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Using our 3D Lya radiation transfer code, we compute the radiation transferof Lya and UV continuum photons including dust. Observational constraints onthe neutral gas (column density, kinematics, etc.) are taken from otheranalysis of this object. RESULTS: The observed Lya profile of MS 1512--cB58 isreproduced for the first time taking radiation transfer and all observationalconstraints into account. The observed absorption profile is found to resultnaturally from the observed amount of dust and the relatively high HI columndensity. Radiation transfer effects and suppresion by dust transform a strongintrinsic Lya emission with EW(Lya)>~ 60 Ang into the observed faint superposedLya emission peak. We propose that the vast majority of LBGs have intrinsicallyEW(Lya)~60-80 Ang or larger, and that the main physical parameter responsiblefor the observed variety of Lya strengths and profiles in LBGs is N_H and theaccompanying variation of the dust content. Observed EW(Lya) distributions, Lyaluminosity functions, and related quantities must therefore be corrected forradiation transfer and dust effects. The implications from our scenario on theduty-cycle of Lya emitters are also discussed.

3D Lya radiation transfer. II. Fitting the Lyman break galaxy MS 1512-cB58 and implications for Lya emission in high-z starbursts