Overshoot Region Research Articles

Observations of Locally Excited Waves in the Low Solar Atmosphere Using the Daniel K. Inouye Solar Telescope

We present an interpretation of the recent Daniel K. Inouye Solar Telescope (DKIST) observations of propagating wave fronts in the lower solar atmosphere. Using MPS/University of Chicago MHD radiative magnetohydrodynamic simulations spanning the solar photosphere, the overshoot region, and the lower chromosphere, we identify three acoustic-wave source mechanisms, each occur at a different atmospheric height. We synthesize the DKIST Visible Broadband Imager G-band, blue-continuum, and Ca ii K signatures of these waves at high spatial and temporal resolution, and conclude that the wave fronts observed by DKIST likely originate from acoustic sources at the top of the solar photosphere overshoot region and in the chromosphere proper. The overall importance of these local sources to the atmospheric energy and momentum budget of the solar atmosphere is unknown, but one of the excitation mechanisms identified (upward propagating shock interaction with down-welling chromospheric plasma resulting in acoustic radiation) may be an important shock dissipation mechanism. Additionally, the observed wave fronts may prove useful for ultralocal helioseismological inversions and promise to play an important diagnostic role at multiple atmospheric heights.

Fixed-time observation and predefined performance regulation for oxygen excess ratio of vehicular fuel cells under input saturation

The efficiency, health and lifetime of vehicle-mounted fuel cells highly rely on the oxygen excess ratio (OER). Faced with urgent research limitations, this article tackles the estimation and regulation for immeasurable OER, while suppressing the influences of dramatic stack current, uncertain system information, actuator saturation and performance constraint. Restricted by high cost and measurement difficulty, two fixed-time adaptive observers are proposed to rebuild unavailable OER and lumped disturbance respectively, which eliminate the dependence of estimation time on initial states and alleviate the peaking issue. Further, a fixed-time prescribed performance controller is developed to elevate the tracking performance for the estimated OER, in which the overshoot, regulation time and convergence region can be quantitatively constrained, regardless of initial conditions. Specially, to exclude undesired control singularity, an improved performance function is established to automatically adjust the predefined constraint boundaries depending on the captured variations of stack current and anti-saturation auxiliary signal. The hardware-in-loop validation results under custom working conditions and a typical vehicle driving cycle exhibit that the estimation and regulation of OER reach stability within 0.2s and 1s respectively, besides, the maximum absolute errors in observing and controlling the OER are limited to around 0.6 and 0.8 respectively, with great adaptability to different scenarios.

Marine heatwaves and cold spells in the Brazil Overshoot show distinct sea surface temperature patterns depending on the forcing

The Brazil Current Overshoot regions feature the strongest sea surface temperature variations over the global ocean but forecast skill for these extreme variations is limited. Here we investigate the drivers of marine heatwaves and cold spells in this region and find that ocean flows and sea surface heat fluxes are the primary drivers. We also find that sea surface temperature extremes driven by air-sea heat fluxes produce consistent changes in sea surface temperature and related atmospheric variables over a wide horizontal area, whereas ocean flow-driven sea surface temperature extremes exhibit low consistency in air variables and limited consistency in the spatial extent of sea variables across most sea surface temperature extreme events. These differing air-sea characteristics associated with extremes driven by different drivers offer potential avenues for improving prediction skills and advancing the understanding of three-dimensional air-sea impacts associated with extreme events.

