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Astron. Astrophys. 363, 476-492 (2000)

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4. Influence of the different parameters on [FORMULA] accuracy

4.1. Templates and Lyman forest blanketing

We have studied the influence of the set of templates used on the final results through a comparison between the hyperz [FORMULA] determinations and real spectroscopic data on HDF. All the other parameters are fixed in this case, and the only difference is the set of templates used to compute [FORMULA]. Table 3 summarizes these results. A similar blind test was recently performed by Hogg et al. (1998) on a sample of HDF-N galaxies at [FORMULA], using different procedures and, in particular, different sets of templates.


[TABLE]

Table 3. Summary of dispersions in the HDF [FORMULA] measurements for the different sets of templates, where [FORMULA], using the Calzetti's law with [FORMULA] ranging from 0 to 1.2 magnitudes. The total number of objects considered in each non-catastrophic sample is given in brackets. See more details in text.


We have computed photometric redshifts for the sample of 108 galaxies on the HDF-N with observed [FORMULA] (Cohen et al. 1996; Cowie 1997; Zepf et al. 1997; Steidel et al. 1996; Lowenthal et al. 1997) considered by Fernández-Soto et al. (1999) plus 4 galaxies from HDF-S (Glazebrook et al. 2000, in preparation). Among these, 83 galaxies are at [FORMULA] and 29 at [FORMULA]. Photometry was obtained from the Stony Brook's group (Fernández-Soto et al. 1999; SUNY web pages http://www.ess.sunysb.edu/astro/hdfs ) using the package SExtractor (Bertin & Arnouts 1996) to detect sources, and consists in 7 filters for the HDF-N (F300W, F450W, F606W, F814W plus near infrared photometry in JHK filters obtained by Dickinson et al. 2000 at the KPNO IRIM camera) and 12 for the HDF-S (F300W, F450W, F606W, F814W, plus an additional shallow optical catalogue UBVRI from NTT SUSI2, and near infrared JHK data obtained with NTT SOFI). Here we consider results obtained using the 7 filters for the HDF-N galaxies and all the 12 available filters for the four objects of the HDF-S subsample. Calculations on the HDF-S using 7 filters do not affect significantly the individual photometric redshift and the overall statistic.

To calculate magnitudes from the available measured fluxes in the catalogues, we considered as non-detection criterion a signal-to-noise ratio [FORMULA]. In this case we assigned a magnitude [FORMULA] and we used the information about the limiting magnitude in the involved filter.

Three different sets of templates are considered in this section: the basic 5 GISSEL98 models with solar metallicity mentioned above (1 delta burst, 3 µ-decaying, 1 constant star-formation system), the CWW set of empirical SEDs, and the CWW set extended with a SED of a very blue galaxy taken from GISSEL library (Miller & Scalo IMF, constant SFR, [FORMULA] Gyr). Adding new very blue spectra to the third set does not change perceptibly the results. As for the simulated catalogues, we search solutions in the redshift interval [FORMULA] - 7 with a step [FORMULA]. In all cases, a crude limit in absolute magnitude has been imposed to compute [FORMULA], with [FORMULA]. Moreover, we checked the age of the template to be consistent with the age of the universe at the considered redshift, depending on the cosmological model. Here we use [FORMULA], [FORMULA] and [FORMULA]. The reddening is assumed to range from [FORMULA] to 1.2, following the Calzetti et al. (2000) law.

The comparison between [FORMULA] and [FORMULA] for the 112 galaxies of the sample is shown in Fig. 4, for the three sets of templates hereafter referenced as (a), (b) and (c), respectively. Each of them produces a fairly good agreement with the measured spectroscopic redshifts, but noticeable differences appear when considering the values of the dispersion, computed as

[EQUATION]

in the two redshift domains ([FORMULA] and [FORMULA]):

  • for [FORMULA] ([FORMULA]) we found: (a) [FORMULA]; (b) 0.21; (c) 0.17. If we exclude objects with [FORMULA], the value of [FORMULA] reduces to 0.06 in case (a) (81 objects), and to 0.08 for (b) and (c) (81 and 82 objects respectively). In case (a), these rejected objects correspond to the two galaxies with uncertain spectroscopic redshifts (see Arnouts et al. 1999). Thus, using GISSEL models in this redshift domain produces more accurate results than CWW templates alone.

