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Properties of z~3-6 Lyman break galaxies. II. Testing star formation histories and the SFR-mass relation with ALMA and near-IR spectroscopy

We examine the dependence of derived physical parameters of distant Lyman break galaxies (LBGs) on the assumed star formation histories (SFHs), their implications on the SFR-mass relation, and we propose observational tests to better constrain these quantities. We use our SED-fitting tool including nebular emission to analyze a large sample of LBGs, assuming five different star formation histories, extending our first analysis of this sample (de Barros et al. 2012, paper I). In addition we predict the IR luminosities consistently with the SED fits. Compared to "standard" SED fits assuming constant SFR and neglecting nebular lines, assuming variable SFHs yield systematically lower stellar masses, higher extinction, higher SFR, higher IR luminosities, and a wider range of equivalent widths for optical emission lines. Exponentially declining and delayed SFHs yield basically identical results and generally fit best. Exponentially rising SFHs yield similar masses, but somewhat higher extinction. We find significant deviations between the derived SFR and IR luminosity from the commonly used SFR(IR) or SFR(IR+UV) calibration, due to differences in the SFHs and ages. Models with variable SFHs, favored statistically, yield generally a large scatter in the SFR-mass relation. We show that the true scatter in the SFR-mass relation can be significantly larger than inferred using SFR(UV) and/or SFR(IR). Different SFHs, and hence differences in the derived SFR-mass relation and in the specific star formation rates, can be tested/constrained observationally with future IR observations with ALMA. Measurement of emission lines, such as Halpha and [OII]3727, can also provide useful constraints on the SED models. We conclude that our findings of a large scatter in SFR-mass at high-z and an increase of the specific star formation rate above z>~3 (paper I) can be tested observationally. (abriged)