3 The emission line spectra

   
3.1 Hydrogen lines

Observed line profiles for the Balmer lines H$\gamma$, H$\delta$, H$\zeta$ and H$\eta$ are presented in Figs. 1-5 for RRSco, RAql, RCar, SScl and RHya (because of its position in the sky and the phase of its light curve, RLeo was not observable near maximum when the Balmer lines were in emission, but we did observe it during two different minima). The line

Figure 1: Left: Line profiles of H$\gamma$, H$\delta$, H$\zeta$, H$\eta$as a function of phase in RRSco. The observations were made with a wide (1500$\mu$m) slit. F $_{\lambda }$ is plotted vertically, with the zero flux level for each spectrum being indicated by a tick mark on the vertical axis. The phase of the observation is indicated next to each tick mark. Note that the height of the profiles is arbitrary as we scaled them with different factors. Table 4 lists the maximum flux level in each line. The horizontal axis corresponds to wavelength $\lambda$(i.e. velocity). The spectra have been positioned horizontally so that line emission in the rest frame of the star will appear at zero velocity (stellar center-of-mass velocities from Table 1 have been adopted). Positive velocities correspond to motion outward from the center-of-mass (i.e. $\lambda$increases to the right). Right: The Balmer line profiles observed with a narrow (300$\mu$m) slit at phase $\phi = 0.29$, shown for comparison with the wide slit observations

Figure 2: Left: Line profiles of H$\gamma$, H$\delta$, H$\zeta$, H$\eta$ as a function of phase in RAql (see Fig. 1 for details). Right: The Balmer line profiles observed with a narrow (300$\mu$m) slit at phase $\phi = 0.01$

Figure 3: Left: Line profiles of H$\gamma$, H$\delta$, H$\zeta$, H$\eta$ as a function of phase in RCar (see Fig. 1 for details). Right: The Balmer line profiles observed with a narrow (300$\mu$m) slit at phase $\phi = 0.11$

Figure 4: Left: Line profiles of H$\gamma$, H$\delta$, H$\zeta$, H$\eta$ as a function of phase in SScl (see Fig. 1 for details). Right: The Balmer line profiles observed with a narrow (300$\mu$m) slit at phase $\phi = 0.02$

Figure 5: Left: Line profiles of H$\gamma$, H$\delta$, H$\zeta$, H$\eta$ as a function of phase in RHya (see Fig. 1 for details). Right: The Balmer line profiles observed with a narrow (300$\mu$m) slit at phase $\phi = 0.12$

Figure 6: From left to right: Line profiles of SiI 4102.94Å (M 2) as a function of phase in RRSco, RAql, RCar, SScl and RHya (plotted as in the left panel of Fig. 1). The feature on the left of each plot is the edge of the nearby H$\delta$ emission line. Table 4 lists the maximum flux level in each SiI line

Figure 7: From left to right: Narrow (300$\mu$m) slit spectra for the SiI 4102.94Å line at phase $\phi = 0.11$ in RCar and $\phi = 0.02$ in SScl, and the MgI 4571.10Å line at phase $\phi = 1.49$ in RLeo and $\phi = 0.12$ in RHya. These plots are shown for comparison with the wide (1500$\mu$m) slit observations in Figs. 6 and 8

Figure 8: From left to right: Line profiles of MgI 4571.10Å (M 1) as a function of phase in RRSco, SScl, RLeo and RHya (plotted as in the left panel of Fig. 1). Table 5 lists the maximum flux level in each line

Figure 9: Left: Line profiles of MgI 4571.10Å (M 1) and MgI 3829.32Å, 3832.35Å and 3838.29Å (all M 3) as a function of phase in RAql (plotted as in the left panel of Fig. 1). Table 5 lists the maximum flux level in each line. Right: Profiles of the MgI multiplet 3 lines observed with a narrow slit (300$\mu$m) at a single phase, shown for comparison with the wide slit (1500$\mu$m) observations. $F_{\lambda }$ is plotted vertically, with the zero flux level for each spectrum being indicated by a tick mark on the vertical axis

