Download Evolution of low- and intermediate mass stars

Evolution of low- & intermed. mass stars
Evolution of low- and intermediate
mass stars
Falk Herwig
Dept. of Physics and Astronomy
University of Victoria
Evolution of low- & intermed. mass stars
2
thermohaline mixing
mass loss and opacities
rotation
convection
13C-pocket
•
12C combustion
proton•
Motivation
Sagittarius
Carina
MW
2.0
a
[Ba/Fe]
1.0
• understanding SFH and chemical
evolution in dSph galaxies
• constrain nucleosynthesis processes,
e.g. Eu vs α-elements
• near-field cosmologie: identify the
building blocks of our galaxy
0
– 1.0
1.5
Annu. Rev. Astro. Astrophys. 2009.47:371-425. Downloaded from arjournals.annualreviews.org
by UNIVERSITY OF VICTORIA on 05/25/10. For personal use only.
b
1.0
[Eu/Fe]
Evolution of low- & intermed. mass stars
3
Sculptor
Fornax
0.5
0
– 47 –
– 0.5
–2
Tolstoy etal 2009 (ARAA)
[Fe/H]
–1
0
Figure 13
Neutron-capture elements (a) Ba, and (b) Eu in the same four dSphs as in Figure 11 compared to the Milky
Way. Sgr (orange: McWilliam & Smecker-Hane 2005; Monaco et al. 2005; Sbordone et al. 2007), Fnx (blue:
Shetrone et al. 2003; Letarte 2007), Scl ( green: V. Hill & DART, in preparation; Shetrone et al. 2003; Geisler
et al. 2005), and Carina ( purple: Shetrone et al. 2003; Koch et al. 2008a). Open symbols refer to single-slit
spectroscopy measurements, whereas filled circles refer to multiobject spectroscopy. A representative
error-bar for the latter is shown on the left-hand side of the picture. The small gray squares are a
compilation of the Milky Way disk and halo star abundances, from Venn et al. (2004a).
• abundances in extremely enriched
very metal-poor stars
• stellar archeology: find the
nucleosynthetic signature of the first
stars in the Universe
Lucatello etal 2004
406
barium (Ba) or lanthanum (La). Among the few exceptions is europium (Eu), which is almost
exclusively an r-process product.
Figure 13 compares Ba and Eu abundances in four dSph galaxies and in the Milky Way. At
first glance, the Eu evolution in dSph galaxies resembles that of their respective α-elements (see
Figure 11), as expected for an r-process originating in massive stars. In the Milky Way, Ba and Y
are dominated by the r-process for [Fe/H] ! −2.0 (e.g., Johnson & Bolte 2002, Simmerer et al.
2004), whereas the s-process dominates at higher metallicities (e.g., more than 80% of the solar
Ba is of s-process origin).
At early times (at [Fe/H] < −1), there seems to be little difference between the various dSphs
and the Milky Way halo in Figure 13. However, there is a hint that at the lowest metallicities
([Fe/H] < −1.8), [Ba/Fe] increases in scatter and starts to turn down. This hint is confirmed in the
plot in Section 4.2, which includes other dSphs, although from much smaller samples (Shetrone,
Côté & Sargent 2001; Fulbright, Rich & Castro 2004; Aoki et al. 2009). In fact, this scatter
and downturn of [Ba/Fe] is a well-known feature in the Milky Way halo (François et al. 2007;
Barklem et al. 2005, and references therein), where it occurs at much lower metallicities ([Fe/H] <
−3.0). So far we have extremely low number statistics for dSphs, and these results need to be
confirmed in larger samples of low-metallicity stars. These low r-process values at higher [Fe/H]
Tolstoy
· ·
Hill
Tosi
Evolution of low- & intermed. mass stars
how?
4
Multi-physics and multi-scale simulations:
Multi-physics:
• nuclear physics, nucleosynthesis
• evolution of the star: atomic, plasma, hydro, EOS under extreme
conditions
• stellar explosion
Multi-scale (e.g. time):
Evolution time: 100 to 103yrs (log t/s = 7 … 11)
Flash-burning (combustion) times: hours to days (log t/s = 3 … 5)
Convective mixing/Nuclear reaction time: minutes (log t/s = 1 … 2)
Sound crossing time: seconds (log t/s = 0 … 1)
n-capture time scale: < seconds (log t/s < 0)
How to respond?
Combine different simulation approaches for different components ...
Evolution of low- & intermed. mass stars
how?
5
The three simulation components
Stellar hydrodynamics
Stellar evolution
Nucleosynthesis
Evolution of low- & intermed. mass stars
6
Stellar evolution:
macroscopic/global
evolution of stars
Assumptions:
• Spherical symmetry
• Hydrostatic equilibrium (u=0)
Complete evolution of intermediate mass star
Conservation laws:
mass
momentum
energy
plus material properties: atomic, nuclear, thermodynamic physics.
Evolution of low- & intermed. mass stars
He-shell flashes in AGB stars
7
Adopted from Herwig, 2005, ARAA, 43.
MESA: modules for experiments in stellar evolution
8
4
low-/intermediate
mass evolution
3
MS to WD through Hecore flash
4
2
log L/Lsun
1
6.0
-1
10.0
-2
1.8
1.5
5
Y = 0.28
Z = 0.02
0
-4
M0.80
M1.00
M1.25
4.8
4.6
4.4
log Teff
1.2
1.0
0.8
4.0
3.8
3.6
log Teff
2
C-star
formation
on the
AGB
2
1.8
1.8
1.6
1.6
1.4
1.4
1
1
stellar mass
CO ratio
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
500000 1e+06 1.5e+06 2e+06 2.5e+06 3e+06 3.5e+06 4e+06 4.5e+06
0
age/yr
0.6
mr/Msun
1.2
1.2
O end
! Si
!
start
!
4
3.8
3.6
!
3.4
! Ne end
! Ne start
and O start
C end
!
C start
!
He end
!
25Msun
He start
!
H end
!
7.5
4.2
H start
0
1
2
3
4
5
6
7
log Central Density (gr cm
−3
8
9
10
)
massive star
evolution
8
MH
log LH
log LHe
7
6
0.58
mr/Msun
4.4
4.2
Si end !
5
0.56
4
0.54
3
0.52
2
0.5
0
1
500000 1e+06 1.5e+06 2e+06 2.5e+06 3e+06 3.5e+06 4e+06 4.5e+06
t/yrs
log L/Lsun
-3
2.0
1000 km/sec infall
9.5
2.3
9.0
2.7
8.5
3.0
8.0
2
4.0
3.5
1
log L/L!
5.0
4.5
0
log Central Temperature (K)
3
7.0
C/O
Evolution of low- & intermed. mass stars
A new, modern, modular, open, fast community stellar evolution code
Paxton etal 2010,
in prep. read the
Manifesto before
using!!!
Evolution of low- & intermed. mass stars
9
Local 3D
simulations of
hydrodynamic
processes on shorter
time scales
The fluid equations of motion
Conservation laws:
mass
momentum
energy
Plus nuclear burn:
Stellar interior convection:
Hydrodynamics and Mixing of
He-shell Flash Convection
(Paul Woodward, LCSE, Minnesota)
Evolution of low- & intermed. mass stars
Extra-mixing aka “cool-bottom processing”
10
Several observations on the AGB
as well as on the RGB indicate
that a certain amount of mixing
between the bottom of the giant
convection envelope and the Hburning shell is needed, e.g.
