Turbulent Convection in Stellar Interiors. I. Hydrodynamic Simulation

By C. Meakin, D. Arnett. 2006

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We describe the results of 3D numerical simulations of oxygen shell burning and hydrogen core burning in a 23 M☉ stellar model. A detailed comparison is made to stellar mixing-length theory (MLT) for the shell-burning model. Simulations in 2D are significantly different from 3D, in terms of both flow morphology and velocity amplitude. Convective mixing regions are better predicted using a dynamic boundary condition based on the bulk Richardson number than by purely local, static criteria like Schwarzschild or Ledoux. MLT gives a good description of the velocity scale and temperature gradient for shell convection; however, there are other important effects that it does not capture, mostly related to the dynamical motion of the boundaries between convective and nonconvective regions. There is asymmetry between upflows and downflows, so the net kinetic energy flux is not zero. The motion of convective boundaries is a source of gravity waves; this is a necessary consequence of the deceleration of convective plumes. Convective "overshooting" is best described as an elastic response by the convective boundary, rather than ballistic penetration of the stable layers by turbulent eddies. The convective boundaries are rife with internal and interfacial wave motions, and a variety of instabilities arise that induce mixing through a process best described as turbulent entrainment. We find that the rate at which material entrainment proceeds at the boundaries is consistent with analogous laboratory experiments and simulation and observation of terrestrial atmospheric mixing. In particular, the normalized entrainment rate E = uE/σH is well described by a power-law dependence on the bulk Richardson number RiB = ΔbL/σ for the conditions studied, 20 ≲ RiB ≲ 420. We find E = ARi, with best-fit values log A = 0.027 ± 0.38 and n = 1.05 ± 0.21. We discuss the applicability of these results to stellar evolution calculations.

Subfields: Astronomy and Astrophysics

View Paper: https://www.semanticscholar.org/paper/bb7ac36033741cf22851eaef6855b32c865e52c7

