A&A 407, 1059-1065 (2003)
DOI: 10.1051/0004-6361:20030925
E. Rodríguez1 - A. Arellano Ferro2 - V. Costa1 - M. J. López-González1 - J. P. Sareyan3
1 - Instituto de Astrofísica de Andalucía, CSIC,
PO Box 3004, 18080 Granada, Spain
2 -
Instituto de Astronomía, UNAM, PO Box 70-264, 4510 Mexico DF,
Mexico
3 -
Observatoire de la Côte d'Azur, BP 4229, 0634 Nice Cedex 4, France
Received 12 February 2003 / Accepted 12 June 2003
Abstract
We present the results of simultaneous
photometry
carried out from 1999 to 2001 of the variable V2109 Cyg
together with a spectroscopic analysis based on one high resolution spectrum
obtained in 2000. From this
study, the star is definitively classified as an evolved
Sct-type
variable with solar metal
abundances. This conclusion is also supported by the detected
multiperiodic pulsational
behaviour and the observed variation of the m1 index over the
pulsation cycle. This variation is slightly reversed relative to the V light
curve, in very good agreement with the m1 variation expected from the
photometric calibrations. Besides the main
frequency
f1=5.3745 cd-1 and its first harmonic 2f1,
a secondary peak is found at
f2=5.8332 cd-1 (
f1/f2=0.92) with f1 identified as a radial
mode and f2 as non-radial. Whereas no significant
variations are found in the amplitude of f1 from season to season,
the amplitude of f2 changes strongly. Moreover, the main period
has remained constant since 1990, within the observational uncertainties.
Additional secondary frequencies may also be excited in this variable.
Key words: stars: variables: Sct - stars: individual: V2109 Cyg -
stars: oscillations - techniques: photometric, spectroscopic
V2109 Cyg (
,
F0) is a pulsating star discovered by the Hipparcos
satellite (ESA 1997). It has a period of
and full amplitude
.
However,
the type of variability has been subject of controversy during the last few
years: in the Hipparcos catalogue it is identified as an RRc-type variable,
but Kazarovets et al. (1999) proposed a
Sct-type
classification whereas
Kiss et al. (1999) claimed again this star as an RRc
pulsator. Finally, Rodríguez et al. (2000)
re-classified this star
as a
Sct variable on the basis of its period and its Strömgren
photometric indices. The importance of this topic arises from the fact that
if this star is an
RR Lyr-type pulsator, it would be the RR Lyr-type variable with the
shortest period known up to date. In order to clarify this point new
photometric and spectroscopic observations have been carried out.
The photometric observations were collected through the years 1999 to 2001 at
Sierra Nevada Observatory (SNO), Spain (
measurements
using the 0.9 m telescope) and in 2000 at San Pedro Mártir
Observatory (SPMO), Mexico
(uvby photometry using the 1.5 m telescope). Both telescopes are
equipped with identical six-channel
spectrophotometers
for simultaneous measurements in uvby or in the narrow and
wide H
channels (Nielsen 1983).
HD 189013 (
,
A2) was used as main comparison star with HD 191022
(
,
G0) as check star. The latter was used as comparison star by
Kiss et al. (1999). Additionally, a few
data
of HD 193701 (
,
F5IV) were also collected at SNO for calibration
purposes. Table 1 lists the journal of the photometric observations.
In the present work no variations, within our
observational errors, were found for any of the comparison stars. No
noticeable nightly zero-point shifts nor short-period periodicities are
present. The mean
values obtained for the C2-C1 differences on each of the nights were always
the same within 0
002, as standard deviation, for any of the vby
filters and 0
004 in the u band. Moreover, when Fourier analyses
are perfomed, no significant peaks are detected in the spectra. No
periodicities with amplitudes larger than about 1.5 mmag are present.
In order to transform our instrumental magnitude
differences into the standard
system, we have used the procedure described in
Rodríguez et al. (1997). The agreement found between the
derived standard
differences from the two observatories was very good among each other and with
those found in the different catalogues available in the
bibliography (Olsen 1983, 1996; Hauck & Mermilliod 1998).
However, large
discrepancies are found for the derived values of V2109 Cyg with respect
to the values published in Kiss et al. (1999),
especially in the m1 and c1 indices.
