Issue |
A&A
Volume 509, January 2010
|
|
---|---|---|
Article Number | A90 | |
Number of page(s) | 7 | |
Section | Stellar structure and evolution | |
DOI | https://doi.org/10.1051/0004-6361/200912914 | |
Published online | 22 January 2010 |
A
Scuti star in the post-MS contraction phase: 44 Tauri
P. Lenz1 - A. A. Pamyatnykh1,2,3 - T. Zdravkov2 - M. Breger1
1 - Institut für Astronomie, University of Vienna,
Türkenschanzstrasse 17, 1180 Vienna, Austria
2 -
Copernicus Astronomical Centre, Bartycka 18, 00-716 Warsaw, Poland
3 -
Institute of Astronomy, Russian Academy of Sciences, Pyatnitskaya Str 48, 109017 Moscow, Russia
Received 17 July 2009 / Accepted 27 October 2009
Abstract
Context. The evolutionary stage of the
Scuti star 44 Tau has been unclear. Recent asteroseismic studies have
examined models on the main sequence, as well as in the expansion phase
of the post-main sequence evolution. However, these models could not
reproduce all of the observed frequencies, the mode instability range,
and the fundamental stellar parameters simultaneously. A recent
photometric study has increased the number of detected independent
modes in 44 Tau to 15, and a newly found gravity mode at
5.30 cd-1 extends the observed frequency range.
Aims. One of the possible evolutionary stages of 44 Tau has
not yet been considered: the overall contraction phase after the main
sequence. We computed asteroseismic models to examine whether models in
this evolutionary stage provide a better fit of the observed frequency
spectrum.
Methods. We used Dziembowski's pulsation code to compute
nonadiabatic frequencies of radial and nonradial modes. Observation of
two radial modes and an avoided crossing of dipole modes put strong
constraints on the models. A two-parameter overshooting routine is
utilized to determine the efficiency of element mixing in the overshoot
layer above the convective core.
Results. We find that pulsation models in the post-MS
contraction phase successfully reproduce the observed frequency range,
as well as the frequency values of all individual radial and nonradial
modes. The theoretical frequencies of the mixed modes at 7.79 cd-1 and 9.58 cd-1 are in better agreement with the observations if efficient element mixing in a small overshoot layer is assumed.
Key words: Sct - stars: oscillations - stars: individual: 44 Tau
1 Introduction
The
Scuti stars are a class of pulsators exhibiting low-order acoustic and
gravity modes driven by the opacity mechanism acting in the HeII
ionization zone. In evolved
Scuti
stars mixed modes, i.e., modes with acoustic behaviour in the envelope
and gravity behaviour in the interior, are common. Since such modes
probe different layers inside a star than purely acoustic modes, the
Scuti stars are excellent targets for asteroseismology.
The Scuti pulsator 44 Tau (spectral type: F2 IV) exhibits an exceptionally slow intrinsic rotation of
km s-1 (Zima et al. 2007) which is much lower than the average value for
Scuti stars. For this group of pulsators, projected rotational velocities,
,
around 100 km s-1
and higher are not unusual. This makes 44 Tau an interesting and
relatively simple target for asteroseismology, because the effects of
rotation are weak and do not complicate mode identification and stellar
modelling.
Table 1: Observed frequencies and mode identifications.
In recent years several ground-based observing campaigns of the Delta Scuti Network (DSN) were organized to retrieve photometric and spectroscopic data of 44 Tau. The first comprehensive frequency analysis of its photometric light variations was published by Antoci et al. (2007). This paper also summarizes all previous observations of the star. With two additional seasons of extensive Strömgren vy photometry, Breger & Lenz (2008) could increase the number of detected frequencies to 49, of which 15 are independent.
Garrido et al. (2007) have determined the spherical degree, ,
for the 10 dominant modes by means of photometric amplitude ratios
and phase differences. Their results were later confirmed by Lenz
et al. (2008). In 2004 a spectroscopic campaign was organized
simultaneously to the photometric observing run. The results of the
line-profile variation analyses and the determination of photospheric
element abundances are discussed in detail by Zima et al. (2007).
