Using Numerical Simulations to explore a Mixing Mechanisms for Nova Enrichment Jonathan Dursi

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1 The Center for Astrophysical Thermonuclear Flashes Using Numerical Simulations to explore a Mixing Mechanisms for Nova Enrichment Jonathan Dursi May 21, 2001 Alan Calder, Alexandros Alexakis, James Truran, Robert Rosner Bruce Fryxell, Kevin Olson, Paul Ricker, Frank Timmes, Mike Zingale An Accelerated Strategic Computing Initiative (ASCI) Academic Strategic Alliances Program (ASAP) Center at The University of Chicago

2 The Standard Model for Classical Novae What are Classical Novae? Thermonuclear explosions in hydrogen-rich envelopes on white dwarfs in close binary systems. How does evolution proceed? Accretion of matter from a companion leads to growth of the envelope until a critical pressure is achieved at its base to trigger a thermonuclear runaway. Why is the outburst so violent? A combination of degenerate conditions at the base of the envelope and the dredge-up of C, O, and Ne fuels from the white dwarf core yields rapid energy release on a dynamic time scale.

3 The Envelope Enrichment Mechanism Ejecta of all studied novae are characterized by enrichment (3040% by mass) in either He, CNO elements, or O, Ne, Mg elements (Truran and Livio 1986). Such enrichment cannot reflect the composition of the matter transferred from the (typically) low-mass stellar companions. Nuclear burning alone will not produce significant conversion of helium to carbon or heavier elements. Also, the degree of degeneracy in not generally significant to allow temperatures at the peak of the runaway to reach values (> Million K) at which breakout from CNO cycles can occur. Requisite enrichment must result from outward mixing (dredge-up) of material from underlying C/O or O/Ne white dwarf. Mechanism for mixing is the most critical issue.

4 Studied Enrichment Mechanisms Proposed mechanisms for out ward mix ing of whit e dwarf matt er int o hydrogen- rich envelopes include (see, e.g., review by Livio and Truran 1991): Shear mixing: Kippenhahn and Thomas 1978; Kutter and Sparks Diffusion-induced convection: Prialnik and Kovetz Convective overshoot-induced flame propagation: Woosley 1986; Glasner et al. 1997; Kercek et al

5 Shear- driven Wave Mixing on White Dwarfs Proposed Mechanism: At the surface of the white dwarf, gravity waves are being generated and amplified due to a resonant interaction with a wind (caused either by accretion or convection). Mixed layer from wind-wave interaction is distributed through the envelope by convection, thereby enriching the envelope.

6 Shear- Driven Wave Mixing on White Dwarfs

7 Shear- Driven Wave Mixing on White Dwarfs Gravity Waves: We have extended the formalism from oceanographic studies to arbitrary density ratios and determined the growth rate of unstable waves, in the linear theory, for the white dwarf case. 2-d simulations of the development and breaking of nonlinear gravity wave and subsequent mixing are underway. Convection: Development of new hydrostatic hydrodynamics module and methods for mapping 1-d models (Zingale, et al. 2002) allows for 2-d simulations of the onset of convection in realistic nova models. Simulations of onset of convection and characteristics of convective flows are underway. Development of subgrid models for the mixing layer based on heavy element fluxes from wind studies.

8 The Flash Code Short ly: Relat ivist ic accret ion ont o NS Flame- vort ex interactions Compressed turbulence Type Ia Supernova The Flash code Gravitat ional collapse/ Jeans instability 2 Is modular Wave breaking on white dwarfs 3 Has a modern CS- influenced architecture 4 Can solve a broad range of (ast ro)physics problems 5 Is highly port able Intracluster a. Can run on alllaserasci platforms driven shock interactions instabilit ies Nova outbursts on white dwarfs RayleighTaylor b. Runs on ot her available m assivelyparallel syst ems instability 5. Can ut ilize all processors on available m achines Scales and performs well Is available on t he web: htt p:/ / flash.uchicago.edu Magnet ic RayleighTaylor Cellular detonation Orzag/ Tang Helium burning on neutron MHD st ars vortex Richtmyer- Meshkov