This seems to be very probably due to calibration problems by these authors
as will be seen in Sect. 4. Our determined standard magnitude differences
of V-C1 versus Heliocentric Julian Day have been deposited
in the Commission 27 IAU Archives of Unpublished Observations, file 350E,
and can also be requested from the authors.
In addition, one high resolution (42 000) spectrum of V2109 Cyg was obtained on October 6, 2000 with the 1.93 m telescope of the Haute-Provence Observatory (France). This telescope is equipped with the echelle spectrograph ELODIE. Details of the instrument are described by Baranne et al. (1996). The spectrum was reduced using the spectroscopic data reduction tasks of the IRAF package.
Table 1: Journal of observations.
Period analysis, using the classical O-C method, was performed with
the new times of maximum derived in the present work together with those
determined by Kiss et al. (1999). The new times of maximum
were
calculated as an average over the three vby bands following the method
described in Rodríguez et al. (1990). If we use a linear
ephemeris, with a period of 0
186049 (from Kiss et al. 1999),
to
phase our data (time span of 1.43 years), we can see that this period does not
work well, suggesting that the true period needs to be longer.
In fact, a new
linear ephemeris with origin in
)
and period
)
was derived in our O-C analysis with the
residuals randomly distributed around zero, as listed in Table 2. This new
value is in very good agreement
with that of 0
1860656 given by the Hipparcos catalogue (ESA 1997)
using
the data collected by this satellite between the years 1990 to 1993.
Thus, it suggests that the main period of V2109 Cyg
has remained constant since 1990 and no sudden period decrease has occurred
between 1991 and 1998, as mentioned by Kiss et al. (1999).
In fact, when a
Fourier analysis is performed to the V+y data of these authors, a
main peak at f=5.3746 cd-1 (that is, period of 0
186060) is found in
good agreement with our results.
On the other hand,
from Table 2 we see that the residuals are too large
(standard deviation of the fit is 0
0040) as compared with the estimated
times of maximum error bars (
0
0007). This means
that a secondary period is probably present in the light curves. This agrees
well with the differences found between the light curves obtained
in different nights, as shown in Fig. 1 for the individual light curves
obtained at &O.
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Figure 1: Nightly light curves of V2109 Cyg collected at San Pedro Mártir Observatory during seven nights in September, 2000. Different symbols correspond to different nights. |
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Table 3: Frequencies and amplitude signal/noise ratios obtained for each uvby filter.
Table 4: Results from the Fourier analysis applied to the uvby data collected in the year 2000.
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Figure 2: Power spectra in the v band before and after removing the frequencies detected in the Fourier analysis. |
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Figure 3: Light curves phased for each frequency after removing the other. Top panel: for f1. Bottom panel: for f2. |
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This was confirmed when a Fourier analysis was made of our data collected in the year 2000 (our largest data set), following the method described in Rodríguez et al. (1998). When the v filter was analysed, a main peak was found at f1=5.3745 cd-1. A secondary peak was also detected at f2=5.8332 cd-1 after f1 and its first harmonic (2f1) were removed from the spectra. The corresponding power spectra are shown in Fig. 2. When these peaks are extracted, no new significant periodicities are present in our data. Similar results were obtained in the other filters.
Table 3 lists the amplitude signal/noise (S/N) ratios obtained for each of the frequencies and filters, following Handler et al. (1996). As shown, the three peaks are intrinsic of the variable (Breger et al. 1993, 1996). Figure 3 shows the 2000 data set phased for each frequency after prewhitening of the other one. The results of the Fourier analysis are listed in Table 4. The amplitude ratios and phase shifts determined for different colours indicate that the secondary peak is also due to pulsation.
From Table 4 it can also be seen that the residuals in vby are smaller when the wavelength is larger. This suggests that more frequencies are remaining. This is also supported by the fact that these residuals are much larger than the white noise found for the C2-C1 spectra (e.g., in the filter v we have 8.7 mmag for V-C1, but only 3.1 mmag for C2-C1) taking into account that C2 and the variable are of similar brightness.
The existence of f2 is also confirmed when the 2000 data sets collected at SPMO and SNO are independently analysed. However, this cannot be found with our 1999 or 2001 data sets, because both the number of points and hours of observation are insufficient.
