We present multidimensional modeling of convection and oscillations in main-sequence stars somewhat more massive than the Sun, using three separate approaches: 1) Using the 3-D planar StellarBox radiation hydrodynamics code to model the envelope convection zone and part of the radiative zone. Our goals are to examine the interaction of stellar pulsations with turbulent convection in the envelope, excitation of acoustic modes, and the role of convective overshooting; 2) Applying the spherical 3-D MHD ASH (Anelastic Spherical Harmonics) code to simulate the core convection and radiative zone. Our goal is to determine whether core convection can excite low-frequency gravity modes, and thereby explain the presence of low frequencies for some hybrid γ Dor/δ Sct variables for which the envelope convection zone is too shallow for the convective blocking mechanism to drive gravity modes; 3) Applying the ROTORC 2-D stellar evolution and dynamics code to calculate evolution with a variety of initial rotation rates and extents of core convective overshooting. The nonradial adiabatic pulsation frequencies of these nonspherical models are calculated using the 2-D pulsation code NRO. We present new insights into pulsations of 1-2 M⊙ stars gained by multidimensional modeling.

The preliminary results of an analysis of the red giant star KIC 5701829 observed for 29 days in short-cadence mode with the Kepler satellite are reported. The oscillation spectrum of this star is characterized by the presence of a well-defined solar-like oscillation pattern due to acoustic modes. The characterization of the power spectrum has been performed following three basics steps commonly used in the analysis of solar-like oscillations: fitting and correcting for the background, estimating the frequency of maximum power (νmax) and the large separation (Δν), and extracting individual frequencies. We have found that the frequency of maximum oscillation power, νmax, and the mean large frequency separation, Δν, are around, 143 and 12 μHz, respectively. The global asteroseismic parameters along with atmospheric parameters from the literature allow us to infer about evolutionary status of the star.

We explore the radial (p-mode) stability of stars across a wide range of mass (0.2 < M < 50 M⊙), composition (0 < X < 0.7, Z = 0.001, 0.02), effective temperature, and luminosity. We identify the instability boundaries associated with low- to high-order radial oscillations (0 ⩽ n ⩽ 13). The instability boundaries are a strong function of both composition and radial order (n). The classical blue edge shifts to higher effective temperature and luminosity with decreasing hydrogen abundance. High-order modes are more easily excited and small islands of high radial-order instability develop, some of which correspond with real stars. Driving in all cases is by the classical κ-mechanism and, at high luminosity-to-mass ratio, strange-mode instability. We identify regions of parameter space where new classes of pulsating variable have recently or may, in future, be discovered. The majority of these are associated with reduced hydrogen abundance in the envelope.

Asteroseismology has been proven to be a successful tool to unravel details of the internal structure for different types of stars in various stages of evolution well after birth. We can now show that it has similar power for pre-main sequence (pre-MS) objects. Pre-MS stars with masses between ~1 and 6 solar masses that have recently been formed and gain their energy mainly from gravitational contraction can become vibrationally unstable during their evolution to the main sequence. Within the past ~15 years, several dozens of pulsating pre-MS stars were discovered using data obtained from ground and from space. Depending on their masses, pre-MS stars can show three different types of pulsations: (i) δ Scuti type p-mode pulsations, (ii) γ Doradus like g-mode oscillations and (iii) g-mode Slowly Pulsating B star pulsations.

Our asteroseismic investigations yielded new insights into the connection between the pulsations and early stellar evolution: We revealed a relation between the stars' oscillatory behavior and their relative evolutionary stages that might lead us to a model-independent determination of the stars' fundamental parameters. With this we will be able to put constraints on theoretical models and help to answer some of the yet open questions in early stellar evolution.