Asteroseismic Investigation on KIC 10526294 to Probe Convective Core Overshoot Mixing

In the overshoot mixing model with an exponentially decreasing diffusion coefficient, the initial value of the diffusion coefficient plays a crucial role. According to the turbulent convective mixing model, the characteristic length of convection in the convection zone differs from that in the overshoot region, resulting in a rapid decrease of the diffusion coefficient near the convective boundary. To investigate this quick decrease, we conducted an asteroseismic study on the intermediate-mass slowly pulsating B-type star KIC 10526294. We generated stellar models with varied input parameters, including the overshoot parameters, and compared the resulting stellar oscillation periods with observations. To mitigate the potential issue arising from large steps in the stellar parameters and stellar age, we employed a comprehensive interpolation scheme for the stellar oscillatory frequencies, considering all stellar parameters and stellar age. Our analysis revealed that the quick decreasing of the diffusion coefficient has discernible effects on the stellar oscillations, and a quick decrease with 4 orders of magnitude shows the best oscillatory frequencies compared with the observations. This provides weak evidence in support of the prediction made by the turbulent convective mixing model. Furthermore, we examined the residuals of the oscillation periods and discovered a potential association between abundance anomalies in the buoyancy frequency profile and the oscillation-like patterns observed in the residuals.

PHANGS–JWST First Results: Massive Young Star Clusters and New Insights from JWST Observations of NGC 1365

A primary new capability of JWST is the ability to penetrate the dust in star-forming galaxies to identify and study the properties of young star clusters that remain embedded in dust and gas. In this Letter we combine new infrared images taken with JWST with our optical Hubble Space Telescope (HST) images of the starbursting barred (Seyfert2) spiral galaxy NGC 1365. We find that this galaxy has the richest population of massive young clusters of any known galaxy within 30 Mpc, with ∼30 star clusters that are more massive than 106 M ⊙ and younger than 10 Myr. Sixteen of these clusters are newly discovered from our JWST observations. An examination of the optical images reveals that 4 of 30 (∼13%) are so deeply embedded that they cannot be seen in the Hubble I band (A V ≳ 10 mag), and that 11 of 30 (∼37%) are missing in the HST B band, so age and mass estimates from optical measurements alone are challenging. These numbers suggest that massive clusters in NGC 1365 remain completely obscured in the visible for ∼1.3 ± 0.7 Myr and are either completely or partially obscured for ∼3.7 ± 1.1 Myr. We also use the JWST observations to gain new insights into the triggering of star cluster formation by the collision of gas and dust streamers with gas and dust in the bar. The JWST images reveal previously unknown structures (e.g., bridges and overshoot regions from stars that form in the bar) that help us better understand the orbital dynamics of barred galaxies and associated star-forming rings. Finally, we note that the excellent spatial resolution of the NIRCAM F200W filter provides a better way to separate barely resolved compact clusters from individual stars based on their sizes.

Characterising the AGB bump and its potential to constrain mixing processes in stellar interiors

Context. In the 1990s, theoretical studies motivated the use of the asymptotic giant branch bump (AGBb) as a standard candle given the weak dependence between its luminosity and stellar metallicity. Because of the small size of observed asymptotic giant branch (AGB) samples, detecting the AGBb is not an easy task. However, this has now been made possible thanks to the wealth of data collected by the CoRoT, Kepler, and TESS space-borne missions. Aims. It is well-known that the AGB bump provides valuable information on the internal structure of low-mass stars, particularly on mixing processes such as core overshooting during the core He-burning phase. Here, we investigate the dependence of the AGBb position on stellar parameters such as the stellar mass and metallicity based on the calibration of stellar models to observations. Methods. In this context, we analysed ∼4000 evolved giants observed by Kepler and TESS, including red giant branch (RGB) stars and AGB stars, for which asteroseismic and spectrometric data are available. By using statistical mixture models, we detected the AGBb both in frequency at maximum oscillation power, νmax, and in effective temperature, Teff. Then, we used the Modules for Experiments in Stellar Astrophysics (MESA) stellar evolution code to model AGB stars and match the AGBb occurrence with observations. Results. From the observations, we were able to derive the AGBb location in 15 bins of mass and metallicity. We noted that the higher the mass, the later the AGBb occurs in the evolutionary track, which agrees with theoretical works. Moreover, we found a slight increase in the luminosity at the AGBb when the metallicity increases. By fitting those observations with stellar models, we noticed that low-mass stars (M ≤ 1.0 M⊙) require a small core overshooting region during the core He-burning phase. This core overshooting extent increases toward high mass; however, above M ≥ 1.5 M⊙, we found that the AGBb location cannot be reproduced with a realistic He-core overshooting alone. Thus, additional mixing processes have to be invoked instead. Conclusions. The observed dependence on metallicity complicates the application of the AGBb as a standard candle. Moreover, different mixing processes may occur according to stellar mass. At low mass (M ≤ 1.5 M⊙), the AGBb location can be used to constrain the He-core overshooting. At high mass (M ≥ 1.5 M⊙), an additional mixing induced, for instance, by rotation is needed to reproduce what is seen in observations.

