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Astron. Astrophys. 325, 1259-1263 (1997)

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2. Basic formulation

Following current formulation (e.g. Bechtold et al. 1987, Meiksin & Madau 1993) the mean specific intensity [FORMULA] of the diffuse radiation field at frequency [FORMULA], as seen by an observer at redshift 0 (outside our Galaxy), writes as

[EQUATION]

where [FORMULA] is the proper volume emissivity (expressed in erg cm-3  s-1  Hz-1) at frequency [FORMULA] and redshift z, and [FORMULA] is the mean transmission of a clumpy medium averaged over all lines of sight. In our application the volume emissivity is the ultraviolet emission resulting from the star formation activity in galaxies. Taking an average over all morphological types and all star formation histories, the luminosity density can be considered continuous with a unique mean spectral shape. In these conditions and following the notations of Bechtold et al. (1987), [FORMULA] can be split into [FORMULA] the current local luminosity density of galaxies at frequency [FORMULA] and [FORMULA] the spectral shape normalized to 1 at the frequency [FORMULA] with a factor [FORMULA] accounting for any proper evolution in the luminosity density (the density variation due to expansion is taken into account by a factor [FORMULA]). Adopting [FORMULA], we get

[EQUATION]

The effective optical depth [FORMULA] due to Lyman continuum absorption of HI and HeII by discrete absorption systems is given by (e.g. Paresce et al. 1980, Moller & Jakobsen 1990, Miralda-Escudé & Ostriker 1990)

[EQUATION]

where [FORMULA] is the redshift and column density distribution of absorbers along the line of sight and [FORMULA] the optical depth through an individual cloud of column density N.

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© European Southern Observatory (ESO) 1997

Online publication: April 28, 1998

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