A&A 400, 599-612 (2003)
DOI: 10.1051/0004-6361:20030068
R. S. Levenhagen 1 - N. V. Leister 1 - J. Zorec 2 - E. Janot-Pacheco 1 - A. M. Hubert 3 - M. Floquet 3
1 - Instituto de Astronomia, Geofísica e Ciências Atmosféricas
da Universidade de São Paulo, CUASO 05508-900 São Paulo, Brazil
2 - Institut d'Astrophysique de Paris, 98bis Boulevard Arago, 75014 Paris, France
3 - Observatoire de Paris-Meudon, GEPI, FRE/2459, 92195 Meudon Cedex, France
Received 8 July 2002 / Accepted 19 December 2002
Abstract
Line profile variations (lpv) in He I, Fe II, Mg II and
Si II transitions were detected in the Be star
Cen (HD 127972)
by means of high resolution and S/N spectroscopic observations obtained in six
epochs from May 1996 to April 2001. They were interpreted in terms of nonradial
pulsations (NRPs). Time analysis was performed using Cleanest algorithm and
showed the following frequencies with high order of significance: 0.61 c/d,
1.48 c/d, 3.81 c/d, 5.31 c/d, 9.24 c/d and 10.35 c/d. From phase variation
diagrams we estimated mode degrees
in the range 3-8. If the 10.35 c/d
frequency is considered the first harmonic of 5.31 c/d, the corresponding
azimuthal number of the mode is
.
Except for 0.61 c/d,
all other frequencies are compatible with NRPs. During the period of
progressive activity enhancement in the He I 6678 line, a strengthening
of Balmer emission lines was observed. From Mar. 12 to Mar. 23, 2000, we
noticed rapid variations of both H
peak separation and V/R ratios.
Using a simple model for the H
line emission formation, we
outlined an explanation for the season-averaged H
emission variation in
terms of changes of the mass density in the circumstellar envelope. The
fundamental parameters of
Cen were analyzed using several methods. The
adopted ones account for the stellar fast rotation, which helped us not only to
estimate the stellar rotational frequency, but also to show that the star is in
the middle of its main sequence life span.
Key words: stars: emission-line, Be - stars: oscillations - stars:
individual:
Cen - stars: fundamental parameters - techniques:
spectroscopic - line: profiles
Epoch | Observing | Telescope | Instrument | Spectral range | No of nights | No of spectra |
season | ||||||
1 | May/June 1996 | LNA 1.60 m | Coudé | He I 6678 Å | 7 | 539 |
2 | May 1997 | LNA 1.60 m | Coudé | He I 6678 Å | 3 | 26 |
3 | June 1998 | LNA 1.60 m | Coudé | He I 6678 Å | 2 | 31 |
4 | April 2000 | ESO 1.52 m | FEROS | 3560-9200 Å | 10 | 33 |
5 | May 2000 | LNA 1.60 m | Coudé | He I 6678 Å | 5 | 56 |
6 | April 2001 | ESO 1.52 m | FEROS | 3560-9200 Å | 3 | 59 |
Long-term (years) photometric variations of Cen were reported by
Jaschek et al. (1964) and Feinstein & Marraco (1979). Short time-scale
photometric variations of this object were first reported by Cuypers et al.
(1989). Though the latter were sometimes interpreted as due to corotating
features, they can also be atributed to NRP due to effects of
compression/expansion phenomena associated with the local temperature
variations caused by the passage of waves through the stellar surface (Smith
1977).
The aim of this paper is to present new Fourier analysis of the lpv in
He I
4026, 4121, 4144, 4388, 4471, 4922, 6678 Å,
Si II
4131 Å, Mg II
4481 Å and
Fe II
5169 Å lines. On the other hand, this star also
underwent photometric monitoring by the Hipparcos satellite from 1990 to
1992. The variations detected are worth studying in some detail. Observations
of
Cen were also made in the BCD spectrophotometric system, which allows
us to derive an independent set of stellar fundamental parameters unperturbed
by CE emission/absorption. Once these parameters are corrected for rotational
effects, we can determine the evolutionary status of the central object. Their
comparison with fundamental parameters derived using stellar model atmospheres
will also help us to discuss the effects induced by the rapid rotation on the
stellar surface. Finally, we will report H
emission line profiles
obtained from 1996 to 2001 whose variations can give us new insights on CE
formation characteristics.
The high resolution and signal-to-noise spectra obtained are distributed over
30 nights. From May 1996 to May 2000 observations were
performed during 17 nights with the Coudé spectrograph at the Brazilian
Laboratório Nacional de Astrofísica (Pico dos Dias) (LNA) 1.60 m (B&C)
telescope using a EMI CCD camera (
pixels). For 13 nights, from April 2000 to April 2001, observations were carried out with the fiber-fed extended
range optical spectrograph (FEROS) at the ESO - La Silla 1.52m telescope. The
LNA spectra were taken with a 1800
grating (first inverse order)
centered on the He I
6678 Å line, with sporadic H
(
Å) measurements. This arrangement yields a spectral
resolution of
with a reciprocal dispersion of 0.08 Å
.
The signal-to-noise ratio is typically
250 for exposure times
around 300 s. Bias, flat-field and Th-Ar comparison lamp were taken during
each night, and observations were reduced with the IRAF
package. ESO
spectra were taken in a spectral coverage of 3560-9200 Å, recorded in 38
orders on the detector, with typical S/N
(near He I 6678 Å). The resolution power of FEROS is
.
