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Astron. Astrophys. 361, 465-479 (2000)

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2. Data-models comparison method

2.1. Determination of the underlying population properties

The optical-near-infrared colors measured for the underlying stellar component (see Sects. 5 and 6.1 in Paper I) have been compared with those predicted by the Bruzual & Charlot (priv. comm.) evolutionary synthesis models. We have obtained the best-fitting model for each point in the color profiles (see Fig. 6 of Paper I) using a maximum likelihood estimator. This maximum likelihood estimator is defined as,

[EQUATION]

where [FORMULA] (with n=1-5) are the [FORMULA], [FORMULA], [FORMULA], [FORMULA] and [FORMULA] colors measured, and [FORMULA] are those predicted by the evolutionary synthesis models. The colors measured were corrected for Galactic extinction using an extinction in the B-band of [FORMULA] (Burstein & Heiles 1982).

We have studied different star formation histories for the formation of this component. In particular, we have considered instantaneous and 1, 3 and 7 Gyr duration bursts and continuous star formation models. This comparison has been restricted to models with metallicity lower than the solar value. We are confident with this assumption since the gas metallicities derived in Sect. 3.4 for the galaxy star-forming regions are lower than one tenth solar.

2.2. Determination of the star-forming regions properties

A more elaborated comparison method has been used in the case of the galaxy star-forming regions. This comparison method is fully described in Gil de Paz et al. (2000b). Briefly, it combines Monte Carlo simulations and a maximum likelihood estimator with Cluster and Principal Component Analysis.

The maximum likelihood estimator employed is very similar to that described in Sect. 2.1, but replacing the [FORMULA] and [FORMULA] colors by the [FORMULA] and [FORMULA] colors. In addition, since these regions have intense H[FORMULA] emission, we have included a new term, defined as [FORMULA]+2.5[FORMULA]log([FORMULA]). This term is equivalent to the H[FORMULA] equivalent width (EW hereafter) term, 2.5[FORMULA]log EW(H[FORMULA]), used in Gil de Paz et al. (2000b). The [FORMULA] magnitudes are those measured within the apertures given in Paper I.

In order to properly derive this new term, we have computed the fraction of H[FORMULA] flux, i.e. the fraction of Lyman photons, due to the stellar continuum measured within the apertures. Two different approaches can be followed. First, we could measure the H[FORMULA] fluxes using these apertures. However, since the H[FORMULA] emission is usually more extended than the continuum emisson, this procedure would sistematically underestimate the H[FORMULA] flux (see, e.g. #8, #13, #18, #50, #70 and #80 regions). Therefore, we have used an alternative method. We measured the total H[FORMULA] using the COBRA program (see Paper I). Then, we assumed that the fraction of photons emitted within the apertures relative to the total emission is equivalent for the Lyman and R-band continuum. Thus, considering that the apertures were obtained at e-, e2- or e3-folding radii and assuming gaussian ligth profiles, this light fraction can be computed for each region. The values obtained for this fraction, f, are given in Table 3.

Then, multiplying these flux ratios by the total H[FORMULA] fluxes given in Table 4 of Paper I, we derive the H[FORMULA] luminosities due to the continuum emission measured within the apertures.

The H[FORMULA] fluxes were corrected for extinction using the [FORMULA] color excesses provided by the H[FORMULA]-H[FORMULA], H[FORMULA]-H[FORMULA] Balmer decrements. In addition, the broad-band magnitudes and colors were corrected for extinction assuming that the extinction affecting the stellar continuum and the gas extinction are related via [FORMULA]=0.44[FORMULA][FORMULA] (Calzetti et al. 1996). In those regions where Balmer line ratios were not measurable we assumed an average extinction of [FORMULA]=[FORMULA]. This value was obtained as the mean of the color excesses given in Table 5 of Paper I for those regions with accessible Balmer line ratios.

Thus, each star-forming region has a point associated in the [FORMULA], [FORMULA], [FORMULA], [FORMULA], [FORMULA], [FORMULA]+2.5[FORMULA]log([FORMULA]) six-dimensional space. However, the corresponding uncertainties transform these points into probability distributions. Using a Monte Carlo method with 103 points and assuming gaussian errors we reconstructed these probability distributions. Then, we compared each of these 103 points with our models using the maximuum likelihood estimator described above. Since these models are parametrized in age, t; burst strength, b; and metallicity, Z, of the burst stellar population, this method effectively provides the (t,b,Z) probability distribution for each input region (see Table 3).

Finally, we studied the clustering pattern present in these distributions using a hierarchical clustering method (see Murtagh & Heck 1987). This method allows to isolate different solutions in the (t,b,Z) space. We grouped the 103 (t,b,Z) points in three clusters of solutions. Then, we performed a Principal Component Analysis (see Morrison 1976) for each individual solution (see Gil de Paz et al. 2000b for a more complete description of this procedure).

For the central starburst component we used a similar procedure. However, since no H[FORMULA] emission was detected for this component, the [FORMULA]+2.5[FORMULA]log([FORMULA]) term was not included in the maximum likelihood estimator. In addition, we introduced the continuum color excess [FORMULA] as a free parameter. Color excesses in the range 0.0-[FORMULA] were studied, where [FORMULA] is the Galactic color excess. For each of the 103 Monte Carlo particles the full range was explored, obtaining the best-fitting color excess and (t,b,Z) array.

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© European Southern Observatory (ESO) 2000

Online publication: October 2, 2000
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