In order to investigate the existence of f2 in other data sets, the measurements collected in 1998 by Kiss et al. (1999), in both Strömgren and Johnson photometry, were analysed. The V and y data were merged and then investigated by means of Fourier analysis. The main peak was found at 5.3746 cd-1 in good agreement with our results. When this frequency and its first harmonic were removed from the spectra, no new peaks were present with amplitudes larger than 6.0 mmag. Similar results are found when the vby and BV data are analysed separately. Table 5 shows the results of the Fourier fitting when f1=5.3745 cd-1 and 2f1 are simultaneously extracted. Hence, f2 is not significant in these data sets, but the vby residuals decrease from filters v to b and y suggesting that some periodicities are still remaining in the light curves. In the case of the BV data, the noise level in the V filter is too high dominating over the eventually remaining signals.
The Hp data collected by the Hipparcos satellite (ESA 1997) were also
investigated. The main peak is detected at
5.3745 cd-1 together with its first harmonic. When f1 and 2f1 are
removed from the amplitude spectra, a flat spectrum remains
with a level of
about 6.0 mmag and no new peaks are detectable. The results of the fitting
are listed in Table 5. The amplitude of f1 in Hp magnitudes is of
) mmag which means an amplitude in the Johnson V filter of
) mmag (Rodríguez 1999).
In summary, the secondary frequency f2=5.8332 cd-1 seems to be well established in the measurements obtained during the year 2000 with an amplitude of 10 mmag in the y=V filter. However, its existence has not been proven in the data collected during 1998 by Kiss et al. (1999) nor during the interval 1990-1993 by the Hipparcos satellite (ESA 1997). If this frequency is present in these data sets, it should be with an amplitude smaller than about 6 mmag. On the other hand, no significant variations are found in the amplitude of the main frequency f1=5.3745 cd-1.
Moreover, the corresponding period ratio P2/P1=0.92 indicates that at least one of the two frequencies corresponds to a nonradial mode. From Table 4, we can also see that the phase differences between the light curves in v and y or b and y are positive for f1 and negative for f2, suggesting that the main frequency corresponds to a radial mode while f2 is nonradial (Garrido et al. 1990). This is also supported by the observed phase shifts between b-y and y. Despite the error bars being too large in the Fourier fitting of the 1998 data sets (Table 5), the observed phase shifts seem to confirm that f1 corresponds to a radial mode.
This resembles the high amplitude Sct
star RY Lep, where besides the main radial mode of constant amplitude, a
secondary non-radial mode with variable amplitude within a time scale of years
has been recently detected (Laney et al. 2003).
Indeed, the secondary
frequency is not detectable in some observing runs. Secondary frequencies with
variable amplitudes are also detected in the medium amplitude
Sct-type
star AN Lyn (Zhou 2002) and strong amplitude variations of the
main frequency
are also found in the low amplitude
Sct variable 28 And
(Rodríguez et al. 1998) where the secondary frequency is
commonly below the limit of photometric detectability.
Table 6:
uvby
indices obtained for V2109 Cyg and comparison
stars. The pairs below the star names are the number of points collected
for each object in uvby and
,
respectively. For comparison,
the values available from the bibliography are listed in the bottom part.
The values listed for the variable are "mean values'' based on the
normal points along the cycle (Table 7). For this star,
the comparison with the earlier available Strömgren indices (bottom part)
must be made at phase 0.15 where the indices are, according to Table 7:
,
,
and
.
With the aim of deriving the uvby
indices for each of
the stars observed in the present work, we followed the method described
in Rodríguez et al. (2003).
Thus, we use the uvby
indices
listed in earlier catalogues for each of the three comparison
stars as zero-points and then, derive the indices for the remaining
objects. In the case of C1 and C3, the more homogeneous catalogue of Olsen
(1996) was used,
but that of Hauck & Mermilliod (1998) was chosen for C2
(this star was not available in the former catalogue).
The corresponding values
are listed in the lower part of Table 6. The new derived indices for each
of the comparison stars are presented in the upper part
of the same table together with the number of points collected and
the errors, as the standard deviations of the magnitude differences relative
to C1. Good agreement is found between our derived indices and
those found in earlier catalogues. This is
also true when we compare with the values of C1 and C3 given in the other
available lists of Olsen (1983) and Hauck & Mermilliod (1998).
