THE BEHAVIOR OF ABSORPTION LINES IN THE SPECTRA OF MIRA VARIABLES AS AN INDICATION OF SHOCK-WAVE PHENOMENA
Richard A. Crowe
Department of Physics and Astronomy
University of Hawaii at Hilo
523 West Lanikaula Street, Hilo, Hawaii
ABSTRACT
It is argued that the irregular behavior of absorption features in the spectra of Mira variables, which traditionally has been difficult to account for, is consistent with the presence of an outward-moving shock front which is probably higher up in the atmosphere than the one producing Balmer emission. This is indicated by a number of observations, including: (a) variable absorption-line weakening near maximum light, (b) the association of strong hydrogen emission with weak-line cycles, and (c) significant changes with phase in the relative radial velocities of absorption-line systems of different excitation. It is suggested that the velocity gradient may be directly responsible for weakening effects by Doppler-shifting pre-shock layers out of the absorbing frame of line photons emerging from shocked gas (the process of escape enhancement). Velocity effects on line absorption should be accounted for in hydrodynamical models of Mira variable envelopes, since in principle, the atmospheric energy balance may be significantly affected.
The Hill-Willson hydrodynamical models have contributed greatly towards a clear understanding of the atmosphere of a Mira variable [1,2]. In the scenario presented by these models, more than one active shock is present at phase 0.2, just after the stellar bolometric magnitude is at maximum. The emission lines and the continuum would originate in the lower shock, which is more regular in nature. This is supported by the relative consistency of the hydrogen emission in strength and phasing from one cycle to the next. The absorption lines, on the other hand, would originate near the upper shock, which is more likely to be aperiodic as successive shocks catch up with one another. Hill and Willson suggest that the aperiodic nature of the upper shock above a certain critical radius is responsible for the irregular changes in the absorption-line strengths and velocities from one cycle to the next [2]. This is the absorption-line weakening which has long defied a consistent explanation [3,4]. The fundamental cause of the line weakening may be the velocity discontinuity across the shock, because it is possible that absorption-line photons trapped in a static atmosphere could escape as the result of a large Doppler shift in the upper layers [5]. If the velocity gradient is responsible for absorption-line weakening, we should expect to see a correlation between the shock strength and the degree of weakening. Such a correlation between emission-line strength and degree of weakening (in the sense that the emission is strongest in weak-line cycles) has been found for o Ceti by Yamashita et al. and for S Carinae by Crowe and Garrison [6,4].
The author began a program several years ago to determine radial velocities for a large group of northern-hemisphere Mira variables. The goal was to match observations of blue-visual spectra with the general features of the Hill-Willson hydrodynamical models. A total of 64 blue spectrograms of 22 Miras were obtained, and six separate systems of lines in each star were studied. Six of these stars (RT Cygni, R Aquilae, R Leonis, U Orionis, Chi Cygni and R Cassiopeiae) were also measured by Wallerstein, and the velocities derived by the author are in very good agreement with the values he obtained [7]. As can be seen in Figure 1, the difference A-E between the mean absorption- and emission-component velocities is always positive (relative to the observer), indicating that the absorption layer is infalling with respect to the emission layer. It should be noted that observations of double-peaked maser emission lines have demonstrated that the stellar center-of-mass velocity is between the absorption-line and emission-line velocities [8]. Unfortunately, because of the fragmented nature of the data, very little information on velocity as a function of phase is available. There are, however, some noticeable trends in the relations between various absorption components in the star R Trianguli (Period = 266 days), for which there is sufficient phase coverage. The differences in velocity between neutral resonance lines (0-1 eV) and subordinate lines (1-3 eV) and between neutral resonance lines and lines produced by ionic species reach their smallest positive values at maximum light and decrease thereafter, becoming negative in post-maximum phases (the resonance-line velocity is algebraically smaller by some 6-8 km/sec). This is what we should expect to see if in fact there is a weak shock wave passing through the absorption-line layers. The lower shock wave would be associated with the emission-line layers, moving at velocities that are about 15 km/sec less positive than the neutral absorption-line layers at maximum light. The layers in which the formation of resonance lines takes place would be above the upper shock at maximum light, but as the disturbance propagates outward and the shock becomes optically thin, layers below the shock would contribute more to the line profile, and the velocity would become less positive. The ionic lines, on the other hand, would be formed between the two discontinuities at maximum light, when the ionic-line velocity is more negative than that of the neutral species. As the upper shock spreads outward and dissipates, the layers in which the formation of ionic lines takes place should achieve a more positive infall velocity with respect to the advancing lower shock. For the R Trianguli data (taken between JD 2444664 and 2445261), this was the case 29 days after maximum (phase 0.1). The advancing lower shock then becomes the ``upper'' shock in the next half-cycle. Thus, although it is not possible to state that the upper shock is present in every Mira variable, there is evidence for its presence in at least one of these stars.
