Issue |
A&A
Volume 520, September-October 2010
|
|
---|---|---|
Article Number | L6 | |
Number of page(s) | 4 | |
Section | Letters | |
DOI | https://doi.org/10.1051/0004-6361/201015442 | |
Published online | 28 September 2010 |
LETTER TO THE EDITOR
Evidence for a sharp structure variation inside a red-giant star
A. Miglio1,
-
J. Montalbán1 -
F. Carrier 2 -
J. De Ridder2 -
B. Mosser3 -
P. Eggenberger4 -
R. Scuflaire1 -
P. Ventura5 -
F. D'Antona5 -
A. Noels1 -
A. Baglin3
1 - Institut d'Astrophysique et de Géophysique de l'Université de Liège, 17
Allée du 6 Août, 4000 Liège, Belgium
2 -
Instituut voor Sterrenkunde, K.U. Leuven, Celestijnenlaan 200D, 3001 Leuven, Belgium
3 -
LESIA, UMR8109, Université Pierre et Marie Curie, Université Denis Diderot, Observatoire de Paris, 92195 Meudon,
France
4 -
Observatoire de Genève, Université de Genève, 51 chemin des Maillettes, 1290 Sauverny, Switzerland
5 -
INAF - Osservatorio di Roma, via Frascati, 33 Monteporzio Catone, RM, Italy
Received 21 July 2010 / Accepted 3 September 2010
Abstract
Context. The availability of precisely determined
frequencies of radial and non-radial oscillation modes in red giants is
finally paving the way for detailed studies of the internal structure
of these stars.
Aims. We look for the seismic signature of regions of sharp
structure variation in the internal structure of the CoRoT target
HR 7349.
Methods. We analyse the frequency dependence of the large
frequency separation and second frequency differences, as well as the
behaviour of the large frequency separation obtained with the envelope
auto-correlation function.
Results. We find evidence for a periodic component in the
oscillation frequencies, i.e. the seismic signature of a sharp
structure variation in HR 7349. In a comparison with stellar
models we interpret this feature as caused by a local depression of the
sound speed that occurs in the helium second-ionization region. Using
solely seismic constraints this allows us to estimate the mass (
M=1.2+0.6-0.4 )
and radius (
R=12.2+2.1-1.8
)
of HR 7349, which agrees with the location of the star in an HR diagram.
Key words: asteroseismology - stars: interiors - stars: oscillations - stars: fundamental parameters - stars: individual: HR 7349
1 Introduction
Red giant stars are cool, highly luminous stars. They play a predominant role in stellar, galactic, and extragalactic astrophysics because they serve as distance and age indicators for globular clusters and nearby galaxies (see e.g. Lee et al. 1993; Girardi & Salaris 2001). Moreover their observed chemical composition is a fundamental ingredient in the study of the chemical evolution of their host galaxy (see e.g. Catelan 2009, and references therein).All red giants have an extended and diluted convective envelope
surrounding a dense core, which makes their structure and therefore
their pulsation properties very different from that of our Sun. As in
solar-like stars however, their convective envelope can stochastically
excite acoustic oscillation modes.
While stochastic oscillations have been firmly detected in a few bright
G and K giants since Frandsen et al. (2002), a major breakthrough was achieved thanks to the photometric space-based observations with the CoRoT satellite (Baglin et al. 2006), leading to the unambiguous detection of radial and non-radial oscillation modes in thousands of red giants (De Ridder et al. 2009; Mosser et al. 2010; Hekker et al. 2009; Carrier et al. 2010).
Moreover, the Kepler
space-telescope has also started monitoring red giants for photometric
variations and has already detected radial and non-radial oscillation
modes in a large number of field giants as well as cluster members (Stello et al. 2010; Bedding et al. 2010a).
As the precise detection of oscillation modes in the Sun fostered
helioseismic inferences in the 1990s, we now have the chance to start
probing the internal structure of these cool evolved stars thanks to
the recent advances in observational stellar seismology.