For 8 modes, the azimuthal order, m, could be determined. Moreover, no indications of a global magnetic field and no anomalous element abundances were found.
The spectroscopically determined
value of
does
not allow for unambiguous determination of the evolutionary status of
44 Tau. In recent studies, both main sequence (hereafter MS)
and post-MS models in the expansion phase have been considered (Garrido
et al. 2007; Lenz et al. 2008). The results by Lenz
et al. (2008) showed that these models fail to reproduce all observable parameters satisfactorily (individual frequencies, observed frequency range, fundamental stellar parameters).
The effective temperature and luminosity of MS models is significantly
lower than the values derived from photometry and Hipparcos data.
Moreover, the positions of predicted modes do not match the observed frequencies (see Fig. 8 in Lenz et al. 2008).
Evolved models in the hydrogen-shell burning stage reproduce the
fundamental stellar parameters well, but theory predicts many more
frequencies than actually observed. While partial mode trapping may
explain the position of the modes, this mechanism should not be very effective for the observed
modes.
Moreover, the frequency range of unstable modes is shifted to higher
frequencies with respect to MS models. Therefore, the mode at
6.34 cd-1 and the newly found mode at 5.30 cd-1 are predicted to be stable by models in the post-MS expansion phase.
We reexamined asteroseismic models of 44 Tau based on the latest frequency solution of Breger & Lenz (2008) and investigated a hitherto neglected possibility: a model in the overall contraction phase after the main sequence.
During the main sequence evolution, a Scuti
star transforms hydrogen into helium in its convective core. The amount
of hydrogen in the core gets very low towards the end of this phase.
The star increases its central temperature by an overall contraction to
keep the energy production from hydrogen burning efficient. At the end
of this overall contraction stage, hydrogen in the core is fully
depleted and the convective core disappears
. A nuclear hydrogen-burning shell is established outside the hydrogen-exhausted core.
The stellar envelope expands again, which leads to a decrease of the effective temperature.
The probability of finding a
Scuti star in the contraction phase after the TAMS is not low. If we
consider the same range of effective temperatures, the evolution during
the overall contraction phase is only approximately 10 times
faster compared to the MS evolution. In the post-MS expansion phase,
the evolution is approximately 16 times faster than on the MS. The
asteroseismic inferences from post-MS contraction models are presented
in this paper.
The paper is organized as follows. In Sect. 2 we briefly summarize the observed parameters of 44 Tau. In Sect. 3 we discuss the computation of our seismic models. The diagnostic power of mixed modes is examined in Sect. 4. Finally, in Sect. 5 we present predictions of post-MS contraction models.
2 Observed frequencies and mode identification
All observed independent frequencies of 44 Tau are given in Table 1, along with their mode identifications, if available. The given Ay amplitudes are mean Strömgren y
amplitudes derived from the five observing seasons between 2000 and
2006. The amplitudes for the first moments are taken from Zima
et al. (2007). The
spherical degrees of the modes were determined by Garrido et al.
(2007) and Lenz et al. (2008). We reinvestigated these mode
identifications with the new full frequency solution of Breger &
Lenz (2008) based on photometric amplitude ratios and phase differences and using the method by Daszynska-Daszkiewicz et al. (2003, 2005). The previous results were confirmed. The new mean amplitude ratios and phase differences between the Strömgren v and y bands are listed in Table 1.
These average values were computed from the annual solutions of the
five observing seasons and weighted by the annual signal-to-noise ratio
of each mode. Taking the observed amplitude modulation in 44 Tau
into account, this weighting scheme is more adequate than the one used
in Lenz et al. (2008). For some modes, in particular for f9, the uncertainties in Av/Ay and
could be reduced significantly.
The spherical degree can be uniquely determined for the 10 dominant modes. The observed mean phase difference of f11 puts this mode midway between the theoretical values of
and 2 modes (see Fig. 5 in Lenz et al. 2008), which prevents an unambiguous identification. The uncertainties in the phase differences of the low-amplitude modes f12-f15 are too large to derive reliable results.
