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Astron. Astrophys. 363, 1065-1080 (2000)

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4. Analysis

4.1. Detection

The 2 µm spectra of Miras, while not as badly blended as the visual spectra of these stars, nevertheless contain a large number of lines, most of which are relatively weak, having central depths less than [FORMULA] 20%. The challenge in identifying H2 is to unambiguously select the H2 lines against this background. For molecules previously identified in these spectra, such as CO, CN, H2O, or SiO, identification is a tractable problem because hundreds of lines are contributed by the species being searched for. However, the number of well placed H2 lines (Table 1) provides a meager selection. A worst case is that encountered by Tsuji (1983) where the column density of H2 is near the detection limit with the result that only a detection of S(1) is likely.

As a first step in identification, the spectra listed in Table 2 were plotted in the regions of the H2 1-0 S(0), S(1), and S(2) line. Two groups of strong atomic lines, neutral titanium from the a5P-z5D transition and neutral scandium from the a4F-z4D transition, lie within a few wavenumbers of the S(0) line. These atomic lines were included in the plots which extended from 4485-4500 cm-1. In cool giants the S(0) region is blanketed with weak features, presumably H2O in the oxygen rich stars and CN in the carbon rich stars.

Using the molecular lines which are present in the 4485-4500 cm-1 plots (but ignoring the candidate H2 lines), the objects in Table 2 can be sorted into five categories with nearly identical spectra shared between the stars in each category. The five categories are strong H2O, moderate H2O, weak H2O, weak H2O/CN, and strong CN. The relation to the normal classifications is obvious: strong-moderate H2O equals to M-type, weak H2O-weak H2O/CN equals to S-type, strong CN equals to C-type. Due to the multidimensional aspect of classification in late type stars (temperature, luminosity and abundance), the Keenan spectral classification, especially among the S-stars, does not necessarily map into C/O abundance (Smith & Lambert 1990). As a result we have found the above classification scheme to be quite useful for the following analysis. The assigned classification category is listed on Table 2. This classification demands comparison of spectra at similar phases since the strength of H2O depends on phase. Note that there are occasional surprising differences between the category we have assigned and the published spectral type. Fig. 1 illustrates some representative spectra.

[FIGURE] Fig. 1. Typical spectra in the 4486-4499 cm-1 region. The spectra range from having strong H2O with no detectable CN (R Cas) through weak H2O and weak CN (R And) through strong CN with no detectable H2O (LX Cyg and S Cep). The classification according to the scheme described in the text is given for each star (see also Table 2). The strong line close to the position of the H2 line visible in R Cas and U Ori is due to H2O. Note the variations in strength of the atomic lines (marked) compared to the molecular lines. Spectra have been shifted to place the lines at laboratory frequencies.

Continua have been set by examining the highest point in each 5 cm-1 interval over the spectral interval observed. Detailed inspection of particular spectral regions shows that this technique produces a consistent continuum level. However, for the strong or moderate H2O spectra the assigned continua are no doubt below the true (i.e. without atomic and molecular lines) continuum level. If the Sc I and Ti I lines in the 4400-4500 cm-1 region are assumed to have similar central depths in both M-type and S-type Miras, then the continuum in the M-type Miras must be well above any existing continuum point in the high resolution 2 µm spectrum. Two micron region atomic lines in S-type Miras have line depths that are relatively constant from phase 0.20 to 0.80. Again if we assume that the atomic lines in the M-type Miras do not weaken near minimum light then the continuum must be placed well above any continuum point in the spectrum at these phases to keep the atomic line depths constant. This is in agreement with water calculations provided by e.g. Aringer et al. (1997).