Stellar global acoustic oscillation modes show up in the
frequency spectrum as discrete peaks. While the average spacing between
the frequencies
of modes of the same spherical degree (large frequency separation,
)
represents an estimate of the mean density of the star (Tassoul 1980; Vandakurov 1967), periodic deviations from a constant
are signatures of so-called acoustic glitches, i.e. regions of sharp-structure variation in the stellar interior.
Any localised region of sharp variation of the sound speed c
induces in the frequencies an oscillatory component with a periodicity
related to the sound-travel time measured from that region to the
surface of the star (Vorontsov 1988; Gough 1990). Its amplitude depends on the sharpness of the glitch and decays with
,
because as the frequency increases, the wavelength of the mode becomes
comparable with or less than the extent of the glitch. These sharp
variations are found in zones of rapidly changing chemical composition,
in ionization zones of major chemical elements, or in regions where the
energy transport switches from radiative to convective.
In the Sun, the detection and interpretation of a large number of acoustic oscillation modes led to the determination of the depth of both the solar convective envelope and of the helium second-ionization zone, and allowed us to estimate the helium abundance in the envelope, otherwise inaccessible by other means (see Christensen-Dalsgaard 2002, for a review).
The possibility and relevance of detecting sharp structure variations in other main-sequence stars, as well as first attempts to look for these signatures, have been addressed in several papers in the literature (see e.g. Théado et al. 2005; Monteiro et al. 2000; Monteiro & Thompson 1998; Mazumdar & Antia 2001; Houdek & Gough 2007; Miglio et al. 2003; Mazumdar 2005; Bedding et al. 2010b; Basu et al. 2004; Roxburgh & Vorontsov 1998; Ballot et al. 2004; Perez Hernandez & Christensen-Dalsgaard 1998; Verner et al. 2006).
Here we report on the detection of a sharp-structure variation in the red giant CoRoT target HR 7349 (HD181907), a star with a physical structure very different from the Sun, yet showing global oscillations modes that allow us to probe its internal structure.
2 Evidence for an oscillatory component in the frequency spacings
Carrier et al. (2010) have determined the eigenfrequencies of HR 7349.
They have shown that the first frequency differences
are
modulated. In order to investigate this modulation, we have
analysed these first frequency differences and compared them to
the function
derived from the method developed by
Mosser & Appourchaux (2009). This envelope autocorrelation function (EACF) is
obtained from the auto-correlation of the times series, performed
as the Fourier spectrum of the windowed Fourier spectrum; the
windows are Hanning filters covering the frequency range where
significant excess power is observed. Because the modulation is
rapid, we had to use narrow filters, with a FWHM varying between 1
and 2 times the mean value of the large separation. An EACF
computed with a narrow filter benefits from the low filtering, but
suffers from larger error bars.
Figure 1 shows the large separations for ,
and 2 superimposed on the function
obtained
with a filter width equal to 1.4 times the mean value of the large
separation, which represents an acceptable compromise between the
filtering of the signal and the noise level. We remark that both values
and error bars of
and
closely agree.
The
modulation seen in the function
is present in all
autocorrelations performed with a filter that is narrow enough to respect
the Shannon criterion.
We have detrended the low-frequency gradient of
in order to emphasize the modulation, which is of the order
of
Hz (a period of about
Ms).
That the modulation is seen with two independent methods, is present over more than 2.5 periods, and remains detectable even if a significant level of noise is added to the spectrum makes us confident that the oscillation found in the frequency differences is genuine.
![]() |
Figure 1:
Large separations
|
Open with DEXTER |
The uncertainty of the period
of the oscillatory component was estimated with a Monte Carlo
simulation. We assumed that the frequencies are independent and are
Gaussian-distributed around their observed value with a standard
deviation equal to their 1-
error bar as listed by Carrier et al. (2010).
We then generated 5000 realizations of the frequencies,
computed the frequency differences, and applied a non-linear regression
procedure.