• large [N/Fe] in C-rich extremely
metal poor stars
• lower 12C/13C on the AGB then
expected from standard models
• abundance correlations with L in
RGB GC stars, e.g. C/N
• Li enhancements in RGB GC
stars
Proposed scenarios include
• “Enhanced Extra Mixing in Low-Mass Red
Giants: Lithium Production and Thermal
Stability” Denissenkov & Herwig (2004)
• magnetic fields: “Can Extra Mixing in RGB and
AGB Stars Be Attributed to Magnetic
Mechanisms?” Busso etal (2007)
• “Magneto-Thermohaline Mixing in Red
Giants” Denissenkov etal (2009)
• followed finally by “Is Extra Mixing Really
Needed in Asymptotic Giant Branch Stars?”
Karakas etal (2010) [best reproduction of
observations with enhanced 16O intershell
abundance]
shell, where a nuclear reaction lowers the mean molecular weight slightly. Thus, we are able to
remove the threat that 3He production in low-mass stars poses to the Big Bang nucleosynthesis
of 3He.
T
he standard evolution of a low-mass star
(Fig. 1) takes it from a short-lived pre–
Main-Sequence (PMS) state, in which it
contracts and heats up but has not yet become
hot enough to burn its nuclear fuel, to the longlived MS state in which slow, steady nuclear
reactions keep the star in thermal equilibrium.
After several gigayears (but depending strongly
on mass), the nuclear fuel is exhausted at and
near the center, the star becomes cooler, larger,
and more luminous, and it starts to climb the red
giant branch (RGB). Its outer layers become
turbulent and convective, and this surface con-
vection zone (SCZ) penetrates deeply into the star,
but the SCZ is forced to retreat again as the fuelexhausted core, surrounded by a thin, hot nuclear-
REPORTS
Fig. 4. A color-coded plot of m on a
cross-section through the initial 3D
model. The shell where the m infrom center
photosphere,
economized on
versiontooccurs
is the yellowwe
region
sandwiched
between a yellow-green
mesh points
by considering
only the region be*To whom
correspondence
should beThe
addressed.
E-mail: is
and
a darker
inversion
low the
SCZ.
It isgreen.
important
for
numerical [email protected]
at a radius of ~5 × 107 m. The base
poses that
the 1D and 3D codes use exactly the
of the SCZ is at ~2 × 109 m, well
1580 approximations for physical
8 DECEMBER
2006 VOLfor
314
same
processes,
outside the frame, and the
surface
example,
of× state,
of theequation
star is at ~2
1010 m.nuclear reaction
11
1
Institute of Geophysics and Planetary Physics, Lawrence
Livermore National Laboratory, 7000 East Avenue,
Livermore, CA 94551, USA. 2Physics and Applied Technologies Division, Lawrence Livermore National Laboratory,
7000 East Avenue, Livermore, CA 94551, USA. 3Centre for
Stellar and Planetary Astrophysics, Monash University,
Australia.
rates, and opacities.
The location of the starting model of the 3D
calculation is shown in Fig. 1. If we had been
clear before starting the 3D calculation that the
1/m bump was going to cause mixing, we would
have started further down, at the point where the
bump first presents itself, which is just above the
point labeled “deepest penetration of convection.” It has become clear that our unexpected
mixing will begin around here, and in practice
we expect that almost all of the 3He in the SCZ
from
center
to photosphere,
economized
on
will have
been
consumed
by thewe
time
the model
mesh points by considering only the region bereaches the point where our 3D calculation
2 August 2006; accepted 25 September 2006
10.1126/science.1133333
burning shell, advances outward. During the
growing phase, the SCZ dredges up and homogenizes material that, at the earlier MS phase, was
processed by nuclear reactions in the interior.
Along the MS, stars burn hydrogen in their
cores by a combination of the proton-proton (pp)
chain (in which four protons unite to form a 4He
nucleus) and the CNO tri-cycle (in which the
same process is catalyzed by carbon, nitrogen,
and oxygen). The former is the more important
in low-mass stars, ≤1 M⊙, and the latter in more
massive stars. However, even in the more massive stars there is still a shell, somewhat outside
the main energy-producing region, where the pp
chain partially operates, burning H to 3He but
not beyond.
Because the pp chain is less sensitive to
temperature than the CNO cycle, cores of lowmass stars are free of convection, but convective
cores develop in higher-mass stars because CNO
energy production is too temperature sensitive
for radiation to stably transport the energy.
Above ~2 M⊙ this convective core is large
Fig. 1. Evolution of a low-mass Pop I
star in a luminosity-temperature diagram. The model was computed in 1D,
that is, spherical symmetry was assumed, using the code of (20, 21) with
updated equation of state, opacity, and
nuclear reaction rates (22). Surface temperature is in kelvins, luminosity in solar
units.
Fig. 5. The development with time of a contour
surface of mean molecular weight near the
peak in the blue curve of Fig. 3. The contour
dimples, and begins to break up, on a time
scale of only ~2000 s.
bulent and has the effect of diluting the inverse
molecular-weight gradient, but it cannot elimi- model makes this very likely. Although the m
nate it. As the turbulent region entrains more of inversion that we find is somewhat above the
the normally stable region outside it, yet below main part of the H-burning shell, it is not far
SCIENCE
www.sciencemag.org
the normal
convective envelope, it brings in fresh above, and we can expect some modest process3
He, which burns at the base of this mixing re- ing of 12C to 13C and 14N. According to (15), it
gion, thus sustaining the inverse molecular- appears to be necessary for some extra mixing to
weight gradient. Ultimately this turbulent region take place beyond the point on the RGB where the
will extend to unite with the normally convective SCZ has penetrated most deeply; that is exactly
envelope, so that the considerable reservoir of the point where our mechanism should start to
3
He there will also be depleted. If its speed of operate. In (15–18) it was suggested that rotation
~500 m/s is maintained, the time for processed in the region between the SCZ and the hydrogenFig. 5. The
development
with be
time
of a contour
material to reach the classically unstable SCZ
burning
shell might
responsible
for the required
surface of mean molecular weight near the
do not
dispute
thecontour
possible importance
is only about 1 month, whereas the time for peak
the in mixing.
the blueWe
curve
of Fig.
3. The
H-burning shell to burn through the ~0.02 M
ofand
rotation;
dimples,
beginshowever,
to break we
up,emphasize
on a timethat the mech⊙
6
scale of anism
only ~2000
s. discovered is not ad hoc but simply
we have
layer is more than 10 years.
The above argument establishes that the arises naturally when the modeling is done in 3D.
bulent
effect
diluting the
inverse
mixingandinhas
thethe
SCZ
is of
extended
below
the clas- This mixing occurs regardless of possible variamolecular-weight gradient, but it cannot elimi- model makes this very likely. Although the m
sical convective limit and that it is very fast com- bles like rotation and magnetic fields. It seems
aded from www.sciencemag.org on February 5, 2010
Evolution of low- & intermed. mass stars
3a
Fig. Deep
4. A color-coded
plot ofof
m on
Mixing
He: Reconciling Big
cross-section through the initial 3D
Bang
and
Stellar
model.
The shell
where
the m in-Nucleosynthesis
2
version
is 1the
yellow
region
Peteroccurs
P. Eggleton,
* David
S. P. Dearborn,
John C. Lattanzio3
sandwiched
between a yellow-green
Low-mass stars, ~1 to 2 solar masses, near the Main Sequence are efficient at producing the helium
3
and aisotope
darker
green.
inversion
isenvelope on the giant branch and should distribute
He, which
they The
mix into
the convective
into the Galaxy by way of 7envelope loss. This process is so efficient that it is difficult to reconcile
at a radius
of ~5 × 10 m. The base
the low observed cosmic abundance of 3He with the predictions of both stellar and Big Bang
a red giant with a fully three-dimensional
m, well
of thenucleosynthesis.
