Issue |
A&A
Volume 507, Number 1, November III 2009
|
|
---|---|---|
Page(s) | L13 - L16 | |
Section | Letters | |
DOI | https://doi.org/10.1051/0004-6361/200913111 | |
Published online | 21 October 2009 |
A&A 507, L13-L16 (2009)
LETTER TO THE EDITOR
A fresh look at the seismic spectrum of
HD49933: analysis of 180 days of CoRoT photometry
,![[*]](/icons/foot_motif.png)
O. Benomar1 - F. Baudin1 - T. L. Campante2,3 - W. J. Chaplin4 - R. A. García5 - P. Gaulme1 - T. Toutain6 - G. A. Verner7 - T. Appourchaux1 - J. Ballot8 - C. Barban9 - Y. Elsworth4 - S. Mathur10 - B. Mosser9 - C. Régulo11,12 - I. W. Roxburgh7 - M. Auvergne9 - A. Baglin9 - C. Catala9 - E. Michel9 - R. Samadi9
1 - Institut d'Astrophysique Spatiale, CNRS, Université Paris XI, 91405
Orsay, France
2 - Danish AsteroSeismology Centre (DASC), Department of Physics and
Astronomy, University of Aarhus, 8000 Aarhus C, Denmark
3 - Centro de Astrofísica da Universidade do Porto, Rua das Estrelas,
4150-762 Porto, Portugal
4 - School of Physics and Astronomy, University of Birmingham,
Edgbaston, Birmingham B15 2TT, UK
5 - Laboratoire AIM, CEA/DSM-CNRS, Université Paris Diderot, IRFU/SAp,
Centre de Saclay, 91191 Gif-sur-Yvette, France
6 - Center for Information Technology, University of Oslo, PO Box 1059
Blindern, 0316 Oslo, Norway
7 - Astronomy Unit, Queen Mary, University of London Mile End Road,
London E1 4NS, UK
8 - Laboratoire d'Astrophysique de Toulouse-Tarbes, Université de
Toulouse, CNRS, 31400 Toulouse, France
9 - LESIA, UMR8109, Université Pierre et Marie Curie, Université Denis
Diderot, Observatoire de Paris, 92195 Meudon, France
10 - Indian Institute of Astrophysics, Koramangala, Bangalore 560034,
India
11 - Instituto de Astrofísica de Canarias, 38205 La Laguna,
Tenerife, Spain
12 - Universidad de La Laguna, Dpto de Astrofísica, 38206
La Laguna, Tenerife, Spain
Received 12 August 2009 / Accepted 15 October 2009
Abstract
Context. Solar-like oscillations have now been
observed in
several stars, thanks to ground-based spectroscopic observations and
space-borne photometry. CoRoT, which has been in orbit since December
2006, has observed the star HD49933 twice. The oscillation spectrum of
this star has proven difficult to interpret.
Aims. Thanks to a new timeseries provided by CoRoT,
we aim to
provide a robust description of the oscillations in HD49933,
i.e.,
to identify the degrees of the observed modes, and to measure mode
frequencies, widths, amplitudes and the average rotational splitting.
Methods. Several methods were used to model the
Fourier
spectrum: Maximum Likelihood Estimators and Bayesian analysis using
Markov Chain Monte-Carlo techniques.
Results. The different methods yield consistent
result, and
allow us to make a robust identification of the modes and to extract
precise mode parameters. Only the rotational splitting remains
difficult to estimate precisely, but is clearly relatively large
(several Hz
in size).
Key words: stars: oscillations
1 Introduction
Stars are now the objects of seismic studies after decades of similar
studies for the Sun, thanks to the advent of space-borne photometric
observations (e.g., MOST, CoRoT and Kepler) and extremely precise
ground-based spectroscopic observations (for a complete review, see for
e.g. Aerts
et al. 2008). This applies in particular to
stars presenting solar-like p modes (acoustic oscillations
stochastically excited by convection), with CoRoT observations of such
stars showing clearly individual peaks in the Fourier spectra
(e.g. Michel et al.
2008). Among these stars, HD49933 has already been
the target of asteroseismic campaigns. It was first observed
spectroscopically from the ground for 10 nights (Mosser et al.
2005). In
2007, a first photometric time series of 60 days was collected
by
CoRoT, followed by a new long run of 137 days in 2008. HD49933
is a F5
main sequence star with an apparent visual magnitude .
It
is hotter than the Sun (
K or
K,
Ryabchikova
et al. 2009; Bruntt
2009; Bruntt
et al. 2008) with an estimated mass of
(Mosser
et al. 2005) and an estimated radius of
(Thévenin
et al. 2006). The surface rotation (
)
was determined to be around 10 km s-1(Mosser
et al. 2005; Solano
et al. 2005). The surface rotation period has also
been
measured at
3.4 days,
using the 60-day CoRoT timeseries
(Deheuvels
et al. 2008; Appourchaux
et al. 2008), from the signatures of photospheric
transiting active regions (e.g., spots) which give rise to a clear
peak in the very low-frequency part of the Fourier spectrum.
