalline (optically-thick) CaF obtained by. ngery —(comparative linear flow method) and by Taylor and Mills (laser pulse method) are in reasonable agreement (Figure 7). However, there is an appreciable discrepancy between the values of k obtained by the ziiQc source method —"— and the single value due to Ogino et al (radial heat source method). 

The second exception is if we are interested in the propagation of a collimated light source (i.e., a laser). In this case, since only one incident direction is to be considered, the problem can be modeled by direct simulation, even for multiple scattering media up to intermediate optical thicknesses (t = 1). In general, the direct simulation of the radiative transfer equation is to be chosen if a fundamental understanding of radiation-combustion or radiation-turbulence interactions is required. 

Mineral dust is an ubiquitous aerosol component. For example, large quantities of dust are routinely transported from sources in North Africa across the tropical Atlantic (Li et al., 1996). Satellite imagery shows that such dust outbreaks take about a week to reach the Caribbean. Mineral dust concentrations in Barbados in April to May 1994 were consistently above 65 /ug m and daily mean values over 100 /xg m are not uncommon there (Li et al., 1996). Optical thickness (t) values during the period seldom dropped below 0.2 (at X — 550 nm) the largest value r occurred during a large dust event. The particle scattering coefficient, varied from 90 x 10 m when the dust concentration was only... 

If this equation is compared to (7.195), we observe immediately that the two relations are of the same form, the only difference being due to the Si which appears at the left of (7.240) (in place of the S ), and the addition of a source term at the right which augments the external sources S. Thus the solution to (7.240) may be obtained by applying the result (7.205). In place of the source function iS which appears in (7.205) w e use the two-term source of (7.240) and modify the definition of the optical thickness /S so that it is given in terms of the total cross section Si in place of Sa- In this way we obtain the solution... 

Figure 2 Spectra of optically thin and thick models with n a r and observed with various apertures. The aperture sizes are for a distance of 500 pc. Note that the optically thin source has a power law spectrum in the near IR and that the wavelength of peak emission is redshifted for larger apertures.

Finally, we estimate that the source becomes optically thick at X Ji 70li. This model is shown in Figure 3. The discrepancy between the model and the observed X = 1 mm flux point is due to our maintaining a dependence in the model emissivity at long wave-... 

Tegen, I. and Fung, I. 1994. Modeling of mineral dust in the atmosphere Sources, transport and optical thickness. Journal of Geophysical Research—Atmospheres 99 (D16) 22897-22914. 

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