arXiv subjects

Paul R. Woodward

Publications and source records attributed to Paul R. Woodward.

15 recordsLinked to original sources

arXiv2026

The physics of deep-interior convective shell boundaries in a massive pre-supernova star: Internal gravity wave mixing at the $N^2$ peak

The physics of convective boundary mixing involves concepts such as penetration and overshooting and has been mostly characterized for envelope and core convection. For the burning shells deep inside massive stars in their final stages, the convective boundary remains poorly understood. 1D stellar-evolution codes typically place a steep entropy gradient and the corresponding narrow \brunt{} ($N^2$) peak at a lower convective shell boundary. Based on high-resolution 3D hydrodynamic simulations of a $25 \rm{M_\odot}$ star 11 days before core collapse, we find that convection excites high-frequency internal gravity waves at the $N^2$ peak representing the C-shell convection bottom. These waves efficiently mix entropy and species and the $N^2$ peak erodes by ${\sim}40\%$ within hours, correspondingly reducing the entropy gradient. The wave-driven diffusion coefficient is $D\approx 5\text{--}6\times 10^{9} \rm{cm}^2 \rm{second}^{-1}$ at the $N^2$ peak in numerically converged simulations. Our simulations show that the dominant physics at this boundary is mixing due to internal gravity waves. Extrapolated with the time-dependent $D$ coefficient from the 3D simulations, the entropy step across the peak decreases by 40--85\% within half a day, thereby reducing the density, temperature and entropy gradients that set the accretion-rate drop a stalled supernova shock encounters. This physics is not included in present-day 1D models and enters the structural parameters that predict explodability. Flattening the gradients days before collapse favors an O--C shell merger, which could reshape pre-collapse nucleosynthesis. Without this physics 1D models carry too sharp gradients that introduce previously unaccounted systematic errors into the explodability surveys, yield tables and chemical-evolution studies built on them.

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arXiv2026

Wave-Driven Mixing Enhanced by Rotation in Red Giant Branch Stars

Stars like our Sun expand as they exhaust their core hydrogen fuel, becoming red giants that eventually reach sizes up to 100 times their original radius. These giants have long presented a puzzle: they show systematic changes in their surface chemical composition that can only be explained by the transport of material from their nuclear-burning interior to their surface. The challenge is that this transport must somehow cross a stable layer that acts as a barrier between the star's outer convective envelope and its nuclear-burning interior. The convective motions in the envelope create internal waves that propagate through this barrier layer, but on their own these waves produce very little material transport. Here we show through high-resolution three-dimensional hydrodynamical simulations that stellar rotation dramatically amplifies how effectively these waves can mix material across this barrier. We find that the mixing rates can exceed those in non-rotating stars by over 100 times, increasing with faster rotation rates. This enhanced mixing provides a natural explanation for the observed chemical signatures in typical red giants. The amplification of wave-driven mixing by rotation may have implications beyond red giants to other types of stars.

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arXiv2026

3D hydrodynamic simulations of massive main-sequence stars -- IV. Internal gravity waves matter for SLF variability

The power spectrum of light curves from satellites like CoRoT and TESS of massive main-sequence stars show stochastic low-frequency (SLF) variability. To investigate the origin of this phenomenon, we conducted high-resolution 3D hydrodynamic \texttt{PPMstar} simulations of a non-rotating \unit{25}{\Msun} zero-age main sequence star, modeling 95\% of the stellar structure with both a core and a thin outer envelope convection zone. The outer envelope convection zone was implemented through modification of the opacity model, shifting the Fe opacity bump inward and enhancing its amplitude for computational feasibility. The luminosity power spectrum from our primary simulation (M424) exhibits qualitative and quantitative characteristics similar to observed SLF variability, with a $\approx2$-dex difference between high- and low-frequency power. The spectrum displays distinct features attributable to internal gravity wave (IGW) eigenmodes. To isolate the contributions of different stellar regions, we performed numerical experiments with suppressed core convection, envelope convection and envelope-only configurations. The comparative analysis demonstrates that outer envelope convection alone produces significantly less low-frequency power than the full-star configuration. In our simulations the outer envelope convection zone excites at its inner boundary a rich IGW eigenmode spectrum in the layer just below. In an otherwise identical simulation where the core convection is not driven by heating, the SLF spectrum is remarkably similar and the integrated power is reduced by only 10\%, suggesting that the envelope convection is the dominant contributor to SLF power spectrum. The IGW spectral characteristics depend on the complete stellar stratification, demonstrating that interior structure could influence observable surface variability.

