4. Constraining the stellar population in H3 and H5
We use the SEDs of H3 and H5, determined from broad-band photometry, to infer the relevant parameters for the stellar population, in particular the total SFR. The SEDs of these objects can be fitted by different synthetic stellar populations, and there is a degeneracy to consider in the SFR-age-metallicity-reddening space. Fig. 5 displays a comparison between the SEDs of H3 and H5. The wavelength interval sampled by the broad-band filters in the restframe of H3 and H5 goes from the Lyman 912 Å break to Å. The region at 1500 Å is sampled by the band, and the bands from R to J give the slope of the UV continuum, whereas the K' band is sensitive to the Balmer and 4000 Å breaks (roughly the restframe B). Thus, we have in principle a good database to roughly constrain the stellar population in these objects. When the IMF and the upper mass limit for star-formation are fixed, the allowed parameter space can be roughly constrained. The presence of Ly in emission points towards a star-forming system. Again, we used the GISSEL98 code for this exercise, taking into account that the two galaxies are necessarily dominated by massive OB stars at the wavelengths seen in the visible bands. Two kinds of SFRs were considered: a single stellar population (instantaneous burst), and a continuous star-forming system, both with the Salpeter (1955) IMF, with upper and lower mass-cutoff of , and an extinction law of SMC type given by Prévot et al. (1984). When computing quantities related to the stellar mass involved in one of these regions, we take the above mass limits for star-formation, but only of the stellar mass corresponds to stars with with this particular IMF.
Figs. 6a and 6b show the likelihood maps corresponding to H3 and H5 respectively, at z=4.05. For each SFR model, we have computed a reduced for 220 different ages of the stellar population, 61 extinction values (ranging between and 3.0 magnitudes), and 5 different metallicities (, , , and ). The most probable regions in this parameter-space are displayed in dark (permitted regions). The scaling directly corresponds to the confidence level as derived from the value. The shaded regions enclose the contours (confidence level of ). The likelihood maps were computed using two independent sets of filters: g,,R,,J,K and g,,r,,J,K, and the averaged intergalactic absorption in the Lyman forest (see Sect. 3.2). In all the cases we use instead of I because the seeing and sampling are better in this filter. The results obtained with each independent set of filters are qualitatively the same, and the two regions in the parameter space coincide. Each point on the likelihood maps presented in Figs. 6a and 6b corresponds to the most restrictive value obtained from the two independent sets (i.e. the lowest likelihood value). We also discuss in each particular case the results obtained when using only the spectral region redwards of Ly (hereafter redSED), a region which is not affected by uncertainties on the intergalactic absorption. In order to retain good resolution at short time scales, a logarithmic scale is used to display the age of the stellar population.
According to Figs. 6a and 6b, the stellar population in H5 is better constrained than in H3 in terms of . The reason for this is probably the relatively redder spectrum of H3 compared to H5. The weight of the old stellar population is more important in H3 than in H5 and, as a consequence, we expect an enlarged set of permitted regions on the reddening-age plane. In a short-burst model without reddening, H3 should be older than H5. Figs. 6a and 6b also display the degeneracy in metallicity versus reddening for the two objects. H3 and H5 do not seem to be highly reddened: the maximum restframe ever attained at a level is magnitudes for H3, and it remains below magnitudes at . This is not surprising given the redshift of these objects and the photometric selection. The age of the stellar population in the constant star-formation models is unconstrained at level in all the cases. Table 3 summarizes the permitted domains in the parameter space for H3 and H5.
Table 3. Permitted domains in the parameter space of H3 and H5. The values given are rough limits, the correlation between the different parameters is displayed in Figs. 6 and 7.
H3 is well fitted by both the burst and the constant star-formation models. Within the confidence level, the metallicity is excluded, whatever the star-formation model, the reddening or the age of the stellar population. All the solutions are compatible at with a moderate 0.4 to 0.6 magnitudes. The best fit at with a burst model is obtained for metallicities below solar: 0.2 metallicity, and age 0.004 Gyr () At , the maximum age for the burst model is 0.1 Gyr, and the maximum value for is 1.1 magnitudes. When we use only the redSED, the domain is enlarged, and the maximum age and permitted for a burst model are 0.29 Gyr and 1.6 magnitudes respectively. The best fits of H3 are given by a constant star-formation model, 0.02 metallicity, with and age 2.4 Gyr (), but this age is in fact incompatible with the age of the universe (1.17(2.16) Gyr with the adopted cosmology and =0.5(0.1)). This is not a problem because the domain for this model encloses solutions up to metallicity, with ages starting at 0.18 Gyr and limited by the age of the universe. ranges between 0.1 and 1.1 magnitudes at , and it increases up to 1.6 magnitudes when using the redSED.
H5 is well fitted by the burst and the constant star-formation models, provided that the value keeps below 0.15 magnitudes typically. The best fit of H5 is given by a constant star-formation model of , age 0.51 Gyr and (). The best fit by the burst model has , age 0.012 Gyr and (). For the burst model, the age and the reddening are well constrained. All the solutions within are compatible with very small values of (), whatever the model or the age of the stellar population. This result is also found when fitting only the redSED. At , the maximum age of the burst is 0.07 Gyr, and up to 0.14 Gyr whith the redSED. The best fit models have solar metallicities or higher than solar. For the constant star-formation model, the reddening is well constrained. The ages are also well constrained (between 0.07 and the age of the universe), provided that we can exclude the highest metallicity.
The best-fit SEDs were used to compute the SFR values and the absolute magnitudes involved in the bursts from the observed magnitudes and mean fluxes. The lens-corrected luminosity observed within the band is erg s-1 for H3, and erg s-1 for H5, with , assuming . In the case of H3, the best fit model has , thus the corrected luminosity in this filter (restframe 1450-1700 Å) is in fact 2.8 times higher. When using the best-fit models to scale the fluxes (Fig. 5), we obtain L(1500 Å)= 1.24 (3.5) erg s-1 Å- 1 for H3 (corrected for ), with , and L(1500 Å)= 1.9 (5.4) erg s-1 Å- 1 for H5 (). These values are not strongly dependent on the model SED used for the scaling. The SFRs derived from the best-fit star-forming models, scaled to the observed L(1500 Å), are for H3 (corrected for ) and for H5 (), and only of these values correspond to stars with . The main uncertainty is the for H3, which could set the SFR to values times lower or higher than the best solution quoted above. The absolute B magnitudes were derived from the observed K magnitudes (restframe 3900-4430 Å), using the best-fit models for a detailed scaling: and for H3 and H5 respectively, with . In the case of H5, this result is almost independent on the model SED because is always small; in the case of H3, the uncertainties in translate into magnitudes of uncertainty in .
The shape of the continuum at wavelengths shorter than Å (restframe Å), up to the I band, is relatively insensitive to the metallicity for metallicities higher than solar. The likelihood map is almost insensitive to age for ages below years, as expected given the sampling in stellar masses in the evolutionary tracks used by GISSEL98. Nevertheless, such time-scales seem irrelevant here, the best solutions being older than this limit. These results also are generally insensitive to the choice of the IMF. Nevertheless, the permitted regions in the likelihood maps show some dependency on the upper mass limit assumed for star-formation. In particular, when this limit is set to a value as low as , the permitted region for burst models is shifted towards younger age values for the stellar population, irrespective of the metallicity. This change on model details has very small influence on the SFRs derived above.
© European Southern Observatory (ESO) 1999
Online publication: May 21, 1999