Heat transfer and behavior of the Reynolds stress in Mach 6 boundary layer transition induced by first-mode oblique waves

This paper investigates a Mach 6 oblique breakdown via direct numerical simulation in conjunction with stability and quadrant analyses. Particular emphasis is placed on, first, the heat transfer and mean flow distortion in the near-wall and outer transitional boundary layer, and, second, the flow events that are responsible for the production of the Reynolds stress. The energy budget reveals that enhancement of viscous dissipation due to mean flow distortion dominates the heat transfer overshoot, while the dissipation due to fluctuations is lesser but not negligible. Downstream of the location of the peak mean heat flux, the wall temperature gradient (non-dimensionalized by the freestream temperature and local boundary layer thickness) varies little, owing to the occurrence of breakdown and the establishment of self-similarity. Renormalized by the boundary layer thickness, a new correlation of the Stanton number shows no overshoot or difference between the original overshoot region and the turbulent region, which indicates the possibility of similarity once breakdown has occurred. In the outer region, enhanced advective heat exchange strongly reshapes the mean temperature profile. Because of successive modal growth and nonlinear saturation, the contributions of the primary oblique mode, streak mode, and a superharmonic to the outer advective heat transfer are found to compete near the location of the peak heat flux. From the perspective of fluid motions, quadrant analysis highlights the evenly and broadly distributed joint probability density function (PDF) of the fluctuating velocities during transition, which results in overproduction of the Reynolds stress, while the PDF is concentrated around zero in the turbulent region. The flow event Q2 (ejection) overtakes Q4 (sweep) in the outer boundary layer of the transitional region, mainly owing to the primary mode, while the two events become attenuated and nearly achieve balance when transition is complete.

On the Spectral Evolution of Hot White Dwarf Stars. III. The PG 1159–DO–DB–DQ Evolutionary Channel Revisited

We continue our comprehensive theoretical investigation of the spectral evolution of white dwarfs based on sophisticated simulations of element transport. In this paper, we focus on the transformation of PG 1159 stars into DO/DB white dwarfs due to the gravitational settling of heavy elements and then into DQ white dwarfs through the convective dredge-up of carbon. We study the impact of several physical parameters on the evolution of the surface carbon abundance over a wide range of effective temperatures. In the hot PG 1159 and DO phases, our calculations confirm that the temperature of the PG 1159-to-DO transition depends sensitively on the stellar mass and the wind mass-loss rate. We show that measured carbon abundances of DOZ white dwarfs are mostly accounted for by our models, with the notable exception of the coolest DOZ stars. In the cooler DB and DQ phases, the predicted atmospheric composition is strongly influenced by the stellar mass, the thickness of the envelope, the initial carbon content, the efficiency of convective overshoot, and the presence of residual hydrogen. We demonstrate that, under reasonable assumptions, our simulations reproduce very well the observed carbon abundance pattern of DQ stars, which thus allows us to constrain the extent of the overshoot region in cool helium-rich white dwarfs. We also argue that our calculations naturally explain a number of recent empirical results, such as the relative excess of low-mass DQ stars and the presence of trace hydrogen and/or carbon at the surface of most DC and DZ stars.

