8 Conclusions

We have examined the spectral properties of the ionising continua, the Lyman-break, and the Ly$\alpha$ and He  II $\lambda$1640 recombination lines in starbursts with metallicities Z from zero - corresponding to primordial, Pop III objects - over low metallicities ( $Z \ga 4 \times 10^{-4}$) observed in nearby galaxies, up to solar metallicity ($Z_{\odot }$  =  0.02).

Our computations, including new sets of stellar evolution models at very low metallicities ( Z = 10^-7, 10^-5) and previously published grids at other Z, allow us in particular to study how spectral properties vary in the transition from Pop III objects to "normal'' currently measurable metallicities.

Various IMFs are treated, including also cases where very massive stars (up to $\sim$500 $M_{\odot }$) are formed, as suggested by hydrodynamical calculations for metallicities $Z \la Z_{\rm crit} \approx 10^{-5}$ (Bromm et al. 2001a; Abel et al. 1998; Nakamura & Umemura 2001).

Predictions are provided for the number of H, He⁰, and He⁺ ionising photons and average photon energies in these continua, the hardness of the ionising spectrum, the amplitude of the Lyman-break, the number of photons able to photodissociate H₂, and finally recombination line luminosities and equivalent widths (mostly for Ly$\alpha$ and He  II $\lambda$1640).

Two limiting cases of star formation histories, instantaneous bursts and constant star formation, are considered. For SFR  =  const., presumably appropriate to describe the average properties of starbursts galaxies or populations thereof, the following main results have been obtained:

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As expected from numerous earlier computations the Lyman continuum flux $Q({\rm H})$ increases with decreasing metallicity. For a universal Salpeter IMF from 1-100 $M_{\odot }$ the enhancement reaches typically a factor of $\sim$3 between solar metallicity and Pop III objects for a constant star formation (Sect. 4, cf. Tumlinson & Shull 2000; Schaerer 2002).

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While for metallicities $Z \ga 1/50$ $Z_{\odot }$ the amplitude of the Lyman-break is rather metallicity independent, a reduction by a factor $\sim$2 is found at lower metallicities, related to the strong increase of the average stellar temperature (Sect. 5).

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The predicted hardness of the ionising fluxes between $\ge$54 eV and $\ge$13.6 eV, i.e. the ability to doubly ionise He, decreases by $\sim$1.5-2 or more orders of magnitude from Z=0 to $\sim$10^-4 depending strongly on the upper mass cut-off of the IMF (Sect. 6).

From empirical constraints we derive a hardness $\log ~$ $Q({\rm He^+})/Q({\rm H})$ $~~ \sim -3.2$ to -2.6 for metal-poor starbursts ( $1/25 \la Z/$$Z_{\odot }$ $~~ \la 1/4$) and softer spectra for higher metallicities (Sect. 6.3). The former should provide the best estimate of $Q({\rm He^+})/Q({\rm H})$; the latter finding is also compatible with recent evolutionary synthesis models of Smith et al. (2002) including line blanketed non-LTE atmospheres for WR and O stars.

We also provide (Sect. 6.2) a simple estimate of the possible impact of hot WR like stars on $Q({\rm He^+})/Q({\rm H})$ at very low metallicities ( $Z \la 10^{-4}$). Such stars could eventually form due to a strong enhancement of mass loss related to rapid rotation (Marigo et al. 2002) or in principle also due very efficient rotational mixing processes (cf. Meynet & Maeder 2002), although we believe that these scenarios are quite unlikely or overall are of minor importance.

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Finally, calibrations for star formation rate determinations from Ly$\alpha$ and other recombination lines at all metallicities and for various IMFs are provided (Sect. 7).

For young bursts, the maximum Ly$\alpha$ equivalent width predicted is shown to increase strongly with decreasing metallicity from W(Ly$\alpha$ $) \sim 240$-350 Å at $Z \ga 1$/50 $Z_{\odot }$ to 400-850 Å or higher at Z between 10^-5 and 0 (Pop III) for the same Salpeter IMF (Sect. 7).

We find that non-negligible He  II $\lambda$1640 emission due to photoionisation from stellar sources appears to be limited to very small metallicities ($\log(Z/$$Z_{\odot }$ $) \la -5.3$) and Population III objects, except if hot WR like stars, whose existence appears very speculative, were frequent.

The detailed model predictions presented here are available on the Web through the CDS and at http://webast.ast.obs-mip.fr/sfr/. In subsequent publications our models are applied to the interpretation of Ly$\alpha$ observations in high redshift galaxies (Valls-Gabaud & Schaerer 2002), modeling of the combined chemical enrichment and re-ionisation history of the Universe (Ferrara & Schaerer 2002), and feasibility studies on the detection of Population III objects (Pelló & Schaerer 2002).

Acknowledgements

I thank Andrea Ferrara, Roser Pelló, David Valls-Gabaud for stimulating discussions and comments on an earlier version of the manuscript. Useful comments from Tom Abel, Daniel Kunth, and Grazyna Stasinska on the draft and related issues were also appreciated. Richard Norris kindly provided model results from his calculations for comparison. Last, but not least, I thank the referee for useful comments which helped to improve the presentation.