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$\begin{figure} \par\epsfig{file=2525f1.eps, width=8.8cm,clip}\end{figure}$ Figure 1: Top: illustration showing the comparison between reddened model spectra (blue) and observations of SN1987A (black) taken on the 24th of February 1987 (Pun et al. 1995; Phillips et al. 1988). Each model flux distribution is scaled for an assumed LMC distance of 52 kpc. In red we show the theoretical continuum energy distribution of the model. Model characteristics are: $L_{\ast} = 3 \times 10^8~L_{\odot}$ , $R_{\rm phot} = 2.74 \times 10^{14}$ cm (or 3940 $R_{\odot }$ ), $v_{\rm phot}=17~700$ km s^-1, $T_{\rm eff} =11~200$ K, n=12, $\rho _{\rm phot} = 1.1 \times 10^{-13}$ g cm^-3. Bottom: montage of rectified spectra computed by including bound-bound transitions of individual species, ordered from the bottom by increasing atomic weight. For species labeled with an "a'', we show $(f_{\lambda }/f_{\rm c}-1) \times x{\rm scale}+1$ , with $x{\rm scale}=4$ beyond 3500 Å and unity elsewhere [color].
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In the text

$\begin{figure} \par\epsfig{file=2525f2.eps,angle=-90,width=8cm,clip}\end{figure}$ Figure 2: Relative ionization for hydrogen (solid), helium (dashed) and iron (dash-dotted line) for the early-stage model of Sect. 3.1 and Fig. 1. The ionization fractions are expressed relative to the abundance of all species. Also shown is the electron density on the top axis [color].
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In the text

$\begin{figure} \par\epsfig{file=2525f3.eps, width=8.8cm,clip}\end{figure}$ Figure 3: Top panel: synthetic fit (color) to HST and Lick observations (black) of SN1999em taken on the 5th of November 1999 (Baron et al. 2000; Leonard et al. 2002a). The red (blue) curve corresponds to a model with $L_{\ast} = 4 \times 10^8~L_{\odot}$ ( $L_{\ast} = 5 \times 10^8~L_{\odot}$ ) and $T_{\rm eff} = 8850$ K ( $T_{\rm eff} = 9200$ K). Other properties are identical: $R_{\rm phot} = 6.6 \times 10^{14}$ cm (or 9540 $R_{\odot }$ ), $v_{\rm phot}=8750$ km s^-1, n=10 and $\rho _{\rm phot} = 4.1 \times 10^{-14}$ g cm^-3. Lower panel: montage of rectified spectra (same as in Fig. 1) [color].
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In the text

$\begin{figure} \par\epsfig{file=2525f4.eps, angle=-90, width=8cm,clip}\end{figure}$ Figure 4: Ionization structure for the intermediate-stage model described in Sect. 3.2 and shown in Fig. 3. The ionization fractions are expressed relative to the abundance of all species [color].
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In the text

$\begin{figure} \par\epsfig{file=2525f5.eps, width=8.8cm,clip}\end{figure}$ Figure 5: Top panel: synthetic fit (blue) to observations (black) of SN1999em taken on the 14th of November 1999 (Leonard et al. 2002a). We also show the continuum flux level (red) computed by ignoring all bound-bound transitions in the formal solution of the radiative transfer equation. The model parameters are: $L_{\ast} = 1.5 \times 10^8~L_{\odot}$ , $R_{\rm phot} = 6.15 \times 10^{14}$ cm (or 8840 $R_{\odot }$ ), $v_{\rm phot}=6350$ km s^-1, $T_{\rm eff} =6800$ K, n=10, $\rho _{\rm phot} = 8.7 \times 10^{-14}$ g cm^-3. In the top panel, we insert a zoom on the Na I5596-5590 Å region: the green curve corresponds to the same model as above (blue) but with the sodium abundance enhanced to four times cosmic. Lower panel: montage of rectified spectra computed by including bound-bound transitions of individual species, limited to those that affect the emergent spectrum [color].
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In the text

$\begin{figure} \par\epsfig{file=2525f6.eps, angle=-90, width=8cm,clip}\end{figure}$ Figure 6: Relative ionization for hydrogen (solid), helium (dashed) and iron (dash-dotted) for the late-stage model of Sect. 3.3. Note that the highest ionization state of iron shown is Fe³⁺ rather than Fe⁴⁺, but the lowest one is now Fe⁰⁺ rather than Fe⁺[color].
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In the text

$\begin{figure} \par\epsfig{file=2525f7.eps, angle=-90, width=8cm,clip}\end{figure}$ Figure 7: Relative ionization for hydrogen (solid), helium (dashed) and iron (dash-dotted) for a very cool model. For clarity, we only show the inner region of the outflow. The radial variation of the electron-density is also shown on the top axis [color].
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In the text

