Context. The observations carried out by the space missions CoRoT and Kepler provide a large set of asteroseismic data. Their analysis requires an efficient procedure first to determine if a star ...reliably shows solar-like oscillations, second to measure the so-called large separation, third to estimate the asteroseismic information that can be retrieved from the Fourier spectrum. Aims. In this paper we develop a procedure based on the autocorrelation of the seismic Fourier spectrum that is capable of providing measurements of the large and small frequency separations. The performance of the autocorrelation method needs to be assessed and quantified. We therefore searched for criteria able to predict the output that one can expect from the analysis by autocorrelation of a seismic time series. Methods. First, the autocorrelation is properly scaled to take into account the contribution of white noise. Then we use the null hypothesis H0 test to assess the reliability of the autocorrelation analysis. Calculations based on solar and CoRoT time series are performed to quantify the performance as a function of the amplitude of the autocorrelation signal. Results. We obtain an empirical relation for the performance of the autocorrelation method. We show that the precision of the method increases with the observation length, and with the mean seismic amplitude-to-background ratio of the pressure modes to the power 1.5 ± 0.05. We propose an automated determination of the large separation, whose reliability is quantified by the H0 test. We apply this method to analyze red giants observed by CoRoT. We estimate the expected performance for photometric time series of the Kepler mission. We demonstrate that the method makes it possible to distinguish $\ell$ = 0 from $\ell$ = 1 modes. Conclusions. The envelope autocorrelation function (EACF) has proven to be very powerful for the determination of the large separation in noisy asteroseismic data, since it enables us to quantify the precision of the performance of different measurements: mean large separation, variation of the large separation with frequency, small separation and degree identification.
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Context. Asteroseismology allows us to probe stellar interiors. In the case of red giant stars, conditions in the stellar interior are such as to allow for the existence of mixed modes, consisting in ...a coupling between gravity waves in the radiative interior and pressure waves in the convective envelope. Mixed modes can thus be used to probe the physical conditions in red giant cores. However, we still need to identify the physical mechanisms that transport angular momentum inside red giants, leading to the slow-down observed for red giant core rotation. Thus large-scale measurements of red giant core rotation are of prime importance to obtain tighter constraints on the efficiency of the internal angular momentum transport, and to study how this efficiency changes with stellar parameters. Aims. This work aims at identifying the components of the rotational multiplets for dipole mixed modes in a large number of red giant oscillation spectra observed by Kepler. Such identification provides us with a direct measurement of the red giant mean core rotation. Methods. We compute stretched spectra that mimic the regular pattern of pure dipole gravity modes. Mixed modes with the same azimuthal order are expected to be almost equally spaced in stretched period, with a spacing equal to the pure dipole gravity mode period spacing. The departure from this regular pattern allows us to disentangle the various rotational components and therefore to determine the mean core rotation rates of red giants. Results. We automatically identify the rotational multiplet components of 1183 stars on the red giant branch with a success rate of 69% with respect to our initial sample. As no information on the internal rotation can be deduced for stars seen pole-on, we obtain mean core rotation measurements for 875 red giant branch stars. This large sample includes stars with a mass as large as 2.5 M⊙, allowing us to test the dependence of the core slow-down rate on the stellar mass. Conclusions. Disentangling rotational splittings from mixed modes is now possible in an automated way for stars on the red giant branch, even for the most complicated cases, where the rotational splittings exceed half the mixed-mode spacing. This work on a large sample allows us to refine previous measurements of the evolution of the mean core rotation on the red giant branch. Rather than a slight slow-down, our results suggest rotation is constant along the red giant branch, with values independent of the mass.
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Period spacings in red giants Vrard, M; Mosser, B; Samadi, R
Astronomy and astrophysics (Berlin),
4/2016, Volume:
588
Journal Article
Peer reviewed
Context. The space missions CoRoT and Kepler have provided photometric data of unprecedented quality for asteroseismology. A very rich oscillation pattern has been discovered for red giants, ...including mixed modes that are used to decipher the red giants' interiors. They carry information on the radiative core of red giant stars and bring strong constraints on stellar evolution. Aims. Since more than 15000 red giant light curves have been observed by Kepler, we have developed a simple and efficient method for automatically characterizing the mixed-mode pattern and measuring the asymptotic period spacing. Methods. With the asymptotic expansion of the mixed modes, we have revealed the regularity of the gravity-mode pattern. The stretched periods were used to study the evenly space periods with a Fourier analysis and to measure the gravity period spacing, even when rotation severely complicates the oscillation spectra. Results. We automatically measured gravity period spacing for more than 6100 Kepler red giants. The results confirm and extend previous measurements made by semi-automated methods. We also unveil the mass and metallicity dependence of the relation between the frequency spacings and the period spacings for stars on the red giant branch. Conclusions. The delivery of thousands of period spacings combined with all other seismic and non-seismic information provides a new basis for detailed ensemble asteroseismology.
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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.
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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.
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Context.
Measuring stellar inclinations is fundamental to understanding planetary formation and dynamics as well as the physical conditions during star formation. Oscillation spectra of red giant ...stars exhibit mixed modes that have both a gravity component from the radiative interior and a pressure component from the convective envelope. Gravity-dominated (
g
-
m
) mixed modes split by rotation are well separated inside frequency spectra, allowing accurate measurement of stellar inclinations.
Aims.
We aim to develop an automated and general approach to measuring stellar inclinations that can be applied to any solar-type pulsator for which oscillation modes are identified. We also aim to validate this approach using red giant branch stars observed by
Kepler
.
Methods.
