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Astron. Astrophys. 364, 517-531 (2000)

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4. Results

4.1. The space-time distribution of K-band selected late-type galaxies

The grid of model spectra has been used to estimate redshifts from spectral fits to the 7-band photometric data for the 16 galaxies lacking a spectroscopic measurement. As typical in cases in which such a wide spectral coverage (0.3 to 2.2 [FORMULA]) and accurate photometry are available, the relative errors in z turn out to be quite small, of the order of [FORMULA]. These broad-band spectral fits allow quite robust estimates of redshifts also for dusty objects, mostly exploiting a well-characterized feature of the optical spectra, the Balmer discontinuity, which is weakly affected by dust extinction (cfr discussion in Sect. 3.2.1 in FA98).

To check the consistency of our method, we compare in Fig. 3 our photometric redshift predictions with the corresponding spectroscopic measures. The vertical error bars refer to different solutions at better than 90[FORMULA] confidence, derived from a [FORMULA] fitting procedure using models (a) and (c). Fig. 3 shows overall good agreement within our modellistic uncertainties of the fits. Added to the 36 spectroscopic redshifts, this procedure enabled us to get quite a reliable redshift distribution for our sample objects.

[FIGURE] Fig. 3. Comparison of photometric redshifts, based on seven-band spectral data, with spectroscopic redshifts. Error bars refer to interval solutions with more than 90[FORMULA] confidence level, derived from [FORMULA] fitting using models [a] and [c].

The distribution in redshift of a source population from a complete flux-limited catalogue provides a powerful constraint on its evolutionary history and formation epoch. This obviously assumes that we control with reasonable confidence all possible selection effects, in particular those due to the surface brightness limit, the cosmological dimming and K-corrections to the fluxes. If some morphological criteria are at play, one needs also to understand how morphological appearance may evolve with redshift. In our case the control of the selection effects is made easier by our primary selection in the K-band, which implies minimal K- and evolutionary corrections as a function of redshift.

The availability of accurate measurements of the effective radii [FORMULA] allows to control the effects of the limiting surface brightness observable in the field in K, which we evaluated from the simulations described in Sect. 2 to be [FORMULA].

Fig. 4 shows the evolution of the observed surface brightness for two objects in our sample (including the galaxy with the faintest surface brightness) as a function of redshift, taking into account the cosmic dimming and using a variety of spectral evolution patterns corresponding to the models described in Sect. 3. It is clear from the figure that the cutoff in surface brightness in the IRIM K band image has no impact in our selection process above our adopted limit in total magnitude of [FORMULA], and the whole redshift space up to at least [FORMULA] is clearly accessible in principle.

[FIGURE] Fig. 4. Scaling of the observed average surface brightness for two faint galaxies in our sample as a function of redshift, according to the evolution models (a) for galaxy # 16 and (c) for # 50 respectively. Note that galaxy # 50 is the one with the lowest observed value of the surface brightness. The deep K-band image used in the primary selection has a [FORMULA] limiting brightness of [FORMULA].

Fig. 5 reports the histogram of the observed redshifts for our complete [FORMULA] sample (including the 16 photometric estimates). The distribution shows pronounced peaks at [FORMULA] and [FORMULA], clearly indicative of strong inhomogeneities in the source distribution due to spatial clustering in the relatively small volume sampled by the HDFN. The uncertainty due to clustering in the limited volume has to be kept in mind when drawing any conclusions from our analysis, which require confirmation from surveys on more extended areas.

[FIGURE] Fig. 5. Redshift distribution for spiral and irregular galaxies brighter than [FORMULA] in the HDFN. The continuous line is the predicted distribution based on canonical local luminosity functions for late-type and irregular galaxies and the spectral evolution model (c) mentioned in Sect. 3.1.

A second relevant feature is apparent in Fig. 5: a cutoff at [FORMULA], with only 2 objects out of 52 found above this limit.

We compared this distribution with a model prediction based on the local luminosity function of galaxies in the K-band (Gardner et al. 1997) complemented with information on the contributions of various morphological classes from optical data (see Franceschini et al. 1998 for more details). The luminosity function is then evolved according to spectral model (c), which provides a conservative estimate of the number of [FORMULA] galaxies (it has the minimal evolution rates among the three models considered). The other assumption we made is that the luminosity function changes as an effect of the evolution of the [FORMULA] ratio (M changes because more mass is turned into stars with time, L follows the evolution of the stellar populations). The onset of star-formation is assumed to happen at [FORMULA].