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arXiv2024

Enhanced extra mixing in low-mass stars approaching the RGB tip and the problem of Li-rich red-clump stars

A few percent of red giants are enriched in Lithium with $A(\mathrm{Li}) > 1.5$. Their evolutionary status has remained uncertain because these Li-rich giants can be placed both on the red-giant branch (RGB) near the bump luminosity and in the red clump (RC) region. However, thanks to asteroseismology, it has been found that most of them are actually RC stars. Starting at the bump luminosity, RGB progenitors of the RC stars experience extra mixing in the radiative zone separating the H-burning shell from the convective envelope followed by a series of convective He-shell flashes at the RGB tip, known as the He-core flash. The He-core flash was proposed to cause fast extra mixing in the stars at the RGB tip that is needed for the Cameron-Fowler mechanism to produce Li. We propose that the RGB stars are getting enriched in Li by the RGB extra mixing that is getting enhanced and begins to produce Li, instead of destroying it, when the stars are approaching the RGB tip. After a discussion of several mechanisms of the RGB extra mixing, including the joint operation of rotation-driven meridional circulation and turbulent diffusion, the Azimuthal Magneto-Rotational Instability (AMRI), thermohaline convection, buoyancy of magnetic flux tubes, and internal gravity waves, and based on results of (magneto-) hydrodynamics simulations and asteroseismology observations, we are inclined to conclude that it is the mechanism of the AMRI or magnetically-enhanced thermohaline convection, that is most likely to support our hypothesis.

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arXiv2024

3D hydrodynamic simulations of massive main-sequence stars II. Convective excitation and spectra of internal gravity waves

Recent photometric observations of massive stars have identified a low-frequency power excess which appears as stochastic low-frequency variability in light curve observations. We present the oscillation properties of high resolution hydrodynamic simulations of a 25 $\mathrm{M}_\odot$ star performed with the PPMStar code. The model star has a convective core mass of $\approx\, 12\, \mathrm{M}_\odot$ and approximately half of the envelope simulated. From this simulation, we extract light curves from several directions, average them over each hemisphere, and process them as if they were real photometric observations. We show how core convection excites waves with a similar frequency as the convective time scale in addition to significant power across a forest of low and high angular degree $l$ modes. We find that the coherence of these modes is relatively low as a result of their stochastic excitation by core convection, with lifetimes on the order of 10s of days. Thanks to the still significant power at higher $l$ and this relatively low coherence, we find that integrating over a hemisphere produces a power spectrum that still contains measurable power up to the Brunt--Väisälä frequency. These power spectra extracted from the stable envelope are qualitatively similar to observations, with same order of magnitude yet lower characteristic frequency. This work further shows the potential of long-duration, high-resolution hydrodynamic simulations for connecting asteroseismic observations to the structure and dynamics of core convection and the convective boundary.