In the case of V2109 Cyg, we list the mean values over the pulsation cycle based on the normal points of Table 7 (the large sigma values are due to the intrinsic variation of the star). These normal points were calculated according to the standard magnitude differences of V-C1 and the indices derived for C1. As it can be seen, some discrepancies seem to be present for the V and c1 values of V2109 Cyg as compared with the indices in the literature (Olsen 1996). However, these indices are based in a few points obtained by Olsen (1983) during only one night and the corresponding phase is unknown, but very probably near the light maximum. In fact, if we compare with our normal points at phase 0.15 (Table 7), the agreement is very good.
The indices listed in Table 6 for each of the comparison stars are also in good
agreement with the spectral types published in the literature
(Simbad 2002).
They indicate that C1 is placed inside the Sct instability region
whereas C2 and C3 are too cool to be both
Dor or
Sct-type pulsators.
Table 8: Reddening and derived physical parameters for V2109 Cyg.
The V light and colour index variations over the main pulsational cycle
were phased in Fig. 4 according to the linear ephemeris derived in Sect. 3.
Normal points every 0.05 units of phase were calculated and
listed in Table 7. Their standard errors are typically of 0
002,
0
001, 0
001, 0
003 and 0
004 in V, b-y, m1, c1 and
,
respectively. The method described in Rodríguez et al.
(2001) was used to estimate the physical parameters of
V2109 Cyg and their
variation along the pulsation cycle. Thus, using the Crawford's
(1979) calibrations,
the reddening can be derived by comparing
the intrinsic and observed b-y values at normal points along the cycle.
In this way, a mean colour excess of
)
is
obtained. The results are summarized in Table 8 indicating
that this star is a normal Population I
Sct-type variable with
approximately solar metal abundances and slightly evolved.
The location of V2109 Cyg in the H-R diagram is shown in Fig. 5, together
with the sample of known
Sct-type variables.
In deriving its luminosity,
the obtained photometric value (Mv(ph) = 1
39(
0.3)) and
the one determined from
its Hipparcos parallax (Mv(
) = 0
88(
0.27), ESA 1997)
were averaged.
The metal content [Me/H]
was calculated from the
m1 parameter
at minimum light (phases between 0.5 and 0.7) where the metal lines are
strongest and m1 is most sensitive to abundance differences. In this
case
m1
and a value of
is
obtained using the Smalley's (1993)
calibration for metal abundances.
Figure 6 presents the changes in effective temperature
and surface gravity in a (c1, b-y) versus (
,
)
grid for
(Smalley & Kupka 1997). If the evolutionary tracks
for Z=0.02 from Claret (1995) are used, the position of the star is
close to the overall contraction phase. Assuming the star is still in the main
sequence stage, a mass of
)
and an age of
) Gyr are estimated. If the star had already evolved off the main
sequence, values of 2.00
and 1.4 Gyr are found.
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Figure 4: Light and colour phase diagrams over the main pulsation cycle. |
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Figure 5:
Location of V2109 Cyg (star) in the H-R
diagram together with the sample of ![]() ![]() |
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The above conclusion on the Sct nature of V2109 Cyg is also supported
by the behaviour of the m1 index along the pulsational cycle.
The metallicity of this variable can also be derived using the observed
variation of the m1 index over the pulsation cycle (Rodríguez et al.
1991).
This variation is slightly reversed with respect to the V light curve,
as shown in Fig. 4, suggesting solar metal abundances for
a star in a similar evolutionary stage as V2109 Cyg (<> =7080 K,
<
> =3.67). The same behaviour is shown in Fig. 1 of Kiss et al.
(1999).
From our data, we find a total variation of
(see
Table 7) along the pulsational cycle (the negative sign means that m1 is
higher when the luminosity or temperature are lower and viceversa). Then, a
variation of 0
012 (in the same sense of the light curve) is found for
the metallicity
m1 parameter
over the pulsation cycle.
This means (the total observed variation in the index
is
= 0
038) a
m1 variation of
0
032 per 0
1 variation in the
index
as shown in Table 9.
This variation is similar to that
found for other high amplitude
Sct stars, in particular RY Lep which
presents
,
<
> = 7010 K and <
> = 3.43
(Rodríguez et al. 1995).