As shown in the figure, these assumptions would imply an expected number of late-type galaxies at [FORMULA] significantly in excess of the observations (9 expected versus only 1 observed). This result parallels a similar finding by FA98 and Rodighiero, Franceschini and Fasano (2000) for the early-type population, showing a demise of objects at redshifts larger than [FORMULA]. One of the possible interpretations of this effect given by FA98, i.e. that the morphological selection could miss galaxies with shapes deviating from the De Vaucouleurs profile in case of merging activity at these redshifts, is no longer acceptable: essentially there are no bright ([FORMULA]) galaxies altogether at [FORMULA] in the HDFN area.

4.2. Evaluating galactic ages and extinction properties

As anticipated, if the photometric measurement of redshift from broad-band spectral fits is weakly affected by dust extinction, the estimates of most other physical parameters of gas-rich systems suffer quite more by the uncertain amount of dust and from the degeneracy between ages of stellar populations and extinction. To check this we have used our large grid of model spectra to study the degeneracy of the spectral-fitting solutions of our sample galaxies.

Fig. 6 plots [FORMULA] contours for the amount of dust-rich gas versus the age for two representative galaxies, as well as the best-fit spectra for two different histories of SF (model [a] and [c]).

[FIGURE] Fig. 6. Examples of different fits to the observed broad-band spectra of object number 1, fitted with the population synthesis models described in Sect. 3. The figure plots [FORMULA] contours for the amount of dust-rich gas versus the age (top panels) and the corresponding best-fit spectra for two different histories of SF (lower panels). The solution on the right refers to the model [a] in Fig. 2 and a value for the escape timescale [FORMULA] of 5 Myr (see Sect. 3.1 for details about these parameters). On the left: solution for model [c] and [FORMULA] Myr. The contours correspond to a [FORMULA] increment of 1,5,10,15 and 20 with respect to the best fit in the grid. Therefore the second innermost contour correspond to the 90% confidence interval.

It is immediately apparent that, even within sets of models based on the same evolutionary SFR(t), a fairly substantial degeneracy exists between the age and amount of dust. Furthermore, rather different star formation histories can lead to equally good fits, as detailed in Fig. 6.

Fig. 7 summarizes some results of our best-fitting procedures for three representative objects in our sample. For each object, it reports various solutions for the rate of on-going SF and the average V-band extinction [FORMULA], including the corresponding values of the [FORMULA]. This figure illustrates the fact that the observed SEDs can be fitted with models differing in the current rate of star-formation by factors up to 5-10: a large amount of SF activity can be easily hidden at wavelengths below a few µm.

[FIGURE] Fig. 7. For three representative objects in our sample ([FORMULA] 1, 30 and 36) located at different redshift (z = 0.199, 1.355 and 0.559 respectively) we plot various solutions for the rate of on-going SF against the average V-band effective extinction [FORMULA]. We report the best-fit solutions for every different history of SF considered (as described in Sect. 3.2) and two more corresponding models: the youngest and the oldest one with [FORMULA]. The labels near the points are the [FORMULA] values for each solution. This figure illustrates the fact that the observed SEDs can be fitted with models differing in the current rate of star formation by factors up to 5-10.

Fig. 8 details the results of two different fits to the observed broadband spectrum for object 30, clearly illustrating the degeneracy existing between SF and extinction. The two SEDs correspond to two solutions reported in Fig. 7, with values of the SFR differing by a factor [FORMULA]. The top panel refers to the solution 1 with [FORMULA] and SFR[FORMULA]. The lower panel refers to solution 2 with [FORMULA], SFR[FORMULA]. It is clear that if the analysis is confined to optical/NIR wavelengths, it cannot clearly discriminate between the two solutions, whose differences are apparent only including the far infrared spectrum, where dust re-emission would be detectable. Only observations of the IR spectral energy distribution, say between a few tenths up to a few hundreds µm, where actively star forming galaxies emit most of the energy, would allow to break the present degeneracy in the solutions.

[FIGURE] Fig. 8. Example of two different fits to the observed broad-band spectrum for object number 30 in our identification. We report the spectral galaxy emission of two dusty environments (Sect. 3.1): dashed line = diffuse ISM (cirrus), dot-dashed line = molecular clouds (MCs). The solid line corresponds to the total integrated spectrum of the galaxy. Solution 1 (top panel) and 2 (bottom panel) refer to that plotted in Fig. 7 for object 30, corresponding to a value of [FORMULA], with SFR [FORMULA], [FORMULA] (for sol1), and SFR [FORMULA], [FORMULA] (for sol2).

