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Astron. Astrophys. 359, 991-997 (2000)
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 ( c/d
where and
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 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 ,
and
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
( near 0.62-0.72) is not the same for
all curves. It is strongest at the Blazhko phase
, of average strength at
and weakest at
. It occurs during the bump observed
in the luminosity curve, which occurs at
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 ( ) and the
last ( ) peaks are strongly variable.
Unfortunately, it is difficult to appreciate the changes to the
highest peak ( ), 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 ( ).
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.
© European Southern Observatory (ESO) 2000
Online publication: July 13, 2000
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