Figure 10: Same as Fig. 9 but for RCar

Figure 11: Line profiles of FeI 4427.30Å (M 828), 4375.93Å (M 2), 4307.90Å, 4202.03Å (both M 42) and 3852.57Å (M 73) as a function of phase in RRSco (plotted as in the left panel of Fig. 1). Tables 6 and 7 list the maximum flux level in each line

Figure 12: Same as Fig. 11 but for R Car, and with FeI 4461.65Å (M 2) replacing FeI 4427.30Å (M 828) in the left panel

Figure 13: Left: Line profiles of FeI 4307.90Å, 4202.03Å (both M 42) and 3852.57Å (M 73) as a function of phase in SScl (plotted as in the left panel of Fig. 1). Tables 6 and 7 list the maximum flux level in each line. Right: The FeI 4202.03Å line profile observed with a narrow (300$\mu$m) slit at phase $\phi = 0.02$, shown for comparison with the wide slit (1500$\mu$m) observations

Figure 14: Left: Same as Fig. 13 but for RHya, and including FeI 4307.90Å (M 42) and 3852.57Å (M 73) in the right panel

Figure 15: Left: Same as Fig. 13 but for RAql, and including FeI 3852.57Å (M 73) in the right panel

Figure 16: Left: Line profiles of FeI 4307.90Å (M 42) as a function of phase in RLeo. Right: Line profiless of FeI 4461.65Å, 4375.93Å (both M 2), 4427.30Å (M 828), 4202.03Å (M 42) and 4216.18Å (M 3) at phase $\phi = 1.49$ in RLeo. Both panels are plotted as in the left panel of Fig. 1. Tables 6 and 7 list the maximum flux level in each line

Figure 17: Left: Line profile of FeII 4583.84Å (M 38) at phase $\phi = 0.29$ in RRSco (1500$\mu$m). Table 7 lists the maximum flux level in the line. Right: Line profiles of FeII 4583.84Å (M38) and of the forbidden transitions [FeII]7F (4359.33Å and 4287.40Å) at phase $\phi =0.39$ in RCar. $F_{\lambda }$ is plotted vertically, with the zero flux level for each spectrum being indicated by a tick mark on the vertical axis. Table 8 lists the maximum flux level in each line

Figure 18: Left: Line profiles of MnI 4030.75Å (M 2), FeII 4583.84Å (M 38) and [FeII]6F 4457.95Å at phase $\phi = 1.49$ in RLeo. $F_{\lambda }$ is plotted vertically, with the zero flux level for each spectrum being indicated by a tick mark on the vertical axis. Tables 5, 7 and 8 list the maximum flux level in each line. Right: Line profiles of the forbidden transitions [FeII]7F (4359.33Å and 4287.40Å) and [FeII]21F (4276.83Å and 4243.97Å) at phase $\phi = 1.49$ in RLeo. Table 8 lists the maximum flux level in each line

profiles are plotted against velocity rather than wavelength, because we want to analyse the atmospheric kinematics associated with pulsation. Zero velocity in the plots corresponds to the center-of-mass velocity of the star and a positive velocity indicates a motion outward from the center of the star, and visa versa. Most of the observations in the plots (left panels) were taken with a wide slit, but we also present selected observations taken with a narrow slit (right panels) to give a comparison. Clearly, since the Balmer lines have intrinsic full widths of $\sim$80 km s^-1, the instrumental broadening of the wide slit (15.3 km s^-1) does not influence the line profiles significantly.

The main result seen in the presented spectra is the change in the overall line shape with phase. The full base width (hereinafter FBW) of the hydrogen lines is around 80 km s^-1 when they first appear. With increasing phase, the hydrogen lines become weaker and more narrow (FBW$\sim$60-70 km s^-1). The emission lines are generally centered around an outward velocity of $\sim$10 km s^-1. Previous studies of the hydrogen lines in Miras (e.g. Fox et al. 1984) have shown similar results.