SCZ is atHere
~2we×find,10by9 modeling
hydrodynamic code and a full nucleosynthetic network, that mixing arises in the supposedly stable
outside
the frame,
andthethe
surface shell and the base of the convective envelope.
and radiative
zone between
hydrogen-burning
10
mixing
to Rayleigh-Taylor
of theThisstar
is isatdue~2
× 10 m.instability within a zone just above the hydrogen-burning
References
bruary 5, 2010
REPORTS
28. L. Bildsten, D. Chakrabarty, Astrophys. J. 557, 292 (2001).
29. P. F. L. Maxted, R. Napiwotzki, P. D. Dobbie, M. R. Burleigh,
Nature 442, 543 (2006).
Downloaded from www.sciencemag.org on February 5, 20
11. V. S. Dhillon et al., Mon. Not. R. Astron. Soc. 314, 826
(2000).
12. S. B. Howell, D. R. Ciardi, Astrophys. J. 550, L57 (2001).
Astronomy
&
Astrophysics
A&A 467, L15–L18 (2007)
DOI: 10.1051/0004-6361:20077274
Evolution of low- & intermed. mass stars
c ESO 2007
!
12
L   E
Thermohaline mixing: a physical mechanism governing
the photospheric composition of low-mass giants
C. Charbonnel1,2 and J.-P. Zahn3
1
2
3
Geneva Observatory, University of Geneva, chemin des Maillettes 51, 1290 Sauverny, Switzerland
e-mail: [email protected]
Laboratoire d’Astrophysique de Toulouse et Tarbes, CNRS UMR 5572, Université Paul Sabatier Toulouse 3, 14 Av. E. Belin,
31400 Toulouse, France
LUTH, CNRS UMR 8102, Observatoire de Paris, 92195 Meudon, France
e-mail: [email protected]
Received 9 February 2007 / Accepted 12 March 2007
ABSTRACT
Aims. Numerous spectroscopic observations provide compelling evidence for a non-canonical mixing process that modifies the surface
abundances of Li, C and N of low-mass red giants when they reach the bump in the luminosity function. Eggleton and collaborators
have proposed that a molecular weight inversion created by the 3 He(3 He, 2p)4 He reaction may be at the origin of this mixing, and
relate it to the Rayleigh-Taylor instability. We argue that one is actually dealing with a double diffusive instability referred to as
thermohaline convection and we discuss its influence on the red giant branch.
Methods. We compute stellar models of various initial metallicities that include thermohaline mixing, which is treated as a diffusive
process based on the prescription given originally by Ulrich for the turbulent diffusivity produced by the thermohaline instability in
stellar radiation zones.
Results. Thermohaline mixing simultaneously accounts for the observed behaviour of the carbon isotopic ratio and of the abundances
of Li, C and N in the upper part of the red giant branch. It significantly reduces the 3 He production with respect to canonical evolution
models as required by measurements of 3 He/H in galactic HII regions.
Conclusions. Thermohaline mixing is a fundamental physical process that must be included in stellar evolution modeling.
Key words. instabilities – stars: abundances – stars: interiors – hydrodynamics
1. Introduction
During the first dredge-up (1dup; Iben 1965), the surface composition of low-mass red giant stars1 is modified due to dilution
Shetrone 2003; Recio-Blanco & De Laverny 2007) that also
modifies the abundances of lithium, carbon and nitrogen (e.g.,
Gratton et al. 2000). This non-canonical process appears to be
universal as it affects at least 95% of the low-mass stars, whether
13
Evolution of low- & intermed. mass stars
1972ApJ...1
1972ApJ...172..
1. study the hydrodynamics of
thermohaline mixing
2. apply results in stellar evolution
and compare with observations
Evolution of low- & intermed. mass stars
NUMERICAL SIMULATIONS OF THERMOHALINE
CONVECTION: IMPLICATIONS FOR EXTRA-MIXING IN
LOW-MASS RGB STARS
14
Pavel A. Denissenkov
– 29 –
Department of Physics & Astronomy, University of Victoria, P.O. Box 3055, Victoria,
B.C., V8W 3P6, Canada
arXiv:1006.5481
[email protected]
ABSTRACT
Ocean
Low-mass stars are known to experience extra-mixing in their radiative zones
on the red-giant branch (RGB) above the bump luminosity. To find out if the
100
salt-fingering transport of chemical composition driven by 3 He burning is efficient
enough to produce the RGB extra-mixing, we have done 2D numerical simulations
of thermohaline convection for physical conditions corresponding to the RGB
200
case. We have found that the effective ratio of salt-finger’s length to its diameter
aeff ! 0.5 is more than ten times smaller than the observationally constrained
300
finger aspect ratio aobs " 7. On the other hand, the thermohaline diffusion
coefficient from the linear stability analysis with a = aobs turns out to describe
the RGB extra-mixing at all metallicities so surprisingly well that it is tempting
400
to believe that it may represent the true mechanism. Given this discrepancy,
we call for the necessity of performing 3D numerical simulations of thermohaline
convection for the RGB case.
500
In ocean conditions
longish finger
structures establish
with an aspect ratio
(vertical to
horizontal) of a few.
Subject headings: stars: abundances — stars: evolution — stars: interiors
600
1.
700
Introduction
A main sequence (MS) star with a mass M ! 1.5 M! , e.g. the Sun, gets its energy
from
thermonuclear fusion reactions of the pp-chains. When its core has run out of the
800
hydrogen fuel, the star leaves the MS and becomes a red giant branch (RGB) star. The red
giant has a compact electron-degenerate helium core of the size of the Earth surrounded by
900 hydrogen burning shell (hereafter, HBS) that provides the star with the energy
a narrow
via a transformation of H into He in the CNO-cycle. The bulk of the red giant’s volume is
1000
100
200
300
400
500
600
700
800
900
1000
RGB: R =1700, " = 400 cm2/s, "
100
200
300
400
500
600
700
– 38 –
800
900
(3D simulations
underway, no
dramatic effect
expected)
1000
100
200
300
400
500
600
700
800
900
1000
2
0.25
log10 [X(12C)/X(13C)]
Application to stellar evolution and
obs:
6
RGB: R =1700, " = 4x10 cm2/s, " =200 cm2/s (black)
1.5
• black lines: aspect! ration according to mol
hydro
1
100
coloured
lines:
aspect
ratios
5-7
best
•
fitting
observations
200
0.5
1
15
In star conditions
the ratio of thermal
diffusivity to
diffusivity of
“salinity” is much
greater PLUS the
viscosity is much
smaller: fingers are
shredded, aspect
ration < 1.
mol
!
300
1.5
2
2.5
log10 (L/Lsun)
a
b
0
[C/Fe]
Evolution of low- & intermed. mass stars
=200 cm2/s (red)
!0.25
!0.5
!0.75
3
3.5
!1
1
1.5
2
2.5
log10 (L/Lsun)
3
3.5
Evolution of low- & intermed. mass stars
Mass loss and opacities in AGB stars
16
An important new ingredient for
AGB stellar evolution are new low-T
opacities and - ideally matching mass loss rates, e.g. from
hydrodynamic wind models (see
Susanne Hoefner’s presentation for
details).
Goal: correctly and predictively
describe the loss of the envelope
when the star becomes C-rich
through 3rd dredge-up, and the
surface temperature evolution.
Routinely employed now, e.g.:
• ”New asymptotic giant branch models for a
range of metallicities” Weiss & Ferguson,
A&A, 2009.