As can be seen from Fig. 1, the H2 1-0 S(0) line is an obvious spectral feature in the S-type minimum light Mira spectra. In the spectra with water vapor present, S(0) is also present but due to the large amount of line blanketing present, the line is not obvious. In the Mira spectra with the strongest H2O lines, the H2 S(0) line cannot be identified because of strong blending with the H2O (0,1,1)[18,9,9]-(0,1,0)[17,7,10] line at 4498.027 cm-1 (Zobov et al. 2000 1). Due to these difficulties, identification of H2 in these stars is based on consistency between the 1-0 S(0) and S(1) lines. While the H2 line appears to weaken as C/O decreases from 1, the strength of the H2 line is difficult to quantify because of uncertainties in the continuum and blending. In carbon rich Miras, line blanketing from CN and possibly polyatomics and scattering of the photospheric spectrum in the circumstellar dust obliterates the recognizable line spectrum and no comment on the existence of the H2 can be made.

Identification of the H2 may be secured by measuring consistent line strengths and velocities among the various lines predicted to be present. In the S-type Miras with the strongest H2 lines in our sample (R And, X And, T Cam, [FORMULA] Cyg, R Cyg, and ST Sgr) all the H2 lines appearing in Table 1 are clearly identifiable and have intensities consistent with the oscillator strength and a 2000-3000 K excitation temperature. The S-type Mira spectra are particularly easy to work with, not only because of the strength of the H2 features but also because there are few blending features. The S(0) line is the freest from blending in all spectral types. However, in the S-type stars S(1) is best for monitoring because it is not blended in S-stars and is much stronger than S(0).

Velocities of the line cores and depths of the observed H2 lines are presented in Table 4 for the spectra where hydrogen lines could be definitely identified. For the other stars we give an upper limit of the line depths. In Table 5 velocities for groups of Ti, CN, high excitation 2-0 CO, and low excitation 2-0 CO lines are listed. The velocity agreement between the Ti, CN, and high excitation CO is generally good. Note that while the lines in each atomic/molecular group have similar central depths, the three groups cover a large range in central depth (average central depth is listed in Table 5). We have not listed the central depth of the CO low excitation lines since these lines are blends of multiple velocity components (HHR). The CO low excitation lines typically have central depths in excess of 70% in late M giants.


[TABLE]

Table 4. Observed H2 Lines. The table lists the depth (percent measured below the continuum; D) and the heliocentric velocity (RV) of each line. For several stars we could measure only upper limits due to blending of the H2 line with an H2O line.



[TABLE]

Table 5. Atomic and Molecular Line Measurements. The table lists the depth (D) and the heliocentric velocity (RV) of each line. Stars for which the H2 line gave only an upper limit (see Table 4) are not included.


The H2 velocities are shifted by as much as -9 km s-1 ([FORMULA]0.1 cm-1) from the velocities of the Ti, CN and high excitation CO lines. The precision with which the laboratory frequencies are known for all these species rules out a velocity shift as the result of the laboratory data. Tsuji (1983) noted a shift of -5 km s-1 (0.08 cm-1) between the predicted and observed position of the H2 S(1) line in a number of non-Mira M giants. Based only on the S(1) line he concluded that the line present was not H2 but an unidentified line near the S(1) frequency. However in our data the strength and number of H2 lines present make the identification secure. We conclude that Tsuji's line is indeed H2 S(1) and that his predicted position based on hydrostatic model atmospheres does not account for velocity fields in the atmosphere. The effects of velocity fields on line profiles and positions are described in Windsteig et al. (1998) and Aringer et al. (1999). Tsuji's observations in SR type variables are consistent with our data. The cause of the velocity shift between H2 and other lines will be discussed below.

4.2. Phase dependent behavior

4.2.1. Central depths

Fig. 2 presents the phase dependent absorption central depth of S(1) as a function of visual light phase in [FORMULA] Cyg. The figure combines measurements from the spectra of HHR with those of Table 3. [FORMULA] Cyg (S7,1e) will be discussed in detail because of the extensive time series of spectra available, although H2 lines are not as strong in this star as in "pure" S-type Miras. In [FORMULA] Cyg the S(1) line appears at about phase 0.0 and strengthens rapidly (the central depth increases nearly 0.5% per day) to an 80% deep line at phase 0.4. The line starts to weaken after about phase 0.6, becoming too weak to differentiate from the weak background lines between phase 1.0 and 1.3. Note, that in Fig. 2 phase 1.0 denotes the next visual light maximum. Near maximum light the line is doubled, i.e. seen at two velocities in the spectrum. Doubled spectral lines near maximum light have been observed in spectral lines of many atomic and molecular features (e.g. HHR) and is a feature found also in dynamical model atmospheres (Windsteig et al. 1998). In summary, H2 can be seen in the spectrum throughout the light cycle with the line strongest near phase 0.5. Near maximum light H2 lines are weak and doubled in the spectrum of [FORMULA] Cyg.