Core overshoot constrained by the absence of a solar convective core and some solar-like stars

ABSTRACT Convective-core overshoot mixing is a significant uncertainty in stellar evolution. Because numerical simulations and turbulent convection models predict exponentially decreasing radial rms turbulent velocity, a popular treatment for overshoot mixing is to apply a diffusion process with an exponentially decreasing diffusion coefficient. It is important to investigate the parameters of the diffusion coefficient because they determine the efficiency of the mixing in the overshoot region. In this paper, we have investigated the effects of the core overshoot mixing on the properties of the core in solar models. We have constrained the parameters of the overshoot model by using helioseismic inferences and the observation of the solar 8B neutrino flux. For solar-mass stars, the core overshoot mixing helps to prolong the lifetime of the convective core developed at the zero-age main sequence. If the strength of the mixing is sufficiently high, then the convective core in a solar model could survive until the present solar age, leading to large deviations of the sound speed and density profiles compared with the helioseismic inferences. The 8B neutrino flux also favours a radiative solar core. These observations provide a constraint on the parameters of the exponential diffusion model of the convective overshoot mixing. A limited asteroseismic investigation of 13 Kepler low-mass stars with 1.0 < M/M⊙ < 1.5 shows a mass-dependent range of the overshoot parameter. The overshoot mixing processes for different elements are analysed in detail. It is found that the exponential diffusion overshoot model leads to different effective overshoot mixing lengths for elements with different nuclear equilibrium time-scales.

On the Dynamics of Overshooting Convection in Spherical Shells: Effect of Density Stratification and Rotation.

Overshooting of turbulent motions from convective regions into adjacent stably stratified zones plays a significant role in stellar interior dynamics, as this process may lead to mixing of chemical species and contribute to the transport of angular momentum and magnetic fields. We present a series of fully nonlinear, three-dimensional (3D) anelastic simulations of overshooting convection in a spherical shell that are focused on the dependence of the overshooting dynamics on the density stratification and the rotation, both key ingredients in stars that however have not been studied systematically together via global simulations. We demonstrate that the overshoot lengthscale is not simply a monotonic function of the density stratification in the convective region, but instead it depends on the ratio of the density stratifications in the two zones. Additionally, we find that the overshoot lengthscale decreases with decreasing Rossby number Ro and scales as Ro0.23 while it also depends on latitude with higher Rossby cases leading to a weaker latitudinal variation. We examine the mean flows arising due to rotation and find that they extend beyond the base of the convection zone into the stable region. Our findings may provide a better understanding of the dynamical interaction between stellar convective and radiative regions, and motivate future studies particularly related to the solar tachocline and the implications of its overlapping with the overshoot region.

Constraining stellar evolution theory with asteroseismology of γ Doradus stars using deep learning

Context. The efficiency of the transport of angular momentum and chemical elements inside intermediate-mass stars lacks proper calibration, thereby introducing uncertainties on a star’s evolutionary pathway. Improvements require better estimation of stellar masses, evolutionary stages, and internal mixing properties. Aims. Our aim was to develop a neural network approach for asteroseismic modelling, and test its capacity to provide stellar masses, ages, and overshooting parameter for a sample of 37 γ Doradus stars; these parameters were previously determined from their effective temperature, surface gravity, near-core rotation frequency, and buoyancy travel time Π0. Here our goal is to perform the parameter estimation from modelling of individual periods measured for dipole modes with consecutive radial order rather than from Π0. We assess whether fitting these individual mode periods increases the capacity of the parameter estimation. Methods. We trained neural networks to predict theoretical pulsation periods of high-order gravity modes (n ∈ [15, 91]), and to predict the luminosity, effective temperature, and surface gravity for a given mass, age, overshooting parameter, diffusive envelope mixing, metallicity, and near-core rotation frequency. We applied our neural networks for Computing Pulsation Periods and Photospheric Observables (C-3PO) to our sample and compute grids of stellar pulsation models for the estimated parameters. Results. We present the near-core rotation rates (from the literature) as a function of the inferred stellar age and critical rotation rate. We assessed the rotation rates of the sample near the start of the main sequence assuming rigid rotation. Furthermore, we measured the extent of the core overshoot region and find no correlation with mass, age, or rotation. Finally, for one star in our sample, KIC 12066947, we find indications of mode coupling in the period spacing pattern which we cannot reproduce with mode trapping. Conclusions. The neural network approach developed in this study allows the derivation of stellar properties dominant for stellar evolution, such as mass, age, and extent of core-boundary mixing. It also opens a path for future estimation of mixing profiles throughout the radiative envelope, with the aim of inferring these profiles for large samples of γ Doradus stars.

