5 Mira S stars, SC and C stars: Intrinsic radial-velocity variations versus orbital motion

 

5.1 Intrinsic radial-velocity variations of Mira variables

  The large velocity jitter observed in Mira S stars (Tables 3d, 3e and 4 in Jorissen et al. 1998) is related to their complex and variable cc-dips (Barbier et al. 1988). In some cases like for the star $\chi$ Cyg, the cc-dip has an inverse P-Cygni shape (Fig. 5a), out of which a meaningful radial velocity is very difficult to extract. In other cases like AA Cyg and R Hya, the cc-dips are featureless, broad and very stable, and these stars have the smallest jitter in our sample of Mira S stars (Table 3d of Jorissen et al. 1998). For stars like R And (= HD 1967) and RZ Peg (= HD 209890), two clearly distinct dips are present. In RZ Peg for example (Figs. 5c-d), the two dips correspond to velocities of -25 and -50 kms^-1, whereas the center of mass of the star (as probed by submm observations of the circumstellar CO rotational lines) moves with a velocity of -35 kms^-1 (Sahai & Liechti 1995), close to the average of the two CORAVEL dips. The two minima observed in the cc-dip are therefore likely associated with upwards- and downwards-moving layers forming a shock in the Mira atmosphere (e.g. Fox et al. 1984; Querci 1986; Bowen 1988; Bessell et al. 1996). The respective weights of the two minima vary with time, and so does the velocity of the resulting blend to which a gaussian is fitted. As an illustration, 2 profiles at different phases ($\phi_{\rm RV}$) are given in Figs. 5c-d for RZ Peg. The derived mean radial velocities are indicated on the figures.

  

Figure 5: Examples of cross-correlation dips for Mira S stars. a-b) Profiles for $\chi$ Cyg, including an inverse P Cygni-like profile; c-d) Two profiles at different phases ($\phi_{\rm RV}$) for the star RZ Peg. The time-varying weights of the two minima induce a variation of the measured radial velocity

  

Figure 6: Phase-folded radial-velocity curves of Mira, SC and S stars with tentative- or pseudo-orbital solutions. Labels ("orb'', "orb?'' or "puls'') are used to characterize our confidence level in the obtained solution or to indicate intrinsic radial-velocity variations. Two stars ( BD $-08^\circ 1900$ and HD286340) have also their radial velocities displayed as a function of Julian dates

When the CORAVEL cc-dip of RZ Peg is fitted by a single gaussian profile, as indicated in Fig. 5, a pseudo-orbital solution is found (Table 8), with a period of 437.3$\pm$ 3.9 d. This radial-velocity period may be identified with the photometric period of 437.8d derived from the AAVSO light curve for the Mira variations (see Sect. 5.2). It is therefore clear that, although they mimick an orbital motion, the radial-velocity variations of RZ Peg are intrinsic to the Mira phenomenon. They will be discussed in more details in Sect. 5.2. The same coincidence between the periods of the light variations and of the velocity variations is obtained for the CS Mira star R CMi (= HD54300) and for the C semi-regular (SRa) star SS Vir (= HD 108105) as well. The radial-velocity variations of R CMi can be fitted with a pseudo-orbital solution of period 337.3 $\pm$ 1.3 d, whereas the GCVS lists P = 337.8d for the associated Mira variations. It is interesting to note that the radial-velocity variations of R CMi are strongly non-sinusoidal in spite of the almost symmetric light curve (the rise time from minimum to maximum light represents 48% of the total cycle, according to the GCVS, compared to 44% for RZ Peg). For SS Vir, the radial-velocity and photometric periods are 361.2$\pm3.4$d and $\sim 364$d, respectively. The relevant parameters of the pseudo-orbits for RZ Peg, R CMi and SS Vir are given in Table 8. The radial-velocity periods have been used to fold the points in phase. The corresponding diagrams are displayed in Fig. 6.

5.2 Intrinsic radial-velocity variations of Mira S stars: The cases of RZ Peg and $\chi$ Cyg

  The radial-velocity curve of RZ Peg is well sampled, and makes it possible to investigate in more details the properties of the double cc-dip phenomenon.