A noticeable feature of the hydrogen lines is that the strengths of superimposed absorption features diminish with advancing phase. Joy (1947) identified absorption lines of TiO in H$\gamma$, of FeI and VI in H$\delta$ and of TiI in H$\zeta$. A decrease in absorption with increasing phase is just as expected in a model where the shock producing the emission lines moves above more of the atmosphere as time progresses. The strength of the absorption features also seems to vary from star to star; for instance, superimposed absorption in H$\gamma$ is stronger in RAql than in SScl at comparable phases (Fig. 2 $\phi = 0.01$ and Fig. 4 $\phi = 0.02$). Fox et al. (1984) noted a similar variation of overlying absorption line strength from star to star and suggested that this could be due to a cycle-to-cycle variation in shock strength: at fainter maxima weaker shocks are formed and they are not able to propagate out through as much overlying absorbing material, leading to stronger absorption.

A remarkable result is the appearance of faint Balmer lines at the very early phase $\phi =0.58$ in RRSco (Fig. 1). These emission lines are dominated by strong overlying absorption, as expected. They could also be evidence for an unusually strong shock emerging from the star in the observed pulsation cycle.

   
3.2 Metal lines

Various metal emission lines can be observed in Mira variables around maximum light and during the post-maximum phases. In the spectral range of our observation, we observed the following emission lines, which are ordered by the mutiplet number M: SiI (M2: 4102.94Å), MgI (M1: 4571.10Å), MgI (M3: 3829.32Å, 3832.35Å and 3838.29Å), FeI (M2: 4461.65Å and 4375.93Å), FeI (M3: 4216.18Å), FeI (M42: 4307.90Å and 4202.03Å), FeI (M73: 3852.57Å), FeI (M828: 4427.30Å), FeII (M38: 4583.84Å) as well as forbidden lines [FeII]6F (4457.95Å), [FeII]7F (4359.33Å and 4287.39Å) and [FeII]21F (4276.83Å and 4243.97Å) and finially MnI (M2: 4030.75Å). We discuss these emission lines in the order of their appearance during the pulsation cycle.

3.2.1 The silicon line

The SiI line of the multiplet 2 at 4102.94Å appears at the same phases as the hydrogen lines, namely around maximum light, and varies in strength in the same way as the Balmer lines. The variation in appearance with phase is presented in Fig. 6 for RRSco, RAql, RCar, SScl and RHya. For comparison of wide and narrow slit spectra, additional observations, taken with a narrow slit, are shown in Fig. 7 for one phase in each of RCar and SScl. We measured a FBW of the silicon line of around 60 km s^-1when it first appears, somewhat less than the FBW of the Balmer lines. As with the Balmer emission lines, the SiI emission line can be seen at the remarkably early phase $\phi =0.58$ in RRSco (Fig. 6, left panel).

   
3.2.2 Magnesium lines

The observed MgI emission lines (M1: 4571.10Å; M3: 3829.32Å, 3832.35Å and 3838.29Å) are presented in Figs. 8-10. Additional narrow slit observations are shown in the same figures for the multiplet 3 lines, and in Fig. 7 for the 4571.10Å line. Note that in some of the spectra, the 4571.10Å line appears totally in absorption.

The lines of the MgI multiplet 3 at 3829.32Å, 3832.35Å and 3838.29Å appear around the phase of maximum when the hydrogen lines are dominant. These lines are high excitation lines (lower state excitation potential 2.7 eV) and the Einstein-coefficient is rather large (see Table 2). The emission lines were detected in RAql and RCar (Figs. 9 and 10) where we observed the early post-maximum phases in detail. We measured a FBW of $\sim$30-40 km s^-1. It is obvious that these lines are always blueshifted. For RAql (Fig. 9) at phase $\phi = 0.01$, the emission lines show equal velocity shifts of $\sim$+10 km s^-1, as can also be seen in the panel of the narrow slit observation in Fig. 9 (all emission line velocities quoted in this paper are measured at half maximum height). For RCar (Fig. 10), the velocity shift of the lines at 3829.32Å and 3832.35Å is about +20 km s^-1 when they first appear ( $\phi =-0.09$): the weak 3838.29Å line appears to be strongly affected by overlying absorption causing it to show a smaller velocity shift of only $\sim$+10 km s^-1. At phase $\phi = 0.11$, all multiplet 3 lines are equally blueshifted by $\sim$+10 km s^-1. For RHya, we could not detect the multiplet 3 MgI lines at phases $\phi =0.08$ and 0.12 although one would expect them to be detectable.

