This lecture on adiabatic oscillations is intended to present the basis of asteroseismology and to serve as an introduction for other lectures of the EES 2014. It also exposes the state-of-the-art of solar-like oscillation analysis, as revealed by the space missions CoRoT and Kepler. A large part of the lecture is devoted to the interpretation of the modes with a mixed character that reveal the properties of the radiative cores of subgiants and red giants.
We have computed linear non-adiabatic oscillations of luminous red giants using a non-local and anisotropic time-dependent theory of convection. The results show that low-order radial modes can be self-excited. Their excitation is the result of radiation and the coupling between convection and oscillations. Turbulent pressure has important effects on the excitation of oscillations in red variables.
Early-type stars generally tend to be fast rotators. In these stars, mode identification is very challenging as the effects of rotation are not well known. We consider here the example of $α$ Ophiuchi, for which dozens of oscillation frequencies have been measured. We model the star using the two-dimensional structure code ESTER, and we compute both adiabatic and non-adiabatic oscillations using the TOP code. Both calculations yield very complex spectra, and we used various diagnostic tools to try and identify the observed pulsations. While we have not reached a satisfactory mode-to-mode ident…
CoRoT and Kepler observations of red giants reveal rich spectra of non-radial solar-like oscillations allowing to probe their internal structure. We compare the theoretical spectrum of two red giants in the same region of the HR diagram but in different evolutionary phases. We present here our first results on the inertia, lifetimes and amplitudes of the oscillations and discuss the differences between the two stars.
A leap forward has been performed due to the space-borne missions, MOST, CoRoT and Kepler. They provided a wealth of observational data, and more precisely oscillation spectra, which have been (and are still) exploited to infer the internal structure of stars. While an adiabatic approach is often sufficient to get information on the stellar equilibrium structures it is not sufficient to get a full understanding of the physics of the oscillation. Indeed, it does not permit one to answer some fundamental questions about the oscillations, such as: What are the physical mechanisms responsible for …
The contour method is a new approach to calculating the non-adiabatic pulsation frequencies of stars. These frequencies can be found by solving for the complex roots of a characteristic equation constructed from the linear non-adiabatic stellar pulsation equations. A complex-root solver requires an initial trial frequency for each non adiabatic root. A standard method for obtaining initial trial frequencies is to use a star's adiabatic pulsation frequencies, but this method can fail to converge to non-adiabatic roots, especially as the growth and/or damping rate of the pulsations becomes large…
Longitudinal oscillations of solar filament have been investigated via numerical simulations continuously, but mainly in one dimension (1D), where the magnetic field line is treated as a rigid flux tube. Whereas those one-dimensional simulations can roughly reproduce the observed oscillation periods, implying that gravity is the main restoring force for filament longitudinal oscillations, the decay time in one-dimensional simulations is generally longer than in observations. In this paper, we perform a two-dimensional (2D) non-adiabatic magnetohydrodynamic simulation of filament longitudinal o…
Since the detection of non-radial solar-like oscillation modes in red giants with the CoRoT satellite, the interest in the asteroseismic properties of red giants and the link with their global properties and internal structure is substantially increasing. Moreover, more and more precise data are being collected with the space-based telescopes CoRoT and Kepler. In this paper we present a survey of the most relevant theoretical and observational results obtained up to now concerning the potential of solar-like oscillations in red giants.