[FIGURE] Fig. 2. Central depth as a function of visual light phase for the H2 S(1) line in [FORMULA] Cyg. The H2 S(1) line has two well separated velocity components from approximately phase 0.1 before maximum light to 0.2 after maximum which are marked by full and open circles, respectively.

Time series of three oxygen rich Miras, R Cas, T Cep and o Cet, also were examined to determine when the H2 S(0) and S(1) lines were at maximum strength. In all cases the H2 lines are deepest at phase 0.60. In R Cas and o Cet H2 lines are very blended with H2O but seem to have phase dependent behavior similar to [FORMULA] Cyg.

Changes in line strength of the H2 lines during the stellar light cycle are not limited to Mira variables. Lambert et al. (1986) noted the abnormally strong H2 in the SRa carbon star WZ Cas. When we re-observed this star the H2 S(0) line was not detectable, with a line depth at most half of the previous value. Both spectra are of high quality and both were obtained on the same spectrometer at the same resolution. An accurate light curve does not exist for this star, but measurements in the AAVSO archive suggest, that the first observation was obtained at a light minimum and the second one close to the light maximum.

4.2.2. Velocity

Fig. 3 shows the velocity of the S(1) line in [FORMULA] Cyg as a function of phase along with that of the neighboring (in frequency) Ti I lines. The behavior of the lines of both species is typical for infrared lines in Miras (HSH; Hinkle & Barnes 1979b). The H2 velocity curve, to a first approximation, duplicates the Ti I velocity curve shifted by 0.1 in phase. Fig. 3 also indicates a slight difference in slope between the Ti or CO velocity curve and the H2 velocity curve.

[FIGURE] Fig. 3. Radial velocity as a function of phase from the deepest point in the line profile for the H2 1-0 S(1), CO 2-0 high J", and Ti I lines in the 2 µm spectrum of [FORMULA] Cyg. The solid curve is representative of the CO [FORMULA]v=3 velocity curve (HHS) from the 1.6 µm spectrum. Note the significant departure of the H2 velocities from the relation established by the other three groups of lines.

Both depth and velocity information as well as line profile information may be displayed three dimensionally, as contours of intensity with velocity (or frequency) as one axis, and phase as the other axis. Fig. 4 and Fig. 5 display H2 S(1) and Ti I 4488.3 intensity-velocity-phase contour maps for [FORMULA] Cyg. Features noted in Fig. 1 may be seen in the contour plots. Note in particular that the H2 originates later than the Ti in a light cycle. When the H2 appears it has nearly the same velocity as the Ti but as phase increases the velocity becomes more negative compared to the Ti. In the description of the velocity as a function of phase (Fig. 3) this effect was represented by a phase shift of about 0.1 with a change of slope between the H2 and Ti velocity curves.

[FIGURE] Fig. 4. Intensity contours as a function of phase and velocity for H2 1-0 S(1) in the [FORMULA] Cyg spectrum. Contours are in steps of 5% in intensity. For orientation the areas representing 50% or less intensity are dotted, while the areas with 90% or more intensity are shaded. Note that the S(1) line is only weakly present in absorption at phase 1.0-1.1 with weak emission at [FORMULA] -10 km s-1 from the absorption.

[FIGURE] Fig. 5. Intensity contours for the Ti I line at 4488 cm-1 in the [FORMULA] Cyg spectrum. Note, compared to Fig. 4, the conspicuous presence of a two absorption velocity components at phases 0.9-1.1, the strong emission between the components, and the narrowness of the Ti line relative to the H2 line.