At later phases, the lines of the multiplet 3 disappear and the MgI 4571.10Å (M1) emission line appears. The lower level of this emission line is the ground state and the Einstein-coefficient is rather low (see Table 2). Because it is a ground state line, it is prominent in absorption as well as emission. Before and around maximum light, two absorption components appear, especially in RCar (Fig. 10, $\phi=-0.16$-0.11), presumably corresponding to material behind, and in front of, the emerging shock front. The majority of the observed MgI 4571.10Å emission lines are affected by obvious overlying absorption on the negative velocity side, although this absorption decreases as the phase advances.

The FBW of the MgI 4571.10Å emission line is generally around 40-50 km s^-1 when it first appears and it is blueshifted by $\sim$+10 km s^-1 with respect to the center-of-mass velocity. There is a general decrease in the blueshift towards minimum light; this is probably due to a combination of a real slowing of the shock and a decrease in overlying absorption on the red edge. In RAql (Fig. 9), the velocity shift around the minimum phase ($\phi=0.50$) seems to increase again, possibly due to some asymmetry in the upper atmosphere being transversed by the shock.

RLeo is an interesting case to study, since there are two minima observed which appear rather different. Around the first minimum, the MgI 4571Å line was very faint and narrow ($FBW\sim30$ km s^-1) with the velocity shift decreasing from +5 km s^-1 to +2 km s^-1 for the phases $\phi=0.43$ to $\phi=0.63$. At the next minimum, the emission line was bright and showed a FBW of $\sim$40 km s^-1 and the line was centered at a velocity shift of $\sim$+3 km s^-1. The AAVSO light curve shows that the light maximum preceding the first minimum was much fainter than the maximum preceding the second minimum. A bright preceding maximum obviously leads to a much wider and stronger MgI 4571.10Å emission line. This is consistent with the hypothesis that a stronger (visually brighter) maximum is associated with a stronger shock.

The development of the MgI 4571Å line in RHya (Fig. 8, right panel), the star with the longest period (389 d) of our sample, is obviously different. The emission line appears at a relatively early phase ($\phi = 0.12$) and it has a sharp low velocity edge indicative of strong overlying absorption. Clearly, velocities derived from this line need to be treated with caution, at least until very advanced phases.

   
3.2.3 Neutral iron lines

Out of the variety of neutral iron emission lines in Mira variables, we studied the following: (M2) 4461.65Å and 4375.93Å, (M3) 4216.18Å, (M42) 4307.90Å and 4202.03Å, (M73) 3852.57Å and (M828) 4427.30Å. Figs. 11-16 show the observed FeI lines for all stars of our sample. For SScl, RHya and RAql we present narrow slit as well as broad slit observations for some of the neutral iron lines.

It is obvious that several of the FeI emission lines, namely FeI 4307.90Å, 4202.03Å and 3852.57Å, appear brightly during the post-maximum phase of every star of our sample. Table 2 shows that these are all high excitation lines (lower level excitation potential 1.5-2.2 eV) with large Einstein-coefficents. It has been suggested that the great strength of all three lines is the result of fluorescence, the lines being pumped by the MgII 2795, 2802Å lines (Thackeray 1937; Willson 1976).

The 3852.57Å line appears around maximum visible light with a very narrow FBW of $\sim$25-30 km s^-1. At later phases it widens up to a FBW of $\sim$40-60 km s^-1. It appears that this is due to overlying absorption at early phases removing the negative velocity side of the line (see RCar, RHya and RAql in Figs. 12, 14 and 15).

The 4202.03Å line also appears near maximum light (see RCar, SScl and RAql in Figs. 12, 13 and 15). At early phases, it shows an obvious inverted P-Cygni profile caused by overlying absorption of infalling material.