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arXiv2023

3D hydrodynamics simulations of a 3 $M_{\odot}$ core-helium burning star

The inner structure of core-helium burning (CHeB) stars remains uncertain due to the yet unknown nature of mixing at the boundary of their cores. Large convective cores beyond a bare Schwarzschild model are favoured both from theoretical arguments and from asteroseismological constraints. However, the exact nature of this extra mixing, and in particular the possible presence of semiconvective layers, is still debated. In this work, we approach this problem through a new avenue by performing the first full-sphere 3D hydrodynamics simulations of the interiors of CHeB stars. We use the PPMstar explicit gas dynamics code to simulate the inner 0.45 $M_{\odot}$ of a 3 $M_{\odot}$ CHeB star. Simulations are performed using different Cartesian grid resolutions (768$^3$, 1152$^3$ and 1728$^3$) and heating rates. We use two different initial states, one based on MESA's predictive mixing scheme (which significantly extends the core beyond the Schwarzschild boundary) and one based on the convective premixing approach (which exhibits a semiconvective interface). The general behaviour of the flow in the convective core and in the stable envelope (where internal gravity waves are observed) is consistent with our recent simulations of core convection in massive main-sequence stars, and so are the various luminosity scaling relations. The semiconvective layers are dominated by strong internal gravity waves that do not produce measurable species mixing, but overshooting motions from the convective core gradually homogenize the semiconvective interface. This process can possibly completely erase the semiconvective layers, which would imply that CHeB stars do not harbour a semiconvection zone.

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arXiv2023

3D hydrodynamic simulations of massive main-sequence stars. I. Dynamics and mixing of convection and internal gravity waves

We performed 3D hydrodynamic simulations of the inner $\approx 50\%$ radial extent of a $25\ \mathrm{M_\odot}$ star in the early phase of the main sequence and investigate core convection and internal gravity waves in the core-envelope boundary region. Simulations for different grid resolutions and driving luminosities establish scaling relations to constrain models of mixing for 1D applications. As in previous works, the turbulent mass entrainment rate extrapolated to nominal heating is unrealistically high ($1.58\times 10^{-4}\ \mathrm{M_\odot/yr}$), which is discussed in terms of the non-equilibrium response of the simulations to the initial stratification. We measure quantitatively the effect of mixing due to internal gravity waves excited by core convection interacting with the boundary in our simulations. The wave power spectral density as a function of frequency and wavelength agrees well with the GYRE eigenmode predictions based on the 1D spherically averaged radial profile. A diffusion coefficient profile that reproduces the spherically averaged abundance distribution evolution is determined for each simulation. Through a combination of eigenmode analysis and scaling relations it is shown that in the $N^2$-peak region, mixing is due to internal gravity waves and follows the scaling relation $D_\mathrm{IGW-hydro} \propto L^{4/3}$ over a $\gtrapprox 2\ \mathrm{dex}$ range of heating factors. Different extrapolations of the mixing efficiency down to nominal heating are discussed. If internal gravity wave mixing is due to thermally-enhanced shear mixing, an upper limit is $D_\mathrm{IGW} \lessapprox 2$ to $3\times 10^4\ \mathrm{cm^2/s}$ at nominal heating in the $N^2$-peak region above the convective core.

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arXiv2023

3D hydrodynamics simulations of core convection in supermassive main-sequence stars

Supermassive stars are Population III stars with masses exceeding $10^4\,M_{\odot}$ that could be the progenitors of the first supermassive black holes. Their interiors are in a regime where radiation pressure dominates the equation of state. In this work, we use the explicit gas dynamics code PPMstar to simulate the hydrogen-burning core of a $10^4\,M_{\odot}$ supermassive main-sequence star. These are the first 3D hydrodynamics simulations of core convection in supermassive stars. We perform a series of ten simulations at different heating rates and on Cartesian grids with resolutions of $768^3$, $1152^3$ and $1728^3$. We examine different properties of the convective flow, including its large-scale morphology, its velocity spectrum and its mixing properties. We conclude that the radiation pressure-dominated nature of the interior does not noticeably affect the behaviour of convection compared to the case of core convection in a massive main-sequence star where gas pressure dominates. Our simulations also offer support for the use of mixing-length theory in 1D models of supermassive stars.

