4 The ERO average spectra

In this letter we limit the discussion to the average spectra of the identified galaxy types in order to derive their main properties that would be otherwise difficult to characterize in the individual noisier spectra. The average spectra shown in Fig. 2, obtained deredshifting (with a 5 Å  rest-frame bin), normalizing and stacking the equally weighted individual spectra, are relative to all spectroscopically identified EROs with $Ks\leq20.0$, but they do not significantly change if only the $Ks\leq19.2$ EROs are used.

4.1 Old EROs

By comparing the average spectrum of old EROs with Bruzual & Charlot (2000, private communication) simple stellar population (SSP) models (Salpeter IMF, $Z=Z_{\odot}$) and no dust extinction, and taking into account the observed average R-Ks color (5.19 $\pm$ 0.06), we derive an average age of 3.3 $\pm$ 0.3 Gyr (Fig. 3). The amplitude of the average D4000 break (1.92 $\pm$ 0.06) is consistent with an age of 2.8 $\pm$ 0.3 Gyr. If we adopt an average age of 3.1 $\pm$ 0.3 Gyr for $Z=Z_{\odot}$, the mean formation redshift is then $z_{\rm f}=2.4 \pm 0.3$. If an e-folding time of star formation $\tau=0.3$ Gyr is adopted, or if a Scalo (1986) IMF is used, the age increases to about 4 Gyr. SSP models with a lower metallicity ( $Z=0.4~Z_{\odot}$) would further increase the age to $\sim$5-6 Gyr leading to extremely high $z_{\rm f}$. On the other hand, a higher metallicity with $Z=2.5~Z_{\odot}$ would reduce the age to $\sim$1.1 Gyr and the formation redshift to $z_{\rm f}\sim 1.5$, but it would underestimate the observed R-Ks colors of old EROs at z>1, thus being an inappropriate possibility for the highest redshift objects.

To summarize, being SSP models with an instantaneous burst of star formation rather unrealistic, the age of $\sim$3 Gyr and $z_{\rm f}=2.4$ should be considered lower limits if $Z=Z_{\odot}$.

4.2 Star-forming EROs

As a first attempt to investigate the nature of the star-forming EROs, we compared the global shape of their average spectrum with template spectra of star-forming galaxies, although the presence of [NeV]$\lambda$3426 emission with an equivalent width $W=3.6 \pm 0.7$ Å  may indicate a more complex picture with also a contribution from dust-obscured AGN activity. A more detailed analysis based on absorption lines with an equivalent width of a few  Å  is not warranted by our data because of the limited signal to noise ratio. Among the Kinney et al. (1996) templates, a good agreement is found only with their so called SB6 spectrum (i.e. the average spectrum of starburst galaxies with 0.6<E(B-V)<0.7 as derived from the H$\alpha$/H$\beta$ ratio), but only if the reddening is increased by an additional $E(B-V)\sim0.5$ (we adopt the Calzetti et al. 2000 extinction curve throughout the paper). Since the stellar continuum and the ionized gas of dusty starbursts suffer different extinctions ( $E(B-V)_{\rm star}\sim 0.44E(B-V)_{\rm gas}$; Calzetti et al. 2000), the net total extinction of the continuum of the ERO average spectrum is $E(B-V)_{\rm star}\sim (0.65 \times 0.44)+ 0.5 \sim 0.8$.

The average spectrum of e(a) VLIGs (Very Luminous Infrared Galaxies; ${\rm log}(L_{\rm IR}/L_{\odot})>11.5$; Poggianti & Wu 2000) also provides a global satisfactory agreement at $\lambda>3600$ Å  without the need of extra dust extinction (the median reddening estimated for the e(a) galaxies is $E(B-V)_{\rm gas}=$ 1.1 based on H$\alpha$/H$\beta$ ratio, corresponding to $E(B-V)_{\rm star}\sim 0.5$; Poggianti & Wu 2000).

Finally, a comparison with synthetic spectra of star-forming galaxies with solar metallicity, Salpeter IMF and constant star formation rate (SB99 models, Leitherer et al. 1999 and Bruzual & Charlot 2000 models) showed that the global shape of the continuum and the average R-Ks color can be reproduced with a wide range of ages and with 0.6<E(B-V)<1.1.

The possibility that a fraction of star-forming EROs have an old bulge component contributing to the red colors (e.g. similar to the red massive disk galaxy at z=1.34 of van Dokkum & Stanford 2001) is not ruled out by our data. In fact, HST imaging already showed that the "non-elliptical'' EROs are morphologically made by a heterogeneous population ranging from highly irregular systems (likely to be the most dusty starbursts) to disky galaxies (Moriondo et al. 2000; Stiavelli & Treu 2000). The noise in our spectra hampers a detailed analysis of the individual EROs. However, by subtracting the average spectrum of old from that of star-forming EROs, we estimate that at most 30-40% of the total light of the star-forming EROs at $\sim$4000 Å  can be due to an old system. In such a case, the average reddening would decrease to $E(B-V)_{\rm star} \sim 0.7$ using the SB6 template to reproduce the "pure'' star-forming component.