• “Evolution and chemical yields of AGB
stars: effects of low-temperature opacities”
Ventura & Marigo, MN, 2009.
• “Molecular Opacities for Low-Mass Metalpoor AGB Stars Undergoing the Third
Dredge-up” Cristallo etal, ApJ, 2007.
• “Low temperature Rosseland opacities with
varied abundances of carbon and nitrogen”
Lederer & Aringer, A&A 2009.
• “Asymptotic Giant Branch evolution at
varying surface C/O ratio: effects of
changes in molecular opacities” Marigo,
A&A, 2002.
2) causes the star to move more or less horizontally to the
right in the HR-diagram (Fig. 1) in all cases except C. Weiss &
Ferguson (2009) obtained a similar migration to the right using
c ESO
Astronomy & Astrophysics manuscript no. evol
!
2009 & Schlattl 2008) with
the GARSTEC code (described
in Weiss
March 22, 2009
the mass-loss formula by Wachter et al. (2002) and the opacities
Fig. 1. Luminosity-temperature diagram (cf. HR-diagram) for Model
of Marigo (2002). In their model, no superwind develops as in
A-D. All tracks are plotted starting from the ZAHB.
our case D, but as mass is eventually lost, the star will start to exL   E
pand rapidly. In case C, which is similar to the models by Weiss
compare the results obtained using the new opacities and mass- & Ferguson (2009), this point has not yet been reached.
loss prescription, described in the previous section, with a track
As previously argued by Mattsson (2008), ε˜C , i.e., the abunEffects
of
Carbon-excess
Dependent
Mass
and Molecular
computed using the opacities by Alexander & Ferguson (1994) danceLoss
of carbon available for dust formation, is a more decisive
and the mass-loss formula
by Blöcker
(1995).
The following
for quantity
than the C/O-ratio for the onset of strong dust-driven
Opacities
on
Models
of C-star
Evolution
cases are considered:
mass
loss.
As shown in Fig. 2 (middle panels), ε˜C continues
3 , and B. Paxton4
L. Mattsson1 ! , F. Herwig2 , S. Höfner1 , R. Wahlin1 , M. Lederer
to grow with every thermal pulse, while C/O levels out due to
A Mass loss according to Blöcker for both M-star phase and the increasing dredge-up of oxygen. Since the mass-loss rate de1 C-star phase. Low-temperature opacities by Alexander &
Dept. Physics and Astronomy, Div. of Astronomy and Space Physics, Uppsala University,
515, SE-751
pend Box
steeply
on ε˜C20inUppsala,
case BSweden
and D (see ? for further details),
2
Dept.
Physics(1994)
and Astronomy,
University
of Victoria,
PO Box
3055,excess.
STN CSC, Victoria BC V8W 3P6, Canada
Ferguson
without
dependence
on
the
carbon
weAustria
have a run-away process: with each thermal pulse more car3
Astronomy,
University
of Vienna,for
Türkenschanzstrasse
17, A-1180,
Vienna,
B4 Dept.
Massof loss
according
to Blöcker
M-star phase and
accordis USA
dredged up, which increases the carbon excess and hence
Kavli Institute for Theoretical Physics, University of California, Santa Barbara, CAbon
93106,
ing to Mattsson et al. (2009) for the C-star phase, and low- also the mass-loss rate, that in turn limits the number of thermal
Received
date; accepted
date as in A.
temperature
opacities
pulses by terminating the AGB.
C Mass loss as in A, but the new low-temperature
opacities
as
ABSTRACT
described in Sect. 2.3.
presentloss
models
of stellar
for a 2M" -star
of initial metallicity
Z = 0.01 (scaled solar), with focus on the carbon-star
DWeMass
as in
B andevolution
low-temperature
opacities
as in C, i.e.,
(C-star)
phase
in
particular,
the
effects
of
increasing
carbon
excess
on
mass
loss and4.
molecular
opacities. We employ a new, stateConclusions
the new opacities and the new mass-loss prescription impleof-the-art theoretical
mass-loss
prescription
for
dust-driven
winds,
which
takes
the
effects
of
the
carbon
intoand
account,
and we
L. Mattsson et al.: Effects of Carbon-excess Dependent Massexcess
Loss
Molecular
Opacities
3
menteda simultaneously.
implement
set of composition-dependent molecular opacities, which incorporates the changes due to the evolution of the carbon
We
have
found
that
including
the
dependence
on
the
carbon
exexcess. We find that the development of the carbon excess is controlling much of the carbon-star evolution. A very pronounced
We
note that
introducing
the new
composition-dependent
cess
of rich,
opacities
andonly
mass
loss
during the C-star phase, may
superwind
forms
and the termination
of the
AGB happens soon after the opacstar becomes
carbon
in fact, after
a few
thermal
Within
less
than
200
Myr
from the onset of the superwind,
pulses.asThe
a consequence
of the carbon-excess
included
in significant
the new
mass-loss
prescription
ities,
insuperwind
case C develops
and D,asleads
to significantly
lower dependence
effec- have
very
effects
on the in
evolution. The new opacities
combination with the lower effective temperature (which favours mass loss) obtained with
the of
newthe
opacities.
The superwind
does
not in case D (see Fig. 2, lower right
half
stellar
mass
is lost
tive
temperatures compared to case A and B (see Fig. 2). leads
to
lower
effective
temperatures,
which is consistent with
arise immediately, since the star has to become sufficiently carbon-rich and, at the same time, have a low enough temperature. The
−8
−5
panel).
note
that
theMarigo
AGB
will probably
terminated even
This
is consistent
withṀprevious
results
e.g.,
2002,
other
studies
2002,
and the newbe
massmass-loss
rate grows from
∼ 10 up to
Ṁ ∼ 10(see,
, while
the Marigo
carbon excess
grows by
a factor
of We
four (Marigo
and
the temperature
drops
by 2007),
close to&1000
K. We conclude
this is C/O-ratio
the probable explanation
the originaof theloss
C-star
superwind.
Weiss
Ferguson
2009) 2that
. The
is also for
showing
prescription/code
by
Mattsson
et
al.
(2009)
in
combination
before the next thermal pulse. Hence the model star experiences
slightly
slower
compared
to the
tracks with
with
these
opacities
lead
topulses
thetransfer
formation
of a very
pronounced
Key words.
Stars:increase,
AGB and post-AGB
– Stars:
atmospheres
– Stars:Alexander
carbon – Stars: mass
loss
–aHydrodynamics
– Radiative
only
few
thermal
as ofC-star.
We
note
also
that in the
& Ferguson (1994) opacities, but the difference is not significant. superwind, due to which the number
thermal
pulses
andTP-AGB,
asFig. 2. Evolution on the
starting at the peak of the first thermal p
beginning
of theevents
C-rich
phase
the
mass-loss
rate
drops
signifiThe overall luminosity evolution is similar for all four cases.
sociated
dredge-up
is very
limited.
The
nucleosynthetic
Middle panels: C/O-ratio (left) and carbon excess (right). Lower panels: mass
1. Introduction
is important,
since
C-stars,
therapidly
duration
the AGBinto
cantly,
but
then
evolves
a superwind.
Regarding the mass-loss evolution, we see ament
dramatic
yields
arefor
thus
probably
lower of
compared
to many
previous mod-In case B the
phase
and
the
number
of
thermal
pulses
is
almost
solely
deterchange.
In case
D, acontain
very pronounced
develops as the els
of C-star evolution,
thisbeen
needsreached
to be verified.
superwind
has
notbut
yet
after five thermal pulses,
Stellar
evolution
models
uncertaintiessuperwind
due to input
mined
by
the
mass-loss
rate.