Figure 7 presents the evolution of the CORAVEL cross-correlation profiles as a function of the radial-velocity phase (derived from the elements listed in Table 8). The evolution of the profiles, from a single cc-dip to a double cc-dip and vice versa, is quite obvious. The radial velocities corresponding to each of the peaks have been extracted by fitting a double-gaussian function to the profile. The resulting velocity curve as a function of the phase is displayed in Fig. 8. Two conclusions may be drawn from this figure: (i) each peak has a rather constant velocity, with the center-of-mass velocity corresponding almost to the average of the two peaks, and (ii) the double dip occurs around velocity phases $\phi_{\rm RV} = 0.7 - 0.9$, and this behaviour repeats from one cycle to the other. The velocity difference between the two peaks is of the order of 20 - 30  kms^-1.

The light curve of RZ Peg has been kindly provided to us by the AAVSO (Mattei 1997), and makes it possible to convert velocity phases into photometric phases. The photometric period appears reasonably stable over the time span covered by the radial-velocity observations, with an average period of 437.8d, very close to the 437.3d period of the velocity variations. Adopting a period of 437.3d, the relation $\phi_{\rm phot} = \phi_{\rm RV} + 0.26$ is derived from the AAVSO maximum (HJD 2448301) closest to the zero point of the radial-velocity phase (HJD 2448413). From this relation, it may be concluded that the double cc-dip occurs just after maximum light ($\phi_{\rm phot} = 0.0 - 0.2$).

  

Figure 7: CORAVEL cc-dips of RZ Peg as a function of the radial-velocity phase ($\phi_{\rm RV}$). Phase 0 (HJD 2448413.3) is close to the epoch of minimum radial-velocity (Fig. 6). The profiles have been fitted with a single or double gaussian function, when appropriate (thin solid line)

  

Figure 8: Radial velocities of RZ Peg as a function of the photometric phase ($\phi_{\rm phot} = \phi_{\rm RV} + 0.26$). Open and filled circles indicate the velocities of the double-line reductions whereas star-like symbols are used for velocities derived from gaussian one-line fitting. The center-of-mass velocity, as probed by submm observations of the CO rotational lines (Sahai & Liechti 1995), is represented by the horizontal dashed line

A similar phenomenon of line doubling near maximum light has been reported in several other Mira stars. In the Mira S star $\chi$ Cyg, Hinkle et al. (1982) reported such a line doubling for the rotation-vibration second overtone ($\Delta v = 3$) infrared CO lines and high-excitation first overtone ($\Delta v = 2$) CO lines. Maehara (1971) also reported the doubling of CN and atomic lines near 800.0nm around maximum light in $\chi$ Cyg, and Gillet et al. (1985) in S Car. This line-doubling phenomenon is the signature of a shock front propagating through the line-forming region (e.g. Gillet et al. 1985; Bessell et al. 1996). Incidentally, in $\chi$ Cyg (Fig. 5), a line-doubling as clear as in RZ Peg is not observed for the blue-violet iron lines sampled by CORAVEL (Baranne et al. 1979). The CORAVEL radial velocities of $\chi$ Cyg (averaging to +3.2  kms^-1; Table 3d of Jorissen et al. 1998), derived from the clean cc-dips (Fig. 5b), agree with the value obtained by Pierce et al. (1979). Hinkle et al. (1982; their Fig. 15) argue that these blue-violet photospheric absorption lines with a constant radial velocity form in the infalling material for the whole pulsation cycle. Nevertheless, the CORAVEL profile of $\chi$ Cyg exhibits some characteristic features that may be related to the shock front propagating through the photosphere. Near visual phases 0.0-0.2, the CORAVEL profile of $\chi$ Cyg has a typical inverse P-Cygni shape (Fig. 5a) with the blue-shifted "emission'' component peaking at -20  kms^-1. This velocity corresponds to that of the outflowing material, as derived from the second overtone CO rotation-vibration lines by Hinkle et al. (1982). A similar inverse P-Cygni profile has been reported by Ferlet & Gillet (1984) for the TiI lines near 1 $\mu$m in Mira near maximum light.

It is very likely that the same physical phenomenon - namely a shock front propagating through the line-forming region - is responsible for the time-dependent features observed in the CORAVEL cc-dips of RZ Peg and $\chi$ Cyg. This conclusion is suggested by the fact that in both stars, the line-doubling occurs near maximum light, and the offset between the two distinct components of the cc-dip is of the same order (20 to 30  kms^-1, corresponding to the shock discontinuity). These observed features are well reproduced by the synthetic FeI and CO line profiles computed by Bessell et al. (1996) in a dynamical Mira atmosphere with a propagating shock. For some reason however, the atmospheric structures of RZ Peg and $\chi$ Cyg must be different, so that only in RZ Peg are the blue-violet iron lines sampled by CORAVEL forming in absorption on both sides of the shock, resulting in a clean double-minima cc-dip.