The 4307.90Å line does not appear as prominently as the previous line for phases 0.2 even though both lines have identical upper states (see Table 2). This is almost certainly due to more overlying absorption affecting this line: around maximum light in RCar, SScl and RAql (Figs. 12, 13 and 15), the line is totally in absorption while the 4202.03Å line shows distinct emission. Multiple absorption components are clearly visible cutting into the emission line except at the latest phases. This may be partly self-absorption by pre- and post-shock material as the 4307.90Å has the largest Einstein-coefficent of the two lines. The large Einstein-coefficent may also explain the fact that the 4307.90Å line persists the longest and has the largest flux (see Table 6) of the two lines.

All other FeI emission lines observed are low excitation lines (see Table 2). The 4375.93Å line of the multiplet 2 appears around the phase of maximum light (see RRSco, RCar and RLeo in Figs. 11, 12, 16), which is an exceptional early appearance for a low excitation line. The line shows an obvious inverted P Cygni profile with a steep red wing: the absorption component decreases towards later phases. The 4461.65Å line was only detected in emission in RCar at the phase $\phi =0.39$ and in RLeo at $\phi = 1.49$ (Figs. 12 and 16). Although it belongs to the same multiplet (2) as the 4375.93Å line, it is not as prominent at early phases as the latter.

The remainder of the observed FeI low excitation lines only appear in some stars and no regularity can be seen. The FeI 4427Å emission line was observed in RRSco and RLeo at just one phase each (see Figs. 11 and 16). Finally, the low excitation line at 4216.18Å was observed in RLeo at the phase $\phi = 1.49$.

   
3.2.4 Ionized iron lines

The permitted FeII 4583.84Å emission line was observed in three of the stars of our sample, namely RRSco, RCar and RLeo (Figs. 17 and 18). This is a high excitation line (lower level excitation potential 2.8 eV) which appears towards the minimum light of the star, at phase $\phi = 0.29$ in RRSco, $\phi =0.39$ in RCar and $\phi = 1.49$ in RLeo. The FBW varies from $\sim$35 km s^-1 in RRSco and RCar to $\sim$45 km s^-1 in RLeo. The velocity shifts of the FeII line are around +2 km s^-1 in these stars. In RLeo and RCar, forbidden [FeII] lines can be clearly seen at the same phase as the permitted FeII line at 4583.84Å (Figs. 17 and 18). In RLeo at phase $\phi = 1.49$, following the bright maximum, we found the transitions [FeII]6F (4457.95Å), [FeII]21F (4276.83Å and 4243.97Å) and [FeII]7F (4359.33Å and 4287.39Å). No forbidden lines could be seen in the previous cycle following a fainter maximum: the cycle-to-cycle variability of the forbidden lines is consistent with the suggestion noted earlier that stronger shocks are associated with brighter maxima.

In RCar at phase $\phi =0.39$, we identified only the two [FeII]7F emission lines at 4359.33Å and 4287.39Å. Unfortunately, the observation for RCar at phase $\phi =0.39$ was taken with a narrow slit in poor weather conditions, so the signal to noise of these faint lines is low. Other forbidden lines were probably present but undetectable. In RRSco we could not identify any of the forbidden lines, although we could clearly detect the permitted FeII line (Fig. 17). The FBW of the [FeII]7F emission lines in RCar is $\sim$21-26 km s^-1. The velocity shift was measured at 0-2 km s^-1, which is the same as for the permitted FeII 4583.84Å emission. In RLeo, all the [FeII] emission lines have a FBW of $\sim$40 km s^-1. The velocity shifts are approximately 0-2 km s^-1 for the 7F and the 21F emission lines, similar to the velocity shift of permitted FeII 4583.84Å line.

   
3.2.5 Manganese line

The manganese line at 4030.75Å is a ground state line. It was observed in just one star, namely RLeo, at phase $\phi = 1.49$(Fig. 18). The MnI emission line shows a FBW of $\sim$28 km s^-1 and has a large velocity shift of 10 km s^-1, unlike the FeII and [FeII] lines at the same phase. As with the neutral Fe lines of low excitation (e.g. FeI 4375.93Å), the sharper red edge of the line indicates absorption by infalling, neutral Mn atoms in the layers above the shock.