Context. The solar-like pulsator HD 49385 was observed with the CoRoT⋆ satellite over a period of 137 days. The analysis of its oscillation spectrum yielded precise estimates of the mode frequencies ...over nine radial orders and distinguished some unusual characteristics, such as some modes outside the identified ridges in the échelle diagram and that the curvature of the ℓ = 1 ridge differs significantly from that of the ℓ = 0 ridge. Aims. We search for stellar models that can reproduce the peculiar features of the oscillation spectrum of HD 49385. After showing that they can be accounted for only by a low-frequency ℓ = 1 avoided crossing, we investigate the information provided by the mixed modes about the structure of the core of HD 49385. Methods. We propose a toy-model to study the case of avoided crossings with a strong coupling between the p-mode and g-mode cavities in order to establish the presence of mixed modes in the spectrum of HD 49385. We then show that traditional optimization techniques are ill-suited to stars with mixed modes in avoided crossing. We propose a new approach to the computation of grids of models that we apply to HD 49385. Results. The detection of mixed modes leads us to establish the post-main-sequence status of HD 49385. The mixed mode frequencies suggest that there is a strong coupling between the p-mode and g-mode cavities. As a result, we show that the amount of core overshooting in HD 49385 is either very small (0 < αov < 0.05) or moderate (0.18 < αov < 0.20). The mixing length parameter is found to be significantly lower than the solar one (αCGM = 0.55 ± 0.04 compared to the solar value α⊙ = 0.64). Finally, we show that the revised solar abundances of Asplund ensure closer agreement with the observations than the classical ones of Grevesse & Noels. At each step, we investigate the origin and meaning of these seismic diagnostics in terms of the physical structure of the star. Conclusions. The subgiant HD 49385 is the first star for which a thorough modeling has been attempted to reproduce all the properties of an avoided crossing. It has provided the opportunity to show that the study of the coupling between the cavities in these stars can provide valuable insight into open questions such as core overshooting, the efficiency of convection, and the abundances of heavy elements in stars.
Context.
The size of convective cores remains uncertain, despite their substantial influence on stellar evolution, and thus on stellar ages. The seismic modeling of young subgiants can be used to ...obtain indirect constraints on the core structure during main sequence, thanks to the high probing potential of mixed modes.
Aims.
We selected the young subgiant KIC10273246, observed by
Kepler
, based on its mixed-mode properties. We thoroughly modeled this star, with the aim of placing constraints on the size of its main-sequence convective core. A corollary goal of this study is to elaborate a modeling technique that is suitable for subgiants and can later be applied to a larger number of targets.
Methods.
We first extracted the parameters of the oscillation modes of the star using the full
Kepler
data set. To overcome the challenges posed by the seismic modeling of subgiants, we propose a method that is specifically tailored to subgiants with mixed modes and uses nested optimization. We then applied this method to perform a detailed seismic modeling of KIC10273246.
Results.
We obtain models that show good statistical agreements with the observations, both seismic and non-seismic. We show that including core overshooting in the models significantly improves the quality of the seismic fit, optimal models being found for
α
ov
= 0.15. Higher amounts of core overshooting strongly worsen the agreement with the observations and are thus firmly ruled out. We also find that having access to two
g
-dominated mixed modes in young subgiants allows us to place stronger constraints on the gradient of molecular weight in the core and on the central density.
Conclusions.
This study confirms the high potential of young subgiants with mixed modes to investigate the size of main-sequence convective cores. It paves the way for a more general study including the subgiants observed with
Kepler
, TESS, and eventually PLATO.
