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Multi-dimensional simulations of helium shell flash convection
F. Herwig1,2, B. Freytag3,2, R. M. Hueckstaedt2, F. Timmes2
1. Keele Astrophysics Group, School of Physical and Geographical Sciences, Keele University, UK;
[email protected]
2. Los Alamos National Laboratory, Los Alamos, NM, USA; [email protected], [email protected]
3. Centre de Recherche Astronomique de Lyon- Ecole Normale Supérieure, Lyon, France;
[email protected]
The Asymptotic Giant Branch (AGB) phase is the most productive evolutionary phase in
terms of nucleosynthesis for low and intermediate mass stars. Nucleosynthesis in these
stars is aided by the mixing and heating triggered by recurrent He-shell flashes (Fig.1).
Extreme nuclear energies (corresponding to 108L) are generated during these
thermonuclear flashes with multiple implications for nucleosynthesis and evolution. 1-d
stellar evolution codes (Fig.1) have to adopt simplifying assumptions on convection
induced mixing, especially at convective boundaries. Here, we report on 2D (Fig.2) and
3D (Fig.3, bottom panel) hydrodynamic models of convective mixing in the AGB He-shell
(Herwig etal. 2006, Freytag etal 2007). As opposed to the shallow surface convection in Atype stars studied by Freytag et al. (1996), coherently moving convective cells do not
cross the convective boundary significantly (Fig.2). In other words, penetration is minimal
for this convection zone. We find that convective motions induce a rich spectrum of
internal gravity waves in the neighboring stable layers (Fig.3, top). Interactions of these
(mainly horizontal) oscillations with the convective boundary, as well as motions with
convective characteristics within the stable layers, do cause a finite amount of mixing
across the convective boundary. Our preliminary analysis of this mixing (Fig.4 and 5) is
consistent with semi-analytical results obtained from observations and 1D stellar evolution
simulations (Werner & Herwig, 2006).
convection
p-modes
g-modes
Fig. 3. Top: Frequency-Wave number (k-) power diagrams for different vertical locations in a 2D
RAGE simulation. Gravity modes are strongest in the stable layers. Convective motions are evident
in the stable layers (marked with red line) as well. Bottom: Horizontal slices through different heights
of a 3D simulation showing vertical velocity (light for upward; dark for downward).
Fig.1: Evolution of convective boundaries and burning shells at the coreenvelope interface where all
of the nucleosynthesis in
AGB stars takes place. Convection regions are green,
the location of the H- and
He-burning shells are shown
with red and purple solid
lines. The data was obtained
with a 1D stellar evolution
code. We use the stratification from a 1D He-shell flash
model (t=0yr) for the vertical
stratification of the 2D and
3D hydrodynamic simulations (Fig. 2, 3).
Fig. 2. Top: Fully-developed convection in a 2-D RAGE simulation shown as color-coded pressure fluctuations around
the horizontal mean with pseudo-streamlines superimposed. Middle: The same result shown as entropy fluctuations. A
brighter color indicates higher entropy (as well as higher temperature). Bottom: Different vertical slices of a 3-d RAGE
simulation showing entropy fluctuations. The structure is similar to that seen in 2-d, albeit at a lower spatial resolution.
Fig. 4. Mixing efficiency f versus the number of vertical grid points for two slopes in the lower overshoot region (left and
center panels) and one slope in the upper overshoot region (left panel). The f-value quantifies the exponential decay of
D (see Fig. 5) across the convective boundaries. Models were run using two different Eulerian adaptive-mesh
refinement codes: RAGE (LANL and SAIC) and FLASH (U. of Chicago), and at two heating rates (g-heat: realistic rate
as in stellar model, d-heat: 30 x g-heat). Compared to RAGE, FLASH has a higher-order method and shows more
small-scale structure; yet the f-values are comparable for the two codes with the exception of one outlier. With respect
to spatial resolution, simulations with the enhanced heating rate converge more quickly than those with a nominal
heating rate.
Fig. 5. Diffusion coefficient
derived with a tracer particle
method from the velocity
fields of a 2D simulation.
Green circles
and
red
crosses
show
diffusion
coefficients derived using
spread evolutions of entropy
and
vertical
coordinate,
respectively. The evolution of
the vertical coordinate is
more appropriate in the
convection zone.
References: Freytag B., Ludwig H.-G., & Steffen M., 1996, A&A 313, 497
Freytag B., Herwig F., Hueckstaedt R.M., etal., 2007, in prep.
Herwig F., Freytag B., Hueckstaedt R.M., & Timmes F.X., 2006, ApJ 642, 1057
Herwig, F. & Werner, K., 2006, PASP 118, 138