Spectra studied
and shown in this paper are reduced to the heliocentric frame.
The log of spectroscopic observations carried out on HD 127972 is presented in Table 1. A selected sample of He I 6678 Å line profiles obtained in each observing epoch is shown in Fig. 1. In the present paper we study only lpv associated with NRP. The temporary appearance of emissions in the outer line wings of the He I 6678 Å line, dimples (Smith & Polidan 1993), central quasi emissions, etc. will be discussed elsewhere.
The search for lpv multiperiodicities in HD 127972 spectra was made by means
of the Fast Fourier Transform (FFT) with the "Cleanest" algorithm (Foster
1995; Emilio 1997). It is known that the use of FFT without a frequency search
criterion yields periodograms with a very large number of frequencies, where
the signal appears convolved with the time sampling (aliasing), and the
detection of periodicities becomes somewhat risky and uncertain. However, some
constraints on the selection of the detected periods can be imposed by
filtering signals from the data sampling with well-founded criteria. One of
such methods is the Cleanest algorithm which considers the series as data
vectors represented linearly on a given vectorial base. The method proceeds by
steps by subtracting sequentially from the residuals, obtained once the FFT was
applied to the vector data, a model function derived using each new frequency
peak considered as statistically significant by a
test. Once the last
significant peak in a step cycle has been found, a new vectorial base is
constructed with the last vectors plus the contribution of the last detected
signal. The process goes on until there are no more statistically significant
peaks or simply because the process reaches a stop condition, such as the
imposed maximum number of possible frequencies. The last model function is
formed by a basis with 2n+1 tentative functions. An important feature of
Cleanest is that it does not assume the average signal present in each time
residual to be zero, as does the "Clean" method (Roberts et al. 1987). The
assumption of zero-averaged signals in time residuals leads to the unprobable
fact that the sample data are modulated by signals with an integer number of
cycles which can hinder the performance of signal detection (Emilio 1997;
Levenhagen 2000).
The reliability of the resulting power spectrum can be questioned by the time
data sampling. It implies a finite extent of observational missions, an unequal
time distribution of data and the strong 24 hours periodicity of data sampling.
It is thus important to test the performance of the algorithm of time analysis
used in adverse sampling conditions. This can be achieved in principle by
applying the method to a set of synthetic spectra affected by the same noise
and time distribution as the real spectra. In this way one can infer the
effects of the convolution of the NRP signals with the spectral window. For
this purpose, we created a set of 652 synthetic spectra composed of four
sinusoidal signals, whose frequencies are the same as those detected in
real data (see Sect. 3.2), namely
= 0.6, 1.5, 3.8 and 5.3 c/d, with
the same time distribution as the 1996-2000 LNA data set. These spectra
have been affected by random noise with a Gaussian distribution, whose FWHMrepresents about 30% of total amplitude of the input signal. The frequencies
used in this test were the same as those found in the actual spectra,
and all the synthetic spectra were generated with phase-dependence along the
wavelength bins. From this set, we constructed 241 time series formed at each 0.1 Å across the line profile in the same way as we had done with real
data. The series were then analyzed with the Cleanest algorithm with
appropriate frequency step, of around 0.0005 c/d, corresponding to the total
time span. The resulting periodogram is shown in Fig. 2.
In order to discover whether the frequencies detected by this method are actually related to the star signal or whether they simply reflect the time sampling of data, we carried out to another test by shuffling the synthetic intensities at random, though taking care that the original time sampling was preserved. The resulting periodogram is shown in Fig. 3. A study of the frequency of detected signals in Fig. 3 shows that none is statistically significant. Further analyses taking different combinations of the data sampling also yielded similar results. This shows that all periods displayed in Fig. 2 are robust against random selection of the data points. On the other hand, as the signals displayed in the periodogram of Fig. 2 as well as the amplitude of the simulation noise are close to those of the real data, our results should not be strongly affected by the window spectrum.
LNA spectra were arranged in four main sets: 1996, 1997 to 1998, 2000 and 1996
to 2000. Each data set was divided into 241 time series, from 6664.9 Å
to 6688.9 Å with steps of 0.1 Å. All series were analyzed with
frequency steps in the range 0.2 to 0.0006 c/d, depending on the sample to
be studied. The lpv frequencies with highest significance (75%
confidence level) detected with Cleanest in all data sets concerning He
I, Fe II, Mg II and Si II lines are shown in Table 2.
Figure 4 shows the resulting periodogram for the 1997 to 1998 data. The
confidence diagram resulting from a
test for the periodicities
found in the He I
6678 Å line is shown in Fig. 5. We can
readily see that, besides a signal with
c/d, frequencies greater
than 6 c/d are of lower significance, so they are less trustworthy. The
He I
6678 Å lpv was analyzed using only LNA spectra, since
ESO spectra presented problems related to bad columns of CCD in that wavelength
region. Results concerning lines other than He I
6678 Å
correspond to the 2000-2001 epoch.
Figure 6 pictures in a grey scale the dynamic spectra of the pulsation cycles
for He I 6678 Å line. A total of 652 spectra from 1996 to
2000 were sorted. All spectra falling into the same phase bin were averaged to
minimize the influence of other variabilities and noise (i.e. no prewhitening
was applied). They are presented as residuals from the respective mean profiles
and folded with frequencies
(left),
(center) and
(right).