![]() |
Figure 1: Mean power spectrum using 3 time series of 60 days (solid grey line), and the fitted model (dashed line). |
Open with DEXTER |
The seismic interpretation of HD49933 has proven to be very difficult. Mosser et al. (2005) could not isolate individual p modes in the Fourier spectrum of observed line-of-sight velocities but were able to find a regular pattern in the spectrum, which is the signature of the large frequency separation between modes of same degree l(but increasing radial order n). The first CoRoT time-series was analysed by Appourchaux et al. (2008), and these data clearly show individual p-mode peaks in the Fourier spectrum. However, the peaks show large widths, making the interpretation less than straightforward: a given peak could be interpreted as being a closely spaced pair of l = 0 and l = 2 modes, or a single (but rotationally split) l = 1 mode. Based on the modeling of the spectrum using a Maximum Likelihood Estimator fitting method, Appourchaux et al. (2008) chose one of these two possible interpretations (hereafter called model A) based on the highest likelihood of each model. This first time-series was the object of other studies. Appourchaux et al. (2009) put into perspective the results of Appourchaux et al. (2008), showing that the likelihood ratio test does not give the probability of the hypothesis given the data, but only the significance of the data given the hypothesis. Benomar et al. (2009), who applied a Bayesian analysis to the same time series, could not definitely favour one interpretation (model A) over the alternate (model B), based on the whole probability distribution of each model. Gruberbauer et al. (2009), using a Bayesian approach too, also consider the identification ambiguous. Gaulme et al. (2009) used a simpler Bayesian approach (Maximum A posteriori, or MAP, approach). The most probable model they found corresponds to the same identification as Appourchaux et al. (2008). More recently, Mosser & Appourchaux (2009) proposed an empirical method to determine the identification of the modes. Its application considers the model B as the more likely when using the two datasets used here.
It should be noted that the case of HD49933 is quite different
from
the solar case: solar modes are very narrow in comparison. Their widths
(1 Hz
for the modes with the highest amplitudes) are much smaller than the
small-frequency separations between l = 0 modes of
order n and the neighbouring l
= 2 modes of order n -1 (being typically around
10
Hz
for the Sun). Moreover, the star inclination angle, if small, tends to
attenuate the visibility of mode components with azimutal order
,
making the mode identification even more difficult.
Here, we use the new long-run CoRoT observations of HD49933, together with the original shorter run timeseries (Fig. 7), in order to properly describe the acoustic oscillations of the star clearly visible in the Fourier spectrum (Fig. 1, Figs. 5 and 8).
2 Methodology
The time series used here were extracted in the same way as in
Appourchaux
et al. (2008). The gaps in the series represent
slightly less than 10% and were filled by linear interpolation.
In order to provide a robust seismic interpretation of the CoRoT
timeseries for HD49933, several analyses were performed, using
different methods (Maximum Likelihood Estimators, or MLE; and various
Bayesian analyses); or the same method applied in an independent
manner. These methods were already used in the same way to analyze the
initial run of 60 days (Benomar
et al. 2009; Appourchaux
et al. 2008). The ``fitters'' of Appourchaux
et al. (2008) and some additional fitters sought to
find a best-fitting model
spectrum. The model has several contributions. There is a contribution
from the background, which includes signatures of convection and
possibly
phenomena with longer time scales (e.g. those related to the stellar
activity) and contributions from the individual p modes. Each mode is
described by a set of parameters: a central frequency, a width and a
height. A single height and width was fitted to each l=0/2
pair and
the closest l=1 mode (in frequency). The relative
heights of the
l = 0, 1 and 2 modes took fixed values,
which were assumed to be
independent of frequency. A single rotational frequency splitting
parameter was fitted to all non-radial modes. The
stellar
inclination, which governs the relative heights of the different mcomponents
for a given (n, l) mode, was
also fitted as a single,
global parameter. The observed spectrum used by the different fitters
was an averaged spectrum (frequency resolution 0.19 Hz) made
from three timeseries of the same duration, which came from the two
CoRoT runs: the first 60-day run, IRa01, and two 60-day long
timeseries from the longer second run, LRa01 (data available at idoc-CoRoT.ias.u-psud.fr).
The different fitters analysed this
spectrum independently, and we then compared the results.
3 Results
The availability of the new longer CoRoT timeseries makes the mode
(degree l) identification significantly less
ambiguous than it was
before. The p-mode peaks are still observed to be very wide (several
Hz), and the
typical signal-to-noise ratio (SNR) (defined as the
ratio of the height of a mode to the level of the background around
the mode) is similar to that for the first, shorter CoRoT
run. However, the additional information provided by the longer second
run is sufficient to allow the modes to be tagged with far greater
confidence than was hitherto possible. There was a very good agreement
between the results of the fitters, with model B (which has an l
= 1mode at 1755
Hz;
see Table 1
for details) favoured
strongly over Model A.