4.3. Colours, sizes and average surface brightness of late-type galaxies at high redshifts

As a first assessment of the age and extinction distributions, we report in Fig. 9 the rest frame (V-K) and (B-J) colours as a function of redshift. As in FA98, the rest frame (B-J) colours are computed by interpolating the observed galaxy spectra using the best-fit models listed in Table 1 (see Sect. 4.4), while the (V-K) colours require a slight extrapolation to longer wavelengths. The left two panels refer to the observed spectra, which include the effects of reddening, while the colour distributions reported in the central panels correspond to "de-reddened" spectra (i.e. taking out the effect of extinction and showing the underlying colour distribution). As we see, extinction plays a significant role: the estimated absorption-subtracted colours appear on average bluer by one magnitude. De-reddened colours are compared with the predictions of single stellar populations with solar metal abundances (dashed horizontal lines). The vertical error bars in the central panels are the mean uncertainties related to our de-reddening procedure based on our grid of models and our adopted 90% confidence level.

[FIGURE] Fig. 9. Rest frame (V-K) (upper panels) and (B-J) (lower panels) colours of late-type field galaxies, compared with predicted values for single stellar populations with solar metallicity. The ages for the latter are indicated as well the mean colours of local galaxies. The left two panels refer to the observed colours, on the center we present the corresponding "de-reddened" colours based on our best-fit SED solutions. On the right we report the rest-frame colours of ellipticals and S0 galaxies from FA98. Filled squares refer to objects with spectroscopic redshift, open circles to those with photometric redshift. The error bars shown in the central panels correspond to the uncertainty in the dereddening at 90% confidence.

A comparison with the early-type galaxy sample studied by FA98 indicates that our late-type field galaxies present redder colours on average, because of extinction. This evidence is stronger in the (V-K) distribution, where a remarkable excess of red late-types is apparent at [FORMULA] and [FORMULA]. This illustrates that selecting by colours is far more sensitive to extinction effects than to intrinsic differences among the stellar populations contributing to the flux.

Once de-reddened, the rest-frame (B-J) colours reveal young stellar populations with ages from 0 to 2 Gyrs, significantly bluer than those of early-type galaxies, indicative of on-going SF. The (V-K) de-reddened colours show a dependence on redshift: while at [FORMULA] they appear blue, those for galaxies at [FORMULA] are constant and quite red on average ([FORMULA]), and as red as those of the early-type population investigated by FA98.

We warn that translation to age-distributions is subject to the uncertainties in the evaluation of the effective extinction (see also next section). However, the similarity in the intrinsic V-K colours of galaxies independent of morphology does indeed support a common age distribution for the spheroidal stellar components in Elliptical/S0s and in spiral bulges, something predicted by the hierarchical formation scenario mentioned in Sect. 1.

Finally, we report in Fig. 10 our measured average surface brightness in the B band ([FORMULA]) versus effective radius [FORMULA] for the bona-fide spirals in our high-z sample, compared with data from a local sample based on the RC3. [FORMULA] was computed for our distant sources applying only the K-correction and the cosmological scaling factors. A further correction has been applied taking into account the effects of internal absorption. While the largest values of [FORMULA] shown by local galaxies are missed by our high-z sample because we are not sampling the rare population of large size galaxies in the HDF limited space volume, there is no evidence of a significant offset in [FORMULA] between the local and distant spirals within the large observed spreads in the data. In particular, the lowest surface brightness galaxies ([FORMULA]) in our sample are highly inclined, probably extinguished, objects. Note that the same relation fitting the Kormendy relation for E/S0 galaxies also fits data for spirals.

[FIGURE] Fig. 10. Kormendy relation in the B band, i.e., the average surface brightness versus effective radius for the bona-fide spirals in our high-z sample (filled cirles), compared with the data from a local spiral sample based on the RC3 (open squares). [FORMULA] was obtained for our distant sources applying the K-correction and a correction for the internal absorption.

4.4. A tentative physical characterization of late-type galaxies in the HDF-N

Though aware of the uncertainties inherent in the spectral modelling of gas-rich systems due to the uncertain extinction, neverthless we attempt here to estimate some basic physical parameters of these sources, or at least to provide some boundary values as found by application of our vast model grid.

