Red giants are evolved stars that have exhausted the supply of hydrogen in their cores and instead burn hydrogen in a surrounding shell 1,2 . Once a red giant is sufficiently evolved, the helium in the core also undergoes fusion 3 . Outstanding issues in our understanding of red giants include uncertainties in the amount of mass lost at the surface before helium ignition and the amount of internal mixing from rotation and other processes 4 . Progress is hampered by our inability to distinguish between red giants burning helium in the core and those still only burning hydrogen in a shell. Asteroseismology offers a way forward, being a powerful tool for probing the internal structures of stars using their natural oscillation frequencies 5 . Here we report observations of gravity-mode period spacings in red giants 6 that permit a distinction between evolutionary stages to be made. We use high-precision photometry obtained by the Kepler spacecraft over more than a year to measure oscillations in several hundred red giants. We find many stars whose dipole modes show sequences with approximately regular period spacings. These stars fall into two clear groups, allowing us to distinguish unambiguously between hydrogen-shell-burning stars (period spacing mostly 50 seconds) and those that are also burning helium (period spacing 100 to 300 seconds).Oscillations in red giants, like those in the Sun, are thought to be excited by near-surface convection. The observed oscillation spectra are indeed remarkably Sun-like, with a broad range of radial and nonradial modes in a characteristic comb pattern [7][8][9][10][11]

Context. Solar-like oscillations have been observed in numerous red giants from ground and from space. An important question arises: could we expect to detect non-radial modes probing the internal structure of these stars? Aims. We investigate under what physical circumstances non-radial modes could be observable in red giants; what would be their amplitudes, lifetimes and heights in the power spectrum (PS)? Methods. Using a non-radial non-adiabatic pulsation code including a non-local time-dependent treatment of convection, we compute the theoretical lifetimes of radial and non-radial modes in several red giant models. Next, using a stochastic excitation model, we compute the amplitudes of these modes and their heights in the PS. Results. Distinct cases appear. Case A corresponds to subgiants and stars at the bottom of the ascending giant branch. Our results show that the lifetimes of the modes are mainly proportional to the inertia I, which is modulated by the mode trapping. The predicted amplitudes are lower for non-radial modes. But the height of the peaks in the PS are of the same order for radial and non-radial modes as long as they can be resolved. The resulting frequency spectrum is complex. Case B corresponds to intermediate models in the red giant branch. In these models, the radiative damping becomes high enough to destroy the non-radial modes trapped in the core. Hence, only modes trapped in the envelope have significant heights in the PS and could be observed. The resulting frequency spectrum of detectable modes is regular for = 0 and 2, but a little more complex for = 1 modes because of less efficient trapping. Case C corresponds to models of even higher luminosity. In these models the radiative damping of non-radial modes is even larger than in the previous case and only radial and non-radial modes completely trapped in the envelope could be observed. The frequency pattern is very regular for these stars. The comparison between the predictions for radial and non-radial modes is very different if we consider the heights in the PS instead of the amplitudes. This is important as the heights (not the amplitudes) are used as detection criterion.

Asteroseismology of stars that exhibit solar-like oscillations are enjoying a growing interest with the wealth of observational results obtained with the CoRoT and Kepler missions. In this framework, scaling laws between asteroseismic quantities and stellar parameters are becoming essential tools to study a rich variety of stars. However, the physical underlying mechanisms of those scaling laws are still poorly known. Our objective is to provide a theoretical basis for the scaling between the frequency of the maximum in the power spectrum (ν max ) of solar-like oscillations and the cut-off frequency (ν c ). Using the SoHO GOLF observations together with theoretical considerations, we first confirm that the maximum of the height in oscillation power spectrum is determined by the so-called plateau of the damping rates. The physical origin of the plateau can be traced to the destabilizing effect of the Lagrangian perturbation of entropy in the upper-most layers, which becomes important when the modal period and the local thermal relaxation time-scale are comparable. Based on this analysis, we then find a linear relation between ν max and ν c , with a coefficient that depends on the ratio of the Mach number of the exciting turbulence to the third power to the mixing-length parameter.

Context. Observations and analysis of solar-type oscillations in red-giant stars is an emerging aspect of asteroseismic analysis with a number of open questions yet to be explored. Although stochastic oscillations have previously been detected in red giants from both radial velocity and photometric measurements, those data were either too short or had sampling that was not complete enough to perform a detailed data analysis of the variability. The quality and quantity of photometric data as provided by the CoRoT satellite is necessary to provide a breakthrough in observing p-mode oscillations in red giants. We have analyzed continuous photometric time-series of about 11 400 relatively faint stars obtained in the exofield of CoRoT during the first 150 days long-run campaign from May to October 2007. We find several hundred stars showing a clear power excess in a frequency and amplitude range expected for red-giant pulsators. In this paper we present first results on a sub-sample of these stars. Aims. Knowing reliable fundamental parameters like mass and radius is essential for detailed asteroseismic studies of red-giant stars. As the CoRoT exofield targets are relatively faint (11−16 mag) there are no (or only weak) constraints on the stars' location in the H-R diagram. We therefore aim to extract information about such fundamental parameters solely from the available time series. Methods. We model the convective background noise and the power excess hump due to pulsation with a global model fit and deduce reliable estimates for the stellar mass and radius from scaling relations for the frequency of maximum oscillation power and the characteristic frequency separation. Results. We provide a simple method to estimate stellar masses and radii for stars exhibiting solar-type oscillations. Our method is tested on a number of known solar-type pulsators.