  • in the high redshift domain, the dispersion in all the considered cases is [FORMULA] ([FORMULA]). If we remove catastrophic identifications (2 objects), characterized by [FORMULA], then [FORMULA] in case (a), 0.08 in (b) and 0.07 in (c). In this case, the CWW set produces slightly better results than GISSEL, probably due to a Lyman blanketing effect. This point is discussed below.

[FIGURE] Fig. 4a-f. Comparison between photometric and spectroscopic redshifts for the HDF spectroscopic sample. Error bars in [FORMULA] correspond to [FORMULA]. Different sets of template spectra are used in the various panels: a the basic 5 GISSEL98 models with solar metallicity; b the CWW set of empirical SEDs; c the CWW set extended with a SED of a very blue galaxy. The lower panels d , e and f present the comparison between template sets of different metallicities. See text for more details.

In general, the reasons of failures can be ascribed to many effects, such as a wrong photometry (systematic errors when measuring magnitudes or underestimated photometric errors) leading to a highly unlikely fit, or a probability function with significant secondary peaks, because of degeneracy among the fit parameters, or a relatively "flat" probability function due to a lack of sufficient photometric information. The last explanation applies particularly to the object at [FORMULA], which is detected only in filter F814W and which is at the limit of detection in F450W, with [FORMULA]. However, if we use all the available photometry, disregarding the [FORMULA] criterion, we obtain [FORMULA]. The object at [FORMULA] is placed at low redshift by other groups (Fernández-Soto et al. 1999; Arnouts et al. 1999). Nevertheless a secondary peak, with a very small [FORMULA] probability, is found at [FORMULA].

We can remark that at high redshift the cases (b) and (c) are better centred around the spectroscopic value. However, their [FORMULA] values are higher than in case (a). The reason suspected for that is the one-to-one relation introduced here between the Lyman-forest absorption and the redshift. We investigate this problem by assigning different values to the Lyman-forest decrement, multiplying the values of the mean line blanketing [FORMULA] and [FORMULA] provided by Madau (1995) by a factor 0.5 and 1.5, then increasing or decreasing the absorption (Furusawa et al. 2000). We found a better fit to the HDF data when the Lyman forest along the line of sight produces a smaller flux decrement with respect to the mean value. In this case we obtain [FORMULA] for the GISSEL case (a), a value which is similar to the value of CWW SEDs. An overestimate of absorption due to neutral hydrogen induces a subsequent and systematic underestimate of redshifts, because the same attenuation of the flux could be reproduced with a solution at lower redshift. Hence a careful knowledge of the UV region of SEDs is essential to accurately assess [FORMULA]; furthermore, the Lyman forest represents the most important signature of spectra in the high redshift regime. Thus it is important to allow the blanketing in the Lyman forest to span a sufficiently wide range of values in order to prevent systematic effects at high-z, which could depend on the line of sight.

It is worth to notice that, even if all the template SEDs reproduce the spectroscopic redshifts on the HDF with sufficient accuracy, the redshift distributions of galaxies could change significantly when we are dealing with objects fainter than the spectroscopic limits, for which no training set is available. When the redshift distribution obtained on the HDF with CWW templates is compared with the equivalent one computed with GISSEL templates, there are no strong differences in the overall distribution. Nevertheless, this result could not apply to all cases. A straightforward example is the case of a deep photometric survey using visible filters only, without near-IR photometry, and designed to probe the low surface-brightness regime. It is easily shown that, in this case, a degenerate solution could exist for the faintest "blue" sources, for which it is impossible to decide between a low-z solution (low surface-brightness object with a very young stellar population, as presented in next subsection) and a relatively bright [FORMULA] galaxy, with ongoing star-formation (no strong signatures on a continuum increasing bluewards). In that case, using the CWW templates alone will tend to select the later solution systematically, whereas including templates spanning a wide range of ages for the stellar population (such as GISSEL) could select the former solution, thus leading to a completely different redshift distribution. We prefer to adopt a relatively large number of GISSEL's templates, to supply a wide baseline for modeling the age effects, rather than to assume the evolution reproduced by the transformation in a different local spectral type.

4.2. Age of the stellar population

Photometric redshifts are efficient when a spectral feature is detected through the filters with an important strength as compared to photometric uncertainties. When we are dealing with the stellar continuum of a young stellar population, the 4000 Å break becomes visible at [FORMULA] years (see Bruzual & Charlot 1993). In most cases, this lack of strong features could not be compensated by the presence of strong emission lines, simply because such lines have a negligible effect on the integrated energy when using broad-band filters (see Sect. 4.7).