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Figure 1: Spectroscopic sampling of LNA spectra, centered on He I 6678 Å line profile. |
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Figure 2: Periodogram of synthetic residuals with time distribution (window spectrum) equal to that of LNA spectra, from 1996 to 2000. |
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Figure 3: Periodogram of synthetic residuals with the same time distribution as Fig. 2, but the input signals were randomly shuffled. Notice that none of the previous frequencies were found, suggesting that they are not strongly dependent on data sampling. |
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Figure 4: Periodogram of He I 6678 Å line profiles obtained at LNA in 1997/1998. |
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Figure 5: Diagram of confidence level for periodicities found in He I 6678 Å line profiles. The horizontal line indicates 75% confidence level. |
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The signals with high degree of confidence are
c/d
(
),
c/d (
),
c/d
(
)
and 5.31
c/d (
). The highest considered
frequencies,
c/d (
)
and
c/d
(
)
were found only in He I
6678 Å. The
uncertainty related to time sampling for these signals is of the order
0.05 c/d, considering the averaged data span of 1996, 1997-1998 and 2000 sets,
weighted by the number of observed spectra. A number of frequencies displayed
in Table 2 are in agreement with our previous results for this star, like
1.48 c/d, 1.78 c/d, 5.31 c/d (Janot-Pacheco et al. 1999). As in Janot-Pacheco
et al. (1999), we have also found a signal at 4.52 c/d, but only in the
He I
4471 line. Since this signal can be an alias of 3.52 c/d,
we do not report it in Table 2. The frequencies found in the lpv analyses
(
to
)
are attributed to NRP modes. The 0.61 c/d signal
(
)
is discussed in Sect. 6, where it is shown that it is compatible
with the presence of an ejected orbiting shell. In Sects. 4.1 and 4.2 it is
shown that the 1.3 c/d signal can be associated with stellar rotation, since it
was determined from the continuum and line spectra, and was also found in the
lpv analyses of He I
4026, 4388 Å and Si II
4131 Å whose detection could be assured through the presence of
inhomogeneities such as spots (Balona 1990).
![]() |
Figure 6:
Grey-scale of spectroscopic residuals centered at
He I 6678 Å, folded with ![]() ![]() ![]() |
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Besides the lpv analyzed in the previous section, variabilities in radial
velocity (RV), equivalent width (EW) and full width half maximum (FWHM)
measurements in He I 6678 Å line profiles were also
detected. Table 3 compares the frequencies obtained from these global line
profile variations with those found in the previous section. Figure 7 shows the
RV, EW and FWHM variations of the He I 6678 line from 1996 to 2000 where
the mid-term variation of the line profile can be seen. There is a noticeable
anticorrelation between the EW and the FWHM of the line.
Photometric data of HD 127972 from the Hipparcos satellite (ESA 1997) obtained
from 1990 to 1992 were also analyzed. In this case, the time series analysis
with Cleanest indicated a strong signal with frequency
c/d. The photometric data folded with this frequency are shown in Fig. 8. These
data cannot be recast into a neat phase-dependent diagram with a lower
frequency, in particular with 1.3 c/d, since the amplitude of the photometric
signal is much more significant than the last one. We argue that 1.55 c/d could
be associated with NRPs rather than with stellar rotation (see Sect. 4.1).
Line Profile | Epoch | Detected frequencies (c/d) | |||||
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||||
Fe II 5169 Å | 4-6 | 0.61 | 1.51 | 5.33 | |||
He I 4026 Å | " | 0.62 | 1.30 | 1.48 | |||
He I 4121 Å | " | 1.49 | |||||
He I 4144 Å | " | 0.58 | 1.47 | 1.78 | |||
He I 4388 Å | " | 1.28 | 3.52 | ||||
He I 4471 Å | " | 0.61 | 1.48 | 1.79 | |||
He I 4922 Å | " | 0.57 | 1.50 | 1.82 | 3.51 | ||
Mg II 4481 Å | " | 0.63 | 1.71 | ||||
Si II 4131 Å | " | 0.62 | 1.29 | 1.50 | 1.70 | 3.81 | |
He I 6678 Å | 5 | 0.58 | 1.47 | 1.71 | 3.52 | 5.31 | |
He I 6678 Å | 2-3 | 0.61 | 1.48 | 3.81 | 5.31 | ||
He I 6678 Å | 1 | 0.61 | 1.48 | 3.81 | 5.31 | ||
He I 6678 Å | 1 to 5 | 0.61 | 1.48 | 3.81 | 5.31 |
An approach to infer the pulsational degree
and the azimuthal order
was proposed by Telting & Schrijvers (1997a) with the
intensity period search method (IPS). This method takes into account the phase
variation across the line profile of a frequency and its first harmonic. It is
mainly an empirical formulation based on analyses of phase diagrams derived
from generated time series of absorption line profiles of a non-radially
pulsating early-type star. For diagnostic purposes, using a Monte Carlo
simulation these authors quantified the relation between
and
(phase difference of main frequency), and that between
and
(phase difference of its first harmonic) for
spheroidal modes. They found that the fitted coefficients are remarkably stable
throughout the parameter space.
