Angular momentum transport efficiency in post-main sequence low-mass stars

Context. Using asteroseismic techniques, it has recently become possible to probe the internal rotation profile of low-mass (~1.1-1.5 Msun) 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 1.25 Msun 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.Comment: 8 pages, 6 figures; accepted for publication in Astronomy & Astrophysic

Accretion from debris disks onto white dwarfs : Fingering (thermohaline) instability and derived accretion rates

Recent observations of a large number of DA and DB white dwarfs show evidence of debris disks, which are the remnants of old planetary systems. The infrared excess detected with \emph{Spitzer} and the lines of heavy elements observed in their atmospheres with high-resolution spectroscopy converge on the idea that planetary material accretes onto these stars. Accretion rates have been derived by several authors with the assumption of a steady state between accretion and gravitational settling. The results are unrealistically different for DA and DB white dwarfs. When heavy matter is accreted onto stars, it induces an inverse $\mu$-gradient that leads to fingering (thermohaline) convection. The aim of this letter is to study the impact of this specific process on the derived accretion rates in white dwarfs and on the difference between DA and DB. We solve the diffusion equation for the accreted heavy elements with a time-dependent method. The models we use have been obtained both with the IRAP code, which computes static models, and the La Plata code, which computes evolutionary sequences. Computations with pure gravitational settling are compared with computations that include fingering convection. The most important result is that fingering convection has very important effects on DAs but is inefficient in DBs. When only gravitational settling is taken into account, the time-dependent computations lead to a steady state, as postulated by previous authors. When fingering convection is added, this steady state occurs much later. The surprising difference found in the past for the accretion rates derived for DA and DB white dwarfs disappears. The derived accretion rates for DAs are increased when fingering convection is taken into account, whereas those for DBs are not modified. More precise and developed results will be given in a forthcoming paper

Strong Approximation of Empirical Copula Processes by Gaussian Processes

We provide the strong approximation of empirical copula processes by a Gaussian process. In addition we establish a strong approximation of the smoothed empirical copula processes and a law of iterated logarithm

Period spacings in red giants I. Disentangling rotation and revealing core structure discontinuities

Asteroseismology allows us to probe the physical conditions inside the core of red giant stars. This 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. 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. 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. We propose a new view on 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. The measurement of the asymptotic period spacing and the signature of the structural glitches on mixed modes are then made easy. This work opens the possibility 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 on the radiative core.Comment: Accepted in A&

Seismic evidence for a weak radial differential rotation in intermediate-mass core helium burning stars

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. Mosser et al. (2012) have measured the rotation rates in the central regions of intermediate-mass core helium burning stars (secondary clump stars). Our aim was 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. We selected a subsample of Kepler secondary clump stars with mixed modes that are clearly rotationally split. By applying a thorough statistical analysis, we showed that the splittings of both gravity-dominated modes (trapped in central regions) and p-dominated modes (trapped in the envelope) can be measured. We then used these splittings to estimate the amount of differential rotation by using inversion techniques and by applying a simplified approach based on asymptotic theory (Goupil et al. 2013). We obtained evidence for a weak radial differential rotation for six of the seven targets that were selected, with the central regions rotating $1.8\pm0.3$ to $3.2\pm1.0$ times faster than the envelope. The last target was found to be consistent with a solid-body rotation. 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.Comment: 16 pages, 8 figures, accepted in A&

Open issues in probing interiors of solar-like oscillating main sequence stars: 2. Diversity in the HR diagram

We review some major open issues in the current modelling of low and intermediate mass, main sequence stars based on seismological studies. The solar case was discussed in a companion paper, here several issues specific to other stars than the Sun are illustrated with a few stars observed with CoRoT and expectations from Kepler data.Comment: GONG 2010 - SoHO 24, A new era of seismology of the Sun and solar-like stars, To be published in the Journal of Physics: Conference Series (JPCS