Each time a cost function S, defined as
![]() |
(1) |
was minimized, where y is the matrix of observed frequency differences, V is the covariance matrix of the observed frequency differences, and

![]() |
(2) |
with








3 Interpretation of the oscillatory component
As recalled in Sect. 1,
the periodicity of the component allows us to infer the location of the
glitch in terms of its acoustic depth or in terms of its relative
acoustic radius (as suggested by Ballot et al. 2004). For HR 7349 we find:
,
where t is the sound travel time from the centre to the glitch, and T is the acoustic radius of the star (
).
To interpret this observational evidence, we consider in Fig. 2 the location of acoustic glitches in the structure of red-giant models computed with the code ATON (Ventura et al. 2008).
We find that at about half the acoustic radius the sound speed has a
sharp variation owing to a local depression of the first adiabatic
exponent
in the helium second-ionization zone. We therefore interpret the
periodic component detected in the frequencies of HR 7349 as the
signature of helium second ionization.
This interpretation is further supported by a direct comparison between
observed and numerically computed pulsation frequencies in models of
red giants (see Sect. 4).
![]() |
Figure 2:
a) Behaviour of |
Open with DEXTER |
We notice that while in the Sun and solar-like stars the base of the convective envelope is located at about half the stellar acoustic radius (see Fig. 2), in red giants it is located at a small relative acoustic radius (typically less than 10-1 for the models considered, depending on the mass and evolutionary state).
Furthermore, we find that in the models the relative acoustic radius of the He second-ionization region (
)
and the average
determine the mass and radius of the star (see Fig. 3).
We ascribe this dependence to the the fact that the temperature
stratification in the envelope of red-giant stars depends mostly on M and R (see e.g. Kippenhahn & Weigert 1990); a thorough discussion on this topic will be reported in detail in a forthcoming paper.
On the basis of seismic constraints only, we can thus derive from Fig. 3 the mass of HR 7349 (
M= 1.2+0.6-0.4 )
and, through the scaling of
with the mean stellar density, its radius (
R= 12.2+2.1-1.8
).
Because the parallax of this nearby red giant is known, an independent
radius estimate of HR 7349 can be obtained via the precise
absolute luminosity and effective temperature (Carrier et al. 2010), leading to
,
in agreement with the seismically inferred radius. We also notice that
the mass and radius estimates are also compatible to those obtained by
the combination of the frequency corresponding to the maximum
oscillation power (
),
,
and
(Carrier et al. 2010).
![]() |
Figure 3:
Behaviour of the relative acoustic radius of the second helium ionization region (
|
Open with DEXTER |
4 Direct comparison with numerically computed oscillation frequencies
We consider a red giant model of 1.2
and 12
computed with the stellar evolutionary code ATON (Ventura et al. 2008). The model has an initial helium mass fraction Y=0.278 and a heavier-elements mass fraction Z=0.02. For this model we computed adiabatic oscillation frequencies of spherical degree
and 2 in the domain 15-40
Hz with an Eulerian version of the code LOSC (Scuflaire et al. 2008).
In a red giant model, differently from the Sun, non-radial
oscillation modes in the frequency domain of solar-like oscillations (Kjeldsen & Bedding 1995) are expected to have a mixed pressure and gravity nature. In the model we considered (see Fig. 3) the spectrum of
and 2 modes is mostly populated by modes with a dominant gravity-like
behaviour. These modes exhibit a high inertia compared to radial modes,
and therefore show surface amplitudes significantly smaller than the
purely acoustic radial modes (Eggenberger et al. 2010; Dupret et al. 2009; Christensen-Dalsgaard 2004; Dziembowski et al. 2001).
Nonetheless, among this large number of non-radial oscillation modes,
few modes are efficiently trapped in the acoustic cavity of the star
and have inertias similar to those of radial modes (see Fig. 4).
We then compute
and
by selecting radial modes and the
modes corresponding to local minima in the inertia, hence strongly
trapped in the acoustic cavity. We find an average value of the large
frequency separation of 3.4
Hz and clear periodic components in
(open squares in Fig. 5) and
.