The mode positions in the diagnostic diagrams for mode identification
depend on the efficiency of convection. By fitting the predicted mode
positions to the observed values, Lenz et al. (2008) determined
the mixing-length parameter,
,
to be
0.2
in 44 Tau. This is also confirmed by the new data. Consequently,
convection in the envelope of 44 Tau is not very efficient.
The azimuthal order of eight modes was derived by Zima et al. (2007) using the moment method. Most modes in 44 Tau are axisymmetric with exception of the two prograde modes f2 and f3. No rotational splitting has been observed. The close pair f6 and f9 at 9.56 and 9.58 cd-1
does not represent a part of a rotationally split multiplet, because
the determined spherical degrees differ. The inclination angle of
44 Tau could be constrained to
.
The effective temperature of 44 Tau is
= 6900
100 K,
= 1.305
0.065, and
= 3.6
0.1.
Due to the use of a more recent estimate for the bolometric correction,
the given mean luminosity is lower than the value in Lenz et al.
(2008).
Table 2: Parameters of post-MS contraction models with a good fit of the 15 frequencies observed in 44 Tau.
3 Seismic models in the post-MS contraction phase
In this study we used the Warsaw-New Jersey evolutionary code, which is a descendant of the Paczynski (1970) code. In this code, envelope convection is described with the standard mixing-length theory of convection. The evolutionary models are computed assuming uniform rotation and conservation of global angular momentum during evolution from the ZAMS.
Aside from the traditional description of overshooting from the
convective core, we also applied a new two-parameter description that
allows for partial element mixing in the overshooting region
(Dziembowski & Pamyatnykh 2008).
It allows us to consider different profiles of the hydrogen abundance
inside the partly mixed region just above the convective core.
One of the parameters,
,
defines the overshooting distance above the convective core. The second parameter, w,
adjusts the profile of the hydrogen abundance between the convective
core and the upper boundary of the overshooting region. It therefore
characterizes the efficiency of mixing in this region. The hydrogen
mass fraction in a stellar layer, X, is defined as a function of fractional mass, q:
X = Xc + (q - qc)w [a+b(q-qc)]. | (1) |
The coefficients a and b are determined from w and

To compute the nonadiabatic radial and nonradial frequencies, we used the most recent version of Dziembowski's pulsation code (1977). This code relies on the frozen convective flux approximation. The effects of rotation on the frequencies were treated up to second order following Dziembowski & Goode (1992).
In this study we used two sources of the Rosseland mean opacities: the OPAL opacity tables (Iglesias & Rogers 1996) and the OP opacities (Seaton 2005). At low temperatures, these tables are supplemented by the Ferguson & Alexander (2005) molecular and grain opacities.
The abundances of some photospheric elements in 44 Tau were determined by Zima et al. (2007). Within the given uncertainties, the abundances of 44 Tau are close to the solar values by Grevesse & Noels (1993, hereafter GN93) and Asplund et al. (2004, 2005, hereafter A04). Since only abundances of 11 elements were measured, we did not utilize a special element mixture for 44 Tau, but examined pulsation models with both solar element mixtures.
3.1 Results with OPAL opacities
Two radial modes are observed in 44 Tau. As discussed in Lenz et al. (2008), this allows us to make use of Petersen diagrams (Petersen & Jørgensen 1972). In these diagrams, the period ratio between two radial modes is plotted against the period of the fundamental mode. The period ratio is sensitive not only to the adopted metallicity but also to rotation as stated by Suárez et al. (2006). Since these quantities are determined well by observations, we can use Petersen diagrams to find the optimum mass of a model.
Another important observation puts tight constraints on the models: the small frequency separation of the two
modes at 9.11 and 9.56 cd-1
indicates that these modes undergo an avoided crossing (Aizenman
et al. 1977). Since both modes are of mixed character, they are
also sensitive to the extent of overshooting from the convective core.