Measuring the extent of convective cores in low-mass stars using Kepler data: towards a calibration of core overshooting

Our poor understanding of the boundaries of convective cores generates large uncertainties on the extent of these cores and thus on stellar ages. 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. We first test and validate a seismic diagnostic that was proposed to probe in a model-dependent way the extent of convective cores using the so-called $r_{010}$ ratios, which are built with $l=0$ and $l=1$ modes. We apply this procedure to 24 low-mass stars chosen among Kepler targets to optimize the efficiency of this diagnostic. For this purpose, we compute grids of stellar models with both the CESAM2k and MESA evolution codes, where the extensions of convective cores are modeled either by an instantaneous mixing or as a diffusion process. Among the selected targets, we are able to unambiguously detect convective cores in eight stars and we obtain 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 obtain 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 show 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 find that it should be valid also for the code MESA, provided the same prescription is used. This study constitutes a first step towards the calibration of the extension of convective cores in low-mass stars, which will help reduce the uncertainties on the ages of these stars.Comment: 27 pages, 15 figures, accepted in A&

Estimating stellar mean density through seismic inversions

Determining the mass of stars is crucial both to improving stellar evolution theory and to characterising exoplanetary systems. Asteroseismology offers a promising way to estimate stellar mean density. When combined with accurate radii determinations, such as is expected from GAIA, this yields accurate stellar masses. The main difficulty is finding the best way to extract the mean density from a set of observed frequencies. We seek to establish a new method for estimating stellar mean density, which combines the simplicity of a scaling law while providing the accuracy of an inversion technique. We provide a framework in which to construct and evaluate kernel-based linear inversions which yield directly the mean density of a star. We then describe three different inversion techniques (SOLA and two scaling laws) and apply them to the sun, several test cases and three stars. The SOLA approach and the scaling law based on the surface correcting technique described by Kjeldsen et al. (2008) yield comparable results which can reach an accuracy of 0.5 % and are better than scaling the large frequency separation. The reason for this is that the averaging kernels from the two first methods are comparable in quality and are better than what is obtained with the large frequency separation. It is also shown that scaling the large frequency separation is more sensitive to near-surface effects, but is much less affected by an incorrect mode identification. As a result, one can identify pulsation modes by looking for an l and n assignment which provides the best agreement between the results from the large frequency separation and those from one of the two other methods. Non-linear effects are also discussed as is the effects of mixed modes. In particular, it is shown that mixed modes bring little improvement as a result of their poorly adapted kernels.Comment: Accepted for publication in A&A, 20 pages, 19 figure

A transmission problem across a fractal self-similar interface

We consider a transmission problem in which the interior domain has infinitely ramified structures. Transmission between the interior and exterior domains occurs only at the fractal component of the interface between the interior and exterior domains. We also consider the sequence of the transmission problems in which the interior domain is obtained by stopping the self-similar construction after a finite number of steps; the transmission condition is then posed on a prefractal approximation of the fractal interface. We prove the convergence in the sense of Mosco of the energy forms associated with these problems to the energy form of the limit problem. In particular, this implies the convergence of the solutions of the approximated problems to the solution of the problem with fractal interface. The proof relies in particular on an extension property. Emphasis is put on the geometry of the ramified domain. The convergence result is obtained when the fractal interface has no self-contact, and in a particular geometry with self-contacts, for which an extension result is proved

Solar-like oscillations in a massive star

Seismology of stars provides insight into the physical mechanisms taking place in their interior, with modes of oscillation probing different layers. Low-amplitude acoustic oscillations excited by turbulent convection were detected four decades ago in the Sun and more recently in low-mass main-sequence stars. Using data gathered by the Convection Rotation and Planetary Transits mission, we report here on the detection of solar-like oscillations in a massive star, V1449 Aql, which is a known large-amplitude (b Cephei) pulsator.Comment: Published in Sience, 19 June 2009, vol. 324, p. 154