5.3 Binaries among Mira variables and SC stars

  Because they are difficult to observe at minimum light, Mira S and C stars were generally insufficiently sampled to attempt a period search on their radial-velocity curve. Well-sampled curves are, however, available for the Mira S stars AA Cyg, $\chi$ Cyg, R Hya, for the C (no Tc) stars SS Vir and S UMa, and for all the SC stars. Some of these stars have already been discussed in Sects. 5.1 and 5.2.

No satisfactory periods emerge for AA Cyg and R Hya. The radial velocity of the absorption lines in $\chi$ Cyg is constant, as discussed in Sect. 5.2. The Mira S star S UMa (= HD 110813) is perhaps a binary, since the radial-velocity period P = 592.2d (Table 8) is well distinct from the 225.9d period of the Mira variations. More measurements are needed, however, before that orbital solution may definitely be accepted.

As far as Tc-poor carbon stars are concerned, X Cnc (= HD 76221) is probably binary, with a 491d orbit (quite distinct from the -uncertain- 195d period quoted by the GCVS for the SRb variations).

A possible orbital solution, with $P = 544.2\pm5.7$d and e = 0.55, has been found for the SC star BD $-08^\circ 1900$ (Table 8 and Fig. 6). A light curve for this star is provided by Jorissen et al. (1997), who find photometric variations on a time scale of about 59d. The absence of coincidence between the radial-velocity and photometric (quasi-)periods may lend some credit to the orbital nature of the radial-velocity variations observed for BD $-08^\circ 1900$. We do not accept this interpretation, however, without the following word of caution: another SC star, GP Ori (= HD286340), exhibits radial-velocity variations of a nature very similar to those of BD $-08^\circ 1900$ (Fig. 6; note especially the drift observed in the early phase of the monitoring, reminiscent of that observed for BD $-08^\circ 1900$), but no orbital solution could be obtained for GP Ori. At this point, we cannot exclude the possibility that the "orbital'' solution found for BD $-08^\circ 1900$ is simply a consequence of a favourable time sampling of irregular, intrinsic variations. One should note in that respect that the $\sigma_{\rm V}/\sigma_{\rm Vr}$ ratio observed for BD $-08^\circ 1900$ fits well the predictions of a simple linear model of adiabatic acoustic oscillations (Jorissen et al. 1997). Finally, the orbital parameters of BD $-08^\circ 1900$ would locate that star in a unusual region of the $(e, \log P)$ diagram (Fig. 4 of Jorissen et al. 1998), which is another argument against that orbital solution.

In fact, relatively large-amplitude radial-velocity variations ($\sigma_{\rm Vr}$ of a few  kms^-1; Table 3e of Jorissen et al. 1998) are a common feature among SC stars. For the two Mira SC stars in our sample (R CMi and RZ Peg), periodic radial-velocity variations were found with the same period as the light curve (Sect. 5.1). For the remaining SC stars, which are of semiregular (SR) or irregular (L) variability types, very irregular radial-velocity variations are indeed observed, with the possible exception of BD $-08^\circ 1900$ discussed above. When the number of measurements is relatively small (<10) and covers a limited time span, these variations may mimick orbital variations.

Note added in proofs: A spectrum of BD $-08^\circ 1900$ has been obtained on the Coude Auxiliary Telescope at ESO (with a resolution of 60 000) and reveals that the $\lambda 4262$TcI line is definitely present. BD $-08^\circ 1900$ is therefore an intrinsic S star. That star ought thus not be binary, and this is another argument to be considered in Sect. 5.3 when evaluating the merits of the possible orbital solution.

Acknowledgements

We thank the AAVSO for communicating us the light curve of RZ Peg. This research has been supported partly by the Fonds National de la Recherche Scientifique (Switzerland, Belgium) and the University of Geneva (Geneva Observatory). S.V.E. is supported by a F.R.I.A. doctoral grant (Belgium). A.J. is Research Associate (F.N.R.S., Belgium).