PPMstar

3D hydrodynamics simulations of a $3 M_{\odot}$ core-helium burning star
Simon Blouin, Falk Herwig, Huaqing Mao, Pavel Denissenkov, Paul R. Woodward. 2023. MNRAS submitted.

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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 $\texttt{PPMstar}$ 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 $\texttt{MESA}$ predictive mixing scheme (which yields a large overshoot region) 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 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.

3D hydrodynamics simulations of core convection in supermassive main-sequence stars.
Blouin, Simon; Mao, Huaqing ; Woods, Tyrone E. ; Denissenkov, Pavel ; Woodward, Paul R. ; Herwig, Falk. 2023. MNRAS, 521, 4605.

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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 spectra 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.

3D hydrodynamics simulations of internal gravity waves in red giant branch stars
Simon Blouin, Huaqing Mao, Falk Herwig, Pavel Denissenkov, Paul R. Woodward, William R. Thompson

• Paper MNRAS 2023
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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.

3D hydrodynamic simulations of massive main-sequence stars
Team: Herwig, Falk; Woodward, Paul; Mao, Huaqing; Thompson, William; Denissenkov, Pavel; Bouin, Simon; Bowman, Dominic; Andrassy, Robert; Lau, Josh et al.

We present 3D hydrodynamic simulations of core convection in a 25 solar mass star. The first three papers of this project are now available on arXiv

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• Paper I (published) Dynamics and mixing of convection and internal gravity waves
• Paper II (submitted) Convective excitation and spectra of internal gravity waves
• Paper III (submitted) The effect of radiation pressure and diffusion leading to a 1D equilibrium model

3D1D hydro-nucleosynthesis simulations. I. Advective-reactive post-processing method and its application to H ingestion into He-shell flash convection in rapidly accreting white dwarfs
Stephens, David; Herwig, Falk; Woodward, Paul; Denissenkov, Pavel; Andrassy, Robert; Mao, Huaqing. 2020. MNRAS 504, 744.

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We present two mixing models for post-processing of 3D hydrodynamic simulations applied to convective-reactive i-process nucleosynthesis in a rapidly accreting white dwarf (RAWD) with [Fe/H] =−2.6, in which H is ingested into a convective He shell. A 1D advective two-stream model adopts physically motivated radial and horizontal mixing coefficients constrained by 3D hydrodynamic simulations. A simpler approach uses diffusion coefficients calculated from the same simulations. All 3D simulations include the energy feedback of the¹²C(p,γ)¹³N reaction from the H entrainment. Global oscillations of shell H ingestion in two of the RAWD simulations cause bursts of entrainment of H and non-radial hydrodynamic feedback. With the same nuclear network as in the 3D simulations, the 1D advective two-stream model reproduces the rate and location of the H burning within the He shell closely matching the 3D simulation predictions, as well as qualitatively displaying the asymmetry of the X_H profiles between the up- and downstream. With a full i-process network the advective mixing model captures the difference in the n-capture nucleosynthesis in the up- and downstream. For example, ⁸⁹Kr and ⁹⁰Kr with half-lives of 3.18 min and 32.3 s differ by a factor 2 - 10 in the two streams. In this particular application the diffusion approach provides globally the same abundance distribution as the advective two-stream mixing model. The resulting i-process yields are in excellent agreement with observations of the exemplary CEMP-r/s star CS31062-050.

3D Hydrodynamic Simulations of C Ingestion into a Convective O Shell
Andrassy R, Herwig F, Woodward P, Ritter C. 2020. MNRAS. 491(1):972-992

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Interactions between convective shells in evolved massive stars have been linked to supernova impostors, to the production of the odd-Z elements Cl, K, and Sc, and they might also help generate the large-scale asphericities that are known to facilitate shock revival in supernova explosion models. We investigate the process of ingestion of C-shell material into a convective O-burning shell, including the hydrodynamic feedback from the nuclear burning of the ingested material. Our 3D hydrodynamic simulations span almost 3 dex in the total lumunosity L_tot. All but one of the simulations reach a quasi-stationary state with the entrainment rate and convective velocity proportional to L_tot and L_tot^1/3 , respectively. Carbon burning provides 14-33 percent of the total luminosity, depending on the set of reactions considered. Equivalent simulations done on 768³ and 1152³ grids are in excellent quantitative agreement. The flow is dominated by a few large-scale convective cells. An instability leading to large-scale oscillations with Mach numbers in excess of 0.2 develops in an experimental run with the energy yield from C burning increased by a factor of 10. This run represents most closely the conditions expected in a violent O-C shell merger, which is a potential production site for odd-Z elements such as K and Sc and which may seed asymmetries in the supernova progenitor. 1D simulations may underestimate the energy generation from the burning of ingested material by as much as a factor 2 owing to their missing the effect of clumpiness of of entrained material on the nuclear reaction rate.

Idealized hydrodynamic simulations of turbulent oxygen-burning shell convection in 4π geometry
Jones S., Andrassy R., Sandalski S., Davis A., Woodward P., Herwig F. 2017. MNRAS. 465:2991.

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This work investigates the properties of convection in stars with particular emphasis on entrainment across the upper convective boundary (CB). Idealized simulations of turbulent convection in the O-burning shell of a massive star are performed in 4π geometry on 768³ and 1536³ grids, driven by a representative heating rate. A heating series is also performed on the 768³ grid. The 1536³ simulation exhibits an entrainment rate at the upper CB of 1.33 × 10^-6 M☉/s. The 768³ simulation with the same heating rate agrees within 17 per cent. The entrainment rate at the upper CB is found to scale linearly with the driving luminosity and with the cube of the shear velocity at the upper boundary, while the radial rms fluid velocity scales with the cube root of the driving luminosity, as expected. The mixing is analysed in a 1D diffusion framework, resulting in a simple model for CB mixing. The analysis confirms that limiting the MLT mixing length to the distance to the CB in 1D simulations better represents the spherically averaged radial velocity profiles from the 3D simulations and provide an improved determination of the reference diffusion coefficient D0 for the exponential diffusion CB mixing model in 1D. From the 3D simulation data, we adopt as the CB the location of the maximum gradient in the horizontal velocity component which has 2σ spatial fluctuations of ≈0.17H_P. The exponentially decaying diffusion CB mixing model with f = 0.03 reproduces the spherically averaged 3D abundance profiles.

Hydrodynamic Simulations of H Entrainment at the Top of He-shell Flash Convection
Woodward P. R., Herwig F., Lin P.-H. 2015. The Astrophysical Journal. 798:49.

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• Simulating Stellar Hydrodynamics at Extreme Scale

We present the first three-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-asymptotic giant branch (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 1024³ cells or more are required to reach a numerical fidelity appropriate for this problem. However, only the result from the 1536³ 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 very stiff convective boundaries. For the representative case we study in detail, we find an entrainment rate of 4.38 ± 1.48 × 10^-13 M_☉/s.

Global Non-spherical Oscillations in Three-dimensional 4π Simulations of the H-ingestion Flash.
Herwig F., Woodward P. R., Lin P.-H., Knox M., Fryer C. 2014. The Astrophysical Journal Letters. 792:L3.

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We performed three-dimensional simulations of proton-rich material entrainment into ¹²C-rich He-shell flash convection and the subsequent H-ingestion flash that took place in the post-asymptotic giant branch star Sakurai's object. Observations of the transient nature and anomalous abundance features are available to validate our method and assumptions, with the aim of applying 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 768³ and 1536³ grids agree well with each other and have been followed for 1500 minutes and 1200 minutes. After an 850 minute 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 of ≈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 one-dimensional 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.