Abstract

The behavior of random band models composed of lines of pure Doppler shape for several irradiance distribution functions is investigated. The particular irradiance distribution functions chosen are: (1) constant irradiance, (2) exponential distribution, (3) truncated <i>S</i><sup>-1</sup> distribution, and (4) the exponential-tailed <i>S</i><sup>-1</sup> distribution. The curves of growth for the first two models are found to have the asymptotic (log) ½behavior characteristic of an isolated Doppler line while the latter two models show a (log)½ dependence.

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  1. W. Malkmus, J. Opt. Soc. Am. 57, 323 (1967).
  2. A. Unsöld, Astrophys. J. 69, 214 (1929).
  3. O. Struve and C. T. Elvey, Astrophys. J. 79, 409 (1934).
  4. S. S. Penner, Quantitative Molecular Spectroscopy and Gas Emissivities (Addison-Wesley Publishing Company, Inc., Reading, Mass., 1959), p. 39. 1214
  5. This result could have been obtained directly from the general expression [R. M. Goody, Atmospheric Radiation. I. Theoretical Basis, (Oxford University Press, London, 1964), p. 133] for a random band model consisting of lines of arbitrary normalized contour f(ω) having an exponential irradiance distribution [Eq. (18)] W¯/d=(1/d) ∫-∞S0f(ω)u[1+S0f(ω)u]-1dω.
  6. This result is also derivable directly from a general expression given by C. D. Rodgers (private communication) for a random band model consisting of lines of arbitary normalized contour f(ω) having an exponential-tailed S-1 irradiance distribution [Eq. (34), R large] W¯/d=(1/d lnR) ∫-∞ ln[1+SMƒ(ω)u]dω.

Elvey, C. T.

O. Struve and C. T. Elvey, Astrophys. J. 79, 409 (1934).

Malkmus, W.

W. Malkmus, J. Opt. Soc. Am. 57, 323 (1967).

Penner, S. S.

S. S. Penner, Quantitative Molecular Spectroscopy and Gas Emissivities (Addison-Wesley Publishing Company, Inc., Reading, Mass., 1959), p. 39. 1214

Struve, O.

O. Struve and C. T. Elvey, Astrophys. J. 79, 409 (1934).

Unsöld, A.

A. Unsöld, Astrophys. J. 69, 214 (1929).

Other

W. Malkmus, J. Opt. Soc. Am. 57, 323 (1967).

A. Unsöld, Astrophys. J. 69, 214 (1929).

O. Struve and C. T. Elvey, Astrophys. J. 79, 409 (1934).

S. S. Penner, Quantitative Molecular Spectroscopy and Gas Emissivities (Addison-Wesley Publishing Company, Inc., Reading, Mass., 1959), p. 39. 1214

This result could have been obtained directly from the general expression [R. M. Goody, Atmospheric Radiation. I. Theoretical Basis, (Oxford University Press, London, 1964), p. 133] for a random band model consisting of lines of arbitrary normalized contour f(ω) having an exponential irradiance distribution [Eq. (18)] W¯/d=(1/d) ∫-∞S0f(ω)u[1+S0f(ω)u]-1dω.

This result is also derivable directly from a general expression given by C. D. Rodgers (private communication) for a random band model consisting of lines of arbitary normalized contour f(ω) having an exponential-tailed S-1 irradiance distribution [Eq. (34), R large] W¯/d=(1/d lnR) ∫-∞ ln[1+SMƒ(ω)u]dω.

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