In the case of V2109 Cyg, <> = 2
740 and
<
> = 3.67. Hence, taking into account the observed variation
m1 = -0
002, we find
a metal content of
using the
(
m1*,
)
grids of Rodríguez et al. (1991).
This is in perfect agreement with the value previously obtained
in Table 8.
However, if the value of
= -0.9 (Kiss et al.
1999) is assumed, a
variation of
m1 = +0
012 should be expected over the pulsation
cycle of V2109 Cyg in bad agreement with the observations. Thus, it is
followed that V2109 Cyg is a Population I
Sct-type variable rather
than a RR Lyr star.
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Figure 6:
Observed loop in the (c1, b-y) diagram. ![]() ![]() ![]() |
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Table 9:
Observed metallicity index variation for V2109 Cyg together with
some known high amplitude Sct-type variables from Rodríguez
et al. (1991).
m1* means variation of the
m1 parameter per each 0
1 variation in the
index.
The same conclusion on the nature of V2109 Cyg is also supported by the analysis of abundances carried out on the high resolution spectrum obtained with the echelle spectrograph ELODIE.
Before performing a line synthesis analysis of the spectrum, we
estimated its effective temperature
by comparing the width of H
at residual intensities between 0.7 and 0.9, with those of the
theoretical profiles calculated by Kurucz (1993)
for all gravities. We found
between 6500 and 6800 K as initial values for the synthesis analysis.
We have used ATLAS9 (Kurucz 1993) model atmospheres as an input to the 1997 version of LTE line synthesis program MOOG first described in Sneden (1973). The procedure assumes plane-parallel atmospheres, hydrostatic equilibrium and LTE.
We have worked without prejudice of the RR Lyr or Sct nature
of the star in assigning initial values to log g. We used excitation
equilibrium of Fe I lines to get a preliminary estimate of
,
requiring
that the derived abundances be independent of the lower excitation potential
of the lines, followed by ionisation equilibrium of Fe I/Fe II, Ti I/Ti II
and Cr I/Cr II to arrive at a satisfactory estimate of
and
.
The microturbulence velocity
was estimated by requiring that weak,
medium and strong lines give a consistent value of abundance. The
atmospheric parameters found were
) K,
) dex and
) km s-1 in good agreement with those values
obtained from photometric calibrations (Table 8).
Table 10: Elemental abundances for V2109 Cyg. The solar abundances are taken from Grevesse et al. (1996). N is the number of lines included in the calculation.
The derived elemental abundances are listed in Table 10. The discussion on the uncertainties in the elemental abundances obtained by the above procedure can be found in Arellano Ferro et al. (2001). The errors in [X/H] elemental abundances can be found by dividing the standard deviations by the square root of the number of lines used given in Table 10.
Recently, Kiss et al. (1999) concluded that the star is a
RR Lyr based upon
their Strömgren photometry and a number of empirical calibrations. These
authors estimated
) K,
)
and
). Our detailed atmospheric analysis does
not support
their conclusions. Based on 122 Fe I and 16 Fe II lines cleanly seen in our
high resolution spectrum, we find that V2109 Cyg has solar iron and calcium
abundance, precluding the classification of this object as an RR Lyr star.
Moreover, a mean value of
) dex is obtained from
Table 10
(calculated as an average with weighting according to the corresponding error
bars) in very good agreement with that of
) dex
derived from photometry.
Therefore our abundances analysis of the atmosphere of V2109 Cyg does not
support its classification as an RR Lyr star but confirms
the Sct classification obtained independently on pulsational
arguments.
As s-process elements can only be formed in the hot bottom burning convection region of stars ascending the AGB (e.g. Arellano Ferro et al. 2001), small overabundances of Y, Zr, Ba and Ce in this mildly evolved star are probably explained as an inheritance of the star from the original star-forming cloud.
Acknowledgements
This research was supported by the Junta de Andalucía and the Dirección General de Investigación (DGI) under project AYA2000-1559 and by DGAPA-UNAM (Mexico) under project number IN110102-3. This research has made use of the Simbad database, operated at CDS, Strasbourg, France. Acknowledgements are made to L. L. Kiss for making available his 1998 data sets on V2109 Cyg.