We report in Table 1 the formal best-fit solutions obtained from fitting the observed SEDs of our sample galaxies: [FORMULA]: V band effective extinction; [FORMULA]: total baryonic mass divided by [FORMULA] solar masses; SFR: observed SFR in solar masses per year.

Fig. 11a plots the rate of ongoing star-formation SFR based on best-fit solutions versus redshift for our sample galaxies. The values derived in our analysis have a median around [FORMULA]. Only one peculiar object (source number 2 in Table 1) shows an extreme value of SF (above [FORMULA]). It is an apparently normal giant spiral viewed face-on, for which our spectral fit predicts a large extinction [FORMULA]. A more standard extinction value ([FORMULA]), still providing an acceptable fit, would still correspond to a large value of SFR[FORMULA].

[FIGURE] Fig. 11a-c. Panel a : Distribution of the on-going star formation rate SFR versus redshift, for the best-fit solutions. Panel b : SFR against the total baryonic mass for best fit solutions. The mean uncertainty on the mass is reported. Panel c : Ratio of the total baryonic mass normalized to the on-going rate of SF for each objects (based on best-fit solutions). This ratio gives an estimate of the timescale for the conversion of gas into stars, showing a substantial spread from a few to 20 Gyrs. The error bars correspond to the mean 90% uncertainty, providing the range of variation for two extreme solutions (the youngest and the oldest one with [FORMULA]).

The apparent scaling of SFR with z in Fig. 11a may be explained as mostly a selection effect concerning the luminosity of our objects. On the other hand, Fig. 11b indicates that the star formation rate is on average proportional to the intrinsic baryonic mass, such that galaxies with higher SFR are typically those more massive. By looking at higher redshifts means to observe only the more luminous sources, those with larger masses. Our K-band selection then operates largely on the stellar mass.

Any dependence on redshift disappears when we normalize SFR to the baryonic mass, as it is done in Fig. 11c. The ratio [FORMULA] appearing in Fig. 11c gives the timescale for the formation of stars in our late-type galaxy sample. The latter does not reveal characteristics of violent starburst, if we consider our observed timescales required to convert all gas in stars: these range from 1 up to 20 Gyrs, and indicate a moderate star formation activity for the present K-selected field galaxies.

4.5. Constraints on the global star formation history: contributions of late-type and early-type field galaxies

A most popular way to represent the evolutionary properties of a population of cosmic sources is through the plot of the total luminosity density (or the stellar formation and metal production rates) in the comoving volume (Madau et al. 1996; Lilly et al. 1996). When referred to the average galaxy population in the field, this function was shown to drastically increase from the present time back to redshift [FORMULA], and to flatten off above.

The separate contribution of galaxies with early-type morphologies to the global star-formation rate per comoving volume [FORMULA] [[FORMULA]] has been estimated by FA98 using the complementary sample in the HDFN and population synthesis results. The outcome was that early-types contribute significantly to the total [FORMULA] mostly at [FORMULA], their fractional contribution decreasing very fast at lower z.

A first reason to perform a similar computation on the complementary sample of spirals and irregulars is to compare the two histories of SF. A further reason of interest to have the full complete sample processed comes from recent reports claiming evidence for a more gradual decline of the galaxy ultraviolet luminosity density at [FORMULA] (Cowie et al. 1999; Treyer et al. 1998), taken as an indication of a modest evolution of the rate of SF during the last [FORMULA] Gyrs of the galaxy cosmic history.

An independent assessment, accounting for dust extinction and exploiting the observed baryonic mass function in stars through a full spectro-photometric fit to the SED's, would then be clearly welcome. We remember that, whereas this computation is relatively straightforward for the classified ellipticals/S0 due to the lack of an ISM complicating the stellar population-synthesis fit, modelling gas rich late-types presents more severe problems due to the presence of dust. We will see later, however, that the corresponding uncertainties tend to average out in the integrated form of the [FORMULA] function, providing a relatively robust result.

We defer to the paper by Franceschini et al. (1998) for all details of the computation. To remind here only the basic steps, for all 52 objects in our complete sample we computed, within our grids of synthetic spectra, the younger and more extinguished solution. In the same way we determined the older solution less affected by absorption. We computed the available comoving volumes [FORMULA] within which the object would still be visible above the sample flux limit (Lilly et al. 1995 , 1996). The contribution of each galaxy to the global SFR has been estimated by dividing the time dependent SF rate (derived from the two fits) by [FORMULA]. A correction to the comoving SF rate is then applied for the portion of the luminosity function not sampled by the present survey. Such correction is based on the K-band luminosity function discussed by Connolly et al. (1997). The global SFR density [FORMULA], is the summed contribution by all galaxies in our sample.

