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Astron. Astrophys. 363, 517-525 (2000)

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5. The template SEDs

5.1. EPS model parameters

A large number of EPS models with different input parameters (IMF, [FORMULA], n and [FORMULA]) are developed, each accounting for both the local properties and evolutionary behaviour of the 4 types of galaxies considered here. For a given spectral type, the model parameters are normalised at [FORMULA] by fitting them to the local observed SED of their respective type. The evolutionary behaviour of the EPS models is then constrained by estimating the photometric redshifts to our calibrating sample in Table 1, considering template SEDs with different parameters (i.e. IMF and [FORMULA]) and allowing for Lyman continuum and Lyman forest absorption for [FORMULA] galaxies. The template SEDs corresponding to the evolutionary parameters which give the closest agreement between the photometric and spectroscopic redshifts are then adopted (see below). The sensitivity of the final results (i.e. photometric redshifts) to the input parameters in the EPS models is studied in the next section while, details of the final templates for individual types, which best satisfy the above requirements, are summarised below:

a) Ellipticals. The synthetic SEDs, representing elliptical galaxies, are constructed taking [FORMULA] and [FORMULA]. This gives an e-folding star formation time scale of 1 Gyr and reproduces the observed local SEDs for the ellipticals (Fig. 2.1a). A formation redshift of 5 is estimated, corresponding to an age of 13 Gyrs. These models predict a noticeable extinction by dust (AB [FORMULA] 4.6 mag) in the first stages of their evolution which are characterized by intense star formation activity, making them powerful far-infrared sources (Fig. 2.2a) (see MDX94 for more details).

[FIGURE] Fig. 2.1a-c. The synthetic Spectral Energy Distributions (SEDs) are predicted and constrained to fit the observed data at [FORMULA], as explained in the text (left panel). Details of each panel and the source of the observational data for each type is given below. Fig. 2.2a-c. The local synthetic SEDs for different types of galaxies from Figs. 2.1a-c (solid lines) are compared with their counterparts at [FORMULA] (dashed lines).
a) Elliptical galaxies: open squares (Burstein et al. 1988); filled triangles (Schild & Oke 1971); filled circles (Oke & Sandage 1968); asterix (Kennicutt 1992); the filled circles at FIR wavelengths correspond to the average local FIR SED for these galaxies (Mazzei & DeZotti 1994b).
b) Starburst galaxies: this corresponds to the observed SEDs of NGC5996 (MK691). The observed data are taken from: filled circles (Kennicutt 1992); asterix in the shorter wavelength region (IUE data from Kinney et al. 1993); asterix in the near-IR region (Balzano 1983); FIR data (IRAS Catalugue Version 2 (Fullmer, L. and Lonsdale, C. 1989)); the IUE data are measured over [FORMULA] aperture and are shifted vertically by a factor of 1.6 to normalise to the optical SED; near-IR data, measured over [FORMULA] aperture has been shifted by a factor of 4.5.
c) Spiral galaxies: this corresponds to the NGC3627 galaxy. The observed data are from Kennicutt (1992) and Rice et al. (1988).

[FIGURE] Fig. 2.1d. The local observed SED of IRR galaxy NGC 4449 (Kennicutt 1992), filled circles, is compared with the synthethic SED of our Irr template at [FORMULA] (continuous line) and that for the starburst galaxies (dashed line). Fig. 2.2d. The SED for irregulars (solid line) is compared with that for the starbursts (dashed line), both at [FORMULA].

b) Spirals. The models which produce synthetic SEDs for spiral galaxies have [FORMULA] and [FORMULA]/yr. They are consistent with an e-folding star formation time scale of 10 Gyrs, corresponding to a formation redshift of 2 (i.e. an age of 10-11 Gyrs). This gives a local value of [FORMULA], very similar to that of our own Galaxy. This model re-produces the local SED of NGC 3627 out to the far-infrared wavelengths (Fig. 2.1c). Spiral galaxies are slowly evolving with time ([FORMULA] beyond [FORMULA]), resulting a smooth evolution for their SED (Fig. 2.2c) - (see MXD92 for more details).

c) Starbursts. The template SEDs for the starburst population are produced taking [FORMULA], [FORMULA] and a formation redshift of 5. This template does not produce powerful far-infrared emission at any redshift and hence, its local SED (Fig. 2.1b) is different from that of local luminous far-infrared starbursts (ie. M82 and Arp 220). The SFR in this model is a gradual process with a smooth time scale, leading to formation of very blue, metal poor systems at [FORMULA] (Fig. 2.1b) and a blue, dust-free ([FORMULA]) system at [FORMULA] (Fig. 2.2b). This mimics a scenario involving frequent but short bursts of star formation, which use a small fraction of gas in these systems (strong bursts of star formation rapidly exhaust the gas, leading to ellitpical like systems). The starburst templates here represent the average evolutionary behaviour expected for this population of galaxies.

d) Irregulars. The Irregular template has been produced with the same recipe as the starburst but with a formation redshift of [FORMULA] (ie. an age of 0.8-0.9 Gyr). The local SED of the irregular galaxy NGC 4449 (Kennicutt 1992) is compared in Fig. 2.1d with our local templates for both irregular and starburst galaxies. These templates are also compared at [FORMULA] (Fig. 2.2d), showing a significant difference beyond [FORMULA].