Stellar inclination impacts the visibility of oscillation modes with azimuthal orders
m
= { − 1, 0, +1}. We used the mean height-to-background ratio of dipole mixed modes with different azimuthal orders to measure stellar inclinations. We recovered the underlying statistical distribution of inclinations in an unbiased way using a probability density function for the stellar inclination angle.
Results.
We derive stellar inclination measurements for 1139 stars on the red giant branch for which Gehan et al. (2018, A&A, 616, A24) identified the azimuthal order of dipole
g
-
m
mixed modes. Raw measured inclinations exhibit strong deviation with respect to isotropy which is expected for random inclinations over the sky. When taking uncertainties into account, the reconstructed distribution of inclinations actually follows the expected isotropic distribution of the rotational axis.
Conclusions.
This work highlights the biases that affect inclination measurements and provides a way to infer their underlying statistical distribution. When a star is seen either pole on or equator on, measurements are challenging and result in a biased distribution. Correcting biases that appear in low- and high-inclination regimes allows us to recover the underlying inclination distribution.
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Using combined asteroseismic and spectroscopic observations of 418 red-giant stars close to the Galactic disc plane (6 kpc < RGal ≲ 13 kpc, | ZGal| < 0.3 kpc), we measure the age dependence of the ...radial metallicity distribution in the Milky Way’s thin disc over cosmic time. The slope of the radial iron gradient of the young red-giant population (−0.058 ± 0.008 stat. ±0.003 syst. dex/kpc) is consistent with recent Cepheid measurements. For stellar populations with ages of 1−4 Gyr the gradient is slightly steeper, at a value of −0.066 ± 0.007 ± 0.002 dex/kpc, and then flattens again to reach a value of ~−0.03 dex/kpc for stars with ages between 6 and 10 Gyr. Our results are in good agreement with a state-of-the-art chemo-dynamical Milky-Way model in which the evolution of the abundance gradient and its scatter can be entirely explained by a non-varying negative metallicity gradient in the interstellar medium, together with stellar radial heating and migration. We also offer an explanation for why intermediate-age open clusters in the solar neighbourhood can be more metal-rich, and why their radial metallicity gradient seems to be much steeper than that of the youngest clusters. Already within 2 Gyr, radial mixing can bring metal-rich clusters from the innermost regions of the disc to Galactocentric radii of 5 to 8 kpc. We suggest that these outward-migrating clusters may be less prone to tidal disruption and therefore steepen the local intermediate-age cluster metallicity gradient. Our scenario also explains why the strong steepening of the local iron gradient with age is not seen in field stars. In the near future, asteroseismic data from the K2 mission will allow for improved statistics and a better coverage of the inner-disc regions, thereby providing tighter constraints on theevolution of the central parts of the Milky Way.
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Among the 19 red-giant stars belonging to eclipsing binary systems that have been identified in Kepler data, 15 display solar-like oscillations. We study whether the absence of mode detection in the ...remaining 4 is an observational bias or possibly evidence of mode damping that originates from tidal interactions. A careful analysis of the corresponding Kepler light curves shows that modes with amplitudes that are usually observed in red giants would have been detected if they were present. We observe that mode depletion is strongly associated with short-period systems, in which stellar radii account for 16%-24% of the semi-major axis, and where red-giant surface activity is detected. We suggest that when the rotational and orbital periods synchronize in close binaries, the red-giant component is spun up, so that a dynamo mechanism starts and generates a magnetic field, leading to observable stellar activity. Pressure modes would then be damped as acoustic waves dissipate in these fields.
Period spacings in red giants Mosser, B; Vrard, M; Belkacem, K ...
Astronomy and astrophysics (Berlin),
12/2015, Volume:
584
Journal Article
Peer reviewed
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.
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Context. With the space-borne missions CoRoT and Kepler, a large amount of asteroseismic data is now available and has led to a variety of work. So-called global oscillation parameters are inferred ...to characterize the large sets of stars, perform ensemble asteroseismology, and derive scaling relations. The mean large separation is such a key parameter, easily deduced from the radial-frequency differences in the observed oscillation spectrum and closely related to the mean stellar density. It is therefore crucial to measure it with the highest accuracy in order to obtain the most precise asteroseismic indices. Aims. As the conditions of measurement of the large separation do not coincide with its theoretical definition, we revisit the asymptotic expressions used for analyzing the observed oscillation spectra. Then, we examine the consequence of the difference between the observed and asymptotic values of the mean large separation. Methods. The analysis is focused on radial modes. We use series of radial-mode frequencies in published analyses of stars with solar-like oscillations to compare the asymptotic and observational values of the large separation. This comparison relies on the proper use of the second-order asymptotic expansion. Results. We propose a simple formulation to correct the observed value of the large separation and then derive its asymptotic counterpart. The measurement of the curvature of the radial ridges in the échelle diagram provides the correcting factor. We prove that, apart from glitches due to stellar structure discontinuities, the asymptotic expansion is valid from main-sequence stars to red giants. Our model shows that the asymptotic offset is close to 1/4, as in the theoretical development, for low-mass, main-sequence stars, subgiants and red giants. Conclusions. High-quality solar-like oscillation spectra derived from precise photometric measurements are definitely better described with the second-order asymptotic expansion. The second-order term is responsible for the curvature observed in the échelle diagrams used for analyzing the oscillation spectra, and this curvature is responsible for the difference between the observed and asymptotic values of the large separation. Taking it into account yields a revision of the scaling relations, which provides more accurate asteroseismic estimates of the stellar mass and radius. After correction of the bias (6% for the stellar radius and 3% for the mass), the performance of the calibrated relation is about 4% and 8% for estimating, respectively, the stellar radius and the stellar mass for masses less than 1.3 M⊙; the accuracy is twice as bad for higher mass stars and red giants.
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