From the stability of the coefficients they concluded that it is possible to
derive good estimates for the pulsation parameters
and
by
evaluating the phase differences across the line profile. The typical
uncertainties on
and
by using the IPS method are
estimated to be
and
,
respectively. Considering the previous
detected lpv frequencies
,
,
,
and
as due to NRP, their pulsation parameters thus derived are given in
Table 4.
Since we did not find first harmonics with significant amplitudes for most
frequencies in the He I 6678 Å line profile, it was not
possible to calculate their
values by this method. We attempted
to do this only for
,
whose detected harmonic was supposed to be
(see Table 4 and Fig. 9). Figure 9 are shown the IPS diagrams
for frequencies
to
.
The upper panels show the phase
diagram across the He I 6678 line profile and the lower panels present
their respective amplitudes. Figure 9 shows clearly the asymmetrical aspect of
the amplitude of signals corresponding to frequencies
and
.
The same phenomenon was also seen by Floquet et al. (2000) in EW Lac. The 10.35 c/d signal could perhaps be considered the first harmonic of
5.31 c/d (scenario A). However, its power distribution does not exhibit the
same behavior over the entire line profile, as can be expected for two
harmonics, even when there are non-adiabatic effects (Schrijvers & Telting
1999). Thus, we also considered the possibility that the two signals are
independent (scenario B). In scenario A, IPS analysis leads to a pulsational
degree l = 5 and order
4, while in scenario B we obtain for
and
l = 5 and l = 8 respectively. It can also be
seen from this figure that the signal
is not symmetrical around the
line center, which should not be the case for NRP. However, the occurrence of
central quasi-emissions in He I 6678 Å transition at the 1996-1998 epoch could be partially responsible for the assymmetry observed in
around the line center.
Once the lpv frequencies are obtained, it is also important to determine
the fundamental parameters of Cen. This will allow us, on the one hand,
to distinguish the periodicities associated with rotation from those related
to NRP and, on the other hand, to determine the evolutionary state of the
star.
To determine the fundamental parameters of HD 127972 we used its BCD
spectrophotometric data (Chalonge & Divan 1952). They were derived from
12 low resolution spectra observed at ESO (La Silla, Chile) in May 1978 with
the "Chalonge spectrograph" (Baillet et al. 1973). The advantages of using
this system for Be stars were widely discussed in Zorec & Briot (1991). It
provides observational parameters that describe the photospheric Balmer
discontinuity (BD) of the star and which are free from interstellar extinction
and circumstellar emission/absorption perturbations. As they concern stellar
layers where the continuum spectrum is formed, they originate in regions that
can be assumed to be less perturbed by the stellar activities affecting the
outermost atmospheric layers and commonly seen in spectral lines.
The
(
)
parameters (
mean spectral position of the BD;
D* = energy jump measured at
3700 Å) represent the
photospheric flux emitted by the observed stellar hemisphere, which in fast
rotators is neither spherical nor has uniform surface temperature and gravity
(Tassoul 1978). The emitted spectrum is then aspect angle dependent and may
depict on average an object cooler and more evolved than it really is (Moss &
Smith 1981). Thus, the observed spectral and photometric parameters do
not reflect the actual stellar mass and its evolutionary stage, if the observed
quantities are interpreted simply using the current calibrations of fundamental
parameters, as it the star were rotationless.
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Figure 7: Radial velocity (RV), equivalent width (EW) and FWHMfor all LNA spectra from 1996 to 2000. |
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lpv's | EW | RV | FWHM | V/R |
0.6 | 0.5 | 0.6 | 0.7 | 0.5 |
1.5 | 1.6 | 1.6 | 1.5 | |
3.8 | 3.6 | |||
5.3 | 5.0 | |||
9.2 | ||||
10.3 |
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Figure 8: Photometric Hipparcos light curve (ESA 1997) of HD 127972 folded modulo with its main detected frequency (1.5 c/d). |
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where ,
and
are respectively the bolometric
luminosity, the BD and the
parameter of the star if it were
rotationless; FL, FD and
are functions calculated
assuming the stars are rigid rotators. M is taken as the "actual'' stellar
mass,
is the angular velocity ratio (
is
the critical angular velocity), i is the stellar aspect angle, t is the
stellar age,
is the critical linear equatorial velocity,
is the
critical equatorial radius and
the "actual'' equatorial radius at its
rotational rate
.
The function FL, FD and
were obtained assuming a Roche model for the stellar deformation and von
Zeipel's law for the effective temperature distribution, as previously done by
many authors (cf. Maeder & Peytremann 1970, 1972; Collins & Sonneborn 1977;
Collins et al. 1991). They were already used in Zorec & Briot (1997), Floquet
et al. (2000, 2002), Frémat et al. (2002), Zorec et al. (2002a,b).
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Figure 9:
IPS diagram for the detected lpv signals from
![]() ![]() ![]() |
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The observed (
)
parameters used to solve Eqs. (1)
are given in Table 5. The corresponding apparent (
parameters obtained with calibrations suited
to normal, rotationless B stars (Divan & Zorec 1982) are also reproduced in
Table 5. The observed bolometric luminosity
introduced in
(1) was estimated, however, using integrated fluxes over the entire
spectrum and the Hipparcos parallax of
Cen. The method used to
obtain it also helps us to test the consistency of the
calibration dependent fundamental parameters. By definition
the flux effective temperature of a star is:
For comparison, let us quote the fundamental parameters of Cen
recently determined by some authors. Harmanec (2000) obtained
K,
,
and
.