The result appears in Fig. 12 in the form of the comoving rate of star formation [FORMULA] versus redshift for the sample considered here (dot-dash line), compared with the evolutionary path for early-type galaxies (dotted lines). The results in panel a and b correspond to the two extreme acceptable (at 90% of confidence) spectral solutions for each object, the one most extinguished and younger for panel a, and the older less extinguished for panel b.

[FIGURE] Fig. 12. Comoving volume star-formation rate density [FORMULA] as a function of redshift for field galaxies. The contribution of late-types to the cosmic SFR (dot dashed line) derived from our sample is compared in the two cases with the evolutionary path for early-type galaxies studied by FA98 (dotted line). The solid line corresponds to the total amount of SF density in the field. The panels correspond to two different extreme solutions (see text for details): the younger and more extinguished (panel a), the older less affected by dust absorption (panel b). The data reported are from Lilly et al. (1996) and Connolly et al. (1997).

The disk-dominated and the irregular galaxies in the present sample display an evolutionary behaviour different from that of bulge-dominated objects. The former appear to form actively stars well below [FORMULA], whereas the rate of SF for the latter is high at [FORMULA] but converges very fast at lower z. Our result for the disk and irregular galaxies is quite consistent with those by Brinchmann et al. (1998, their Fig. 15), in showing a comoving SFR modestly increasing between [FORMULA] and 1. On the contrary, our results differ significantly from Brinchmann et al. as far as the early-type systems are considered (in their case E/S0 have a flat [FORMULA] in the same z-interval): we explain this as due to the very different procedures adopted to measure the function [FORMULA], in our case it was a global fit to the UV-optical-NIR SED, in their case the use of the OII EW as a tracer of SF. Indeed, the latter should more likely trace a negligible residual of SF due to low-level merging activity or stellar recycling, than the global history of SF in these galaxies.

Note that, despite the large uncertainties on the single object, the overall result is fairly well constrained between the two extreme solutions depicted by the shaded region in Fig. 13. This is due to a sort of compensation intervening in the adopted solutions: the younger-more extinguished one tends to have a more intense ongoing SF activity but less protracted in time, while the contrary happens for the older less-extinguished solutions. In other words, the baryonic mass already converted into stars and sampled by the near-IR (JHK) flux measurements as a function of redshift, provides a more robust evaluation of the evolutionary SFR than the instantaneous SFR mapped by the short-wavelength flux. In a sense, the errorbar appearing in Fig. 11 does not translates into a similarly large uncertainty in the prediction of Fig. 13, because the ongoing rate of SF (SFR in panel a of Fig. 11) and the timescale of SF ([FORMULA] in panel c) scale inversely to the galaxy mass function observed at various redshifts.

[FIGURE] Fig. 13. The total star formation rate density per unit comoving volume for field galaxies (late+early-types) is compared with the prediction of Cowie et al. (1999), who found a dependence of [FORMULA] on z in the range [FORMULA] of the form [FORMULA] (continous line). The shaded region is bracketed by the two solutions based on the younger-high extinction (upper histogram) and the older less extinguished (lower histogram) models. See also caption to Fig. 12.

This prompted us to compare our results with those published by Cowie et al. (1999). This is done in Fig. 13 where our results appear as the shaded region, which is bracketed by the two solutions based on the younger-high extinction (upper histogram) and the older less extinguished (lower histogram) models. The continuous line is a polynomial function [[FORMULA]] quoted by Cowie et al. (1999) as best-fitting their and Treyer's et al. (1998) data on the time-dependent UV luminosity density. Within the uncertainties, our results are in quite better consistency with the Cowie et al. (1999) evolutionary law than with the dataset compiled by Madau et al. (1996), based on the CFRS (Lilly et al. 1996) and the low-z [FORMULA] survey by Gallego et al. (1995).

While some discussions can be found in Cowie et al. (1999) about possible origins for this discrepancy and on the consequences on this new evaluation of the evolutionary SFR, we only take note here of the nice agreement between our results and those of Cowie et al. (1999), based on quite independent grounds.

It is remarkable that UV and near IR selected galaxy samples show such similar evolution of the comoving SFR density [FORMULA].

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Online publication: January 29, 2001