5 Evolutionary synthesis models

In order to derive the physical properties of the different stellar populations in Mrk 86 we have built a complete set of evolutionary synthesis models based in those developed by Bruzual & Charlot (priv. comm.).

First, we have assumed that the optical-near-infrared spectral energy distribution (SED) in any region of Mrk 86 can be described by a young star-forming burst superimposed on an underlying stellar population. The burst strength parameter, b, will describe the mass ratio between both stellar populations. Then, using this parameter and the evolution with time of the stellar continuum prediced by the Bruzual & Charlot (priv. comm.) models, we derive the colors and number of Lyman photons emitted for different composite stellar populations, with b ranging between 10^-4 and 1. We have studied models with metallicities 1/50 $Z_{\hbox{$\odot$ }}$, 1/5 $Z_{\hbox{$\odot$ }}$, 2/5 $Z_{\hbox{$\odot$ }}$, $Z_{\hbox{$\odot$ }}$ and 2 $Z_{\hbox{$\odot$ }}$, and Scalo (1986) IMF with $M_{\rm low}=0.1\,M_{\hbox{$\odot$ }}$ and $M_{\rm up}=125\,M_{\hbox{$\odot$ }}$. The underlying population has been parametrized using the optical-near-infrared colours measured in the outer regions of Mrk 86. We use, B-V=0.69, V-R=0.52, R-J=1.27, J-H=0.99 and R-K=2.35, as underlying stellar population colors, assuming that no significant color gradients are present (see Fig. 6). In addition, the mass-to-light ratio adopted for this stellar population in the K-band was $0.87\,M_{\hbox{$\odot$ }}/L_{K,\hbox{$\odot$ }}$ (see Paper II).

Figure 6: Color profiles in the outer regions of Mrk 86

Now, following the procedure described by Gil de Paz et al. (2000b) and Alonso-Herrero et al. (1996) we included the contribution to the total flux and colors arising from the nebular continuum and the most intense emission-lines (i.e., [O II] $\lambda\lambda$3726, 3729 Å, H$\beta$, [O III]$\lambda$4959 Å, [O III]$\lambda$5007 Å and H$\alpha$, etc.).

We have assumed, in order to compute the nebular continuum emission, an electron density, n_e, of 10²cm^-3 and a temperature, T_e, of 10⁴K. In addition, from the analysis of our spectroscopic data (see Paper II), we adopted a $N[He{\sc ii}]/N[H{\sc ii}]$ abundance ratio of 0.12. We have also assumed that the He III abundance is so low that the emission from recombination to He II is negligible.

Finally, we have included the contribution of the emission lines to the total flux. The contribution of the H$\beta$, H$\alpha$, Pa$\beta$, $\rm Br_{10}-Br_{19}$ and Br$\gamma$ hydrogen emission lines to the BVRJHK bands was obtained assuming the case-B of recombination (Osterbrock 1989) and using the relation given by Brocklehurst (1971). The contribution of the most intense forbidden lines have been estimated using average [O II] $\lambda\lambda$3726, 3729/[O III]$\lambda$5007 and [O III]$\lambda$5007/H$\beta$ line ratios, as provided by our spectroscopic data. Fortunately, the contribution of all the forbidden lines to the B and V bands is very small. Using the higher and lower line-ratios measured in the galaxy, this contribution would range between 1 and 8 per cent for the B-band and 2 and 8 per cent for the V-band, for a H$\alpha$ equivalent width (EW hereafter) of 100 Å.

The output of the models will be the optical-near-infrared colors B-V, V-R, V-J, J-H and J-K of the composite stellar population, its H$\alpha$ luminosity and equivalent width, and mass-to-light ratio, parametrized as a function of the burst age, burst strength and stellar metallicity (t, b, Z).

The Cousins-R magnitudes originally given by the Bruzual & Charlot (priv. comm.) models have been converted to Johnson-R magnitudes using the relation given by Fernie (1983). However, if we compare the correction predicted by Fernie (1983) in the case of very red stars ( $R_{\rm C}-R_{\rm J}\simeq0.25^{\mathrm{m}}$) with that measured by Fukugita et al. (1995) for early-type galaxies, typically of 0.1 ^m -with no correction for extinction applied-, we find differences of about 0.15 ^m. Since the change in $R_{\rm C}-R_{\rm J}$ due to the correction for extinction can not be higher than 0.02 ^m, this difference has to be attributed to a difference in the correction between evolved stellar populations and individual very-red stars. Thus, in the case of the underlying population analysis, we have applied the mean correction given by Fukugita et al. (1995).