The clear detection with CoRoT and KEPLER of radial and non-radial solar-like oscillations in many red giants paves the way to seismic inferences on the structure of such stars. We present an overview of the properties of the adiabatic frequencies and frequency separations of radial and non-radial oscillation modes, highlighting how their detection allows a deeper insight into the properties of the internal structure of red giants. In our study we consider models of red giants in different evolutionary stages, as well as of different masses and chemical composition. We describe how the large a…
One of the largest sources of uncertainty in stellar models is caused by the treatment of convection in stellar envelopes. One dimensional stellar models often make use of the mixing length or equivalent approximations to describe convection, all of which depend on various free parameters. There have been attempts to rectify this by using 3D radiative-hydrodynamic simulations of stellar convection, and in trying to extract an equivalent mixing length from the simulations. In this paper we show that the entropy of the deeper, adiabatic layers in these simulations can be expressed as a simple fu…
A growing number of solar-like oscillations has been detected in red giant stars thanks to CoRoT and Kepler space-crafts. The seismic data gathered by CoRoT on red giant stars allow us to test mode driving theory in physical conditions different from main-sequence stars. Using a set of 3D hydrodynamical models representative of the upper layers of sub- and red giant stars, we computed the acoustic mode energy supply rate (Pmax). Assuming adiabatic pulsations and using global stellar models that assume that the surface stratification comes from the 3D hydrodynamical models, we computed the mode…
We present results of an ongoing study of the pulsational properties of sdB stellar models aimed at exploring the consequences of detailed chemical transitions for radial, $p-$ and $g-$ modes. In particular, we focus on the effects of diffusion at the H-He transition and of He-burning at the convective cores. We find that diffusion of He and H has a strong impact on the period spectrum of sdBVs stars, leading to less efficient mode trapping. Our results also suggests that asteroseismology of sdBVs stars might offer a very good opportunity to constrain extramixing processes in the He-burning co…
We are developing a 3D radiation hydrodynamics code to simulate the interaction of convection and pulsation in classical variable stars. One key goal is the ability to carry these simulations to full amplitude in order to compare them with observed light and velocity curves. Previous 2D calculations were prevented from doing this because of drift in the radial coordinate system, due to the algorithm defining radial movement of the coordinate system during the pulsation cycle. We remove this difficulty by defining our coordinate system flow algorithm to require that the mass in a spherical shel…
We introduce GYRE, a new open-source stellar oscillation code which solves the adiabatic/non-adiabatic pulsation equations using a novel Magnus Multiple Shooting (MMS) numerical scheme. The code has a global error scaling of up to 6th order in the grid spacing, and can therefore achieve high accuracy with few grid points. It is moreover robust and efficiently makes use of multiple processor cores and/or nodes. We present an example calculation using GYRE, and discuss recent work to integrate GYRE into the asteroseismic optimization module of the MESA stellar evolution code.
Roche-lobe overflow and common envelope evolution are very important in binary evolution, which is believed to be the main evolutionary channel to hot subdwarf stars. The details of these processes are difficult to model, but adiabatic expansion provides an excellent approximation to the structure of a donor star undergoing dynamical time scale mass transfer. We can use this model to study the responses of stars of various masses and evolutionary stages as potential donor stars, with the urgent goal of obtaining more accurate stability criteria for dynamical mass transfer in binary population …
The Nobel prize in physics 2015 has been awarded "... for the discovery of neutrino oscillations which show that neutrinos have mass". While SuperKamiokande (SK), indeed, has discovered oscillations, SNO observed effect of the adiabatic (almost non-oscillatory) flavor conversion of neutrinos in the matter of the Sun. Oscillations are irrelevant for solar neutrinos apart from small $ν_e$ regeneration inside the Earth. Both oscillations and adiabatic conversion do not imply masses uniquely and further studies were required to show that non-zero neutrino masses are behind the SNO results. Phenome…
Effects of decoherence by wave packet separation on collective neutrino oscillations in dense neutrino gases are considered. We estimate the length of the wave packets of neutrinos produced in core collapse supernovae and the expected neutrino coherence length, and then proceed to consider the decoherence effects within the density matrix formalism of neutrino flavour transitions. First, we demonstrate that for neutrino oscillations in vacuum the decoherence effects are described by a damping term in the equation of motion of the density matrix of a neutrino as a whole (as contrasted to that o…
We present a new oscillation code, GYRE, which solves the stellar pulsation equations (both adiabatic and non-adiabatic) using a novel Magnus Multiple Shooting numerical scheme devised to overcome certain weaknesses of the usual relaxation and shooting schemes appearing in the literature. The code is accurate (up to 6th order in the number of grid points), robust, efficiently makes use of multiple processor cores and/or nodes, and is freely available in source form for use and distribution. We verify the code against analytic solutions and results from other oscillation codes, in all cases fin…
Recent numerical and theoretical considerations have shown that low-degree acoustic modes in rapidly rotating stars follow an asymptotic formula and recent observations of pulsations in rapidly rotating delta Scuti stars seem to match these expectations. However, a key question is whether strong gradients or discontinuities can adversely affect this pattern to the point of hindering its identification. Other important questions are how rotational splittings are affected by the 2D rotation profiles expected from baroclinic effects and whether it is possible to probe the rotation profile using t…
High-quality data from space-based observatories present an opportunity to fit stellar models to observations of individually-identified oscillation frequencies, not just the large and small frequency separations. But such fits require the evaluation of a large number of accurate stellar models, which remains expensive. Here, we show that global-mode oscillation frequencies interpolated in a grid of stellar models are precise and accurate, at least in the neighbourhood of a solar model.