The detection of mixed modes in red giants with space missions C
O
R
O
T and
Kepler
has revealed their deep internal structure. These modes allow us to characterize the pattern of pressure modes ...(through the measurement of their asymptotic frequency separation Δ
ν
) and the pattern of gravity modes (through the determination of their asymptotic period spacing ΔΠ
1
). It has been shown that red giant branch (RGB) stars regroup on a well-defined sequence in the Δ
ν
− ΔΠ
1
plane. Our first goal is to theoretically explain the features of this sequence and understand how it can be used to probe the interiors of red giants. Using a grid of red giant models computed with
MESA
, we demonstrate that red giants join the Δ
ν
− ΔΠ
1
sequence whenever electron degeneracy becomes strong in the core. We argue that this can be used to estimate the central densities of these stars, and potentially to measure the amount of core overshooting during the main sequence part of the evolution. We also investigate a puzzling subsample of red giants that are located below the RGB sequence, in contradiction with stellar evolution models. After checking the measurements of the asymptotic period spacing for these stars, we show that they are mainly intermediate-mass red giants. This is doubly peculiar because these stars should have nondegenerate cores and they are expected to be located well above the RGB sequence. We show that these peculiarities are well accounted for if these stars result from the interaction between two low-mass (
M
≲ 2
M
⊙
) close companions during the red giant branch phase. If the secondary component has already developed a degenerate core before mass transfer begins, it becomes an intermediate-mass giant with a degenerate core. The secondary star is then located below the degenerate sequence, which is in agreement with the observations.
Context. The detection of mixed modes that are split by rotation in Kepler red giants has made it possible to probe the internal rotation profiles of these stars, which brings new constraints on the ...transport of angular momentum in stars. Rotation rates in the central regions of intermediate-mass core helium burning stars (secondary clump stars) have recently been measured. Aims. Our aim is to exploit the rotational splittings of mixed modes to estimate the amount of radial differential rotation in the interior of secondary clump stars using Kepler data in order to place constraints on angular momentum transport in intermediate-mass stars. Methods. We select a subsample of Kepler secondary clump stars with mixed modes that are clearly rotationally split. By applying a thorough statistical analysis, we show that the splittings of gravity-dominated modes (trapped in central regions) and of p-dominated modes (trapped in the envelope) can be measured. We then use these splittings to estimate the amount of differential rotation by using inversion techniques and by applying a simplified approach based on asymptotic theory. Results. We obtain evidence for a weak radial differential rotation for six of the seven targets that were selected, with the central regions rotating from 1.8 ± 0.3 to 3.2 ± 1.0 times faster than the envelope. The last target is found to be consistent with a solid-body rotation. Conclusions. This demonstrates that an efficient redistribution of angular momentum occurs after the end of the main sequence in the interior of intermediate-mass stars, either during the short-lived subgiant phase or once He-burning has started in the core. In either case, this should bring constraints on the angular momentum transport mechanisms that are at work.
Context.
Asteroseismic measurements of the internal rotation of subgiants and red giants all show the need for invoking a more efficient transport of angular momentum than theoretically predicted. ...Constraints on the core rotation rate are available starting from the base of the red giant branch (RGB) and we are still lacking information on the internal rotation of less evolved subgiants.
Aims.
We identify two young
Kepler
subgiants, KIC 8524425 and KIC 5955122, whose mixed modes are clearly split by rotation. We aim to probe their internal rotation profile and assess the efficiency of the angular momentum transport during this phase of the evolution.
Methods.
Using the full
Kepler
data set, we extracted the mode frequencies and rotational splittings for the two stars using a Bayesian approach. We then performed a detailed seismic modeling of both targets and used the rotational kernels to invert their internal rotation profiles using the MOLA inversion method. We thus obtained estimates of the average rotation rates in the
g
-mode cavity (⟨Ω⟩
g
) and in the
p
-mode cavity (⟨Ω⟩
p
).
Results.
We found that both stars are rotating nearly as solid bodies, with core-envelope contrasts of ⟨Ω⟩
g
/⟨Ω⟩
p
= 0.68 ± 0.47 for KIC 8524425 and ⟨Ω⟩
g
/⟨Ω⟩
p
= 0.72 ± 0.37 for KIC 5955122. This result shows that the internal transport of angular momentum has to occur faster than the timescale at which differential rotation is forced in these stars (between 300 Myr and 600 Myr). By modeling the additional transport of angular momentum as a diffusive process with a constant viscosity
ν
add
, we found that values of
ν
add
> 5 × 10
4
cm
2
s
−1
are required to account for the internal rotation of KIC 8524425, and
ν
add
> 1.5 × 10
5
cm
2
s
−1
for KIC 5955122. These values are lower than or comparable to the efficiency of the core-envelope coupling during the main sequence, as given by the surface rotation of stars in open clusters. On the other hand, they are higher than the viscosity needed to reproduce the rotation of subgiants near the base of the RGB.