The author has applied a histogram technique (Willson et al. [9].) to the velocity data obtained for the program Mira stars. In this procedure, the velocities of individual lines are ``binned'' in velocity space; the size of the velocity bin used was 2.5 km/sec, an interval that is roughly the error in the velocities of individual lines. The majority of absorption-line velocities in R Trianguli (Figure 2) are grouped between 63-65 km/sec, while the emission-line velocities (not corrected for limb-brightening effects) are distributed around a mean value of 50 km/sec. There are two noticeable trends on the rising branch. First, the subordinate lines generally have more positive velocities than the resonance lines at phase -34 days and at +29 days, but the two sets of velocities become comparable at -8 days. Secondly, the lines of ionized metals appear to be grouped at the same velocity as the subordinate lines at -34 days and at +29 days, but become smaller (more negative) as maximum light is approached. These two trends suggest that, just prior to maximum light, a weak shock passes through the layer in which the subordinate lines are formed. On the descending branch, the subordinate lines of neutrals and the ionized lines of metals must arise from adjacent layers, which would be between the shock discontinuities in the model of Hill and Willson. Subsequent to phase 0.1, these layers would start infalling toward the lower shock, while the upper shock passes through the region of resonance line formation. Thus, the velocity data for R Trianguli are at least consistent with a two-shock model, although this may not be the only possible interpretation.
There are other reasons to suspect that a two-shock model may be applicable to the atmospheres of Mira variables, as discussed by Crowe and Garrison [4]. Briefly, they are: (i) CaI 4226 line strengths show a strong correlation with spectral type in late-type (M5e-M9e) Miras, but not in early-type (M0e-M4e) Miras; this suggests that smaller line opacities in early-type Miras allow us to see down to deeper layers between the discontinuities in the line core; (ii) the CaI resonance line weakens dramatically (getting narrower and shallower) at phase 0.8, coincident with the strengthening of Balmer emission; this may be due to escape enhancement, whereby an upper velocity field Doppler-shifts preshock layers out of the absorbing frame of line-center photons emerging from shocked gas, thus making the line profile shallower; (iii) there is more variation in Ca I line strength before maximum light than after, suggesting that a weak shock wave affects line strengths before maximum, then moves through the line-forming region; (iv) the appearance of MgI 4571 emission at late post-maximum phases (0.3) suggests the presence of a weak shock moving through cooler molecular layers. It should be added that the escape-enhancement process, discussed above, may be very important in cool stellar atmospheres blanketed by many strong lines. Velocity effects on line absorption should thus be accounted for in hydrodynamical models of Mira variable envelopes, since in principle, atmospheric energy balance may be significantly affected.
REFERENCES
1. Willson, L.A., and Hill, S.J., 1979, Ap.J., 228, 854.
2. Hill, S.J. and Willson, L.A., 1979, Ap.J., 229, 1029.
3. Merrill, P.W., Deutsch, A.J. and Keenan, P.C., 1962, Ap.J., 136, 21.
4. Crowe, R.A. and Garrison, R.F., 1988, Ap.J. Suppl., 66, 69.
5. Mihalas, D., Kunasz, P.B. and Hummer, D.G., 1976, Ap.J., 203, 647.
6. Yamashita, Y., Maehara, H. and Norimoto, Y., 1981, Ann. Tokyo Astron. Obs., 18, 142.
7. Wallerstein, G., 1975, Ap.J. Suppl., 29, 375.
8. Reid, M.J. and Dickinson, D.F., 1976, Ap.J., 209, 505.
9. Willson, L.A., Wallerstein, G. and Pilachowski, C.A., 1982, MNRAS, 198, 483.
FIGURE CAPTIONS
Figure 1: The difference A-E between absorption- and emission-component velocities for 23 Miras. Each star is indicated by a different plot symbol. The period in days is given to the right of the label for each star in parentheses; this can be used to locate the positions of stars with the same symbol.
Figure 2: Velocity histograms for
R Trianguli at phases -34 days (JD 2445198) and -8 days
(JD 2445224). The individual line velocities have been
``binned'' in 2.5 km/sec velocity space units. The
excitation for each line is indicated by a different plot
symbol on the right.
(Note: DDO = David Dunlap
Observatory, Toronto).