As compared with our determination, the slightly higher
value of
obtained by Harmanec (2000) could be due to its
determination, which carries a difference of 0.23 mag in the
bolometric correction (BC) used (Code et al. 1976). On the other hand, Code's
et al. (1976) were calculated from the OAO-2 satellite far-UV energy
measurements, which are overestimated as compared to those obtained since
then with TD1 and IUE satellites. They may endanger the reliability of BC
estimates for hot stars. The difference noticed in
might be due
to the use of
Strömgren's photometry and the calibrations by Moon
& Dworetsky (1985), which can lead to systematic deviations in the estimation
of fundamental parameters (Frémat & Zorec 2002). Stefl et al. (1995)
obtained
K also using
photometry,
but with Napiwotzki's et al. (1993) calibration. The use of photometric data
can easily lead to overestimated effective temperatures, mostly for hot Be
stars, because even a slight CE emission, which is difficult to clear up, can
affect the u magnitude. Stefl et al. (1995) obtained
K by fitting spectral lines with model atmospheres. This value is no
far from the temperature we derived by a similar method (Sect. 4.2), but which
we did not adopt for the present study. The stellar mass and radius determined
by Harmanec (2000) are similar to those we inferred in this paper, but neither
the starting
and
parameters nor the methods
used to obtain them are the same in the two attempts.
The system (1) was solved using a Monte Carlo method for the
trials of the input set of parameters (
). Each parameter, X, was sampled in turn between two extreme values,
where the amplitudes
are quoted in Table 5. We discarded
about 10% of the solutions obtained, those which lead to
and/or
.
The average values of reliable solutions of (1) derived
from the remaining 90% trials are given in Table 5. The quoted dispersions do
not represent errors, but the range of acceptable solutions. The relations
between luminosities, masses and stellar ages used are from the evolutionary
tracks of non-rotating stars calculated by Schaller et al. (1992) for Z = 0.02.
Noting that
is a key parameter to solve relations (1) and
that the difference between Chauville's et al. (2001) and Slettebak's (1982)
determinations is of the same order as their uncertainties, we sought the
higher
that, together with the above quoted uncertainties, still
leads to reliable solutions of (1). We thus obtained
km s-1. Solutions presented in Table 5 encompass the input
values centered once on
310 km s-1 that range from 266 to
354 km s-1 and then values centered on
km s-1
ranging from 326 to 414 km s-1.
Finally, we calculated the rotational frequency
c/d, also given in Table 5, which can be compared
with those obtained from time series analysis of lpv. They are, however,
average values of only 27 determinations from the possible combinations of
(
)
parameters,
where each parameter takes in turn three values
,
X and
.
The frequency derived from lpv time series analysis that more
closely resembles
is
c/d. A frequency
c/d was
actually observed by Janot-Pacheco et al. (1999). Finally, we note that not
only the rotational frequency
is far from the "critical''
rotational frequency
,
which ranges from 1.34 c/d to 1.39 c/d,
depending on the value of
adopted, but that it only marginally
approaches the frequency
c/d suited for some lpv and the
photometric variations.
Since for a star with mass
the main sequence (MS) life
time is
yr, the ages estimated imply that
Cen displays the Be phenomenon at
,
roughly the
earliest epoch at which this phenomenon seems to appear in open clusters
(Fabregat & Torrejón 2000). Only if we adopted the observed fundamental
parameters (
)
without correcting them from rotational
effects would the star apparently be at the end of its MS life span (
yr), as expected from theoretical predictions (Maeder &
Meynet 2000). In these models, the high stellar rotation and hence, the Be
phenomenon, are meant to appear as the consequence of the evolution of the
stellar internal rotational law.
Unfortunately the only spectra we have at our disposal of HD 127972 covering a
large spectral range are for the years 2000 and 2001, when this star displayed
well developed H
emission. In spite of the fact that the estimation of
fundamental parameters from these spectra brings in the influence of the CE, it
can in principle furnish an extreme limit for these values. We calculated a
grid of models with
and
around the values displayed in
Table 5 with steps
K and
dex using the codes of non LTE model atmospheres TLUSTY (Hubeny 1988) and
SYNSPEC (Hubeny et al. 1994) to synthesize line profiles. Fundamental parameter
determination was attempted employing Wolf's (1973) method with a
controlled fit of H
and H
absorption lines combined with
reproduction of the Si II
/Si III
and
He I
/He II
equivalent width ratios. The
results are summed up in Fig. 10. From this figure it seems that from the
spectral lines used, the stellar parameters are
K and
dex (marked "x'' in Fig. 10).
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Figure 10:
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The difference between the solutions attempted for the H
and H
lines is explained by a different amount of line filling in with circumstellar
emission. It can also be noted that H
is not clean from this emission.
In both cases the residual emission leads to a lower gravity and to a hotter
stellar temperature estimation.