To find the optimum fit for the dipole modes, a series of computations with different overshooting distances,
,
and different efficiencies of partial element mixing in the overshoot layer (w=2.0
and 8.0) were made. Models that exhibited a good fit of all dipole
modes also showed very good agreement for the quadrupole modes. For
models obtained with X=0.70, the frequency separation between the dipole modes at 9.11 and 9.56 cd-1 is predicted to be slightly larger than observed. An increase in the initial hydrogen mass fraction, X,
helps to decrease the predicted frequency separation to the observed
values and provides the best agreement for all observed
15 frequencies.
The best pulsation models for OPAL opacities and the GN93 and A04 element mixture are given in Table 2.
All models were computed with a mixing length parameter
.
Model 4 was computed with the traditional description of
overshooting. Starting with an initial rotation rate of
3.5 km s-1, the tabulated evolved models exhibit rotation rates close to 3 km s-1. The effects of rotation were also taken into account in the calculation of the pulsation frequencies.
A comparison between predicted and observed frequencies for Model 4 in Table 2 is shown in Fig. 1. It can be seen that this pulsation model allows all observed modes to be explained solely with
modes. In some cases modes with
or 4 are also close to observed values, but photometric cancellation effects clearly favour low degree modes.
To describe the goodness of the fit, we used a dimensionless merit function similar to the one used in Brassard et al. (2001):
![]() |
(2) |
where










![]() |
Figure 1: Comparison between observed frequencies (vertical lines) and predicted unstable frequencies (circles) for a post-MS contraction model (Model 4 in Table 2). If the spherical degree of a mode was not observationally determined, a full vertical line is shown. Predicted frequencies that match observed frequencies are marked as filled circles. The rotational splitting is smaller than the size of the symbols. |
Open with DEXTER |
The position of OPAL models in the HR diagram is shown in Fig. 2 for models obtained with the GN93 and the A04 element mixture. The effective temperatures of these pulsation models are somewhat cooler than the values derived from photometric and spectroscopic measurements.
![]() |
Figure 2: HR diagram with evolutionary tracks for models with a good fit of all 15 observed modes. The models were constructed with OPAL opacities and two different solar element mixtures: the GN93 element mixture a) and the A04 element mixture b). |
Open with DEXTER |
The pulsation models obtained with the A04 mixture are closer to the TAMS. A 15-frequency fit with w=2.0
is not possible, because the required overshooting distance would be
less than possible for models in the overall contraction phase. The
main reason for the differences between pulsation models obtained with
the GN93 and the A04 mixture is the slightly different opacity in
the overshoot layer that affects the size of the convective core. The
uncertainties in the element abundances (and opacities) in 44 Tau
therefore lead to an uncertainty in the determination of the
overshooting distance,
.
The predicted frequency range of unstable modes agrees well with the observed frequency range as shown in Fig. 3
for one of the models that can be considered representative of all OPAL
models. Additional unstable modes are predicted between 13 and
17 cd-1. The mode instability at these high frequencies is sensitive to the efficiency of convection. If
is decreased from 0.2 to lower values, the highest frequencies
become stable. In our study we relied on the standard mixing-length
theory of convection and the frozen flux approximation. Time-dependent
convection models, such as those used in some other recent studies
about
Scuti stars (e.g., Montalbán & Dupret 2007; Dupret et al. 2005), would yield a more accurate determination of the high-frequency border of instability.
3.2 Results with OP opacities
Lenz et al. (2007) found
that post-MS expansion models of 44 Tau constructed with OP
opacities have significantly lower temperature and luminosity values
than observed. This problem persists for post-MS contraction models.
Montalbán & Miglio (2008) explain this by differences of 10% between OPAL and OP opacities at temperatures around
.
This corresponds to the temperature region in which the period ratio is
a sensitive probe as can be seen in the two uppermost panels in
Fig. 4.
The diagram shows the kinetic energy density of the radial fundamental
and first overtone mode inside the star. Pulsation modes are sensitive
to the conditions in temperature regions in which the kinetic energy
density is high.