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arXiv2023

3D hydrodynamics simulations of internal gravity waves in red giant branch stars

We present the first 3D hydrodynamics simulations of the excitation and propagation of internal gravity waves (IGWs) in the radiative interiors of low-mass stars on the red giant branch (RGB). We use the PPMstar explicit gas dynamics code to simulate a portion of the convective envelope and all the radiative zone down to the hydrogen-burning shell of a 1.2$M_{\odot}$ upper RGB star. We perform simulations for different grid resolutions (768$^3$, 1536$^3$ and 2880$^3$), a range of driving luminosities, and two different stratifications (corresponding to the bump luminosity and the tip of the RGB). Our RGB tip simulations can be directly performed at the nominal luminosity, circumventing the need for extrapolations to lower luminosities. A rich, continuous spectrum of IGWs is observed, with a significant amount of total power contained at high wavenumbers. By following the time evolution of a passive dye in the stable layers, we find that IGW mixing in our simulations is weaker than predicted by a simple analytical prescription based on shear mixing and not efficient enough to explain the missing RGB extra mixing. However, we may be underestimating the efficiency of IGW mixing given that our simulations include a limited portion of the convective envelope. Quadrupling its radial extent compared to our fiducial setup increases convective velocities by up to a factor 2 and IGW velocities by up to a factor 4. We also report the formation of a $\sim 0.2\,H_P$ penetration zone and evidence that IGWs are excited by plumes that overshoot into the stable layers.

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arXiv2018

Simulating 3-D Stellar Hydrodynamics using PPM and PPB Multifluid Gas Dynamics on CPU and CPU+GPU Nodes

The special computational challenges of simulating 3-D hydrodynamics in deep stellar interiors are discussed, and numerical algorithmic responses described. Results of recent simulations carried out at scale on the NSF's Blue Waters machine at the University of Illinois are presented, with a special focus on the computational challenges they address. Prospects for future work using GPU-accelerated nodes such as those on the DoE's new Summit machine at Oak Ridge National Laboratory are described, with a focus on numerical algorithmic accommodations that we believe will be necessary.

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arXiv2014

Hydrodynamic simulations of H entrainment at the top of He-shell flash convection

We present the first 3-dimensional, fully compressible gas-dynamics simulations in $4π$ geometry of He-shell flash convection with proton-rich fuel entrainment at the upper boundary. This work is motivated by the insufficiently understood observed consequences of the H-ingestion flash in post-AGB stars (Sakurai's object) and metal-poor AGB stars. Our investigation is focused on the entrainment process at the top convection boundary and on the subsequent advection of H-rich material into deeper layers, and we therefore ignore the burning of the proton-rich fuel in this study. We find that, for our deep convection zone, coherent convective motions of near global scale appear to dominate the flow. At the top boundary convective shear flows are stable against Kelvin-Helmholtz instabilities. However, such shear instabilities are induced by the boundary-layer separation in large-scale, opposing flows. This links the global nature of thick shell convection with the entrainment process. We establish the quantitative dependence of the entrainment rate on grid resolution. With our numerical technique simulations with $1024^3$ cells or more are required to reach a numerical fidelity appropriate for this problem. However, only the result from the $1536^3$ simulation provides a clear indication that we approach convergence with regard to the entrainment rate. Our results demonstrate that our method, which is described in detail, can provide quantitative results related to entrainment and convective boundary mixing in deep stellar interior environments with veryvstiff convective boundaries. For the representative case we study in detail, we find an entrainment rate of $4.38 \pm 1.48 \times 10^{-13}M_\odot \mathrm{/s}$.

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arXiv2014

Global non-spherical oscillations in 3-D $4π$ simulations of the H-ingestion flash

We performed 3-D simulations of proton-rich material entrainment into \czw-rich He-shell flash convection and the subsequent H-ingestion flash that took place in the post-AGB star Sakurai's object. Observations of the transient nature and anomalous abundance features are available to validate our method and assumptions, with the aim to apply them to very low metallicity stars in the future. We include nuclear energy feedback from H burning and cover the full $4π$ geometry of the shell. Runs on $768^3$ and $1536^3$ grids agree well with each other and have been followed for $1500\mathrm{min}$ and $1200\mathrm{min}$. After a $850\mathrm{min}$ long quiescent entrainment phase the simulations enter into a global non-spherical oscillation that is launched and sustained by individual ignition events of H-rich fluid pockets. Fast circumferential flows collide at the antipode and cause the formation and localized ignition of the next H-overabundant pocket. The cycle repeats for more than a dozen times while its amplitude decreases. During the global oscillation the entrainment rate increases temporarily by a factor $\approx 100$. Entrained entropy quenches convective motions in the upper layer until the burning of entrained H establishes a separate convection zone. The lower-resolution run hints at the possibility that another global oscillation, perhaps even more violent will follow. The location of the H-burning convection zone agrees with a 1-D model in which the mixing efficiency is calibrated to reproduce the light curve. The simulations have been performed at the NSF Blue Waters supercomputer at NCSA.