4.2.3. Line profiles

Fig. 4 and Fig. 5 provide another dimension of information since the intensity information, i.e. the line profiles, is plotted. The H2 S(1) line is broader than the Ti I line. The lines of both Ti and H2, but particularly H2, are asymmetric. In [FORMULA] Cyg, the positive wing is noticeably broader than the negative wing. Both the H2 and the Ti lines have inverse P-Cygni line profiles between phases [FORMULA] 0.7 and 1.10. In the case of [FORMULA] Cyg the emission is not strong.

To further investigate the cause of the line asymmetry we have examined the HSH R And time series spectra. R And has very strong H2 lines. In Fig. 6 and Fig. 7 a time series of S(1) line profiles for the S-type Miras [FORMULA] Cyg and R And are presented. In R And the asymmetry, seen in the [FORMULA] Cyg lines at phases 0.3 through 0.8, is even more marked. The R And S(1) line cores show a strong asymmetry. An additional asymmetry is caused by the near maximum light emission negative of the S(1) and Ti absorption lines, which is present in [FORMULA] Cyg at a phase as early as 0.8. In R And the emission in the Ti line is observed at phase 0.8, too, while the emission in the H2 line is not detectable before light maximum.

[FIGURE] Fig. 6. Time series of line profiles in [FORMULA] Cyg as a function of phase for (left to right) H2 1-0 S(1), CO 2-0 R(21), H2 1-0 S(7), and Ti I 4488 cm-1. The dotted line marks the center-of-mass velocity. The arrows above the spectrum locate the CO [FORMULA]v=3 photospheric velocity. Phase is labeled under the S(1) spectrum. Note the emission at phase 0.83 and 0.98 in the S(1) and Ti lines. Time increases upward.

[FIGURE] Fig. 7. R And line profiles. Spectra taken at phase 0.86 and 0.97 did not include the S(7) line. This line is shown at the slightly different phases 0.80 and 0.96.

In Fig. 6 and Fig. 7 we include a line profile of a low excitation CO line (12C16O 2-0 R21) as well as a high excitation H2 line (1-0 S(7)) and a Ti line. In both stars the S(1) line profiles are similar in breadth and velocity to the low excitation 2-0 CO line profiles. In the preceding section we noted in our sample of [FORMULA]20 stars the agreement of velocities between H2 S(1) and the low excitation 2-0 CO lines. The H2 S(7) line is similar to the Ti line.

4.3. Line intensities

In order to investigate the dependence of H2 intensity on the intensity of metal lines and C, N, O group lines, a representative set of lines from Ti, CN, and CO were measured (Table 5). As a first approximation, the average depth of each group of lines was used as an index. In stars with strong H2O and strong CN, blending reduced the line list to less then a usable number of lines. The strong H2O and strong CN stars will not be discussed below. Among the remaining stars, which cover a restricted range in C/O, the Ti, CO, and CN line strengths are fairly well correlated. H2 is not correlated with these line strengths.

In Fig. 8 the H2 S(0) central depths are plotted as a function of period. At a given period, S and SC stars show stronger H2 lines than M stars. Therefore we note that a higher C/O ratio leads to stronger H2 lines. The period of the Mira, shown by Keenan (1966) to be related to the temperature, is a second factor. Over the range of periods examined, P[FORMULA]200 to 500 days, we find that long period is a necessary condition for strong H2 lines.

[FIGURE] Fig. 8. The central depth of H2 S(1) as a function of period. The filled symbols are oxygen rich stars, the open circles are S stars and the crosses mark SC stars.

The envelope of points in Fig. 8 suggests that for C/O=1, the H2 S(0) central depth increases by [FORMULA]20% for each 100 day increase in period. The line saturates at a period of about 400 days. The data suggest that the H2 line strength among the Miras can be parameterized as a set of lines parallel to this relation, with each line being defined by the C/O. However, more data on C/O and more measurements of H2 lines are needed to confirm this.

Of course, one has to be aware that H2O can severely modify the height of the continuum and may therefore influence this relation between intensity and C/O.

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Online publication: December 5, 2000
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