$\begin{figure} \par\epsfig{file=2525f8.eps, width=8.8cm,clip}\end{figure}$ Figure 8: Comparison between emergent spectra computed with identical parameters but differing in the adopted maximum radius, chosen at 2 (blue), 3 (red) and 6, 10 and 15R₀ (overlapping perfectly to form the black curve). To facilitate the comparison of the relative synthetic fluxes for the different models, these have all been normalised to unity, at 10 000 Å ( left panel) and 20 000 Å ( right panel). R₀ is identical in all cases. Note also that the red and black curve overlap perfectly everywhere except in the UV. We employ a small model atom for this investigation, i.e. solely H I, He I, C II, N I, O I, Fe II, Fe III [color].
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In the text

$\begin{figure} \par\epsfig{file=2525f9.eps, width=8.8cm,clip}\end{figure}$ Figure 9: Comparison of the emergent flux from models with identical parameters apart from a different adopted metallicity. The black curve describes a model with solar metal abundance. The red (blue) shows the resulting emergent spectra when all metal abundances are scaled by a factor of two (one half). The model spectra beyond H $\alpha$ are relatively insensitive to changes in metallicity - therefore for ease of comparison we have normalised the fluxes to unity at 7000 Å [color].
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In the text

$\begin{figure} \par\epsfig{file=2525f10.eps, width=8.8cm,clip}\end{figure}$ Figure 10: Comparison of the emergent flux from models differing in luminosity, enhanced and decreased by a factor of ten compared to the model in black. Also, we scale the radius and the base density up or down by $\sqrt {10}$ , to maintain the same photospheric velocity for all (see text for details). The model atom used is small, including only the most abundant species, i.e. H I, He I, C II, N I, O I, Fe II and Fe III [color].
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In the text

$\begin{figure} \par\epsfig{file=2525f11.eps, width=15cm,clip}\end{figure}$ Figure 11: Illustration of the influence of the density exponent n on the synthetic flux distribution for n=6, 8, 10 and 12. All other model parameters are kept identical. The model atom used is small, including only the most abundant species, i.e. H I, He I, C II, N I, O I, Fe II and Fe III.
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In the text

$\begin{figure} \par\epsfig{file=2525f12.eps, width=8.8cm,clip}\end{figure}$ Figure 12: Illustration of the influence of the density exponent n on the synthetic flux distribution for n=6, 8, 10 in a cool model where hydrogen recombines near the base. All other model parameters are kept identical. Note that the most striking effect is on the set of Ca II lines near 8500 Å, the line appearing broader and stronger for smaller density exponents [color].
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In the text

$\begin{figure} \par\epsfig{file=2525f13.eps, width=8.8cm,clip}\end{figure}$ Figure 13: Illustration of the relative line emission occurring at a given height in the outflow, both for one of the three components of the Ca II feature at ca. 8500 Å, i.e. Ca II8662 Å (solid line) and H $\alpha$ (broken line). We use a color coding to differentiate between models with different density exponent. Note how extended the line formation region of the Ca II line is compared to that of H $\alpha$ . The other two components of the Ca II triplet show a similar behavior and are thus not shown. $\xi$ is defined such that line flux is proportional to $\int \xi {\rm d}\log r$ [color].
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In the text

$\begin{figure} \par\epsfig{file=2525f14.eps, width=8cm,clip}\end{figure}$ Figure 14: Synthetic fits (broken line) to observations (solid line) of SN1999em taken on the 30th of October (A), and the 1st (B), 5th (C) and 8th (D) of November 1999 (Leonard et al. 2002a), showing the He I 5875 Å line region. Note how well CMFGEN manages to reproduce the observed profile using only a modest helium enrichment over the cosmic value ( ${\rm H/He}=5$ by number), in agreement with stellar evolutionary predictions for Blue/Red supergiants, progenitors of type II SN. This capability of CMFGEN is in stark contrast with failures to reproduce this He I line in the works of Schmutz et al. (1990) and Eastman & Kirshner (1989), suggesting the importance of treating all species in non-LTE.
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In the text

$\begin{figure} \par\epsfig{file=2525f15.eps, width=8cm,clip}\end{figure}$ Figure 15: Zoom into the optical spectroscopic observations (black) of SN1999em taken on the 30th of October 1999 (Leonard et al. 2002a) showing synthetic fits for a model comprising all species as given in Table 1 (blue) or only bound-bound transitions of hydrogen (turquoise), helium (green) and nitrogen (red). We strongly support the idea that the observed features around 4600 Å and 5500 Å are due to N II lines [color].
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In the text

$\begin{figure} \par\epsfig{file=2525f16.eps, width=7.4cm,clip}\end{figure}$ Figure 16: Hot star model (WN5). Bottom: grayscale image of the quantity $p \cdot I(p)$ as a function of pand scaled wavelength $x=(\lambda /\lambda _0-1)c$ , where p is the impact parameter (in units of the hydrostatic radius $R_{\ast }$ ), I(p) the specific intensity along p (at x). Here, $\lambda _0$ corresponds to the rest wavelength of C IV 1548 Å and cis the speed of light. The terminal velocity of the model is 2000 km s^-1. Top: line profile flux, directly obtained by summing $p \cdot I(p)$ over the range of p. Thus, the line flux at x in the top panel corresponds to the cumulative sum of all contributions $p \cdot I(p)$ at x shown in the bottom panel, giving a vivid illustration of the sites at the origin of the observed line profile.
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In the text