Table
1:
Frequencies of the fitted modes. The 1 and 2-intervals correspond to
confidence levels of 68% and 95%,
respectively.
We also established, using the Bayesian approach, that models that include l=2 modes are strongly favoured over those which do not (at a confidence level over 99.9%). To check for evidence in the Fourier spectrum of l=3 modes, we instead used a collapsed spectrum. We could find no evidence for a significant excess of power in the wings of the l=1 modes. Evidently, the SNR in the l=3 modes is too low for them to be observed.
We make one final remark regarding the identification problem. Appourchaux et al. (2008), who favoured model A, made their choice based solely on a comparison of the maximum likelihoods given by a classical MLE analysis. When the fitting problem is non-trivial, this type of analysis can converge on a subsidiary maximum (not the true, global maximum), biasing any statistical comparison of two possible models. In addition to MLE, we also applied for the work in this paper the Markov Chain Monte-Carlo (MCMC) analysis, which circumvents the above problem by giving a complete sampling of the parameter space. Both MCMC and MLE now clearly favour Model B. The present results are due to the conjunction of two facts. First, the extra information provided by the new observations (adding 137 days to the first 60 days of observation). Second, the confirmation given by the use of Bayesian analysis about a robust comparison of the associated probabilities to each model. All this ensures the identification without ambiguity, whatever the method used.
Most of the frequencies for model B returned by the different fitters
lie within a 1-
error interval (which corresponds to a level
of confidence of 68%), and all do so within a 1.5-
interval. These error
intervals are particularly small in the
frequency range
where the modes
have relatively large heights. Agreement is particularly good at l
= 1(
Hz; see
Fig. 9).
This is because these modes are not affected by prominent nearby modes,
as is the case for the closely spaced l=0 and
2 modes (which show
significant overlap in frequency). The l=2 modes
have lower
amplitudes than their l=0 neighbours and
consequently have the
largest errors of any of the observed l (
Hz,
see Fig. 9).
Table 1
lists Model B frequencies from one of the
analyses used here (a Bayesian analysis coupled to MCMC
sampling; see for example Benomar
et al. 2009). The échelle diagram of
these frequencies is shown in Fig. 3. From
the most
reliable l = 0 and l = 1 modes,
it is possible to estimate the large
frequency separations
and
and their variation
with frequency (see Fig. 2). The
uncovered frequency
variation may be regarded as being significant, given the good
precision on the estimated frequencies. Any estimate of the frequency
difference
between neighbouring l = 0 and l
= 2 modes is
much less reliable because of the difficulty of fitting these modes
(see above). Thus, the only result that can be provided is the
average:
Hz.
![]() |
Figure 2: Large frequency separation computed from l = 0 (crosses linked by a dashed line) and l = 1 (diamonds linked by a solid line) modes. |
Open with DEXTER |
The widths of the modes, which are related to the damping, are also
listed in Table 1
and shown in Fig. 4.
This
figure illustrates the main difficulty of interpreting the spectrum:
the relatively high values of the widths. As on the Sun, an increase
in width with increasing frequency is visible, but the level of
precision prevents a more detailed analysis. The amplitudes of the
modes, which depend on the balance between damping and excitation, are
listed in Table 1.
The l=0 amplitudes are plotted in
Fig. 6.
The maximum is about 3.7 ppm,
which, while
higher than the maximum amplitude of low-l solar
oscillations, is
still lower than predicted by a scaling of amplitude on
(with
0.7,
see Samadi et al.
2007). Extraction of the rotational frequency splitting,
,
of the modes remains very difficult: the analyses of the
different fitters failed to converge on a unique solution. Estimated
values were in the range
Hz
Hz, i.e.,
high
compared to the solar value, but as expected given the surface
rotation period estimated from the low-frequency part of the Fourier
spectrum (
days).
Finally, we were able to extract robust values for the angle of
inclination of the star. All analyses converged on an angle of of
.
This is in agreement with an independent determination made using
measurements of the stellar
,
radius and period (Solano et al.
2005; Mosser
et al. 2009). However, as mentioned earlier, such a
small angle greatly favours the visibility of m=0
mode components, rendering the splitting measurement very difficult.
