The Structure and Evolution of the Sun by Giuseppe Severino

Author:Giuseppe Severino
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Using the Eddington-Barbier approximation and LTE to express the emergent intensity and denoting with τ c the continuum optical depth and with τ l the additional optical thickness due to the line opacity, we get

where we have neglected the smooth variation of the Planck function over the line width. For a weak line τ l ≪ 1, hence we can approximate the difference between the values of the Planck function at two depths by means of the differential, that is,

Moreover, it is

where N a is the number of atoms capable of absorbing and σ l is the transition cross section. Inserting the last two results in W, we find

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