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Citations in the corpus

Mass Loss: Its Effect on the Evolution and Fate of High-Mass Stars (2014, background): “…(Woosley et al. 2002, 2007), other explosive shell burning instabilities (Dessart et al. 2010, Smith & Arnett 2014), wave-driven 20 Smith mass loss (Meakin & Arnett 2007, Quataert & Shiode 2012, Shiode & Quataert 2013), and stellar collisions or mergers in a binary system (Podsiadlowski et al.…”
TOWARD REALISTIC PROGENITORS OF CORE-COLLAPSE SUPERNOVAE (2011, methodology): “However, simulations in 3D will have essentially the same driving mechanisms as in 2D. Based upon existing simulations (e.g., Meakin & Arnett 2007b), it is unlikely that the increased damping will eliminate dynamic behavior entirely.”
PREPARING FOR AN EXPLOSION: HYDRODYNAMIC INSTABILITIES AND TURBULENCE IN PRESUPERNOVAE (2013, methodology): “Simulations show vigorous wave production at convective boundaries (Meakin & Arnett 2007b).”
Pre-supernova outbursts via wave heating in massive stars – I. Red supergiants (2017, background): “Remarkably, these estimates of convective velocities and turnover frequencies typically match those seen in 3D simulations of a variety of burning phases (e.g. Meakin & Arnett 2007a; Alvan et al. 2014; Couch & Ott 2015; Lecoanet et al. 2016; Jones et al. 2017) to within a factor of 2.”
Multidimensional supernova simulations with approximative neutrino transport. II. Convection and the (2007, background): “…whose size and amplitude are not well known because threedimensional, long-time stellar evolution simulations for fullsphere models until the onset of core collapse have not been possible so far (see, e.g., Bazan & Arnett 1998; Murphy et al. 2004; Young et al. 2005; Meakin & Arnett 2006, 2007a,b).”
A MODEL FOR GRAVITATIONAL WAVE EMISSION FROM NEUTRINO-DRIVEN CORE-COLLAPSE SUPERNOVAE (2009, methodology): “For one, in steady-state stellar convection, the eddies are larger and have faster speeds in 2D simulations (Arnett et al. 2009; Meakin & Arnett 2007b, and the references therein).”
Colloquium: Perspectives on core-collapse supernova theory (2012, background): “In a very real sense, “progenitor is destiny,” a mapping complicated only by the randomness associated with chaotic turbulence and instability dynamics and with the unknown initial perturbation spectrum imposed by pre-collapse convective burning (Meakin & Arnett 2006,2007ab).”
Luminous blue variable eruptions and related transients: diversity of progenitors and outburst properties (2010, background): “Initial simulations suggest that boundary layers within the star may be susceptible to dynamic disturbances (Meakin & Arnett 2007; Guzik et al. 1999, 2005).”
REVIVAL OF THE STALLED CORE-COLLAPSE SUPERNOVA SHOCK TRIGGERED BY PRECOLLAPSE ASPHERICITY IN THE PROGENITOR STAR (2013, methodology): “The 3D oxygen burning simulations of Meakin & Arnett (2007) suggest that in 3D the Mach numbers of fluctuations may be only half as large as in 2D.”
Type II-Plateau supernova radiation: dependences on progenitor and explosion properties (2013, unknown): “The treatment of convection by means of the mixing-length theory (MLT), or core overshooting at theedge of convective regions, is far from satisfactory (Meakin & Arnett 2007).”
Dawes Review 6: The Impact of Companions on Stellar Evolution (2016, methodology): “Convection in giant stars was studied using 3D models by Meakin & Arnett (2007) and more recently by Chiavassa et al. (2011) with CO5BOLD (Freytag, Steffen, & Dorch, 2002) at relatively low resolution, but high enough for a meaningful comparison with VLTI observations of Wittkowski et al. (2016).”
THE COMPACTNESS OF PRESUPERNOVA STELLAR CORES (2013, methodology): “Simulations by Meakin and collaborators (e.g. Meakin & Arnett 2007; Viallet et al. 2013) confirm that some type of mixing will always take place at convective boundaries defined by either the Ledoux or Schwarzschild criterion, although the exact formulation of this mixing remains uncertain.”
THE ROLE OF TURBULENCE IN NEUTRINO-DRIVEN CORE-COLLAPSE SUPERNOVA EXPLOSIONS (2014, background): “…in the Si/O shell not unlike the fluctuations 6 Some data for unperturbed models are taken from Couch & O’Connor (2014). found in realistic, multi-dimensional simulations of convective nuclear burning in massive stars in both scale and strength (Meakin & Arnett 2007; Arnett & Meakin 2011).”
A PANCHROMATIC VIEW OF THE RESTLESS SN 2009ip REVEALS THE EXPLOSIVE EJECTION OF A MASSIVE STAR ENVELOPE (2013, background): “Finally we mention that direct numerical simulations of pre-collapse hydrodynamics by Meakin (2006), Meakin & Arnett (2007) and Arnett & Meakin (2011a,b) found eruptive instabilities due to the interaction of oxygen and silicon burning shells.”
MODULES FOR EXPERIMENTS IN STELLAR ASTROPHYSICS (MESA): PLANETS, OSCILLATIONS, ROTATION, AND MASSIVE STARS (2013, background): “A dependency on the evolutionary stage seems also likely (Herwig et al. 1997; Meakin & Arnett 2007; Tian et al. 2009).”
A High-resolution Study of Presupernova Core Structure (2017, background): “…bifurcations may not be real and might be overcome, or at least smoothed out (Alexakis et al. 2004), by increasing the convective overshoot or doing a multi-dimensional calculation (e.g., Meakin & Arnett 2007; Viallet et al. 2013; Arnett & Meakin 2016; Jones et al. 2017; Cristini et al. 2017).”
The Status of Multi-Dimensional Core-Collapse Supernova Models (2016, methodology): “First numerical experiments based on the entrainment law of Meakin & Arnett (2007b) were performed by Staritsin (2013) for massive stars on the main sequence 14 and did not reveal dramatic differences in the size of the convective cores compared to more familiar, calibrated recipes for core…”
GENERAL-RELATIVISTIC SIMULATIONS OF THREE-DIMENSIONAL CORE-COLLAPSE SUPERNOVAE (2012, methodology): “In short, Meakin & Arnett (2007a) found that the root-mean-square (rms) density fluctuations are largest at the convective boundaries.”