Notice the difference between the solutions obtained for the Si and He
equivalent width ratios. Both series of lines are currently assumed to be
little affected by circumstellar emission/absorption. On the other hand,
according to von Zeipel's theorem, the local effective temperature of
Cen ranges from 22 700 K at the pole to 19 900 K at the equator. As
equivalent widths of the studied lines are increasing functions of
in this range of temperatures, the difference between solutions for the
Si and He line ratios means that the stellar polar region more strongly favors
the radiation fluxes in the Si than in He lines. This selection effect on
formation region is also seen in the
estimates, since from the Si
we obtain
km s-1, while from He lines it assumes
km s-1. This fact warns against the use of
photospheric lines for
determinations in fast rotators whose
intensity increases with higher temperatures, since this parameter may result
in underestimation.
HD 127972 showed H
emission intensity strengthening from 1996 through
2000 and a slight fading in 2001; this last was accompanied by increased
central absorption. The average H
emission line profiles observed in
the 1996, 1997, 1998, 2000 and 2001 epochs are shown in Fig. 11. This pattern
of H
line profiles variation resembles that displayed by the star in
the 1987-1993 period (Hanuschik et al. 1996), but in the opposite sense.
Putting both patterns together, a kind of cyclic emission variation of about
6-7 years appears.
From 34 H
emission line profiles obtained from Mar. 12 to Mar. 23,
2000, a rapid cyclic variability of the V/R emission peak intensity ratio (Fig.
12) and a rough increase, followed by a rapid decrease in the
separation of the emission peaks, was observed (Fig. 13). The total
peak separation change is not greater than 15 km s-1. Let us note also
that the highest peak separation corresponds to the highest V/R value. After
this maximum, the V/R ratio and the peak separation decreased. These changes
were accompanied by a general wiggling of the line emission profile,
characterized by a noticeable pulling down of the whole blue emission wing that
produced the observed V/R decreasing ratio. This drop of the emission intensity
on the blue side of the emission line profile was followed by an increase of
the red wing, but of much smaller amplitude. The maximum intensity changes in
the blue wing were
(I is the intensity
normalized to the local continuum) and they were produced in the spectral
region from
to -800 km s-1, while the intensity
variation in the remaining profile was
.
Transient
sharp absorption spikes were also observed far out in the wings.
Each epoch corresponding to four season-averaged H
emission line
profiles shown in Fig. 11 is also characterized by a different
spectral extent of the He I 6678 lpv. Figure 14 displays the
mean absolute deviations of the lpv across the He I 6678 line profile,
as defined by Walker (1991). It can be seen in this figure that the
wavelength interval showing profile variability systematically widens from
1996 through 2000. The wavelength interval where the variability of highest
significance extends beyond the
limit, from roughly
390 km s-1 in 1997 to about
450 km s-1 in 2000. This behavior was
also observed in other Be stars and in particular in
Eri by Kambe et al. (1993 and references therein).
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310 | 370 | ![]() |
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0.86 | 0.90 | ![]() |
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8.5 | 8.7 | ![]() |
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6.2 | 6.3 | ![]() |
i = | 66o | 70o | ![]() |
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5.3 | 5.2 | ![]() |
t/108 yr = | 0.199 | 0.178 | ![]() |
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1.12 | 1.24 | ![]() |
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485 | 494 | ![]() |
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1.34 | 1.39 | ![]() |
Regarding the uncertainties in the determination of
we can adopt,
using the data in Table 5,
km s-1 as
the reference value for the projected critical rotational velocity. Then, the
line activity that extends up to
450 km s-1 could imply that the
stellar layers where the He I 6678 line is formed may be in critical
rotation. However, this rotation is somewhat puzzling, because from the
He I 4471 line observed in April and May 2000 we obtained
km s-1 (Sect. 4.2).
At least two explanations can be put forward for
this discrepancy: 1) the main contributions to He I 6678 and He
I 4471 lines come respectively from different atmospheric layers [as expected
from the ratio of their respective oscillator strengths
f(6678)/f(4471) =5.6], so that while the uppermost layers are accelerated to the critical
rotational velocity, the lower ones would be left unscathed; 2) the
contribution to the He I 6678 line wings at velocities
is due to exophotospheric or circumstellar material travelling at
velocities up to
km s-1. The first possibility recalls the scenario proposed by Osaki
(1986) and Saio (1994), where the prograde NRP modes accelerate the outer
stellar atmospheric equatorial layers up to the critical rotational velocity.
These layers may give rise to mass loss and the NRP modes decrease in
intensity as the mass dissipates in the extended envelope.
We studied the He I 6678 lpv beyond the
limit. In order to
obtain the characteristic frequencies, the red and the blue sides of the
line profiles were folded into a unique positive velocity scale. The
periodograms that resulted for the periods 1996, 1997/1998 and 2000, and the
respective diagrams of confidence levels of the signals found are shown in Fig. 15. In the confidence level estimations we excluded the points at V < 310 km s-1. Since roughly in the interval
to
km s-1
the emission shoulders seen in the line profiles are probably formed in the
circumstellar regions, we can consider frequencies
as due
to circumstellar orbiting matter. If so,
c/d could
represent a perturbation produced at distances 3.3 to 6.4R* away from the
star, depending on whether we consider Keplerian or angular momentum
conservation rotation law respectively. From the diagrams of Fig. 15 we see
that the signal
c/d disappears gradually from 1996 to 2000,
as it would be overtaken by matter gathered elsewhere and with a more
significant contribution to the line profile. On the contrary, the signal
c/d is ubiquitous and its significance grows from 1996 to 2000
(the confidence peaks must be regarded relative to each other only within a
given diagram). It may correspond to perturbations centered from 1.3 to
2.0R* in the CE, depending on the rotational law assumed. As emission in the
H
line also grows from 1996 to 2000, we may consider there is an
increasing amount of matter gathered in these CE regions. This picture seems
to be confirmed by an increasing CE density derived using a simple model of the H
line emission presented in Sect. 5.2. The widening of the wavelength
interval of lpv in the He I 6678 line could be then associated with a
period of increased mass ejection.