We investigate induced oscillations by the gravitational field of a fast stellar object, such as a neutron star or a black-hole in a near miss collision with another star. Non-adiabatic collision conditions may lead to large amplitude oscillations in the star. We show that for a solar-type star a resonant condition can be achieved by a fast moving stellar object with velocity in the range of 100 km/s to 1000 km/s, passing at a distance of a few multiples of the star radius. Although such collisions are rare, they are more frequent than head-on collisions, and their effects could be observed th…
We have developed a new stellar evolution and oscillation code YNEV, which calculates the structures and evolutions of stars, taking into account hydrogen and helium burning. A nonlocal turbulent convection theory and an updated overshoot mixing model are optional in this code. The YNEV code can evolve low- and intermediate-mass stars from pre-main sequence (PMS) to thermal pulsing asymptotic branch giant (TP-AGB) or white dwarf. The YNEV oscillation code calculates the eigenfrequencies and eigenfunctions of the adiabatic oscillations of given stellar structure. The input physics and the numer…
The space-borne missions have provided a wealth of highly accurate data. However, our inability to properly model the upper-most region of solar-like stars prevents us from making the best of these observations. This problem is called "surface effect" and a key ingredient to solve it is turbulent pressure for the computation of both the equilibrium models and the oscillations. While 3D hydrodynamic simulations help to include properly the turbulent pressure in the equilibrium models, the way this surface effect is included in the computation of stellar oscillations is still subject to uncertai…
The purpose of this short paper is to give a summary of the derivation of a perturbative method to assess the impact of an arbitrary 3D magnetic field configuration, whose energy is everywhere small relative to the gravitational binding energy, on the form and value of the eigenfrequencies and eigenfunctions of stellar oscillations.
We calculate the dynamical tides raised by a close planetary companion on non-rotating stars of $1$ $\text{M}_{\odot}$ and $1.4$ $\text{M}_{\odot}$. Using the Henyey method, we solve the fully non-adiabatic equations throughout the star. The horizontal Lagrangian displacement is found to be 10 to 100 times larger than the equilibrium tide value in a thin region near the surface of the star. This is because non--adiabatic effects dominate in a region that extends from below the outer edge of the convection zone up to the stellar surface, and the equilibrium tide approximation is inconsistent wi…
Effects of stellar rotation on adiabatic oscillation frequencies of pressure modes are discussed. Methods to evaluate them are briefly exposed and some of their main results are presented.
We report the observations of X-ray oscillations during the flare in a cool active star XI Boo for the first time. XI Boo was observed by EPIC/MOS of the XMM-Newton satellite. The X-ray light curve is investigated with wavelet and periodogram analyses. Both analyses clearly show oscillations of the period of 1019 s. We interpret these oscillations as a fundamental fast-kink mode of magnetoacoustic waves.
Here we present CAFein, a new computational tool for investigating radiative dissipation of dynamic tides in close binaries and of non-adiabatic, non-radial stellar oscillations in isolated stars in the linear regime. For the latter, CAFein computes the non-adiabatic eigenfrequencies and eigenfunctions of detailed stellar models. The code is based on the so-called Riccati method, a numerical algorithm that has been successfully applied to a variety of stellar pulsators, and which doesn't suffer of the major drawbacks of commonly used shooting and relaxation schemes. Here we present an extensio…
Two different mechanisms may act to induce quasi-periodic pulsations (QPP) in whole-disk observations of stellar flares. One mechanism may be magneto-hydromagnetic (MHD) forces and other processes acting on flare loops as seen in the Sun. The other mechanism may be forced local acoustic oscillations due to the high-energy particle impulse generated by the flare (known as `sunquakes' in the Sun). We analyze short-cadence Kepler data of 257 flares in 75 stars to search for QPP in the flare decay branch or post-flare oscillations which may be attributed to either of these two mechanisms. About 18…
Adiabatic oscillation frequencies of stellar models, computed with the standard mixing-length formulation for convection, increasingly deviate with radial order from observations in solar-like stars. Standard solar models overestimate adiabatic frequencies by as much as ~ 20 μHz. In this letter, we address the physical processes of turbulent convection that are predominantly responsible for the frequency differences between standard models and observations, also called `surface effects'. We compare measured solar frequencies from the MDI instrument on the SOHO spacecraft with frequency calcula…