Because of the position of its node, the radial first overtone mode
probes the temperature region between = 4.5 and 7.0 with different weights than the radial fundamental mode.
The differences between OPAL and OP opacities are shown in the middle panel of Fig. 4.
The lower panel shows the location of opacity bumps inside the star. We
artificially enhanced the OP opacities by up to 15% around = 6.0 and tested the impact on models in the contraction phase after the main sequence.
The results are shown in Fig. 5. The corresponding model parameters can be found in Table 2.
Contrary to models constructed with standard OP opacities, models
obtained with enhanced OP opacities are closer to the photometric error
box in the HR diagram. This may indicate that the Rosseland mean
opacities of the OP tables are currently underestimated in the
temperature region around
.
For models constructed with standard OP opacities, a fit of all 15
frequencies is only possible with the GN93 element mixture. Adopting OP
instead of OPAL opacities shifts the models that fit all 15 frequencies
closer to the TAMS (e.g., compare the models in Fig. 2a with Model 7 in Fig. 5).
The models constructed with OPAL A04 are already situated at the TAMS (Fig. 2b). To fit the avoided crossing of modes and the
modes in standard OP A04 models,
would have to be reduced more than possible for a model in the overall
contraction phase. However, the use of enhanced OP opacities in
combination with the A04 element mixture allows for a 15-frequency
fit. The corresponding models are listed in Table 2.
4 Mixed modes as probes of the stellar core
The partial mixing processes at the convective core boundary are currently not fully understood. During the hydrogen core burning phase, we expect a region around the convective core that is partially mixed due to several mechanisms: (i) overshooting from the convective core; (ii) rotationally induced mixing (the core rotates faster than the envelope leading to additional mixing).
Unfortunately, until now no rotational splittings could be detected in 44 Tau. Therefore, we cannot derive the profile of differential rotation that would be necessary to disentangle the effects of rotation in element mixing.
An excellent probe of the size of the overshoot layer is the g1 mode for
as
stated by Dziembowski & Pamyatnykh (1991). This mode is partially
trapped in the overshoot region, so its frequency has high diagnostic
value. However, in 44 Tau models in the contraction phase after
the TAMS, this mode already moved to higher frequencies outside the
observed frequency range.
However, we observe many mixed modes in 44 Tau which are
also sensitive to the conditions in the chemically inhomogeneous
overshoot layer above the convective core. Table 3 lists the fraction of oscillation kinetic energy confined in the g-mode cavity,
,
for all predicted unstable modes in Model 3. Since the given values of
are very similar for the different OPAL and OP models, they can be
considered representative of all post-MS contraction models. Moreover,
the differences between calculated and observed frequencies are given.
If the azimuthal order of an observed mode is unknown, the frequency
difference to the theoretical m=0 modes
is given and the value is enclosed by brackets. The uncertainty in
frequency due to unknown azimuthal order may be as high as 0.05 cd-1 for
modes.
![]() |
Figure 3:
Instability parameter, |
Open with DEXTER |
![]() |
Figure 4: Radial fundamental and first overtone mode as probes for opacities. Upper panel: kinetic energy density inside the star. Middle panel: comparison between OPAL and OP opacities for the same model. Lower panel: absolute values of Rosseland mean opacities from OPAL and OP data. |
Open with DEXTER |
![]() |
Figure 5: HR diagram with evolutionary tracks of two models constructed with enhanced and standard OP opacities. Both models provide a good 15-frequency fit. |
Open with DEXTER |
Table 3: Theoretical frequencies and mode properties of unstable modes predicted by Model 3.
The mixed
mode at 7.79 cd-1
has strong g-mode characteristics. Almost 87% of its kinetic
energy is confined in the g-mode cavity in the stellar interior. This
also explains why the observed amplitude of this mode is significantly
smaller than that of other dipole modes in 44 Tau. Consequently,
this and other mixed modes are sensitive to the shape of the hydrogen
profile in the partially mixed layer above the convective core.