![]() |
Figure 11:
Average H![]() |
Open with DEXTER |
There is also the prevalent frequency
c/d that could be
due to the central star, which as seen in Sect. 3.2. is quite outstanding in
the data analyzed in the present paper.
Let us finally note that if
actually changed from 310 to 450 km s-1, this would represent a variation of only 14% in
,
while the 45% variation of
is provided mainly by rotational stretching of the
equatorial radius
.
One of the most difficult questions relating to Be stars concerns their CE
formation. It is then important to determine the relevant parameters that
characterize the CE structure at each observed emission phase. This may help us
to estimate the effects of stellar activity on the observed CE changes.
In particular, if the apparently increasing activity detected in the He
I 6678 line from 1996 to 2000 also implied conspicuous mass ejections, the
average density of the CE must have changed perceptibly, so that we can detect
it by studying the emission in the H
line. In order to obtain a rough
insight on the scale factors characterizing the CE structure, we use first
physical principles and a simple representation of the envelope. From Sect. 4.2 it seems that
Cen is seen nearly equator-on. We assume then that the CE is represented by a rotating cylindrical disc seen edge-on. It can also be
simultaneously expanding or contracting. Since the main radiation transfer
effects are controlled by the optical depth, which is an integrated quantity,
the disc can be treated in a first approximation as a rotating/expanding (or
contracting) ring with the same radial optical depth as the CE is thought to
have (Floquet et al. 2000). The ring has a radius R and a total height
.
It has long been known that the source function
of the H
line in B stars is strongly dominated by radiative ionization and recombination
processes (Thomas 1965; Jefferies 1968). In a slab, as the one represented by
the ring facing the central star, we can then use the following dependence of
the source function with the optical depth (Mihalas 1978):
The wavelength-dependent H
line optical depth was assumed to
be:
From (5) we see that the radiation field of the underlying star
determines the value of the source function, so that
0.05. The rotationally broadened photospheric absorption line
profile is obtained using the flux
calculated for
km s-1 from Kurucz' codes and using the fundamental stellar parameters
presented in Table 5. The fit of each observed mean
line
profile (Fig. 11) is then obtained using R, H,
,
and
as free parameters.
determines the
eventual asymetry seen in the emission peaks. It was determined only for the
1996 line profile; in other cases we considered
km s-1.
The separation of the emission peaks is determined mainly by
,
but
it also depends on
.
The full width of the emission line on its half
intensity and on the low side of wings approaching the continuum level is fixed
by R and
.
For a given value of R, H and
determine the
emission intensity in the peaks. The ratio H/R and
establish the
depth of the central absorption. The fits thus obtained are shown in Fig.
16 (dashed lines) and the corresponding CE parameters are given
in Table 6. We considered the 1998 H
emission line profile as
essentially the same as in 1997, so we did not produce a fit for this line.
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Figure 12:
H![]() |
Open with DEXTER |
![]() |
Figure 13:
H![]() |
Open with DEXTER |
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Figure 14:
Time evolution of mean absolute deviations of line
profile variations detected in He I![]() ![]() ![]() |
Open with DEXTER |
In our previous work (Janot-Pacheco et al. 1999), a signal with 0.78 c/d was
detected and interpreted as due probably to a NRP mode. Keeping in mind the
mechanism of mass ejection based on prograde modes proposed by Osaki (1986),
such a signal is not expected to produce mass ejection, as it is retrograde.
A similar signal was not detected in this work, but another was
found with 0.6 c/d. According to the fundamental stellar parameters presented in Table 5, the frequency
c/d can also be interpreted as being
due to an orbiting perturbation either at
for a Keplerian
velocity law or at
if an angular momentum conservation law
is prevailing.
For comparison, we give in Table 6 the semi-separation of emission peaks
(in km s-1) in the H
line profiles and the radius
associated with
assuming the CE is in Keplerian
rotation. We see that
while
(
and
are both aspect
angle projected velocities). This peculiar behavior is due to the CE opacity
effect (Hummel 1994; Chauville et al. 2001), according to which for line
profiles of 1996-1998 type our simulations show that keeping the parameters
(
)
unchanged, the line emission peak separation widens as
increases from
to 1.0. It stretches down again for still
higher values of
.
In line profiles of 2000-2001 type, the separation
of the emission peaks reduces for increasing values of
.
Due to this
effect, it is difficult to infer from the present numerical simulation the
characteristics of the CE rotational law. Such a deduction is further hindered
by the fact that
is an average rotational velocity that probably
resumes the kinematic characteristics of the whole CE from the star up to an
external radius
R/R*. Let us still note that for
,
because of the
-dependence of the source
function, our model line profiles become bottle-shaped.