Conclusions.
Our results yield further evidence that the efficiency of the internal redistribution of angular momentum decreases during the subgiant phase. We thus bring new constraints that will need to be accounted for by mechanisms that are proposed as candidates for angular momentum transport in subgiants and red giants.
Context. Using asteroseismic techniques, it has recently become possible to probe the internal rotation profile of low-mass (≈1.1−1.5 M⊙) subgiant and red giant stars. Under the assumption of local ...angular momentum conservation, the core contraction and envelope expansion occurring at the end of the main sequence would result in a much larger internal differential rotation than observed. This suggests that angular momentum redistribution must be taking place in the interior of these stars. Aims. We investigate the physical nature of the angular momentum redistribution mechanisms operating in stellar interiors by constraining the efficiency of post-main sequence rotational coupling. Methods. We model the rotational evolution of a 1.25M⊙ star using the Yale Rotational stellar Evolution Code. Our models take into account the magnetic wind braking occurring at the surface of the star and the angular momentum transport in the interior, with an efficiency dependent on the degree of internal differential rotation. Results. We find that models including a dependence of the angular momentum transport efficiency on the radial rotational shear reproduce very well the observations. The best fit of the data is obtained with an angular momentum transport coefficient scaling with the ratio of the rotation rate of the radiative interior over that of the convective envelope of the star as a power law of exponent ≈3. This scaling is consistent with the predictions of recent numerical simulations of the Azimuthal Magneto-Rotational Instability. Conclusions. We show that an angular momentum transport process whose efficiency varies during the stellar evolution through a dependence on the level of internal differential rotation is required to explain the observed post-main sequence rotational evolution of low-mass stars.
Context. First-ascent red giants in the approximate mass range 0.7 ≲ M/M⊙ ≲ 2 ignite helium in their degenerate core as a flash. Stellar evolution codes predict that the He flash consists of a series ...of consecutive subflashes. Observational evidence of the existence of the He flash and subflashes is lacking. The detection of mixed modes in red giants from space missions CoRoT and Kepler has opened new opportunities to search for such evidence. Aims. During a subflash, the He-burning shell is convective, which splits the cavity of gravity modes in two. We here investigate how this additional cavity modifies the oscillation spectrum of the star. We also address the question of the detectability of the modes, to determine whether they could be used to seismically identify red giants passing through the He flash. Methods. We calculate the asymptotic mode frequencies of stellar models going through a He subflash using the Jeffreys-Wentzel-Kramers-Brillouin (JWKB) approximation. To predict the detectability of the modes, we estimate their expected heights, taking into account the effects of radiative damping in the core. Our results are then compared to the oscillation spectra obtained by numerically calculating the mode frequencies during a He subflash. Results. We show that during a He subflash, the detectable oscillation spectrum mainly consists of modes trapped in the acoustic cavity and in the outer g-mode cavity. The spectrum should thus at first sight resemble that of a core-helium-burning giant. However, we find a list of clear, detectable features that could enable us to identify red giants passing through a He subflash. In particular, during a He subflash, several modes that are trapped in the innermost g-mode cavity are expected to be detectable. We show that these modes could be identified by their frequencies or by their rotational splittings. Other features, such as the measured period spacing of gravity modes or the location of the H-burning shell within the g-mode cavity could also be used to identify stars going through a He subflash. Conclusions. The features derived in this study can now be searched for in the large datasets provided by the CoRoT and Kepler missions.
Period spacings in red giants Mosser, B; Vrard, M; Belkacem, K ...