![]() |
Figure 6: Comparison of the theoretical frequencies of two pulsation models with different hydrogen profile modelling, w=8.0 (filled circles) and w=2.0 (open circles). Modes that are most affected are marked with a dotted circle. The parameters of the models are given in Table 2 (see Models 2 and 3). |
Open with DEXTER |
We computed pulsation models using two different assumptions for element mixing in the overshoot layer: weak element mixing (w=2.0) and efficient element mixing (w=8.0). For comparisons we also calculated models with the standard description of overshooting, which assumes no element mixing in the overshooting region.
In Fig. 6 we compare the predicted frequency spectra for Models 2 and 3 (obtained with w=2.0 and w=8.0,
respectively). The corresponding overshooting distances were adjusted
to values that provide the best fit of the observed frequencies. As can
be seen, the frequencies of some modes are sensitive to the differences
in the overshooting region. The frequency of the g4 mode at 7.79 cd-1 shifts most significantly. The frequency difference
cd-1
is larger than the expected maximum frequency separation between
components of a rotational splitting. Consequently, our results suggest
preference for more efficient mixing in a small partially mixed region (w=8.0) over less efficient mixing in a larger partially mixed region (w=2.0).
![]() |
Figure 7:
Impact of different efficiency of element mixing in the overshoot layer on the profile of the hydrogen abundance ( upper panel) and on the Brunt-Väisälä frequency ( middle panel).
Lower panel: relative Lagrangian pressure perturbation for two mixed
|
Open with DEXTER |
The corresponding profile of the hydrogen abundance for the discussed pulsation models is given in the upper panel of Fig. 7.
The different hydrogen profiles lead to a modification of the
Brunt-Väisälä frequency, as shown in the panel in the middle of the
diagram. In the lower panel the eigenfunction of the relative
Lagrangian pressure variation is given for the mixed modes: g4 at 7.79 cd-1 and p1 at 7.01 cd-1.
Its larger amplitude in the partially mixed region makes the gravity
mode very sensitive to the conditions in this region. The change in the
Brunt-Väisälä frequency due to the different chemical profile slightly
adjusts the size of the g-mode cavity and, therefore, also influences
the values of the frequencies.
5 Predictions of the post-MS contraction model
Post-MS contraction models of 44 Tau predict a few additional dipole and quadrupole modes that may be found by future observations. After fitting the observed 15 modes, the frequencies of the remaining modes no longer strongly depend on the input parameters. However, small deviations may be found, especially for g-modes that will provide additional constraints on mixing in the overshoot layer. The expected frequencies of hitherto not observed modes can be found in Table 3. The detection of these modes would help in refining our models.
A reexamination of our photometric data indeed shows a prominent peak at the predicted position of the second radial overtone (11.198 cd-1). With an SNR of 2.72, this peak is below the significance limit of 4.0 but may be confirmed with new additional data. A reexamination of radial velocity data did not show any reliable prominent peaks at the predicted position of modes. Many of the predicted modes that lack an observational counterpart are gravity modes for which we only expect low amplitudes. Therefore, more accurate data are needed to extract these frequencies.
Moreover, the model predicts the spherical degree of some of the observed modes:
for 7.79 cd-1 and
for 5.30, 8.64, 11.30, 12.69 cd-1. These predictions also need to be confirmed by high-resolution spectroscopic data.
The computed evolutionary relative period changes,
,
are approximately
yr-1. Such changes are too small to be measured with the 5 year time-base of our data.
6 Conclusions
We constructed seismic models of the Scuti
star 44 Tau in the overall contraction phase after the main
sequence. The two observed radial modes and an avoided crossing of a
pair of dipole modes put strong constraints on pulsation models. Unlike
models on the main sequence or in the post-MS expansion phase, these
models successfully reproduce all 15 independent frequencies
observed in 44 Tau and predict that all detected modes are
unstable. This makes 44 Tau an example for determining the
evolutionary stage by means of asteroseismology.
The observed frequency spectrum (obtained from ground-based data) can be solely explained with modes with spherical degrees of 0, 1 and 2. This result is what we expect for the given accuracy of the data.