The
evolution
of
the
internal
struccarbon
increases.
fact,to the
mass-lossrather
rate becomes so
Our
stellar
evolution
sequence
with
ab
initio
inputdecrease
physics in effective
physics
that, excess
for practical
reasons,Inneed
be prescribed
is due(Blöcker
to a combination
of a slower
ture also dependswhich
on the mass-loss
1995), which
in turn
References
Co
that the
average timeMass-loss
step drops
orders
thanhigh
computed
simultaneously.
on three
the AGB
is aof magnitude
is reproducing
the superwind
quantitatively
in the amount obaffects the fundamental
stellar
parameters.
Since
the
mass-loss
temperature
and a steep
dependence
−2 of mass loss on temperature
process
is of to
great
importance
for stellar
evolution
mod- not
and that
appears
continue
to drop.
We have
therefore
ratecontindepends onserved
these stellar
be −4
aM
feedmassparameters,
loss ( Ṁ =there
10−5will
− Alexander
10
). Extrapolating
the 1994, ApJ, 437, 897
& Ferguson J.W.,
" yrD.R.
Fer
els, ued
but any
is usually
by asome
empirical,
according
to
Mattsson
et
al.
(2009).
The
origin
of
the superwind
of theimplemented
tracks beyond
few simple
thermal
pulses in back,
the C-star
which means
that
the
mass-loss
prescription
put
into
a
mass
loss
to
the
end
of
the
end
of
the
AGB
(by
looking
at
the
Blöcker
T.,
1995,
A&A,
297,
727
He
semi-empirical
or theoretical
The mass
loss of to
AGB
stellar evolutionremaining
model
ismodel
critical.
In
particular,
since
the
massregime, since
the dropformula.
in the time
step needs
be investigated
in
the
is
due
to
the
combination
of
low
effective
temperamass
in
case
D)
will
bring
us
up
to
the
observed
level
Bowen
G.H.,
1988,
ApJ,
329,
299
stars is thought to be driven by radiation pressure on dust- loss rate is found to increase significantly with the carbon ex−5
more
in outer
detailstellar
and atmospheres.
the numericsVarious
of themass-loss
code may
modifi- of
a few
times
M"pulse
yr−2and
. The
mass-loss ratemass-loss
in the beginning
grains
in the
for-need
tures
and
a 10
carbon-excess
dependent
rate.
cess (Mattsson et
al.
2008),
each
thermal
correspondcation.
The
time
step
drops
significantly
in
case
B
as
well,
as
mulae/recipes have been used previously, e.g., a scaled Reimers- ing dredge-up event
of the
C-star
phase
drops
to
a
very
low
level
(see
Fig.
2,
lower
will take a C-star closer to the termination
The
relatively
decline
in temperature (again, see Fig.
as a1975)
strong
begins
toHoek
develop,
although noofsuch
pro- This
law soon
(Reimers
waswind
used by
van den
& Groenewegen
leftwill
panel),
then risesrapid
over
the AGB.
lead tobut
a mechanism
that isroughly
limiting three
the orders of magnitude,
(1997),
while Karakas
& Lattanzio
(2007)
used thetoformula
by amount
−8
−5 of AGB
nounced
superwind
as in case
D seems
be developing
at this
2)andcauses
the
star
more
or less
horizontally
to the
of carbon
other
nucleosynthesis
products
from
Ṁ
∼ 10
up to
Ṁ ∼to
10move
, while
the carbon
excess
grows
Vassiliadis
&
Wood
(1993),
and
Herwig
(2002;
2004)
used
the
most notably
the
s-process
elements,
that
can
be
expelled
stage, which one can expect due to the higher effectivestars,
temperaa factor
of four.
right
in the
HR-diagram (Fig. 1) in all cases except C. Weiss &
theoretical prescription by Blöcker (1995), derived from early by a carbon star.by
ture
of
the
star
(an
effect
of
the
opacities).
wind models by Bowen (1988). Recently, Weiss & Ferguson
Mass loss and opacities in AGB stars
Evolution of low- & intermed. mass stars
Mattson, Herwig,Hoefner, Wahlin, Lederer, Paxton
mass loss vs. age
“forwardmodeling”
superwind?!!
Ferguson
(2009)
similar migration to the right using
The implementation
of opacities
that obtained
depend on theachemi(2009)2 made use of the theoretical formula by Wachter et al. cal composition of the star (which changes as the star evolves)
Note that
Rosseland
opacities are used. Since the diffusion Acknowledgements.
MTLcode
has been
supported byintheWeiss
Austrian&
Academy
of 2008) with
the GARSTEC
(described
Schlattl
(2002), which
is probably
moremean
realistic.
can how
affectthe
the structure
and surface
temperature
significantly.
Sciences (DOC
programme)
and acknowledges
funding by the Austrian Science
approximation
does
not
apply
to
the
surface
layers,
it
is
unclear
Mattsson et al. (2009) have recently made an effort to de- Marigo (2002) and
the
mass-loss
formula
by Wachter
Marigo
& Girardi
(2007) have shown
that us- et al. (2002) and the opacities
Fund
FWF
(project
P-18171).
effective
temperature
affected
quantitatively.
Fig. 1. Luminosity-temperature
(cf.
HR-diagram)
Model
termine
how the
mass lossisofdiagram
carbon-rich
AGB
stars (C-stars) for
ing composition-dependent
opacities
leads toIn
an improvement
of no superwind develops as in
of Marigo
(2002).
their model,
A-D. All tracks
areonplotted
starting from
ZAHB. wind the agreement between
depends
stellar parameters,
using the
a state-of-the-art
models and observations (e.g., colours,
caseC-star
D, but
as mass
is eventually
lost, the star will start to exmodel including time-dependent dust formation and frequency- initial-final massour
relation,
luminosity
functions
etc.) but
dependent radiative transfer. That work has provided a new also to significantly
lower
effective In
temperatures,
to similar to the models by Weiss
pand
rapidly.
case C, compared
which is
mass-loss prescription, which includes steep dependences on earlier work. Since the mass-loss rate depends steeply on the ef-
17
total
mass vs.
age
600 -400 -200 0
200 400 600 600 -400 -200 0
11.74 yrs
200 400 600 600 -400 -200 0
11.74 yrs
200 400 600 600 -400 -200 0
11.74 yrs
200 400 600
11.74 yrs
Evolution of low- & intermed. mass stars
Hydrodynamic simulations of AGB envelopes
18
Freytag & Hoefner (2008)
density
temperature
velocity field
grey intensity
600 -400 -200 0
200 400 600 600 -400 -200 0
200 400 600 600 -400 -200 0
200 400 600 600 -400 -200 0
200 400 600
600 -400 -200 0
200 400 600 600 -400 -200 0
200 400 600 600 -400 -200 0
200 400 600 600 -400 -200 0
200 400 600
600 -400 -200 0
200 400 600 600 -400 -200 0
200 400 600 600 -400 -200 0
200 400 600 600 -400 -200 0
200 400 600
12.06 yrs
12.37 yrs
12.06 yrs
12.37 yrs
12.06 yrs
12.37 yrs
12.06 yrs
12.37 yrs
Fig. 1. Time sequence of five snapshots for model S (st28gm06n02). The model age in years is indicated on top of each frame. The axes are in solar
radii. Shown from left to right are log density (color range from 10−13 to 2 × 10−7 g/cm3 ), log temperature (color range from 800 K to 50 000 K),
velocity field (pseudo-streamlines of the velocity components within the image plane integrated over 5× 106 s) and grey intensity.