![]() |
Figure 3:
Echelle diagram built from the fitted frequencies for a large
separation of 85 |
Open with DEXTER |
![]() |
Figure 4:
Widths of the fitted modes, with 1 |
Open with DEXTER |
4 Conclusion
The two CoRoT observation runs on the star HD49933 - the first 60-day run, and the more recent longer run - have now provided enough data to resolve the identification of modes in the oscillation spectrum at a very high confidence level. This identification relied on several independent analyses. The new data have also allowed us to improve the precision in the mode parameters, with fractional improvements being in the range from 40% to 70% depending on the parameter. It is now possible to determine precise mode frequencies for l = 0 and 1 modes. The l = 2 mode parameters are more difficult to estimate because of the overlap with the stronger, neighbouring l = 0modes. The widths and amplitudes of the modes are well determined, as is the inclination angle of the star. The rotational frequency splitting remains the only mode parameter that is poorly constrained. However, it is clearly much higher than the solar value, and similar or larger in size to the inverse of the surface rotation period. In summary, this new information on the acoustic oscillations of HD49933 now opens the possibility for detailed seismic modeling of the star.
AcknowledgementsW.J.C. and Y.E. wish to thank the UK Science and Technology Facilities Council (STFC) for support under grant ST/F00204/1. I.W.R. and G.A.V. also thank STFC, for support under grant PP/E001793/1. J.B. acknowledges support through the ANR project Siroco. We thank J. Leibacher for very useful comments.
References
- Aerts, C., Christensen-Dalsgaard, J., Cunha, M., et al. 2008, Sol. Phys., 251, 3 [CrossRef] [NASA ADS]
- Appourchaux, T., Michel, E., Auvergne, M., et al. 2008, A&A, 488, 705 [EDP Sciences] [CrossRef] [NASA ADS]
- Appourchaux, T., Samadi, R., & Dupret, M. A. 2009, A&A, 506, 1 [EDP Sciences] [CrossRef]
- Benomar, O. 2008, Commun. Asteroseismol., 157, 98 [NASA ADS]
- Benomar, O., Appourchaux, T., & Baudin, F. 2009, A&A, 506, 15 [EDP Sciences] [CrossRef]
- Bruntt, H. 2009, A&A, 506, 235 [EDP Sciences] [CrossRef]
- Bruntt, H., De Cat, P., & Aerts, C. 2008, A&A, 478, 487 [EDP Sciences] [CrossRef] [NASA ADS]
- Deheuvels, S., Michel, E., & Mosser, B. 2008, Commun. Asteroseismol., 157, 297 [NASA ADS]
- Gaulme, P., Appourchaux, T., & Boumier, P. 2009, A&A, 506, 7 [EDP Sciences] [CrossRef]
- Gruberbauer, M., Kallinger, T., Weiss, W. W., et al. 2009, A&A, 506, 1043 [EDP Sciences] [CrossRef]
- Michel, E., Baglin, A., Auvergne, M., et al. 2008, Science, 322, 558 [CrossRef] [NASA ADS]
- Mosser, B., & Appourchaux, T. 2009, A&A, accepted
- Mosser, B., Baudin, F., Lanza, A., et al. 2009, A&A, 506, 245 [EDP Sciences] [CrossRef]
- Mosser, B., Bouchy, F., Catala, C., et al. 2005, A&A, 431, L13 [EDP Sciences] [CrossRef] [NASA ADS]
- Ryabchikova, T., Fossati, L., & Shulyak, D. 2009, A&A, 506, 203 [EDP Sciences] [CrossRef]
- Samadi, R., Georgobiani, D., Trampedach, R., et al. 2007, A&A, 463, 297 [EDP Sciences] [CrossRef] [NASA ADS]
- Solano, E., Catala, C., Garrido, R., et al. 2005, AJ, 129, 547 [CrossRef] [NASA ADS]
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Online Material
![]() |
Figure 5:
Echelle diagram computed for a large separation of 85 |
Open with DEXTER |
![]() |
Figure 6:
Amplitude (
|
Open with DEXTER |
![]() |
Figure 7: Lightcurves of HD49933 for the 60-day long initial run ( left) and the 137-day long run ( right). |
Open with DEXTER |
![]() |
Figure 8: Detail of the spectrum (solid grey line), and of the fitted model (dashed line) with a pair l=0/2 on the left and an l=1 on ther right. |
Open with DEXTER |
![]() |
Figure 9:
Mean ( upper and lower) 1 |
Open with DEXTER |
Table
2:
Amplitudes and widths of the fitted modes. The 1-
intervals correspond to confidence levels of 68%.
Footnotes
- ... photometry
- The CoRoT space mission, launched on 2006 December 27, was developed and is operated by the CNES, with participation of the Science Programs of ESA, ESA's RSSD, Austria, Belgium, Brazil, Germany and Spain.
- ...
- Figures 5-9 and Table 2 are only available in electronic form at http://www.aanda.org
All Tables
Table
1: Frequencies of the fitted modes. The 1 and 2-intervals
correspond to confidence levels of 68% and 95%,
respectively.
Table
2: Amplitudes and widths of the fitted modes. The 1-
intervals correspond to confidence levels of 68%.
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