Convective Overshooting in the Envelopes of A-type Stars Using the k-ω Model

Abstract Mixing between convective zones is quite uncertain in the envelopes of A-type stars. To study the mixing in A-type envelopes, we use a new convection model, the k-ω model, in the MESA stellar evolution code. Using the k-ω model, we find that the overshooting regions of the He ii and H/He i convection zones are integrated with each other. There is material exchange between the He ii and H/He i convection zones through overshooting, in agreement with recent numerical simulations.We obtain the overshooting distance of about 3.5H p below the base of the H/He i convection zone in a 2.3 M ⊙ star. There are two overshooting regions beyond the He ii convection zone in the same stellar model. We obtain that the overshooting distance of the upper one is about 3.9H p and about 2.0H p for the lower one. We find that the turbulent diffusion effect is particularly strong in the convective envelopes of A-type stars. In addition, we find that the typical size of the convective rolling cells is restricted by the actual thickness of the convective zones, because the thickness of the convection zones are usually smaller than or approximately equal to the local pressure scale height. Through comparisons with the results of the k-ω model, we find that a suitable value of f ov is about 0.45 for the H/He i convective overshooting region. It is about 0.27 for the upper He ii convective overshooting region and about 0.25 for the lower one.

Wall slip in primitive chain network simulations of shear startup of entangled polymers and its effect on the shear stress undershoot

In some recent experiments on entangled polymers of stress growth in the startup of fast shear flows, an undershoot in the shear stress is observed following the overshoot, i.e., before approaching the steady state. Whereas tumbling of the entangled chain was proposed to be at its origin, here, we investigate another possible cause for the stress undershoot, i.e., slippage at the interface between the polymer and solid wall. To this end, we extend the primitive chain network model to include slip at the interface between entangled polymeric liquids and solid walls with grafted polymers. We determine the slip velocity at the wall, and the shear rate in the bulk, by imposing that the shear stress in the bulk polymers is equal to that resulting from the polymers grafted at the wall. After confirming that the predicted results for the steady state are reasonable, we examine the transient behavior. The simulations confirm that slippage weakens the magnitude of the stress overshoot, as reported earlier. The undershoot is also weakened, or even disappears, because of a reduced coherence in molecular tumbling. Disentanglement of grafted chains from bulk ones, taking place throughout the stress overshoot region, does not contribute to the stress undershoot.

On the dynamical interaction between overshooting convection and an underlying dipole magnetic field – I. The non-dynamo regime

ABSTRACT Motivated by the dynamics in the deep interiors of many stars, we study the interaction between overshooting convection and the large-scale poloidal fields residing in radiative zones. We have run a suite of 3D Boussinesq numerical calculations in a spherical shell that consists of a convection zone with an underlying stable region that initially compactly contains a dipole field. By varying the strength of the convective driving, we find that, in the less turbulent regime, convection acts as turbulent diffusion that removes the field faster than solely molecular diffusion would do. However, in the more turbulent regime, turbulent pumping becomes more efficient and partially counteracts turbulent diffusion, leading to a local accumulation of the field below the overshoot region. These simulations suggest that dipole fields might be confined in underlying stable regions by highly turbulent convective motions at stellar parameters. The confinement is of large-scale field in an average sense and we show that it is reasonably modelled by mean-field ideas. Our findings are particularly interesting for certain models of the Sun, which require a large-scale, poloidal magnetic field to be confined in the solar radiative zone in order to explain simultaneously the uniform rotation of the latter and the thinness of the solar tachocline.