Evolution of low- & intermed. mass stars
19
1. Formation and
2. evolution
of the 13C-pocket
Gravity waves
(Denissenkov & Tout, 2002)
Mixing processes for the radiative
s-process (partial mixing of
protons with 12C at the base of
the convective envelope during/
after 3DUP)
Rotation (Langer etal. 1999)
Hydrodynamic
overshooting
(Herwig etal. 1997)
Evolution of low- & intermed. mass stars
Hydrodynamic simulations of AGB envelope convection
focus on beneath-atmosphere, deeper layers
20
Woodward & Porter, LCSE, U Minnesota, http://www.lcse.umn.edu
temperature
fluctuation
Evolution of low- & intermed. mass stars
Rotation and magnetic
fields
4
21
Suijs et al.: White
• Rotation in 1D stellar evolution,
e.g. Maeder & Meynet, Heger etal,
Langer etal.
• plus magnetic fields, e.g. Taylor &
Spruit dynamo, questioned by
Zahn etal (2007)
Compare to observations in late
phases:
• Rotation rates of neutron stars
and white dwarfs
• Implications from nucleosynthesis,
e.g. s-process in TP-AGB stars
(Herwig etal 2003, Siess etal 2004)
Fig. 5. Average core specific angular momentum of our initial
etalinitial
(2008)
and final models (cf. Table 1 and Fig.Suijs
4), versus
stellar
mass (full drawn lines). Points for 15 M! stars computed with
the same physics from Heger et al. (2005) have been added. The
upper line corresponds to the initial models. Filled triangles corresponds to the final models of the non-magnetic sequences, and
filled squares to the final models of the magnetic sequences. The
“Seismic evidence
forhorizontal
the loss
stellar
dashed
lineof
indicates
the angular
spectroscopic upper limit on
the white
dwarf
spins obtainedstage”
by Berger et al. (2005). Star symmomentum before
the
white-dwarf
bols represent astroseismic measurements from ZZ Ceti stars
Charpinet, S.; Fontaine, G.;
Brassard, P.,
2009.
(Bradley 1998, 2001;
Dolez 2006; Nature,
Handler 2001,
Handler et al.
2002, Kepler et al. 1995, Kleinmann et al. 1998, Winget et al.
1994), where smaller symbols correspond to less certain measurements. The green hatched area is populated by magnetic
white dwarfs (Ferrario & Wickramasinghe 2005; Brinkworth et
al. 2007). The three black open pentagons correspond to the
la
to
Y
b
la
s
5
W
to
g
th
m
p
s
m
tw
F
re
W
la
T
a
a
A
N
A
w
C
R
zone of #10 M$ that has formed at the end of the third
! ¼ ðt & t0 Þ=Dt, where the previous pulse, i.e., the maximum He-burning
contraction
andofthe
angular
velocity in the
dredge-up
phaseresumes
as a result
timeand depth-dependent
luminosity, has occurred at t0; the interpulse period is Dt ¼ 3 ' 104 yr. Two
intershell
region
increases
accordingly
(profiles
!
¼
0:0122–
hydrodynamic overshoot (top panel, Fig. 6). In this model
different mixing periods resulting from rotation occur in the partial mixing
0.1706).
The
angular
velocity
profiles
at
later
times
show
zone during
the interpulse
period (see text).
no mixing takes place during the interpulse phase. InImplications
the
from
nucleosynthesis,
againpanel
the formation
a plateau
between
0.746
0.749
13C neutron
source
hasand
started
middle
of Figure of
6 the
the H and
shellup
is now
located,
of deposition
M!, where
e.g.
in TP-AGB stars
13C abundance
has s-process
releasing
neutrons,
to 10%
of thebecause
In Table 2 we give the mixing properties in the partial
of H-shell
ashes
of the
core.
been
consumed.
Inon
thetop
upper
part
of the partial mixing zone,
(Herwig
etal
mixing 2003)
zone at three different times: an early phase soon
the evolution
of the angular
velocity
rotating
14N dominates,
the majority
of neutrons
are in
absorbed
whereFrom
after the pulse, a phase just before the release of neutrons
can anticipate
the following
mixing
propp)14we
C reaction.
This can
be seen from
the probyTP-AGB
the 14N(n,stars
starts, and a phase after the neutron source 13C is exhausted.
erties.
Efficient
shear
mixing
will
take
place
at
#0.746
M
14
"3
!
6
file of C. The maximum neutron density is 5:7 % 10 cm
after the formation of the large angular velocity gradient.
This gradient
because two convective regions extend
no forms
rotation
with rotation
to *these mass coordinates from below and above in short
!
succession.
The
He
flash
convection
first
taps
the
reservoir
!)
="
of!(high angular momentum in the core. Then the convective
=#
envelope
establishes contact between the fast-rotating inter!'
=$
shell
and
the
slow-rotating
envelope.
At
this
interface
rota!&
=%
tionally
induced shear mixing will be most efficient in acting
!%
=&
on!$abundance gradients. The timescale to establish a partial
=+
12
<
D
mixing
zone
of hydrogen and C as needed for the forma!#
=(
!<!'!%)
)(
"#
=13
E
tion
!" of the C pocket is limited to the time interval when the
=)
*+$(*'
*+$(*&
*+$(*%
*+$(*$
*+$(*#
!'(%&)
!'(%&*
!'(%+
!'(%+"
envelope and the intershell are in contact, i.e., between the
end
* of the third dredge-up and the reignition of the H-shell.
!
)'
"$
=
E
This
lasts
2000–3000
yr
(Fig.
1).
However,
as
can
be
!) period
="
)&
"%
?
G
?6
G;
seen
7,
the
steep
angular
velocity
gradient
remains
!( in Figure
=#
)&
"%
=
E
at!'this mass
coordinate after the formation of the partial
=$
!&
=%
mixing
zone, and shear mixing at this location will persist
!%
=&
throughout
the intershell period.
!$
=+
Correspondingly, two mixing periods during the inter!# phase resulting from rotation can be distinguished, as
=(
!<!'$)#
pulse
!"
=)
shown
by the temporal evolution of the mixing coefficient
*+$(*'
*+$(*&
*+$(*%
*+$(*$
*+$(*#
!'(%&)
!'(%&*
!'(%+
!'(%+"
presented in Figure 8. During the initial envelope-core con"
tact)period at the end of the third dredge-up, a partial mix12
ing*+"zone of protons and C forms (top panel, Fig. 9). The
!')
mixing efficiency in Eulerian coordinates at this time is
!'+
log*+$Dr # 5 (in cgs units), but decreasing rapidly at a timescale
*+& of #1000 yr. However, after the TP the mass gradient
!'%
in the partial mixing zone increases steadily as the intershell
*+(
!'#
layers
contract and evolve toward a preflash structure. For
!<!'+**
assessing
the effect on the abundance evolution, the
*
!
*+$(*'
*+$(*&coefficient
*+$(*%
!'(%&)
!'(%&*
!'(%+
!'(%+"
Lagrangian
mixing
should be *+$(*$
considered: *+$(*#
,1EF.A6
71895:;
! "2
dm
2 2
Fig. 9.—Same as Fig. 6 for the simulation at the 25th interpulse phase
¼
Drpartial
¼ ð4"#r
Þ D
ð6Þ
Dm profiles
Fig. 6.—Abundance
in the
mixing
zone
r ; at three times
dr
including rotation and no hydrodynamic overshoot. The middle panel
during the seventh interpulse phase of the model with hydrodynamic over-
•
,-.ABCF/,-.AG;C=)
7589:;>/7589?6;!"