Astronomy and astrophysics (Berlin),
12/2015, Volume:
584
Journal Article
Peer reviewed
Open access
Context Asteroseismology allows us to probe the physical conditions inside the core of red giant stars. This process relies on the properties of the global oscillations with a mixed character that ...are highly sensitive to the physical properties of the core. However, overlapping rotational splittings and mixed-mode spacings result in complex structures in the mixed-mode pattern, which severely complicates its identification and the measurement of the asymptotic period spacing. Aims. This work aims at disentangling the rotational splittings from the mixed-mode spacings in order to open the way to a fully automated analysis of large data sets. Methods. An analytical development of the mixed-mode asymptotic expansion is used to derive the period spacing between two consecutive mixed modes. The echelle diagrams constructed with the appropriately stretched periods are used to exhibit the structure of the gravity modes and of the rotational splittings. Results. We propose a new view of the mixed-mode oscillation pattern based on corrected periods, called stretched periods, that mimic the evenly spaced gravity-mode pattern. This provides a direct understanding of all oscillation components, even in the case of rapid rotation. In this way, the measurement of the asymptotic period spacing and the signature of the structural glitches on mixed modes can be performed easily. Conclusions. This work makes it possible to derive all seismic global parameters in an automated way, including the identification of the different rotational multiplets and the measurement of the rotational splitting, even when this splitting is significantly larger than the period spacing. Revealing buoyancy glitches provides a detailed view of the radiative core.
Context. The Kepler space mission has made it possible to measure the rotational splittings of mixed modes in red giants, thereby providing an unprecedented opportunity to probe the internal rotation ...of these stars. Aims. Asymmetries have been detected in the rotational multiplets of several red giants. This is unexpected since all the red giants whose rotation profiles have been measured thus far are found to rotate slowly, and low rotation, in principle, produces symmetrical multiplets. Our aim here is to explain these asymmetries and find a way of exploiting them to probe the internal rotation of red giants. Methods. We show that in the cases where asymmetrical multiplets were detected, near-degeneracy effects are expected to occur, because of the combined effects of rotation and mode mixing. Such effects have not been taken into account so far. By using both perturbative and non-perturbative approaches, we show that near-degeneracy effects produce multiplet asymmetries that are very similar to the observations. We then propose and validate a method based on the perturbative approach to probe the internal rotation of red giants using multiplet asymmetries. Results. We successfully apply our method to the asymmetrical l = 2 multiplets of the Kepler young red giant KIC 7341231 and obtain precise estimates of its mean rotation in the core and the envelope. The observed asymmetries are reproduced with a good statistical agreement, which confirms that near-degeneracy effects are very likely the cause of the detected multiplet asymmetries. Conclusions. We expect near-degeneracy effects to be important for l = 2 mixed modes all along the red giant branch (RGB). For l = 1 modes, these effects can be neglected only at the base of the RGB. They must therefore be taken into account when interpreting rotational splittings and as shown here, they can bring valuable information about the internal rotation of red giants.
Context. Our poor understanding of the boundaries of convective cores generates large uncertainties on the extent of these cores and thus on stellar ages. The detection and precise characterization ...of solar-like oscillations in hundreds of main-sequence stars by CoRoT and Kepler has given the opportunity to revisit this problem. Aims. Our aim is to use asteroseismology to consistently measure the extent of convective cores in a sample of main-sequence stars whose masses lie around the mass limit for having a convective core. Methods. We first tested and validated a seismic diagnostic that was proposed to probe the extent of convective cores in a model-dependent way using the so-called r010 ratios, which are built with l = 0 and l = 1 modes. We applied this procedure to 24 low-mass stars chosen among Kepler targets to optimize the efficiency of this diagnostic. For this purpose, we computed grids of stellar models with both the Cesam2k and mesa evolution codes, where the extensions of convective cores were modeled either by an instantaneous mixing or as a diffusion process. Results. We found that 10 stars in our sample are in fact subgiants. Among the other targets, were able to unambiguously detect convective cores in eight stars, and we obtained seismic measurements of the extent of the mixed core in these targets with a good agreement between the Cesam2k and mesa codes. By performing optimizations using the Levenberg-Marquardt algorithm, we then obtained estimates of the amount of extra mixing beyond the core that is required in Cesam2k to reproduce seismic observations for these eight stars, and we showed that this can be used to propose a calibration of this quantity. This calibration depends on the prescription chosen for the extra mixing, but we found that it should also be valid for the code mesa, provided the same prescription is used. Conclusions. This study constitutes a first step toward calibrating the extension of convective cores in low-mass stars, which will help reduce the uncertainties on the ages of these stars.
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