In order to study the effects of age on [FORMULA] estimates as a function of redshift, we have produced different sets of catalogues corresponding to different ages, all of them with a uniform distribution in z for the delta burst SED (single stellar population model). Fig. 6 displays the general trends of [FORMULA] versus [FORMULA] for representative ages and the UBVRIJHK set of filters. In this case the set of templates used is the basic GISSEL one with solar metallicity. At [FORMULA], the redshift determination is accurate for any age because of the presence of Lyman break in the filter U. At smaller redshifts, [FORMULA] is based on the 4000 Å break as the strongest spectral signature, and it is visible only in systems which are a few [FORMULA] years old.

The results obtained applying hyperz to these catalogues are summarized in Fig. 5, where we show the effect described above by means of the dispersion in four redshift bins: the value of [FORMULA] decreases increasing the redshift and the age of the stellar population.

[FIGURE] Fig. 5. The dispersion [FORMULA] as a function of the mean redshift of the considered range. Ages are [FORMULA] and [FORMULA] yr from top to bottom.

[FIGURE] Fig. 6. Comparison between [FORMULA] and [FORMULA] for simulated catalogues of single burst galaxies with [FORMULA], filters set UBVRIJHK and ages of galaxies [FORMULA] and [FORMULA] yr.

4.3. Cosmology

The effects of cosmological parameters ([FORMULA], [FORMULA] and [FORMULA]) are only related to the age allowed to the stellar population at a given redshift. When using hyperz , the age of the stellar population can be optionally limited to the age range permitted by the cosmological parameters. In order to quantify such effect on [FORMULA], if any, we have compared the results previously obtained on the HDF (with the crude age limitation given above) with those obtained without age constraints, and also with a different set of cosmological parameters ([FORMULA], [FORMULA] and [FORMULA]). These results show that the effect of the cosmological parameters on the [FORMULA] estimate is negligible, because they affect [FORMULA] by less than 1%.

4.4. Reddening

The five reddening laws presently implemented in hyperz are:

  1. Allen (1976) for the Milky Way (MW);

  2. Seaton (1979) fit by Fitzpatrick (1986) for the MW;

  3. Fitzpatrick (1986) for Large Magellanic Cloud (LMC);

  4. Prévot et al. (1984) and Bouchet et al. (1985) for Small Magellanic Cloud (SMC);

  5. Calzetti et al. (2000) for starburst galaxies.

The different laws are presented in Fig. 7.

[FIGURE] Fig. 7. Extinction curves [FORMULA] for the different reddening laws implemented in hyperz .

Recent studies on high redshift galaxies and star formation obscured by dust have shown the importance of reddening in the high-z universe. In order to probe this issue on [FORMULA] computations, we have compared the results previously obtained on the HDF to those obtained assuming no reddening, all the other parameters being fixed. We found [FORMULA] without catastrophic objects) for the low-z bin and [FORMULA] for the high-z one, but with a much higher percentage of catastrophic identifications: 10 objects at [FORMULA] are erroneously identified as low redshift galaxies.

Therefore, keeping a wide range of reddening values seems to be essential to reproduce the SEDs of high redshift galaxies. According to Steidel et al. (1999), the typical [FORMULA] for galaxies to [FORMULA] is 0.15 mags, thus [FORMULA] mags when using a Calzetti's law. The maximum [FORMULA] allowed in our calculations is about 2 times this value.

Moreover, we conducted a test to study the influence of the different reddening laws, using all the implemented possibilities. We found that the laws reproducing the extinction of the Milky Way and the Large Magellanic Cloud are not appropriate to fit the SEDs of high redshift galaxies ([FORMULA]), whereas they leave the low redshift region unaffected. Instead, the fourth law, corresponding to the Small Magellanic Cloud, produces results similar to those obtained with the curve provided by Calzetti et al. (2000). It correctly assigns the [FORMULA] to the high redshift objects, but it places a couple of low [FORMULA] objects at higher [FORMULA]. The last effect is probably due to the higher and steeper [FORMULA] at short wavelength as compared to Calzetti's, which mimics the additional effect of the UV attenuation induced by the Lyman forest. At high redshift, the most important wavelength region is the UV, between 1000 Å and 3000 Å, where the considered laws give quite different trends, thus modifying in a different way the magnitudes and producing different values of [FORMULA]. In fact, most of the fits to the HDF sample using reddening laws from 1 to 4 produce worse [FORMULA] values than the Calzetti's law, in particular for those objects requiring [FORMULA]. These galaxies cannot be reproduced by the MW and LMC laws, even when the limit of [FORMULA] is increased up to [FORMULA].