7>55/?1>42@-;/,-.ABC
,-../01-23456/7589:;
Rotation and
magnetic fields
="
;H:21-;/HIJ-5:1H/"/A7K>1; C
6@A3156/@BC5.A1@/!/9,D-16!);
Evolution of low- & intermed. mass stars
utionary
ered the
ies have
e mixing
imply a
gion by
approxitend by
ferences
of 0.7Hp
location
o-dimentag et al.
ion zone
ccording
nvection
oxygenArnett
hing 1Hp
there is
not the
convecg as the
thermal
oundary.
expect a
pported
ons by
oot dismass.
meter for
nvective
applied
or effect
hing the
14N proneutron
n in the
de effect
y #20%.
analysis
with oth-process
ult 22
from
shoot and no rotation. Top: First postprocessing model after the end of the
13
13
16
shows the same interpulse phase as the middle panel in Fig. 6 with respect
13
Evolution of low- & intermed. mass stars
Rotation and
magnetic fields
next generation ?!?
odynamical Processes in Rotating Main Sequence Stars
reach the
ravity, and
ind which
Meynet et
magnetism.
netic field
lities, that
entum and
ud 2002a;
ynet 2004;
Mathis &
Zahn et al.
ito-inertial
zones may
um. They
deposit anmped, thus
cal distrialon et al.
harbonnel
t al. 2007;
n of rotatmical abunnitude diaalso modll soon be
r range of
pted to the
m to comhe present
magnetic
he angular
usively by
These di-
23
Time scales
(log tchar)
Secular scales
(evolution;
! : 109 yrs)
Dynamical
scales
(convection,
instabilities,
turbulence;
!: month)
Rotational transport
equations coupled with
stellar evolution codes
“A Model of Magnetic Braking of Solar Rotation
That Satisfies Observational Constraints”
Denissenkov (2010)
• improving on Charbonneau & MacGregor
Global numerical
simulations
prescriptions and
constraints on
theoretical hypothesis
lth(<10)
lnum
Angular resolution
lnat (!: 4000) (log l)
Fig. 1. Modelling strategy to study dynamical stellar evolution. The diagram presents timescales of the typical physical
processes as a function of the angular resolution necessary to
properly describe these processes. The angular resolution is
expressed in terms of the l index of the spherical harmonics
Yl,m (θ, φ). lnum ! 600 indicates the maximum angular resolution (in term of spherical harmonics nodes) presently achieved
in global numerical simulations.
bulent motions in the vertical direction. This leads to a strongly
anisotropic turbulent transport that is more efficient in the horizontal direction (along isobars) than in the vertical one. As a
result, the horizontal gradients of all scalar fields (temperature,
angular velocity. . . ) are much smaller than their vertical gradients, which allows their expansion in a few spherical harmonics.
This scale separation, both in space and in time, is illustrated in
Fig. 1.
Considering the axisymmetric case, each scalar field is thus
written as the sum of its horizontal average on an isobar, and its
“Secular hydrodynamic processes in
rotating stars” Decressin et al (2009)
(1993)
• strongly anisotropic rotation-driven turbulent
diffusion with dominating horizontal
components
• numerical solution of the azimuthal components
of the coupled momentum and magnetic
induction equations in 2D
“Numerical Simulations of a Rotating Red
Giant Star. I. Three-dimensional Models of
Turbulent Convection and Associated Mean
Flows” Brun & Palacios, 2009
Rayleigh Taylor instability (Weiss
et al. 2004). With ∆ρ/ρ ∼
M. Mocák, S. W. Campbell, E. Müller and K. Kifonidis: The core helium flash revisited
−4
5 × 10 , inferred from our simulation (Fig. 6 a), we find
v2 ∼ gΛ
∆ρ
∼ 7 × 105 cm s−1
ρ
(1)
Evolution of low- & intermed. mass stars
where g ∼ 108 cm s−2 is the gravitational acceleration at the base
of the convection zone, and Λ ∼ 107 cm the approximate length
of the fingers (Fig. 7).
The above estimate agrees well with the results of an analysis of our simulation, where the gas inside the fingers sinks
at a bit smaller velocities ranging from ∼ 1 × 105 cm s−1 up
to 3.5 × 105 cm s−1 (Fig. 6 and 7). It confirms that the “buoyancy work” (∼ v2 ) is consistent with the acceleration of gas
seen in the simulation, and suggests that the mixing is the result
of the Rayleigh-Taylor instability. Hence, we propose to call it
Rayleigh-Taylor finger instability mixing (RTFI). The velocities
observed inside the finger-like structures (Fig. 6 e) are smaller
than those predicted by Eq. (1), likely because of the friction
caused by our numerical scheme between the ambient medium
and the sinking overdense blob.
Note that the initial density fluctuations can result from wrinkling of the contact discontinuity at the boundary of the convection zone due to the convective flow, turbulence, g-modes or
p-modes.
Eggleton et al. (2006) also found Rayleigh-Taylor instabilities driven by a molecular weight inversion caused by the
3
He (3 He,2p) 4 He reaction in hydrodynamic simulations of the
hydrogen-rich layers residing above the hydrogen burning shell
in low-mass red giants. The corresponding mixing is qualitatively similar to RTFI mixing. The mixing velocities observed
by Eggleton et al. (2006) agree very well with those theoretically estimated for a RT instability according to the formula
v2 ∼ gH p ∆µ/µ, where equal relative density and composition fluctuations,
i.e., ∆ρ/ρ = ∆µ/µ, were assumed. However,
Fig. 12. Temporal evolution of the radial distribution of the
2
any density fluctuation
necessarily
lead toaveraged
composition
(color coded)will
logarithm
of the angular
radial (vand
r /2;
2
temperature fluctuations
∆T angular
as well.
Moreover,
the component
formula of
upper panel) and
vθ /2;
lower panel)
of
−1
the(2006)
specificholds
kinetic
energy
(in ideal
erg ggas,
) of
theonly
2D if
model
Eggleton et al.
only
for an
and
the
heflpopIII.2d.2.
blobs are in pressure equilibrium with the ambient medium and
have the same temperature as the surrounding matter.
The finger-like
structures
RTFI
mixing
in our
is roughly
eight timesresulting
higher thanfrom
that due
to triple-α
burning
in
9
−1 −1
the
inner
zone #̇etal
∼ 1.72010a,b
× 10 erg
g the
s ),surrounding
convective motions
max
simulations are
in
pressure
equilibrium
with
gas,
Mocak
first appear within the inner convection zone after about 200 s.
as they moveThe
with subsonic velocities (the speed of sound is
8
−1 onset of convection in the outer zone is delayed until about
c s ∼ 10 cm s500 sin(Fig.
the12,
corresponding
layers).
However,
theyinto
area
Fig. 16). After some
time the
model relaxes
where
the r.m.s values
always
thansteady-state,
the ambient
medium,
i.e., Tof>theTangular
+ ∆T ,
24 coolerquasi
1 ≡ T velocity
11
He-core flash simulations (here 2D) at low Z show Hingestion
main results
• hydrodynamic results do not agree with 1D stellar
evolution
• entrainment at bottom of He-core flash convection
zone (cf. ‘overshooting’ at bottom of He-shell flash
convection zone)
Fig. 13. Adiabatic temperature gradient ∇ad (solid-black), temperature gradient of the 2D model heflpopIII.2d.2 averaged from
1000 s to 3200 s (dashed-red), and temperature gradient of the
initial model SC (solid-blue), respectively, as a function of radius.
