Probing the core structure and evolution of red giants using gravity-dominated mixed modes observed with Kepler

We report for the first time a parametric fit to the pattern of the \ell = 1 mixed modes in red giants, which is a powerful tool to identify gravity-dominated mixed modes. With these modes, which share the characteristics of pressure and gravity modes, we are able to probe directly the helium core and the surrounding shell where hydrogen is burning. We propose two ways for describing the so-called mode bumping that affects the frequencies of the mixed modes. Firstly, a phenomenological approach is used to describe the main features of the mode bumping. Alternatively, a quasi-asymptotic mixed-mode relation provides a powerful link between seismic observations and the stellar interior structure. We used period \'echelle diagrams to emphasize the detection of the gravity-dominated mixed modes. The asymptotic relation for mixed modes is confirmed. It allows us to measure the gravity-mode period spacings in more than two hundred red giant stars. The identification of the gravity-dominated mixed modes allows us to complete the identification of all major peaks in a red giant oscillation spectrum, with significant consequences for the true identification of \ell = 3 modes, of \ell = 2 mixed modes, for the mode widths and amplitudes, and for the \ell = 1 rotational splittings. The accurate measurement of the gravity-mode period spacing provides an effective probe of the inner, g-mode cavity. The derived value of the coupling coefficient between the cavities is different for red giant branch and clump stars. This provides a probe of the hydrogen-shell burning region that surrounds the helium core. Core contraction as red giants ascend the red giant branch can be explored using the variation of the gravity-mode spacing as a function of the mean large separation.Comment: Accepted in A&

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&

Theoretical power spectra of mixed modes in low mass red giant stars

CoRoT and Kepler observations of red giant stars revealed very rich spectra of non-radial solar-like oscillations. Of particular interest was the detection of mixed modes that exhibit significant amplitude, both in the core and at the surface of the stars. It opens the possibility of probing the internal structure from their inner-most layers up to their surface along their evolution on the red giant branch as well as on the red-clump. Our objective is primarily to provide physical insight into the physical mechanism responsible for mixed-modes amplitudes and lifetimes. Subsequently, we aim at understanding the evolution and structure of red giants spectra along with their evolution. The study of energetic aspects of these oscillations is also of great importance to predict the mode parameters in the power spectrum. Non-adiabatic computations, including a time-dependent treatment of convection, are performed and provide the lifetimes of radial and non-radial mixed modes. We then combine these mode lifetimes and inertias with a stochastic excitation model that gives us their heights in the power spectra. For stars representative of CoRoT and Kepler observations, we show under which circumstances mixed modes have heights comparable to radial ones. We stress the importance of the radiative damping in the determination of the height of mixed modes. Finally, we derive an estimate for the height ratio between a g-type and a p-type mode. This can thus be used as a first estimate of the detectability of mixed-modes

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&

Seismic diagnostics for transport of angular momentum in stars 2. Interpreting observed rotational splittings of slowly-rotating red giant stars

Asteroseismology with the space-borne missions CoRoT and Kepler provides a powerful mean of testing the modeling of transport processes in stars. Rotational splittings are currently measured for a large number of red giant stars and can provide stringent constraints on the rotation profiles. The aim of this paper is to obtain a theoretical framework for understanding the properties of the observed rotational splittings of red giant stars with slowly rotating cores. This allows us to establish appropriate seismic diagnostics for rotation of these evolved stars. Rotational splittings for stochastically excited dipolar modes are computed adopting a first-order perturbative approach for two $1.3 M_\odot$ benchmark models assuming slowly rotating cores. For red giant stars with slowly rotating cores, we show that the variation of the rotational splittings of $\ell=1$ modes with frequency depends only on the large frequency separation, the g-mode period spacing, and the ratio of the average envelope to core rotation rates (${\cal R}$). This leds us to propose a way to infer directly ${\cal R}$ from the observations. This method is validated using the Kepler red giant star KIC 5356201. Finally, we provide a theoretical support for the use of a Lorentzian profile to measure the observed splittings for red giant stars.Comment: 15 pages, 15 figures, accepted for publication in A&

SYMPA, a dedicated instrument for Jovian Seismology. II. Real performance and first results

Context. Due to its great mass and its rapid formation, Jupiter has played a crucial role in shaping the Solar System. The knowledge of its internal structure would strongly constrain the solar system formation mechanism. Seismology is the most efficient way to probe directly the internal structure of giant planets. Aims. SYMPA is the first instrument dedicated to the observations of free oscillations of Jupiter. Principles and theoretical performance have been presented in paper I. This second paper describes the data processing method, the real instrumental performance and presents the first results of a Jovian observation run, lead in 2005 at Teide Observatory. Methods. SYMPA is a Fourier transform spectrometer which works at fixed optical path difference. It produces Doppler shift maps of the observed object. Velocity amplitude of Jupiter's oscillations is expected below 60 cm/s. Results Despite light technical defects, the instrument demonstrated to work correctly, being limited only by photon noise, after a careful analysis. A noise level of about 12 cm/s has been reached on a 10-night observation run, with 21 % duty cycle, which is 5 time better than previous similar observations. However, no signal from Jupiter is clearly highlighted.Comment: 13 pages, 26 figure

Asteroseismic surface gravity for evolved stars

Context: Asteroseismic surface gravity values can be of importance in determining spectroscopic stellar parameters. The independent log(g) value from asteroseismology can be used as a fixed value in the spectroscopic analysis to reduce uncertainties due to the fact that log(g) and effective temperature can not be determined independently from spectra. Since 2012, a combined analysis of seismically and spectroscopically derived stellar properties is ongoing for a large survey with SDSS/APOGEE and Kepler. Therefore, knowledge of any potential biases and uncertainties in asteroseismic log(g) values is now becoming important. Aims: The seismic parameter needed to derive log(g) is the frequency of maximum oscillation power (nu_max). Here, we investigate the influence of nu_max derived with different methods on the derived log(g) values. The large frequency separation between modes of the same degree and consecutive radial orders (Dnu) is often used as an additional constraint for the determination of log(g). Additionally, we checked the influence of small corrections applied to Dnu on the derived values of log(g). Methods We use methods extensively described in the literature to determine nu_max and Dnu together with seismic scaling relations and grid-based modeling to derive log(g). Results: We find that different approaches to derive oscillation parameters give results for log(g) with small, but different, biases for red-clump and red-giant-branch stars. These biases are well within the quoted uncertainties of ~0.01 dex (cgs). Corrections suggested in the literature to the Dnu scaling relation have no significant effect on log(g). However somewhat unexpectedly, method specific solar reference values induce biases of the order of the uncertainties, which is not the case when canonical solar reference values are used.Comment: 8 pages, 5 figures, accepted for publication by A&