The model SEDs at [FORMULA] for the four galaxy types discussed above, agree well with the local observed SEDs, as shown in Figs. 2.1a-2.1d. The effects of Lyman break and Lyman forest opacities are included to the template SEDs, using the relations [FORMULA] vs. z for different wavelengths, given in Madau (1995). These relations were fitted to parametric forms, which were then used to estimate the respective correction (due to absorption by inter galactic medium) to the SEDs at any given redshift. The correction due to Lyman break and Lyman forest absorption ranges from [FORMULA] mag. at [FORMULA] to [FORMULA] mag. at [FORMULA].

5.2. Sensitivity of the template SEDs on the model parameters

In this section we study the dependence of the results (i.e. the photometric redshifts) to the model parameters which most strongly affect the final template SEDs and hence, the predicted photometric redshifts. These parameters consist of the shape of the IMF and its lower mass limit, the total number of templates (i.e. spectral types) and the formation redshift for each galaxy type. New template SEDs are generated corresponding to EPS models for elliptical, spiral, starburst and irregular galaxies, using the parameters listed in Table 2, with the rest of the parameters taken to be the same as discussed in Sect. 5.1. For each set of the new templates, the photometric redshifts are estimated for galaxies in the calibrating sample (Table 1) with the rms scatter in the quantity [FORMULA] (ie. between the photometric and spectroscopic redshifts) calculated and listed in Table 2. The templates corresponding to the model which gives the smallest rms estimate in Table 2 (i.e. model 4) is then adopted. The photometric redshifts estimated for the calibration sample, using the adopted template SEDs (model 4 in Table 2), are listed in Table 1 and compared with their spectrosopic counterparts in Fig. 3. The rms scatter of 0.11 here is taken as the uncertainty in the photometric redshift estimates in the range [FORMULA]. The uncertainties in correcting for intergalactic absorption at [FORMULA] indirectly affect the optimisation of the EPS model parameters in this section. To explore this, we constrained the calibration sample only to galaxies with [FORMULA] (which are much less affected by the IGM absorption) and estimated the EPS model parameters so that to minimise the rms scatter in Fig. 3. No change is found in the EPS model paremeters. Also, we explored the sensitivity of the rms scatter in Fig. 3 to the number of template SEDs used (ie. including templates for different sub-classes of spirals), taking the number of SEDs as a free parameter. This did not reduce the optimum rms scatter, derived using the four templates.

[FIGURE] Fig. 3. Comparison between the spectroscopic redshifts with the photometric values estimated here for 73 HDF galaxies from Table 1. The spectroscopic redshifts are taken from Cohen et al (1996); Steidel et al (1996); Lowenthal et al (1997); Dickinson (1998). The UV drop-out objects for which a U-band limiting magnitude of 28.01 is used to estimate the photometric redshifts, are also included. The crosses are HDF3646+1408 and HDF3659+1222 galaxies which have uncertain published spectroscopic redshifts of [FORMULA] and 0.47 respectively. The lines have a slope of unity. The photometric redshifts are based on model 4 in Table 2. The rms scatter is estimated in [FORMULA] and corresponds to 0.11 with the dashed lines corresponding to [FORMULA] error.


Table 2. Sensitivity of the rms scatter between the photometric and spectroscopic redshifts on the EPS model parameters (i.e. template SEDs)

Considering the results in Table 2, it seems that one set of models (Salpeter IMF with [FORMULA][FORMULA]), give a considerably better fit to observations. This was extensively tested by exploring the parameter space, consisting of the IMF shape and its mass limits, total number of templates and formation redshifts. It was found that this is not due to sampling a particular region of the parameter space or the number of templates, and is indeed, a real effect. A similar study, using a different set of EPS models and the optimised parameters in Table 2, would be extremely valuable.

The galaxies in the calibration sample in Table 1 also have near-IR data (Fernández-Soto et al. 1999). The above procedure was repeated, using the combined optical and near-IR magnitudes (UBVIJK) for the calibrating sample. This did not change the optimized EPS model parameters in Sect. 5.1 and Table 2. As an independent test of the template SEDs here, we include the near-IR magnitudes to the observed SEDs of the calibrating sample in Table 1 and estimate their photometric redshifts, using the template SEDs predicted in Sect. 5.1 (model 4 in Table 2). Compared to their spectroscopic counterparts, an rms scatter of 0.13 is found, in agreement with 0.11 from Fig. 3.

The amount of dust and its evolution with redshift is an important characteristic of the EPS models in this study. This, at any time, is computed self-consistently, accounting for both the SFR and the IMF parameters. By extending the IMF to low [FORMULA] values ([FORMULA] [FORMULA]), the gas depletion rate becomes faster, reducing the dust enrichment rate. This leads to higher optical depth in the early evolutionary phase of our elliptical models (templates)-(see also Mazzei & DeZotti 1996 for more details). The UV extinction ([FORMULA]) corresponding to different IMF and [FORMULA] values is estimated for both elliptical and spiral templates at different redshifts and are listed in Table 3. By changing the shape of the IMF and its lower mass limit, the UV extinction for ellipticals at [FORMULA] changes in the range [FORMULA] mag. Considering the optimised model in Table 2 (model 4), the extinction in spirals is significantly larger than in ellipticals at [FORMULA] while, at higher redshifts ([FORMULA]), ellipticals are obscured more than the spirals. Using our optimised model in Sect. 5.1, the template SEDs at [FORMULA] are compared in Fig. 2.2 with their counterparts at [FORMULA]. These show a significant dust contribution to the elliptical SEDs at [FORMULA], as indicated from the peak at the far-IR wavelengths.


Table 3. Changes in UV extinction ([FORMULA]) with redshift, corresponding to EPS models for Elliptical and Spiral galaxies.

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© European Southern Observatory (ESO) 2000

Online publication: December 11, 2000