Aims. We extend semi-analytical computations of excitation rates for solar oscillation modes to those of other solar-like oscillating stars to compare them with recent observations Methods. Numerical 3D simulations of surface convective zones of several solar-type oscillating stars are used to characterize the turbulent spectra as well as to constrain the convective velocities and turbulent entropy fluctuations in the uppermost part of the convective zone of such stars. These constraints, coupled with a theoretical model for stochastic excitation, provide the rate P at which energy is injected into the p-modes by turbulent convection. These energy rates are compared with those derived directly from the 3D simulations.Results. The excitation rates obtained from the 3D simulations are systematically lower than those computed from the semi-analytical excitation model. We find that P max , the P maximum, scales as (L/M) s where s is the slope of the power law and L and M are the mass and luminosity of the 1D stellar model built consistently with the associated 3D simulation. The slope is found to depend significantly on the adopted form of χ k , the eddy time-correlation; using a Lorentzian, χ L k , results in s = 2.6, whereas a Gaussian, χ G k , gives s = 3.1. Finally, values of V max , the maximum in the mode velocity, are estimated from the computed power laws for P max and we find that V max increases as (L/M) sv . Comparisons with the currently available ground-based observations show that the computations assuming a Lorentzian χ k yield a slope, sv, closer to the observed one than the slope obtained when assuming a Gaussian. We show that the spatial resolution of the 3D simulations must be high enough to obtain accurate computed energy rates.

Context. The advent of space-borne missions such as CoRoT or Kepler providing photometric data has brought new possibilities for asteroseismology across the H-R diagram. Solar-like oscillations are now observed in many stars, including red giants and mainsequence stars. Aims. Based on several hundred identified pulsating red giants, we aim to characterize their oscillation amplitudes and widths. These observables are compared with those of main-sequence stars in order to test trends and scaling laws for these parameters for mainsequence stars and red giants.Methods. An automated fitting procedure is used to analyze several hundred Fourier spectra. For each star, a modeled spectrum is fitted to the observed oscillation spectrum, and mode parameters are derived. Results. Amplitudes and widths of red-giant solar-like oscillations are estimated for several hundred modes of oscillation. Amplitudes are relatively high (several hundred ppm) and widths relatively small (very few tenths of a μHz). Conclusions. Widths measured in main-sequence stars show a different variation with the effective temperature from red giants. A single scaling law is derived for mode amplitudes of red giants and main-sequence stars versus their luminosity to mass ratio. However, our results suggest that two regimes may also be compatible with the observations.

Context. Solar-like oscillations are stochastically excited by turbulent convection at the surface layers of the stars. Aims. We study the role of the surface metal abundance on the efficiency of the stochastic driving in the case of the CoRoT target HD 49933. Methods. We compute two 3D hydrodynamical simulations representative-in effective temperature and gravity-of the surface layers of the CoRoT target HD 49933, a star that is rather metal poor and significantly hotter than the Sun. One 3D simulation has a solar metal abundance, and the other has a surface iron-to-hydrogen, [Fe/H], abundance ten times smaller. For each 3D simulation we match an associated global 1D model, and we compute the associated acoustic modes using a theoretical model of stochastic excitation validated in the case of the Sun and α Cen A. Results. The rate at which energy is supplied per unit time into the acoustic modes associated with the 3D simulation with [Fe/H] =-1 is found to be about three times smaller than those associated with the 3D simulation with [Fe/H] = 0. As shown here, these differences are related to the fact that low metallicity implies surface layers with a higher mean density. In turn, a higher mean density favors smaller convective velocities and hence less efficient driving of the acoustic modes. Conclusions. Our result shows the importance of taking the surface metal abundance into account in the modeling of the mode driving by turbulent convection. A comparison with observational data is presented in a companion paper using seismic data obtained for the CoRoT target HD 49933.

Asteroseismology of evolved solar-like stars is experiencing a growing interest due to the wealth of observational data from space-borne instruments such as the CoRoT and Kepler spacecraft. In particular, the recent detection of mixed modes, which probe both the innermost and uppermost layers of stars, paves the way for inferring the internal structure of stars along their evolution through the subgiant and red giant phases. Mixed modes can also place stringent constraints on the physics of such stars and on their global properties (mass, age, etc...). Here, using two Kepler stars (KIC 4351319 and KIC 6442183), we demonstrate that measurements of mixed mode characteristics allow us to estimate the mode inertias, providing a new and additional diagnostics on the mode trapping and subsequently on the internal structure of evolved stars. We however stress that the accuracy may be sensitive to non-adiabatic effects.