Noting that for the sake of a simple order of magnitude estimation we can
write
,
where
is the total electron number in the CE
region studied, we can draw the following conclusion concerning the CE
evolution as derived from the H
line emission changes: from 1996 to
1997 these changes implied an increase of the emitting region by about 40% and
an increase of
by 60%; the 1997-2000 transition is
characterized by an increase of the emitting region extent by a factor 5.5 and
by a factor 2.2; the 2000-2001 transition is almost passive
as the emitting region shrank by about 60%, while
changed
very little. The high NRP activity noticed in this work in the 2000 epoch
may then correspond to an effective CE replenishing phase. Moreover, it is
worth noticing that the nearly spectroscopic "shell" aspects of the H
line in the 1996 and 1997 epochs that could be interpreted at first glance as
due to an extended, highly absorbing disc, are actually produced by a CE region
which accretes the ejected mass from the star in such a way that the region is
rather close to the central star and that the extent of the region changes
little.
![]() |
Figure 15:
Periodograms and confidence level diagrams for epochs 1996, 1997/98
and 2000 of periodicities found in the wings of the He I 6678 line
beyond ![]() |
Open with DEXTER |
![]() |
Figure 16:
Fits of observed H![]() |
Open with DEXTER |
In this paper we presented Fourier analysis of lpv of He I, Fe
II, Mg II and Si II lines in the Be star Cen (HD 127972)
observed in six epochs at high resolution and S/N ratio from May 1996 to April
2001. The lpv were interpreted in terms of nonradial pulsations (NRPs). Time
analysis was performed using Cleanest algorithm and showed the following
frequencies with high order of significance: 0.61 c/d, 1.48 c/d, 3.81 c/d,
5.31 c/d, 9.24 c/d and 10.35 c/d. All signals except the first are interpreted
as due to NRP modes. From phase variation diagrams we estimated
parameters in the range 3-7. If the 10.35 c/d frequency is considered the
first harmonic of 5.31 c/d, the corresponding azimuthal number of the mode is
.
The observed multiperiodicity is in agreement
with our latest works (Janot-Pacheco et al. 1999). The detected signal with
1.48 c/d is probably due to an NRP mode rather than to rotation, which is
1.12 to 1.24 c/d (at most
1.39 c/d if the
star were to be regarded as a critical rotator). The 3.81 c/d frequency could
be interpreted as the multiple of 1.8 c/d (
), but 1.8
c/d was not found in LNA spectra (He I 6678 Å). It was detected in
other wavelengths of ESO spectra. If this signal really existed, 3.81 c/d could
be also interpreted as due to NRP. The only instance where we detected at the
same time both a signal and its first harmonic was in the case of 5.31 c/d and
10.35 c/d signals, though the significance level of the latter frequency is
less than 75%. In this case, the IPS method yields a tesseral mode
,
.
Epoch |
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R/R* | H/R* |
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(R/R*)K |
km s-1 | |||||||
1996 | 0.9 | 3.5 | 3.1 | 260 | 40 | 210 | 2.2 |
1997 | 1.5 | 3.9 | 3.6 | 280 | 0 | 230 | 1.8 |
2000 | 0.7 | 7.3 | 5.5 | 260 | 0 | 150 | 4.3 |
2001 | 1.3 | 6.3 | 4.7 | 260 | 0 | 140 | 4.9 |
The photometric variations of HD 127972 observed by Hipparcos from 1990 to
1992 were also considered. They could be folded with a frequency
1.55 c/d. According to the fundamental stellar parameters, this signal
cannot be attributed to stellar rotation.
The fundamental stellar parameters were determined by taking into account the first order effects produced by fast stellar rotation on the BCD spectrophotometric quantities used to estimate them. According to these parameters, the star should be in the midst of its MS life span as expected by Fabregat & Torrejon (2000) for Be stars in open clusters. This also implies that, if the star becomes a fast rotator due to evolutionary effects as predicted by Maeder & Meynet (2001), the object would need to be a rapid rotator on the ZAMS.
The H
line profile was observed from May 1996 to April 2001. Its
emission increased from 1996 to 2000 and then decreased slightly in 2001. The
season-averaged H
line emission strengthening was correlated with an
increase of the lpv wavelength extent in the He I
6678 line
(Figs. 11 and 14). The activity with high confidence level extended beyond
the
limit by 26% in 1997 and 45% in 2000. The signal
in the He I
6678 line wings beyond the
limit has an increasing level of significance from 1996 to 2000, which may
indicate that the amount of matter gathered in the CE regions near the central
star was growing during this period.
We used a simple model to study the characteristics of the season-averaged
H
line emission profiles. The fit of model emission line profiles
indicates that the H
variation from 1996 to 2000 is consistent with an
increase of the amount of accumulated matter in the emitting region and with
an enlargement of its extent. The 2000 to 2001 transition phase can be
interpreted as due to shrinkage of the CE emitting region, where the amount of
stored mass remained nearly unchanged.
Acknowledgements
RSL expresses his thanks to Dr. S. Andrievsky for fruitful discussions and help with line profile synthesis. He also thanks Dr. I. Hubený and Dr. T. Lanz for assistance with SYNSPEC and TLUSTY codes. We greatly appreciate and are greatful for the valuable comments and suggestions made by an anonymous referee. This research was supported by Fundação de Amparo à Pesquisa do Estado de São Paulo through grants no. 98/00497-0 and 00/10029-6 and Conselho Nacional de Desenvolvimento Científico e Tecnológico through grant no. 130710/1998-9.