The NASA Kepler spacecraft data revealed a large number of multimode nonradially pulsating γ Dor and δ Sct variable star candidates. The Kepler high precision long time-series photometry makes it possible to study amplitude variations of the frequencies. We summarize recent literature on amplitude and frequency variations in pulsating variables. We are searching for amplitude variability in several dozen faint γ Doradus or δ Scuti variable-star candidates observed as part of the Kepler Guest Observer program. We apply several methods, including a Matlab-script wavelet analysis developed by J. Jackiewicz, and the wavelet technique of the VSTAR software (http://www.aavso.org/vstar-overview). Here we show results for two stars, KIC 2167444 and KIC 2301163. We discuss the magnitude and timescale of the amplitude variations, and the presence or absence of correlations between amplitude variations for different frequencies of a given star. Amplitude variations may be detectable using Kepler data even for stars with Kepler magnitude > 14 with low-amplitude frequencies (~100 ppm) using only one or a few quarters of long-cadence data. We discuss proposed causes of amplitude spectrum variability that will require further investigation.

We present the new interpretation of the oscillation spectrum of HD 163899 based on the new determinations of the effective temperature, mass-luminosity ratio and rotational velocity. These new parameters strongly prefer the more massive models than previously considered. Now it is also possible that the star could be in the main sequence stage. Using the oscillation spectrum as a gauge, we intend to establish which stage of evolution corresponds better to HD 163899.

Massive stars pulsate in various modes; radial and nonradial p-modes, g-modes, and strange modes including oscillatory convective (non-adiabatic g−) modes. Those modes are responsible for the light and velocity variations of β Cephei stars, slowly pulsating B (SPB) stars, and α Cyg variables. The instability mechanisms for these pulsations are discussed. We also discuss the relation between the evolution of massive stars and the excitation of strange modes, which are considered responsible for the pulsation in most of the α Cyg variables. The surface He and CNO abundances of hotter α Cyg variables seem to indicate that the Ledoux criterion of convection is better than the Schwarzschild criterion, although the latter is extensively used in stellar evolution computations.

The evolved, core helium burning, extreme horizontal branch stars (also known as hot B subdwarfs) host several classes of pulsators showing either p- or g-modes, or both. They offer particularly favorable conditions for probing with asteroseismology their internal structure, thus constituting arguably the most interesting seismic window for this intermediate stage of stellar evolution. G-modes in particular have the power to probe deep inside these stars, down to the convective He-burning core boundary where uncertain physics (convection, overshooting, semi-convection) is at work. Space data recently obtained with CoRoT and Kepler are offering us the possibility to probe these regions in detail and possibly shed new light on how these processes shape the core structure. In this short paper, we present the most recent advances that have taken place in this field and we provide hints of the foreseen future achievements of hot subdwarf asteroseismology.

During Kepler's main mission, nearly 20 pulsating subdwarf B (sdB: extreme horizontal branch stars) were discovered. Many of these stars were observed for three years, accumulating over 1.5 million observations. Only through these extended observations have we been able to identify pulsation modes, applying constraints for structure models. Discoveries include nearly-evenly-spaced asymptotic period overtones which represent the interior structure and rotationally-induced frequency multiplets from which we have learned that rotation periods are long, even when in short-period binaries. This paper reviews progress on observational constraints and highlights some of our discoveries including radially differential rotation, conflicting stratification indicators and mode lifetimes.

We present a brief progress report in our quest for deriving seismic models of pulsating white dwarfs that can account simultaneously for all the observed periods at the precision of the observations. We point out that this is possible from a pratical point of view only if parametrized models are used to complement evolutionary models. We adopt a double optimization procedure that insures that the best possible model in parameter space is found objectively and automatically. Our ultimate goal is to be able to account for the exquisite period data gathered with Kepler and Kepler-2 on key pulsating white dwarfs of both the DA (ZZ Ceti) and DB (V777 Her) type.

Just how good are modern stellar models? Providing a rigorous assessment of the uncertainties is difficult because of the multiplicity of input physics. Some of the ingredients are reasonably well-known (like reaction rates and opacities). Others are not so good, with convection standing out as a particularly obvious example. In some cases, it is not clear what the ingredients should be: what role do atomic diffusion, rotation, magnetic fields, etc. play in stellar evolution? All this is then compounded by computational method. In converting all this physics into something we can implement in a 1D evolution code, we are forced to make choices about the way the equations are solved, how we will treat mixing at convective boundaries, etc. All of this can impact the models one finally generates. In this review, I will attempt to assess the uncertainties associated with the ingredients and methods used by stellar evolution modellers, and what their impacts may be on the science that we wish to do.

