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Astron. Astrophys. 359, 991-997 (2000)

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5. Discussion

5.1. A multiperiodic origin?

It was recently shown that the presence of a Blazhko effect in RR Lyrae introduces a multiperiodic behavior of the pulsation (Chadid et al. 1999). Indeed, the detection of a frequency triplet structure in the line-profile variations ([FORMULA] c/d where [FORMULA] and [FORMULA] are the pulsation and Blazhko periods respectively) points out that the two additional periods can produce cycle to cycle variations. The suspected presence of a quintuplet could be also contribute, at least some part of it but necessary weaker, to this modulation. Nevertheless, the corresponding components need an observational confirmation. Also, the harmonics of the base frequency [FORMULA] could have multiplet structure increasing the cycle to cycle variations. Thus, in the framework of this effect, the variations would not irregular but multiperiodic.

Chadid et al. (1999) report the amplitude of the triplet components which are [FORMULA], [FORMULA] and [FORMULA] km/s. Taking into account the three first harmonics of the basic frequency together with the two secondary components of the triplet, giving a fraction of the variance explained by the fit near 94%, the maximum velocity shift over five pulsation periods (the observation does not exceed three nights) is close or smaller than 1 km/s. This is not large enough because we report a shift up to 4 km/s (see Sect. 3). Nevertheless, it is not possible to conclude because our previous observations (Chadid et al. 1999) were not enough to determine with a good accuracy the component intensities of the triplet and to check if a quintuplet was present or not. New observations are required.

5.2. A dynamical origin?

The radial velocity secondary maximum ([FORMULA] near 0.62-0.72) is not the same for all curves. It is strongest at the Blazhko phase [FORMULA], of average strength at [FORMULA] and weakest at [FORMULA]. It occurs during the bump observed in the luminosity curve, which occurs at [FORMULA] and just before the minimum photospheric radius. This is the consequence of the progressive deceleration of the upper atmosphere during contraction. Fokin & Gillet (1997) showed that a shock wave (s3+s4) produces, at this time, an additional local compression of the atmospheric layers in which metallic lines are formed. This shock was called the "early shock" by Hill (1972), who was the first to detect it in his nonlinear pulsating model of RR Lyrae. This dynamical phenomenon induces a secondary photospheric acceleration as observed (see Table 2). Thus, although the motion of layers located just above the photosphere are regular, we can expect that the motion of atmospheric layers well above the photosphere, where the core of absorption lines are formed, will be irregular. These layers, which represent a small part of the total mass of the atmosphere, are strongly affected by supersonic ballistic motion. As a consequence, the subsequent outward propagating shock waves (s1 and s2, see Fokin & Gillet 1997) must be altered. A dynamical coupling, which does not necessarily induce a stationary state, between the motion of atmospheric layers located above the photosphere and those at the photospheric level must be present. This phenomenon, which also includes the interplay with shock waves, could be in part at the origin of the irregularities detected in the radial velocity curves presented in this paper.

As recently shown by Chadid et al. (2000), irregularities in the motion of atmospheric layers in which metallic absorption lines are formed are not large enough to produce a completely decoupled motion between these layers and the photosphere where the continuum and line wings are formed. This is well supported by the fact that the pulsation period deduced from metallic radial velocity curves is close to the broad band photometric period. Thus, the time scale determined from the ballistic motion of the outermost metallic region is certainly not different from the period. Consequently, "irregular" motion means here that some departures may occur at some specific phases of the pulsation instead that it exists a true decoupled motion between the upper envelope of the star, which certainly is present, but it does not concern metallic layers.

Because the FWHM of the Fe II line profile is very sensitive to physical conditions (temperature, velocity field, etc.) within the atmosphere, we must expect that the poor repetitiveness of the FWHM curves reported here can be also due to this dynamical atmospheric process. As demonstrated in Figs. 7-11, the width and the intensity of the first ([FORMULA]) and the last ([FORMULA]) peaks are strongly variable. Unfortunately, it is difficult to appreciate the changes to the highest peak ([FORMULA]), because of the very rapid passage of the shock wave responsible for line doubling. Even the FWHM of the Fe II line, which returns to about the same value (between 18 and 20 km/s) at the maximum radius, does not occur at the same pulsation phase ([FORMULA]).

5.3. A combined effect?

The multiperiodicity induced variation can be amplified in the upper atmosphere by dynamical effects such as shock wave interactions. Consequently, it is plausible that the two above mentioned effects combine together to produce the observed irregularities. In this case, the investigated variations would be irregular.

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© European Southern Observatory (ESO) 2000

Online publication: July 13, 2000