In this paper, third of a series of three dealing with a model of auroral H and H2 emission in the giant planets, we focus on the characteristics of the emergent emission, the only one which can be compared with observations. As the Jovian atmosphere is optically thick at 1215.67 ¿, modeling of emergent auroral Lyman α line profiles requires the use of a radiative transfer code to model the transport of photons from the auroral source to the top of the atmosphere. Here, radiative transfer effects are modeled using the doubling and adding method. This radiative transfert code is self-consistently coupled with the energy degradation code used in the first two papers to compute the excitation rate along the path of precipitating particles as a function of wavelength. Input parameters are the identity and the energy of the incoming particles. We find that the auroral Lyman α line profile shows a central reversal due to the atmospheric H overlying the emitting layer. The shape of the emergent line is almost only sensitive to the column of H in the line of sight to the emission, related, via the atmospheric model used, to the the particle penetration depth (i.e. their energy). In addition, in the case of proton precipitation, charge exchange produces fast H atoms (Hf) which precipitate with the protons. Hf can also be excited and radiate Lyman α photons. This produces a second, Doppler shifted, component, of the Lyman α profile. This component may represent as much as 77.4% of the total Lyman α intensity for 10 keV protons, and it decreases with incident proton energy. It also extends over a broad wavelength range (up to 56 ¿ for 1 MeV proton). Detection of this component would unambiguously identify protons as the particles responsible for the Jovian aurorae. However, for high proton energies, the escaping flux may be too weak to be detected. Finally, following earlier analyses of IUE auroral spectra, we compute the color ratio C between the fluxes escaping in two particular wavelength ranges of the H2 Werner and Lyman bands, 1230--1300 ¿ and 1557--1619 ¿. We also compute the ratio CLyα between the H2 short-wavelength range and the line integrated Lyman α flux. C and CLyα are sensitive to the CH4 and the H column densities, respectively, overlying the auroral source along the line of sight. Once an atmospheric model is assumed, energies of the precipitating particles can be derived. Each of these ratios shows a specific variation with the energy of the particles. In addition, CLyα is sensitive to the identity of precipitating particles as well, so that, combined together, they can, in principle, provide a unique diagnostic of the Jovian aurorae. ¿ 1999 American Geophysical Union