Thus, the slope of the selected reddening law at short wavelengths must be defined carefully; the extrapolation used here to extend the laws 1 to 4 towards wavelengths not covered by data is rather poor. These considerations get stronger evidence that the modeling of the UV region of SEDs is essential to recover correctly the high z galaxies. The re-emission of energy coming from dust heated by massive star formation does not affect the present results, because we concentrate on the UV to near-IR bands.

4.5. Metallicity

We have also checked the influence of the metallicity on the [FORMULA] estimates using the same HDF training sample. The same computations have been done using different and extreme assumptions for the metallicity of the stellar population, with values ranging from [FORMULA] to [FORMULA] (as allowed by Bruzual & Charlot's models). We have also developed a self-consistent set of templates, where the evolution in metallicity of the stellar population is explicitly taken into account (cf. Mobasher & Mazzei 1999). In other words, there is a natural link between the age of the stellar population and its mean metallicity. For all metallicity cases, we have built up the same closed-box systems presented before: a constant star-forming galaxy and six µ-models.

Three sets of templates were considered: the 3 different metallicities together (solar and the 2 extreme values), the two extreme values alone, and the self-consistent model. A comparison among all these cases is given in Fig. 4 (d,e,f). The dispersions at low redshift without failed objects are [FORMULA] respectively, for the 3 different sets. At high redshift we found [FORMULA], under the same assumptions. A slight improvement on the accuracy of [FORMULA] at [FORMULA] is observed when several different metallicities are used together, and the self-consistent model (f) produces the best fit in this redshift range. On the other side, including different metallicities does not affect the high redshift determinations.

4.6. Initial mass function

The influence of the IMF has also been tested on the HDF spectroscopic sample. We have used the self-consistent modeling, which takes into account the evolution in metallicity of the stellar population and produces the best fit to the HDF data when using the Miller & Scalo IMF (1979). We have built up the same closed-box models for 2 additional IMFs, Salpeter (1955) and Scalo (1986), keeping the same upper mass limit for star formation. When applying these new templates to the HDF sample, we find exactly the same results in terms of [FORMULA] accuracy. Looking more carefully to the results obtained for individual objects, we find that the [FORMULA] estimates are approximatively the same, whatever the IMF used. This result is easy to understand because the changes induced on the stellar continuum by the different IMF slopes are compensated in most cases by the other parameters (reddening, age, ...), thus giving the same [FORMULA] result but a different solution in the parameter space.

When we compute [FORMULA] on simulated data, the [FORMULA] accuracy is the same when we use a unique IMF in model galaxies and templates and when we use a different IMF in both settings. In addition, we have checked on possible systematic changes on the spectral types derived by hyperz in the later case, with negative results. In particular, a model catalogue built with Miller & Scalo IMF was analysed with Salpeter and Scalo IMFs, and the results were the same as in the Sect. 4.8 below. This strengthens the idea of the IMF being a secondary parameter in [FORMULA] estimates.

4.7. Emission lines

As long as we are dealing here with broad-band photometry, the presence of emission lines on the spectra has a relatively small effect on the integrated fluxes, and thus a small influence on the [FORMULA] results. This can be easily quantified when we consider the sample of blue compact galaxies at [FORMULA] studied by Guzmán et al. (1997), and the samples of star-forming galaxies described by Cowie et al. (1995), Glazebrook et al. (1995) and Terlevich et al. (1991). At relatively low redshift, the main emission lines to consider are [OII ][FORMULA], H[FORMULA], H[FORMULA] and [OIII ][FORMULA], [OII ] and H[FORMULA] being the most important contributions to the integrated fluxes. According to Guzmán et al. (1997), the [OII ][FORMULA] luminosity of star-forming galaxies can be approximated by [FORMULA], where [FORMULA] is the equivalent width and [FORMULA] is the blue luminosity in solar units.