On the H-type transition to turbulence—Laboratory experiments and reduced-order modeling

A series of experiments were conducted to understand the sources of local, high-amplitude velocity fluctuations produced at the late stages of boundary-layer flow transition to turbulence. The laboratory experiments considered the controlled injection of Tollmien–Schlichting (TS) waves into a nearly zero pressure gradient, laminar boundary layer, resulting in H-type transition to turbulence. Proper orthogonal decomposition (POD) was used to extract the energetic coherent structures within the transitional flow field obtained with particle image velocimetry. The first three modes were observed to feature spatial mode shapes consistent with a cross-section of a canonical hairpin vortex structure and were associated with time-dependent amplitudes having consistent peak frequencies with the fundamental TS wave frequency. Higher-order modes exhibited a combination of sub- and super-harmonics of the TS wave frequency and were attributed to flow interactions produced by a hairpin packet. A conditional averaging method was used to establish a reduced-order model for the overshoot phenomena in Reynolds shear stress and turbulence kinetic energy observed at the late transition stage. The lower portion of the large-scale hairpin vortex structure was observed to be primarily responsible for the overshoot mechanisms, which was well captured in a reduced-order model of the velocity field. The first four POD modes were used to create this reduced-order model, which, while only consisting of ≈15% of the total turbulence kinetic energy of the original velocity field, was able to capture ≈85% of the peak Reynolds stress amplitude across the overshoot region.

From hydrogen to helium: the spectral evolution of white dwarfs as evidence for convective mixing

ABSTRACT We present a study of the hypothesis that white dwarfs undergo a spectral change from hydrogen- to helium-dominated atmospheres using a volume-limited photometric sample drawn from the Gaia-DR2 catalogue, the Sloan Digital Sky Survey (SDSS), and the Galaxy Evolution Explorer (GALEX). We exploit the strength of the Balmer jump in hydrogen-atmosphere DA white dwarfs to separate them from helium-dominated objects in SDSS colour space. Across the effective temperature range from 20 000 to 9000 K, we find that 22 per cent of white dwarfs will undergo a spectral change, with no spectral evolution being ruled out at 5σ. The most likely explanation is that the increase in He-rich objects is caused by the convective mixing of DA stars with thin hydrogen layers, in which helium is dredged up from deeper layers by a surface hydrogen convection zone. The rate of change in the fraction of He-rich objects as a function of temperature, coupled with a recent grid of 3D radiation-hydrodynamic simulations of convective DA white dwarfs – which include the full overshoot region – lead to a discussion on the distribution of total hydrogen mass in white dwarfs. We find that 60 per cent of white dwarfs must have a hydrogen mass larger than MH/MWD = 10−10, another 25 per cent have masses in the range MH/MWD = 10−14–10−10, and 15 per cent have less hydrogen than MH/MWD = 10−14. These results have implications for white dwarf asteroseismology, stellar evolution through the asymptotic giant branch and accretion of planetesimals on to white dwarfs.

3D Modeling of the Structure and Dynamics of a Main-Sequence F-type Star

AbstractCurrent state-of-the-art computational modeling makes it possible to build realistic models of stellar convection zones and atmospheres that take into account chemical composition, radiative effects, ionization, and turbulence. The standard 1D mixing-length-based evolutionary models are not able to capture many physical processes of the stellar interior dynamics. Mixing-length models provide an initial approximation of stellar structure that can be used to initialize 3D radiative hydrodynamics simulations which include realistic modeling of turbulence, radiation, and other phenomena.In this paper, we present 3D radiative hydrodynamic simulations of an F-type main-sequence star with 1.47 solar mass. The computational domain includes the upper layers of the radiation zone, the entire convection zone, and the photosphere. The effects of stellar rotation is modeled in the f-plane approximation. These simulations provide new insight into the properties of the convective overshoot region, the dynamics of the near-surface, highly turbulent layer, and the structure and dynamics of granulation. They reveal solar-type differential rotation and latitudinal dependence of the tachocline location.