The comparison between the model and observed frequency separations clearly supports the interpretation that the periodic component is caused by the local depression in the sound speed in the second helium ionization zone. This feature is well represented by current models that have a mass and radius determined from the periodicity of the component and the average value of the large frequency separation (see Fig. 3).
![]() |
Figure 4:
Mode inertias of radial modes (full dots), |
Open with DEXTER |
We notice that the periodic component related to the He
second-ionization zone is expected to have an amplitude decaying with
frequency, as shown in numerically computed frequencies (open squares
in Fig. 5) and in analytical approximations (Monteiro & Thompson 1998; Houdek & Gough 2007). Although current error bars are too large to draw a firm statement, the amplitude of the observed component computed with
and 1 modes seems to show the expected behaviour, while we notice that the observed
modes show a larger scatter.
5 Conclusions
In summary, we have shown that the acoustic pulsation modes detected by CoRoT in the red giant star HR 7349 bear the signature of a sharp-structure variation inside the star. Comparison with stellar models allows us to interpret this feature as caused by a local depression of the sound speed occurring in the helium second-ionization region.![]() |
Figure 5:
Open squares represent
|
Open with DEXTER |
Besides representing the first seismic inference of a local feature
in the internal structure of an evolved low-mass star, this detection
allows a mass (
M=1.2+0.6-0.4 )
and radius (
R=12.2+2.1-1.8
)
estimate based solely on seismic constraints. Moreover, for this nearby
star, we could also check that our radius estimate is compatible with
the one based on luminosity and effective temperature (
).
This additional test reinforces the proposed interpretation and
approach, which could be applied to the thousands of pulsating giants
of unknown distance that are currently being observed with the space
satellites CoRoT (see Hekker et al. 2009 and; in particular, Fig. 6 in Mosser et al. 2010) and Kepler (Bedding et al. 2010a; Borucki et al. 2010; Gilliland et al. 2010).
A reliable seismic estimate of the mass and radius of these stars would
represent an essential ingredient for stellar population studies (Miglio et al. 2009) and for characterizing planets orbiting around these evolved distant stars (see e.g. Hatzes & Zechmeister 2007).
We finally recall that the detectability of the signature of He ionization can potentially lead us to a seismic estimate of the envelope helium abundance in old stars. Indeed, as shown for the Sun and solar-like stars, the amplitude of the periodic component depends on the envelope helium abundance (see e.g. Basu et al. 2004; Houdek & Gough 2007, and references therein). While CoRoT and Kepler observations will provide other targets and further reduce the uncertainty on the oscillation frequencies, a thorough study on the required precision in terms of seismic and non-seismic observational constraints, as well as and in terms of models, should be undertaken to aim for reliable seismic estimate of the envelope helium abundance in giants.
AcknowledgementsJ.M. acknowledges the Belgian Prodex-ESA for support (contract C90310). F.C. is a postdoctoral fellow of the Funds for Scientific Research, Flanders (FWO).
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Footnotes
- ...
- Postdoctoral Researcher, Fonds de la Recherche Scientifique - FNRS, Belgium.
- ... CoRoT
- The CoRoT space mission, launched on December 27th 2006, has been developed and is operated by CNES, with the contribution of Austria, Belgium, Brazil, ESA (RSSD and Science Programme), Germany and Spain.
- ... exponent
-
, where p,
, and s denote pressure, density, and specific entropy.
All Figures
![]() |
Figure 1:
Large separations
|
Open with DEXTER | |
In the text |
![]() |
Figure 2:
a) Behaviour of |
Open with DEXTER | |
In the text |
![]() |
Figure 3:
Behaviour of the relative acoustic radius of the second helium ionization region (
|
Open with DEXTER | |
In the text |
![]() |
Figure 4:
Mode inertias of radial modes (full dots), |
Open with DEXTER | |
In the text |
![]() |
Figure 5:
Open squares represent
|
Open with DEXTER | |
In the text |
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