Stellar convection is customarily described by the mixing-length theory, which makes use of the mixing-length scale to express the convective flux, velocity, and temperature gradients of the convective elements and stellar medium. The mixing-length scale is taken to be proportional to the local pressure scale height, and the proportionality factor (the mixing-length parameter) must be determined by comparing the stellar models to some calibrator, usually the Sun. No strong arguments exist to suggest that the mixing-length parameter is the same in all stars and all evolutionary phases. Because of this, all stellar models in the literature are hampered by this basic uncertainty.

In a recent paper (Pasetto et al. 2014) we presented a new theory that does not require the mixing length parameter. Our self-consistent analytical formulation of stellar convection determines all the properties of stellar convection as a function of the physical behaviour of the convective elements themselves and the surrounding medium. The new theory of stellar convection is formulated starting from a conventional solution of the Navier-Stokes/Euler equations, i.e. the Bernoulli equation for a perfect fluid, but expressed in a non-inertial reference frame co-moving with the convective elements. In our formalism, the motion of stellar convective cells inside convective-unstable layers is fully determined by a new system of equations for convection in a non-local and time-dependent formalism.

We obtained an analytical, non-local, time-dependent solution for the convective energy transport that does not depend on any free parameter. The predictions of the new theory are compared with those from the standard mixing-length paradigm with positive results for atmosphere models of the Sun and all the stars in the Hertzsprung-Russell diagram.

Measurements of oscillation frequencies of the Sun and stars can provide important independent constraints on their internal structure and dynamics. Seismic models of these oscillations are used to connect structure and rotation of the star to its resonant frequencies, which are then compared with observations, the goal being that of minimizing the difference between the two. Even in the case of the Sun, for which structure models are highly tuned, observed frequencies show systematic deviations from modeled frequencies, a phenomenon referred to as the “surface term.” The dominant source of this systematic effect is thought to be vigorous near-surface convection, which is not well accounted for in both stellar modeling and mode-oscillation physics. Here we bring to bear the method of homogenization, applicable in the asymptotic limit of large wavelengths (in comparison to the correlation scale of convection), to characterize the effect of small-scale surface convection on resonant-mode frequencies in the Sun. We show that the full oscillation equations, in the presence of temporally stationary 3D flows, can be reduced to an effective “quiet-Sun” wave equation with altered sound speed, Brünt–Väisäla frequency, and Lamb frequency. We derive the modified equation and relations for the appropriate averaging of 3D flows and thermal quantities to obtain the properties of this effective medium. Using flows obtained from 3D numerical simulations of near-surface convection, we quantify their effect on solar oscillation frequencies and find that they are shifted systematically and substantially. We argue therefore that consistent interpretations of resonant frequencies must include modifications to the wave equation that effectively capture the impact of vigorous hydrodynamic convection.

Asteroseismology is among the most powerful observational tools to determine fundamental properties of stars. Space-based photometry has recently enabled the systematic detection of oscillations in exoplanet host stars, allowing a combination of asteroseismology with transit and radial-velocity measurements to characterize planetary systems. In this contribution I will review the key synergies between asteroseismology and exoplanet science such as the precise determination of radii and ages of exoplanet host stars, as well as applications of asteroseismology to measure spin-orbit inclinations in multiplanet systems and orbital eccentricities of small planets. Finally I will give a brief outlook on asteroseismic studies of exoplanet hosts with current and future space-based missions such as K2 and TESS.

The study of eclipsing binaries is our primary source of measured properties of normal stars, achieved through analysis of light and radial velocity curves of eclipsing systems. The study of oscillations and pulsations is increasingly vital for determining the properties of single stars, and investigating the physical phenomena active in their interiors. Combining the two methods holds the promise of establishing stringent tests of stellar evolutionary theory, and of calibrating model-dependent asteroseismology with empirically measured stellar properties. I review recent advances and outline future work.