Collapse of particle-laden buoyant plumes

Particle loading affects the dynamics of buoyant plumes, since the difference between particle and fluid densities is much greater than that in the fluid alone. In stratified environments, plume rise is density limited; after initial overshoot, the plume reaches a terminal level and spreads radially. Particles dropping from this horizontal intrusion may be re-entrained. This recycling of dense matter reduces plume buoyancy and intrusion height and, for sufficient load, can lead to plume collapse. Entrainment-based formulae yield a steady-state plume rise. We identify a new conserved quantity for such plumes. Integrating paths of particles dropping from the intrusion yields the fraction re-entrained. A simple mathematical model predicts from buoyancy ratio at source ($P=$ negative particle buoyancy divided by positive fluid buoyancy) whether a particle-laden plume will collapse. Under this model, for small settling velocity, a particle-laden plume will not collapse if $P<0.368$. Above this, collapse depends also on the amount of particle-free ambient fluid entrained in the overshoot region. For pure plumes, experimental evidence suggests that this is small. For forced plumes, more substantial overshoot and entrainment is shown to increase the critical ratio. An extension, based on successive recycling, estimates time to collapse. To investigate further we develop a simple computational model, coupling a ‘top-hat’ plume model, an analytical formula for radially decaying concentrations in the intrusion and an axisymmetric finite-volume solution for time-dependent settling and entrainment. The model can predict the impact of particle load on final rise, as well as the occurrence and time scales of plume collapse.

The Effect of Dynamic Capillarity in Modeling Saturation Overshoot during Infiltration

Core Ideas We provide detailed analysis of various forms of the dynamic capillarity coefficient. We focus on the region of saturation overshoot at larger saturation. The results are evaluated with the aid of experimental observations. Gravity‐driven fingering has been observed during downward infiltration of water into dry sand. Moreover, the water saturation profile within each finger is non‐monotonic, with a saturation overshoot at the finger tip. As reported in the literature, these effects can be simulated by an extended form of the Richards equation, where a dynamic capillarity term is included. The coefficient of proportionality is called the dynamic capillarity coefficient. The dynamic capillarity coefficient may depend on saturation. However, there is no consensus on the form of this dependence. We provide a detailed traveling wave analysis of four distinctly different functional forms of the dynamic capillarity coefficient. In some forms, the coefficient increases with increasing saturation, and in some forms, it decreases. For each form, we have found an explicit expression for the maximum value of saturation in the overshoot region. In current formulations of dynamic capillarity, if the value of the capillarity coefficient is large, the value of saturation in the overshoot region may exceed unity, which is obviously nonphysical. So, we have been able to ensure boundedness of saturation regardless of the value of the dynamic capillarity coefficient by extending the capillary pressure–saturation relationship. Finally, we provide a qualitative comparison of the results of traveling wave analysis with experimental observations.

Binary asteroseismic modelling: isochrone-cloud methodology and application toKeplergravity mode pulsators

The simultaneous presence of variability due to both pulsations and binarity is no rare phenomenon. Unfortunately, the complexities of dealing with even one of these sources of variability individually means that the other signal is often treated as a nuisance and discarded. However, both types of variability offer means to probe fundamental stellar properties in robust ways through asteroseismic and binary modelling. We present an efficient methodology that includes both binary and asteroseismic information to estimate fundamental stellar properties based on a grid-based modelling approach. We report parameters for three gravity mode pulsating {\it Kepler} binaries , such as mass, radius, age, as well the mass of the convective core and location of the overshoot region. We discuss the presence of parameter degeneracies and the way our methodology deals with them. We provide asteroseismically calibrated isochrone-clouds to the community; these are a generalisation of isochrones when allowing for different values of the core overshooting in the two components of the binary.