INFLUENCE OF THE CONVECTION-PULSATION COUPLING
ON THE PHOTOMETRIC OBSERVABLES FOR δ SCT and γ DOR STARS
A. Grigahcène1, M.-A. Dupret1, R. Garrido1 and M. Gabriel2
2
1 Instituto de Astrofísica de Andalucía-CSIC, Granada, Spain
Institut d’Astrophysique et de Géophysique de l’Université de Liège, Belgium
Abstract
In a non radial- non adiabatic pulsation code, the perturbation of the convective flux, the turbulent pressure and the heat dissipation of the kinetic energy of turbulence are taken into account, following the theory of M. Gabriel (1996),
in the mixing length frame.
The sensitivity of the treatment to mixing length parameter value is studied exhaustively.
Better determination of the photometric amplitude ratios and phase differences permit the reduction of discrepancies between theoretical results and observations which allows better mode identification.
δ Scuti stars
Our TDC models succeed to explain the modes stabilization at the δ Scuti instability strip red edge, this is
impossible with FC models. In these figures, we give the theoretical blue and red edges computed with our TDC
non-adiabatic models, for radial (left panel) and l = 2 (right panel) modes of different radial order, with MLT
parameter α=1.8. Dots are the observed positions of δ Scuti stars from the catalogue of Rodriguez et al. (2000).
In this figure, we give the contributions
of the different physical terms to the
work integral of the radial mode p3, for
a model at the instability strip red edge.
WFR (radiation) has a driving effect at
the convective envelope (CE) base (flux
blocking). The effect of convective flux
variations (WFc) is significant in all CE
and compensates the driving effect of
WFR. Turbulent pressure variation has a
driving effect in this model (Wpt). But it
is compensated by the effect of
turbulent kinetic energy dissipation
(Wε2), which has a damping effect on
the oscillations. Hence, Wtot and WFR +
WFc are not very different.
γ Doradus stars
Instability strips
γ Doradus are a recently discovered class of long periods variable stars. Our TDC models succeed to explain the
driving of their high order gravity modes. In the left panel, we give the theoretical instability strips obtained
with different values of the MLT parameter α. Small circles are the observed positions of bona fidae γ Doradus
stars (Handler 2002). Good agreement is obtained for models with α = 2. In the right panel, we give the periods
of all the unstable modes obtained as function
of Teff, for 1.6 M0 models. Theoretical periods
of unstable modes are in agreement with typical
observed periods of γ Doradus stars.
In this figure, we give the contributions
of the radiative and convective flux
variation terms to the work integral of
the l=1 g50 mode of a γ Doradus model.
WFR (radiation) has a significant driving
effect, while WFc (effect of convective
flux variations) does not play a
significant role at the CE base. This
supports the flux blocking mechanism
proposed by Guzik et al. (2000). The
effect of transversal components of flux
variations (WFch and WFRh) is very
small because the horizontal wavelength is much larger than the T, ρ and
P scale heights in these superficial
layers.
M = 1.6 M0
Teff = 6930 K
a = 2.
M = 1.8 M0
Teff = 6680 K
a = 1.8
Multi-color photometric observables
α=1
α = 1.5
M = 1.8 M0 Teff = 7150 K
α = 1 Q = 0.033 d
α = 1.5 Q = 0.033 d
l=2
l=3
l=3
l=3
l=2
l=2
l=2
l=0
l=1
l=0
l=3
α = 1.5
Linear non-adiabatic computations enable to determine the
amplitude ratio and phase difference between the local
effective temperature variation and the radial displacement at
the photosphere: |δ Teff/Teff| and ψT. In the top panels we give
the values obtained for δ Scuti (left) and γ Doradus (right)
models with different α, as function of Q=P*tdyn0/tdyn (days)
and of frequency (c/d) respectively. For both types of stars,
TDC results (red) are less sensitive to α than FC results (blue).
The TDC phase-lags are more realistic than the FC ones.
l=1
l=0
|δ Teff/Teff| and ψT are basic ingredients for the determination of
the photometric amplitude ratios and phase differences
between different color passbands (Dupret et al. 2003). In the
bottom panels are the results obtained for Stroemgren
photometry: amplitude ratios versus phase difference diagrams
at left and amplitude ratios versus wavelength at right. The
FC results obtained with l = 2, 3 and α=1.5 are completely
unrealistic for the δ Scuti model (left). In the right bottom
panels, confrontation to observations for the γ Doradus star
HD164615 (magenta squares, f = 1.233 c/d) shows much better
agreement with the TDC models than with the FC models.
Conclusions
The red edge of the δ Scuti instability strip is obtained by our TDC models, for radial as well as for non-radial modes. Good
agreement with observations is obtained with MLT parameter α = 1.8. The driving of the γ Doradus gravity modes is also explained
by our TDC models. A theoretical instability strip in agreement with observation is obtained with α = 2. Confrontation to multicolor photometric amplitude ratios and phase differences shows better agreement with our TDC models than with FC models.
TDC
M = 1.5 M0 Teff = 6980 K
α = 1.8
FC
REFERENCES
Dupret, M.-A., De Ridder, J., De Cat, P., et al., 2003, A&A 398, 677
Dupret, M.-A., Grigahcène, A., Garrido, R., et al., 2004, A&A 414, L17
Gabriel, M., 1996, Bull. Astron. Soc. Of India, 24, 223
Guzik, J., Kaye, A., Bradley, P., et al., 2000, ApJ 542, L57
Handler, G., 2002, http://www.astro.univie.ac.at/~dsn/gerald/gdorlist.html
Rodriguez, E., Lopez-Gonzalez, M., & Lopez de Coca, P., 2000, A&AS 144, 469