9 Resonant Gravity Wave Breaking on White Dwarfs Two-dimensional simulation of a resonant gravity wave breaking Wind profile: U = Umax (1 e-y/δ), δ = 1.0 x 105 cm Densities: ρc/o = 10,000 g/cm3 50/50% C/O ρh/he = 1,000 g/cm3 75/25% H/He Simulation Domain: 1.0 x 106 cm X 1.0 x 106 cm Acceleration due to gravity: 4.5x 109 cm/s2

10 Resonant Gravity Wave Breaking on White Dwarfs

11 Shear- Driven Wave Mixing on White Dwarfs

12 Shear- Driven Wave Mixing on White Dwarfs

13 Previous work on Convection What has been learned from simulations performed to date? 2-D simulations (Livne and Glasner 1997; Kercek and Hillebrandt 1998) found comparable degrees of dredge-up and peak temperatures consistent with those of 1-D studies. 3-D numerical simulations (Kercek and Hillebrandt 1999) indicate that envelope enrichment via dredge-up proceeds slowly - if at all - and that the temperatures achieved in the hottest regions never approach those of the 1-D and 2-D studies. (Efficient cooling?). What can we hope to learn from further numerical studies? Do there exist conditions under which significant mixing can occur? Are the results obtained above robust? Multi-dimensional simulations are being performed from 1-D initial conditions from Ami Glasner, taken just before runaway.

14 Onset of Convection Want to understand what early convection looks like before runaway. 1-d initial model from A. Glasner. same as used in multi-dimensional runaway simulations, but earlier time (Tmax = 4e7 K). At this point, atmosphere is convectively unstable. Mapped into 2-d (planar) domain with the FLASH code. Initially perturbed with some extra thermal energy. Convective motions investigated. Simulations that follow: 320x960 uniform grid. Few seconds evolution time.

15 Onset of Convection Three t emperat ure perturbation strengths: 2, 5, 10%

16 Onset of Convection Tot al Velocit y cm/ s

17 Heavy element mixing from subgrid model

18 Conclusions Now have the ability to reliably address these problems (Zingale, et al. 2002). Shear-driven mixing is a promising model. Simulations show wave breaking to be effective at mixing. We will get quantitative results (Alexakis, et al.). Currently performing simulations of the onset of convection (Dursi et al.). We hope to use these simulations to calibrate 1-d mixing-length codes for prerunaway evolution. Simulations with a preliminary gravity wave flux subgrid model show promise for enrichment mechanism. We hope to develop prescriptions for subgrid models that will be made available.

19 Shear- Driven Wave Mixing on White Dwarfs Proposed Mechanism: At the surface of the white dwarf, gravity waves are being generated and amplified due to a resonant interaction with a wind (caused either by accretion or convection). What have we done? Motivated by oceanographic studies, where it has been shown that Kelvin-Helmholtz is not the instability responsible for the generation of waves, we have reexplored the nature of the instability. Linear Theory: We have extended the formalism for the generation of gravity waves to arbitrary density ratios and determined the growth rate of the unstable waves for the white dwarf case. Non-Linear Theory: We calculated the changes in the wave amplitude as they became non-linear. Using the Flash code, we were able to generate and follow the non-linear evolution of both the Kelvin Universit y of Chicago Helmholtz and thetheresonant modes.

20 Shear Driven Mixing of White Dwarf Surfaces Mixing model assumptions (Rosner et al. 2001): A fast envelope wind over the stellar surface drives gravity wave instabilities, leading to a well mixed layer. Such an effective wind may arise as a consequence of accretion-driven shear flows or of convective flows which accompany the final stages of the thermonuclear runaway. The envelope becomes unstable to convection at a time of order 10 to 100 years prior to outburst (at a temperature ~ 20 to 30 million K) Mixing timescale estimates give ~10 years, which is less than or comparable to the timescale for which convective instability is found to occur during the final stages of a nova thermonuclear runaway.