Stellar oscillations can be of topological origin. We reveal this deep and so-far hidden property of stars by establishing a novel parallel between stars and topological insulators. We construct an hermitian problem to derive the expression of the stellar $\mathrm{\textit{acoustic-buoyant}}$ frequency $S$ of non-radial adiabatic pulsations. A topological analysis then connects the changes of sign of the acoustic-buoyant frequency to the existence of Lamb-like waves within the star. These topological modes cross the frequency gap and behave as gravity modes at low harmonic degree $\ell$ and as …
Slow magnetoacoustic oscillations in stellar coronal loops with gravitational stratification are analyzed with a numerical solution of the boundary-value problem for eigenvalues and eigen functions. In this study, we only focus on the resonant periods. The effects of the gravitational stratification, star mass, loop temperature, and loop length on the properties of slow magnetoacoustic oscillations are investigated. It is shown that the discrepancy between stratified and non-stratified loops is higher in density perturbations than velocity perturbations. When the star has larger mass, higher c…
Where is the solar dynamo located and what is its modus operandi? These are still open questions in solar physics. Helio- and asteroseismology can help answer them by enabling us to study solar and stellar internal structures through global oscillations. The properties of solar and stellar acoustic modes are changing with the level of magnetic activity. However, until now, the inference on subsurface magnetic fields with seismic measures has been very limited. The aim of this paper is to develop a formalism to calculate the effect of large-scale toroidal magnetic fields on solar and stellar gl…
We have recently developed a new method for adjusting weights to minimize sidelobes in the spectral window. Here we show the results of applying this method to published two-site velocity observations of three stars (alpha Cen A, alpha Cen B and beta Hyi). Compared to our previous method of minimizing sidelobes, which involved adjusting the weights on a night-by-night basis, we find a significant improvement in frequency resolution. In the case of alpha Cen A, this should allow the detection of extra oscillation modes in the data.
Radial adiabatic perturbations of stellar compact objects
Universidade de Lisboa - UL（里斯本大学）；Escola Superior Náutica Infante D. Henrique（因凡特·唐·亨利克斯高等航海学院）；Charles University（查理大学）；Università di Genova（热那亚大学）；INFN Sezione di Genova（意大利国家核物理研究所热那亚分部）
We have calculated the equilibrium properties of a star in a circular, equatorial orbit about a Super-Massive Black Hole (SMBH), when the star fills and overflows its Roche lobe. The mass transfer time scale is anticipated to be long compared with the dynamical time and short compared with the thermal time of the star, so that the entropy as a function of the interior mass is conserved. We have studied how the stellar entropy, pressure, radius, mean density, and orbital angular momentum vary when the star is evolved adiabatically, for a representative set of stars. We have shown that the stell…
The Kepler space telescope observed over 15,000 stars for asteroseismic studies. Of these, 75% of dwarfs (and 8% of giants) were found to show anomalous behavior: such as suppressed oscillations (low amplitude) or no oscillations at all. The lack of solar-like oscillations may be a consequence of multiplicity, due to physical interactions with spectroscopic companions or due to the dilution of oscillation amplitudes from "wide'" (AO detected; visual) or spectroscopic companions introducing contaminating flux. We present a search for stellar companions to 327 of the Kepler asteroseismic sample,…
We calculate the conversion from non-adiabatic, non-radial oscillations tidally induced by a hot Jupiter on a star to observable spectroscopic and photometric signals. Models with both frozen convection and an approximation for a perturbation to the convective flux are discussed. Observables are calculated for some real planetary systems to give specific predictions. Time-dependent line broadening and the radial velocity signal during transit are both investigated as methods to provide further insight into the nature of the stellar oscillations. The photometric signal is predicted to be propor…
Starting from the equations of modified gravity hydrodynamics, we derive the equ tions of motion governing linear, adiabatic, radial perturbations of stars in scalar-tensor theories. There are two new features: first, the eigenvalue equation for the period of stellar oscillations is modified such that the eigenfrequencies are always larger than predicted by General Relativity. Second, the General Relativity condition for stellar instability is altered so that the adiabatic index can fall below 4/3 before unstable modes appear. Stars are more stable in modified gravity theories. Specialising to…