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arXiv2011

Convective-reactive proton-C12 combustion in Sakurai's object (V4334 Sagittarii) and implications for the evolution and yields from the first generations of stars

Depending on mass and metallicity as well as evolutionary phase, stars occasionally experience convective-reactive nucleosynthesis episodes. We specifically investigate the situation when nucleosynthetically unprocessed, H-rich material is convectively mixed with a He-burning zone, for example in convectively unstable shell on top of electron-degenerate cores in AGB stars, young white dwarfs or X-ray bursting neutron stars. Such episodes are frequently encountered in stellar evolution models of stars of extremely low or zero metal content [...] We focus on the convective-reactive episode in the very-late thermal pulse star Sakurai's object (V4334 Sagittarii). Asplund etal. (1999) determined the abundances of 28 elements, many of which are highly non-solar, ranging from H, He and Li all the way to Ba and La, plus the C isotopic ratio. Our simulations show that the mixing evolution according to standard, one-dimensional stellar evolution models implies neutron densities in the He that are too low to obtain a significant neutron capture nucleosynthesis on the heavy elements. We have carried out 3D hydrodynamic He-shell flash convection [...] we assume that the ingestion process of H into the He-shell convection zone leads only after some delay time to a sufficient entropy barrier that splits the convection zone [...] we obtain significantly higher neutron densities (~few 10^15 1/cm^3) and reproduce the key observed abundance trends found in Sakurai's object. These include an overproduction of Rb, Sr and Y by about 2 orders of magnitude higher than the overproduction of Ba and La. Such a peculiar nucleosynthesis signature is impossible to obtain with the mixing predictions in our one-dimensional stellar evolution models. [...] We determine how our results depend on uncertainties of nuclear reaction rates, for example for the C13(α, n)O16 reaction.

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arXiv2009

The Hydrodynamic Environment for the s Process in the He-Shell Flash of AGB Stars

The He-shell flash convection in AGB stars is the site for the high-temperature component of the s-process in low- and intermediate mass giants, driven by the Ne22 neutron source. [...] The upper convection boundary plays a critical role during the H-ingestion episode that may lead to neutron-bursts in the most metal-poor AGB stars. We address these problems through global 3-dimensional hydrodynamic simulations including the entire spherical He-shell flash convection zone (as oposed to the 3D box-in-a-star simulations). An important aspect of our current effort is to establish the feasibility of our appoach. We explain why we favour the explicit treatment over the anelastic approximation for this problem. The simulations presented in this paper use a Cartesian grid of 512^3 cells and have been run on four 8-core workstations for four days to simulate ~5000s, which corresponds to almost ten convective turn-over times. The convection layer extends radially at the simulated point in the flash evolution over 7 H_p pressure scale-heights and exceeds the size of the underlying core. Convection is dominated by large convective cells that fill more than an entire octant. [...]

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arXiv2007

Convective and non-convective mixing in AGB stars

We review the current state of modeling convective mixing in AGB stars. The focus is on results obtained through multi-dimensional hydrodynamic simulations of AGB convection, both in the envelope and the unstable He-shell. Using two different codes and a wide range of resolutions and modeling assumptions we find that mixing across convective boundaries is significant for He-shell flash convection. We present a preliminary quantitative analysis of this convectively induced extra mixing, based on a sub-set of our simulations. Other non-standard mixing will be discussed briefly.

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