For our purposes, an emission line can be overlooked when [FORMULA], where [FORMULA] and [FORMULA] are, respectively, the integrated fluxes within the emission line and the stellar continuum through the filter, and [FORMULA] is the photometric uncertainty in magnitudes. A realistic value of [FORMULA] to 0.1 mags ([FORMULA] to 10% uncertainty) imposes [FORMULA] to 0.1. The limit in equivalent width for galaxies in the Guzmán et al. sample is a few times 100 Å, thus most compact star-forming galaxies fulfill this condition. Even when we consider the typical luminosities of vigorous star-forming sources ([FORMULA] erg/s, Cowie et al. 1995, Glazebrook et al. 1995), emission lines are found to be negligible in most of them. Also the large majority of HII galaxies in the Terlevich et al. (1991) local sample fulfill the condition.

Thus, emission lines do not seem to influence significantly the [FORMULA] results on star-forming galaxies. On the contrary, this is not the general case when we are dealing with AGNs, or when the photometry is obtained through narrow-band filters. We have not considered here neither the contribution of AGN to the simulated samples, nor the influence of such templates on the final accuracy when we are dealing with real data. AGN SEDs could be easily introduced in our present scheme, and this particular application is presently under development (Hatziminaoglou et al. 2000).

4.8. Recovering the main SED parameters through hyperz

As mentioned before, hyperzallows to obtain the [FORMULA] and the best fit parameters across the whole space. The fitting procedure does not favour any parameter in particular. The homogeneous simulations presented in Sect. 3 could be used to briefly discuss on the efficiency to recover the most relevant input parameters: the spectral types, the age of the stellar population and [FORMULA]. Because of the degeneracy between these parameters, and the lack of spectral resolution, we only expect a rough spectral type to be retrieved from broad-band photometry. We have considered the 8 spectral types presented in Sect. 2 to illustrate the case. A general trend appears when comparing the model and retrieved spectral types, whatever the redshift, filter combination and photometric accuracy, with single bursts and early types being more easily identified than late types at all redshifts. Fig. 8 displays an example obtained with the UBVRIJK filter combination and 10% photometric accuracy, excluding catastrophic identifications (less than 1% in this case). The trend remains the same whatever the distribution in types, from these detailed 8 types to a rough Burst-E/S/Im distribution. Lowering the [FORMULA] or the number of filters slightly increases the trend in terms of contrast between the early type and late type behaviour. Late type misidentifications are due to the degeneracy between age of the stellar population and spectral type, such galaxies being incorrectly assigned to younger and earlier types. In other words, there is often a burst-like template, of suitable age and length, which is able to fit the dominant stellar population of a galaxy observed through broad-band filters. The results are the same whatever the configuration in the parameter space, in particular, changing the order or the position of the different templates in the space produces the same results. Degenerate solutions in the redshift dimension are systematically displayed by hyperz , but this is only an option for the other dimensions of the parameter space. There is no systematic trend in the case of catastrophic identifications, but more than 90% of such objects in these simulations have misidentified spectral types as well.

[FIGURE] Fig. 8. Comparison between the model spectral types and the best-fit templates recovered by hyperz , for the simulations computed in Sect. 3. Spectral types, from 1 to 8, correspond to galaxies ranging from early (Bursts/E) to late (Im) types. Circle sizes scale with the number of objects. Ideally only the diagonal region should have been populated.

In the case of [FORMULA], the procedure will choose the best and the lowest possible value. The results in this case are much better, whatever the [FORMULA], provided that near IR filters are included. Using a grid of [FORMULA] to explore the parameter space, the typical value of [FORMULA] ranges between [FORMULA] and 0.3, for photometric accuracies between 5 and 30%, for all the filter combinations including J, H or K (or a combination of them). In all the other cases, [FORMULA] to 0.45, for photometric accuracies between 5 and 30%. These values are an average through all the spectral types and redshifts, excluding catastrophic identifications. Similar estimates on catastrophic objects show an increase between [FORMULA] and [FORMULA] on [FORMULA], depending on the filter set.

In summary, it is difficult to obtain detailed information on the spectral types from broad-band photometry alone, and this is probably the result of the poor spectral resolution. Near IR photometry allows to constraint the [FORMULA] value for all spectral types. Only early type galaxies could be reliably identified by this method. For later types, only a rough estimate of the SED type could be obtained, in terms of "blue" or "red" continuum. The classification in this case shall either include the spectral type and the age of the stellar population, or be based on a simple set of templates such as CWW.

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Online publication: December 11, 2000
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