The frequency spectrum of 44 Tau consists mainly of modes of mixed character, i.e., modes with acoustic behaviour in the envelope and gravity behaviour in the interior. These modes allow examination of the efficiency of partial element mixing in the overshoot layer around the stellar core. We find that the theoretical frequencies of several modes (e.g. the dipole g4 mode at 7.79 cd-1 and the quadrupole mode g5 at 9.58 cd-1) are in better agreement with efficient mixing in a thin overshoot layer than with less efficient mixing in an extended overshoot layer.
The main source of uncertainty in the asteroseismic modelling
of 44 Tau are the stellar opacities. Determination of the size of
the overshooting region above the convective core, therefore, depends
on the source of opacity data and, to a smaller extent, on the choice
of the element mixture.
Pulsation models in the post-MS contraction phase constructed with
standard OP data are more than two standard deviations outside the
photometric error box in the HR diagram. Following a suggestion by
Montalbán & Miglio (2008), we computed a model with artificially enhanced
OP opacities around the temperature region = 6.0.
Such a model indeed agrees better with the fundamental parameters of
44 Tau derived from photometry and Hipparcos data.
The pulsation models presented in this paper not only provide an excellent fit of all observed modes but also allow several predictions, which may be confirmed with additional observational data. A few of the theoretically predicted modes are not observed. The question arises whether the amplitudes of these modes are below the noise threshold of the current data or whether they are even excited at all. Moreover, we predict the spherical degree of already observed modes for which our mode identification techniques did not succeed because the uncertainties in amplitudes and phases are too large. The excellent fit of the individual frequencies is very promising, and we are confident that additional data will lead to even more asteroseismic inferences about this star.
AcknowledgementsWe thank Wolfgang Zima for searching for our predicted frequencies in the radial velocity data of 44 Tau. This investigation has been supported by the Austrian Fonds zur Förderung der wissenschaftlichen Forschung. A.A.P. and T.Z. acknowledge partial financial support from the Polish MNiSW grant No. N N203 379636.
References
- Aizenman, M., Smeyers, P., & Weigert, A. 1977, A&A, 58, 41 [Google Scholar]
- Antoci, V., Breger, M., Rodler, F., & Bischof, K., & Garrido, R. 2007, A&A, 463, 225 [Google Scholar]
- Asplund, M., Grevesse, N., Sauval, A. J., et al. 2004, A&A, 417, 751 [Google Scholar]
- Asplund, M., Grevesse, N., & Sauval, A. J. 2005, ASPC, 336, 25 [Google Scholar]
- Brassard, P., Fontaine, G., Billères, M., et al. 2001, ApJ, 563, 1013 [CrossRef] [Google Scholar]
- Breger, M., & Lenz, P. 2008, A&A, 488, 643 [Google Scholar]
- Daszynska-Daszkiewicz, J., Dziembowski, W. A., & Pamyatnykh, A. A. 2003, A&A, 407, 999 [Google Scholar]
- Daszynska-Daszkiewicz, J., Dziembowski, W. A., Pamyatnykh, A. A., et al. 2005, A&A, 438, 653 [Google Scholar]
- Dupret, M.-A., Grigahcène, A., Garrido, R., et al. 2005, MNRAS, 361, 476 [NASA ADS] [CrossRef] [Google Scholar]
- Dziembowski, W. A. 1977, AcA, 27, 95 [Google Scholar]
- Dziembowski, W. A., & Goode, P. R. 1992, ApJ, 394, 670 [NASA ADS] [CrossRef] [Google Scholar]
- Dziembowski, W. A., & Pamyatnykh, A. A. 1991, A&A, 248, 11 [Google Scholar]
- Dziembowski, W. A., & Pamyatnykh, A. A. 2008, MNRAS, 385, 1061 [Google Scholar]
- Ferguson, J. W., Alexander, D. R., Allard, F., et al. 2005, ApJ, 623, 585 [NASA ADS] [CrossRef] [Google Scholar]