$\begin{figure} \par\epsfig{file=2525f17.eps, width=7.4cm,clip}\end{figure}$ Figure 17: Hot star case (WN8) Same set as in Fig. 16 but for the H $\alpha$ line in a WN8 model with a terminal velocity of 840 km s^-1.
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In the text

$\begin{figure} \par\epsfig{file=2525f18.eps, width=8cm,clip}\end{figure}$ Figure 18: Type II SN model Same set as in Figs. 16 and 17 for the H $\alpha$ line formed in a SN outflow with similar properties to those described in Sect. 3.2.
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In the text

$\begin{figure} \par\epsfig{file=2525f19.eps, width=8.8cm,clip}\end{figure}$ Figure 19: Radial and velocity variation of the logarithm of the line source function normalized to the continuum source function at a continuum optical depth of two third (see text for details). We show the cases corresponding to Figs. 16-18, i.e. for C IV 1548 in the WN5 model ( top), H $\alpha$ in the WN8 model ( middle) and H $\alpha$ in the SN model ( bottom).
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In the text

$\begin{figure} \par\epsfig{file=2525f20.eps , width=8cm,clip}\end{figure}$ Figure 20: Same as Fig. 18 for a model with n=8.
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In the text

$\begin{figure} \par\epsfig{file=2525f21.eps, width=8cm,clip}\end{figure}$ Figure 21: Same as Fig.18 but for a model with n=14.
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In the text

$\begin{figure} \par\epsfig{file=2525f2.eps,angle=-90,width=8cm,clip}\end{figure}$	Figure 2: Relative ionization for hydrogen (solid), helium (dashed) and iron (dash-dotted line) for the early-stage model of Sect. 3.1 and Fig. 1. The ionization fractions are expressed relative to the abundance of all species. Also shown is the electron density on the top axis [color].
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$\begin{figure} \par\epsfig{file=2525f4.eps, angle=-90, width=8cm,clip}\end{figure}$	Figure 4: Ionization structure for the intermediate-stage model described in Sect. 3.2 and shown in Fig. 3. The ionization fractions are expressed relative to the abundance of all species [color].
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$\begin{figure} \par\epsfig{file=2525f6.eps, angle=-90, width=8cm,clip}\end{figure}$	Figure 6: Relative ionization for hydrogen (solid), helium (dashed) and iron (dash-dotted) for the late-stage model of Sect. 3.3. Note that the highest ionization state of iron shown is Fe³⁺ rather than Fe⁴⁺, but the lowest one is now Fe⁰⁺ rather than Fe⁺[color].
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$\begin{figure} \par\epsfig{file=2525f7.eps, angle=-90, width=8cm,clip}\end{figure}$	Figure 7: Relative ionization for hydrogen (solid), helium (dashed) and iron (dash-dotted) for a very cool model. For clarity, we only show the inner region of the outflow. The radial variation of the electron-density is also shown on the top axis [color].
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$\begin{figure} \par\epsfig{file=2525f11.eps, width=15cm,clip}\end{figure}$	Figure 11: Illustration of the influence of the density exponent n on the synthetic flux distribution for n=6, 8, 10 and 12. All other model parameters are kept identical. The model atom used is small, including only the most abundant species, i.e. H I, He I, C II, N I, O I, Fe II and Fe III.
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$\begin{figure} \par\epsfig{file=2525f12.eps, width=8.8cm,clip}\end{figure}$	Figure 12: Illustration of the influence of the density exponent n on the synthetic flux distribution for n=6, 8, 10 in a cool model where hydrogen recombines near the base. All other model parameters are kept identical. Note that the most striking effect is on the set of Ca II lines near 8500 Å, the line appearing broader and stronger for smaller density exponents [color].
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$\begin{figure} \par\epsfig{file=2525f17.eps, width=7.4cm,clip}\end{figure}$	Figure 17: Hot star case (WN8) Same set as in Fig. 16 but for the H $\alpha$ line in a WN8 model with a terminal velocity of 840 km s^-1.
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$\begin{figure} \par\epsfig{file=2525f18.eps, width=8cm,clip}\end{figure}$	Figure 18: Type II SN model Same set as in Figs. 16 and 17 for the H $\alpha$ line formed in a SN outflow with similar properties to those described in Sect. 3.2.
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$\begin{figure} \par\epsfig{file=2525f19.eps, width=8.8cm,clip}\end{figure}$	Figure 19: Radial and velocity variation of the logarithm of the line source function normalized to the continuum source function at a continuum optical depth of two third (see text for details). We show the cases corresponding to Figs. 16-18, i.e. for C IV 1548 in the WN5 model ( top), H $\alpha$ in the WN8 model ( middle) and H $\alpha$ in the SN model ( bottom).
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$\begin{figure} \par\epsfig{file=2525f20.eps , width=8cm,clip}\end{figure}$	Figure 20: Same as Fig. 18 for a model with n=8.
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$\begin{figure} \par\epsfig{file=2525f21.eps, width=8cm,clip}\end{figure}$	Figure 21: Same as Fig.18 but for a model with n=14.
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