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Recovering galaxy stellar population properties from broad-band spectral energy distribution fitting II. The case with unknown redshift

(Abridged) In a recent work we explored the dependence of galaxy stellar population properties derived from broad-band spectral energy distribution fitting on the fitting parameters, e.g. SFHs, age grid, metallicity, IMF, dust reddening, reddening law, filter setup and wavelength coverage. In this paper we consider also redshift as a free parameter in the fit and study whether one can obtain reasonable estimates of photometric redshifts and stellar population properties at once. We use mock star-forming as well as passive galaxies placed at various redshifts (0.5 to 3) as test particles. Mock star-forming galaxies are extracted from a semi-analytical galaxy formation model. We show that for high-z star-forming galaxies photometric redshifts, stellar masses and reddening can be determined simultaneously when using a broad wavelength coverage and a wide template setup in the fit. Masses are similarly well recovered (median ~ 0.2 dex) as at fixed redshift. For old galaxies with little recent star formation masses are better recovered than in the fixed redshift case, such that the median recovered stellar mass improves by up to 0.3 dex whereas the uncertainty in the redshift accuracy increases by only ~ 0.05. However, a failure in redshift recovery also means a failure in mass recovery. As at fixed redshift mismatches in SFH and degeneracies between age, dust and now also redshift cause underestimated ages, overestimated reddening and underestimated masses. Stellar masses are best determined at low redshift without reddening in the fit (median underestimation ~ 0.1 dex for similarly well recovered redshifts). Not surprisingly, the recovery of properties is substantially better for passive galaxies. In all cases, the recovery of physical parameters is crucially dependent on the wavelength coverage adopted in the fitting. Scaling relations for the transformation of stellar masses are provided.