- Garrido, R., Suárez, J. C., Grigahcène, A., Dupret, M. A., & Moya, A. 2007, CoAst, 150, 77 [NASA ADS] [CrossRef] [Google Scholar]
- Grevesse, N., & Noels, A. 1993, in Origin and Evolution of the Elements (CUP), ed. N. Prantzos, E. Vangioni-Flam, & M. Casse, 15 [Google Scholar]
- Iglesias, C. A., & Rogers, F. J. 1996, A&A, 464, 943 [Google Scholar]
- Lenz, P., Pamyatnykh, A. A., & Breger, M. 2007, AIP Conf. Proc., 948, 201 [NASA ADS] [CrossRef] [Google Scholar]
- Lenz, P., Pamyatnykh, A. A., Breger, M., & Antoci, V. 2008, A&A, 478, 855 [Google Scholar]
- Montalbán, J., & Dupret, M.-A. 2007, A&A, 470, 991 [Google Scholar]
- Montalbán, J., & Miglio, A. 2008, CoAst, 157, 160 [NASA ADS] [Google Scholar]
- Paczynski, B. 1970, AcA, 20, 47 [Google Scholar]
- Petersen, J. O., & Jørgensen, H. E. 1972, A&A, 17, 367 [Google Scholar]
- Seaton, M. J. 2005, MNRAS, 362, L1 [NASA ADS] [CrossRef] [Google Scholar]
- Suárez, J. C., Garrido, R., & Goupil, M. J. 2006, A&A, 447, 649 [Google Scholar]
- Zima, W., Lehmann, H., Stütz, Ch., et al. 2007, A&A, 471, 237 [Google Scholar]
Footnotes
- ... disappears
- Of course, convective overshooting also disappears, but we keep the term ``model with overshooting'' or ``the overshooting case'' for later evolutionary stages to distinguish this case from models constructed without convective overshooting.
All Tables
Table 1: Observed frequencies and mode identifications.
Table 2: Parameters of post-MS contraction models with a good fit of the 15 frequencies observed in 44 Tau.
Table 3: Theoretical frequencies and mode properties of unstable modes predicted by Model 3.
All Figures
![]() |
Figure 1: Comparison between observed frequencies (vertical lines) and predicted unstable frequencies (circles) for a post-MS contraction model (Model 4 in Table 2). If the spherical degree of a mode was not observationally determined, a full vertical line is shown. Predicted frequencies that match observed frequencies are marked as filled circles. The rotational splitting is smaller than the size of the symbols. |
Open with DEXTER | |
In the text |
![]() |
Figure 2: HR diagram with evolutionary tracks for models with a good fit of all 15 observed modes. The models were constructed with OPAL opacities and two different solar element mixtures: the GN93 element mixture a) and the A04 element mixture b). |
Open with DEXTER | |
In the text |
![]() |
Figure 3:
Instability parameter, |
Open with DEXTER | |
In the text |
![]() |
Figure 4: Radial fundamental and first overtone mode as probes for opacities. Upper panel: kinetic energy density inside the star. Middle panel: comparison between OPAL and OP opacities for the same model. Lower panel: absolute values of Rosseland mean opacities from OPAL and OP data. |
Open with DEXTER | |
In the text |
![]() |
Figure 5: HR diagram with evolutionary tracks of two models constructed with enhanced and standard OP opacities. Both models provide a good 15-frequency fit. |
Open with DEXTER | |
In the text |
![]() |
Figure 6: Comparison of the theoretical frequencies of two pulsation models with different hydrogen profile modelling, w=8.0 (filled circles) and w=2.0 (open circles). Modes that are most affected are marked with a dotted circle. The parameters of the models are given in Table 2 (see Models 2 and 3). |
Open with DEXTER | |
In the text |
![]() |
Figure 7:
Impact of different efficiency of element mixing in the overshoot layer on the profile of the hydrogen abundance ( upper panel) and on the Brunt-Väisälä frequency ( middle panel).
Lower panel: relative Lagrangian pressure perturbation for two mixed
|
Open with DEXTER | |
In the text |
Copyright ESO 2010
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.