Measuring the obliquities of exoplanet-host stars provides invaluable diagnostic information for theories of planetary formation and migration. Most of these results have so far been obtained by measuring the Rossiter–McLaughlin effect, clearly favoring systems that harbor hot Jupiters. While it would be extremely helpful to extend these measurements to long-period and multiple-planet systems, it is also true that the latter systems tend to involve smaller planets, making it ever so difficult to apply such techniques. Asteroseismology provides a powerful method of determining the inclination of the stellar spin axis — from an analysis of the rotationally-induced splittings of the oscillation modes — whose applicability is ultimately determined by the stellar parameters and not by the signal-to-noise ratio of the transit data. Here we present the first statistical analysis of an ensemble of asteroseismic obliquity measurements obtained for solar-type stars with transiting planets. The sample consists of 25 Kepler planet-candidate host stars, 14 of which are multi-transiting systems. We seek empirical constraints on the spin-orbit alignment of exoplanet systems and discuss the implications for theories of planetary formation and migration.

Continuous and precise space-based photometry has made it possible to measure the orbital frequency modulation of pulsating stars in binary systems with extremely high precision over long time spans. We present the phase modulation (PM) method for finding binaries among pulsating stars. We demonstrate how the orbital elements of a pulsating binary star can be obtained analytically from photometry alone, without spectroscopic radial velocity measurement. Frequency modulation (FM) caused by binary orbital motion also manifests itself in the Fourier transform, as a multiplet with equal spacing of the orbital frequency. The orbital parameters can also be extracted by analysing the amplitudes and phases of the peaks in these multiplets. We derive analytically the theoretical relations between the multiplet properties and the orbital parameters, and present a method for determining these parameters, including the eccentricity and the argument of periapsis. This, too, is achievable with the photometry alone, without spectroscopic radial velocity measurements. We apply these two methods to Kepler mission data and demonstrate that the results are in good agreement with each other. These methods are used to search for invisible binary companions, including planets and invisible massive objects such as neutron stars and stellar-mass black holes.

δ Scuti stars are generally fast rotators and their pulsations are not in the asymptotic regime, so the interpretation of their pulsation spectra is a very difficult task. Binary stars, especially eclipsing systems, offer us the opportunity to constrain the space of fundamental stellar parameters. Firstly, we show the results of KIC9851944 and KIC4851217 as two case studies. We found the signature of the large frequency separation in the pulsational spectrum of both stars. The observed mean stellar density and the large frequency separation obey the linear relation in the log-log space as found by Suarez et al. (2014) and García Hernández et al. (2015). Second, we apply the simple ‘one-layer model’ of Moreno & Koenigsberger (1999) to the prototype heartbeat star KOI-54. The model naturally reproduces the tidally induced high frequency oscillations and their frequencies are very close to the observed frequency at 90 and 91 times the orbital frequency.

The last decade has given rise to several tensions between calculated and (sometimes indirectly) measured stellar opacities. I discuss the current and future capacity for the asteroseismology of B-type oscillators (slowly-pulsating B-type stars and β Cepheids) and main-sequence solar-like oscillators to test stellar opacities. I briefly highlight two methods by which the B-type oscillators already constrain opacities, though they do not yet identify a superior set of tables. I then consider how the main-sequence solar-like oscillators might also test opacities, using the 16 Cygni system as an example. There are currently greater uncertainties than the opacities (in this example, the atmospheric structure) but many of these will be separately constrained in the near future.

The rotation rates in the interior and at the surface is determined for the 22 main-sequence stars with masses between 1.0 and 1.6 M⊙. The average interior rotation is measured using asteroseismology, while the surface rotation is measured by the spectroscopic v sin i or the periodic light variation due to surface structures, such as spots. It is found that the difference between the surface rotation rate determined by spectroscopy and the average rotation rate for most of stars is small enough to suggest that an efficient process of angular momentum transport operates during and/or before the main-sequence stage of stars. By comparing the surface rotation rate measured from the light variation with those measured by spectroscopy, we found hints of latitudinal differential rotation. However, this must be confirmed by a further study because our result is sensitive to a few data points.