• mixing due to
Nevertheless, the convective flow decays fast in both convection zones – at a rate of 4 × 1040 erg s−1 (Fig. 16), probably
because the initial conditions represented by the stabilized initial model are too different from those of the original stellar
model. They disfavor convection since the stabilized model has a
slightly lower temperature gradient than the original one (Fig. 2,
Fig. 13). However, we note that stabilization of the initial model
was essential to prevent it from strongly deviating from hydrostatic equilibrium.
Shortly after convection is triggered in both the outer and the
inner zone this double convection structure vanishes, and after
about 2000 s there is no evidence left for two separate convection
zones (Fig. 12).
Due to the relatively short temporal coverage of the evolution and due to the decaying convective flow, we did not analyze the energy fluxes and turbulent entrainment of this model.
Penetrating plumes do not exist in the convection zone (initially
determined by the Schwarzschild criterion), as it is dominated
rather by g-modes. Hence, firm conclusions are difficult to deFig.but
8. we
Relative
angular
mean molecular
rive,
plan to address
this fluctuations
issue elsewhere.ofWethe
are now
going
to introduce
basic
internal
gravity
weight
∆µ/µ =some
(µ−%µ&
/ %µ&θ at theofbase
of the
convection zone
θ ) characteristic
waves
or
g-modes
that
are
required
to
draw
further
conclusions.
in the 2D model hefl.2d.3 at t = 30 000 s (a), t = 60 000 s (b),
1
2
and t3 = 120 000 s (c), respectively. In each panel the black solid
G-modes
In the
a convectively
stable region,
any displaced
mass of the mean
line gives
angular averaged
radial
distribution
RT finger
instabilities at
the bottom of
convective
shells
Evolution of low- & intermed. mass stars
Multi-dimensional stars
25
abundance of H-rich material entrained from above
into convection zone at ~20ks
Next generation He-shell flash
convection
i. 3D 4π star-in-a-box
simulations (e.g. Herwig etal
2010, arXiv:1002.2241)
ii.compressible gas dynamics
PPM code Paul Woodward
(http://www.lcse.umn.edu)
iii.high accuracy PPB advection
scheme
iv.2 fluids, with individual,
realistic material densities
v.5763 cartesian grid, simulated
time total 60ks
vi.Ma ~ 0.03, 11Hp in conv.
zone
http://www.lcse.umn.edu/index.php?c=movies
26
20
log D [cgs]
horizontal and vertical vrms
<uθ,φ>
<ur>
18
16
14
0
12
-1
10
-2
8
-3
6
-4
D(t0)
D(t1)
2 XH(t0)
XH(t1)
0
0.597 0.598 0.599
-5
4
14
12
10
8
6
-6
-7
0.6
0.601 0.602 0.603 0.604
mr/Msun
4
2
0
10
15
20
25
30
radius / Mm
comparison 1D and 3D
averaged profiles
See poster for details on
nucleosynthesis implications:
NIC_XI_224, see also arXiv:
1002.2241
log XH [mass fraction]
1D mixing profiles
3D 4π star-in-a-box simulations
velocity / km/s
Evolution of low- & intermed. mass stars
Multi-dimensional stars
Busso, M., Gallino, R., Lambert, D. L., Travaglio, C., & Smith, V
Evolution of low- & intermed. mass stars
Calder, A. C., Fryxell, B., Plewa, T., Rosner, R., Dursi, L. J., We
Convective-reactive proton-12C combustion J.
in O.,
Sakurai’s
object
(V4334
Remington,
B. A.,
Drake, Sagittarii)
R. P., Dimonte, G., Zing
and implications for the evolution and yields P.,
from
the first
stars
MacNeice,
P., generations
& Tufo, H. M.of
2002,
ApJS, 143, 201
27
–3–
Campbell,
S. W. & Lattanzio, J. C. 2008, A&A, 490, 769
(arXiv:1002.2241
for details)
Cassisi, S., Iben, I. J., & Tornambe, A. 1998, ApJ, 496, 376
of highly exothermic nuclear reaction and the convective fluid flow time scales are of the same order.
Colella, P. & Woodward, P. R. 1984, Journal of Computational Ph
The ratio of the mixing time scale and the reaction time scale is called the Damköhler number:
Dillmann,
τmix I., Heil, M., Käppeler, F., Plag, R., Rauscher, T., & Thie
Dα =
(1)
of. Physics Conference Series, Vol. 819, Capture Gammaτreact
A. Woehr & A. Aprahamian, 123–127
MLT is concerned with averaged properties both in time over many convective turn-overs and in space over
Dimotakis, P. E. 2005, Annu. Rev. Fluid Mech., 37, 329
the order of a pressure scale height. In the categories
of Dimotakis (2005) diffusion coeffiecients derived
from MLT may describe level-1 mixing (while mixing
induced
rotation
involves
dynamics
that
Duerbeck,
H. W.,by
Liller,
W., Sterken,
C., flow
Benetti,
S., van Gendere
fully mixed burning, MLT appropriate Voskes,
• Dα <<1:
T., Brogt,
E., Arentoft,
T., vantime-dependent
der Meer, A., & D
are altered
by mixing processes and labeled in this scheme
as level-2
mixing).
Therefore,
• Dα ~1 : combustion regime, MLT and 1D spherical symmetry assumption
mixing through a diffusion algorithm with diffision coefficients derived from MLT is appropriate for regimes
inappropriate because:
with Dα ! ★
1. The difficulty of simulating convective-reactive phases in present one-dimensional stellar
MLT describes convection only in a time and spatially averaged sense
evolution codes
appears asfuels
the inability
MLT (or any
similar convection theory) to properly account
★ inthen
combustion
are not of
completely
mixed
for the additional
dynamic
effectsfeedback
introduced
through
rapidburn
and dynamically
relevant
nuclear energy release
★ localized
energy
from
nuclear
feeds back into
hydro
in level-3
mixing associated
numbers
Dαcommon,
≈ 1.
in low- with
and Damköhler
zero-metallicity
stars
including both low-mass and
• combustion
massive, rotating and non-rotating stars, X-ray bursts, SD SN Ia projenitors, etc
Convective-reactive episodes can be encountered in numerous phases of stellar evolution, including
the He-shell flash of AGB stars of extremely low metal content (e.g. Fujimoto et al. 2000; Iwamoto et al.
2004), the He-core flash in extremely low metallicity low-mass stars (e.g. Hollowell et al. 1990; Schlattl
et al. 2002; Campbell & Lattanzio 2008), young white dwarfs of solar metallicity (e.g. Iben et al. 1983;
Evolution of low- & intermed. mass stars
How nucleosynthesis? Different strategies:
28
• synthetic stellar structures (i.e. fit-
formula to full stellar evolution)
and more or less complete
processing
• Stellar evolution first, then
nucleosynthesis post-processing of
a few key locations, e.g. the 13Cpocket etc (the Gallino etal
approach)
• Stellar evolution with an inlined
network
✴ smaller network of charged
particles, plus co-processing of
heavier elements in separate
larger network (e.g. Lattanzio,
Karakas etal)
✴inlining of complete network
into stellar evolution code (e.g.
Cristallo etal)
• NuGrid approach: stellar
evolution first with energy
suficient network, write out all
strucutre information, complete
post-processing of all zones and
timesteps for dynamic and
complete network of entire
evolution (made possible vie
parallel computing)
Evolution of low- & intermed. mass stars
How nucleosynthesis?
29
Why
http://nugrid.phys.uvic.ca
?
• create a framework that allows to
process large, internally consistent
and comprehensive yield sets
• facilitate easy and routine production
of large sets of observables that allow
simultaneous validation of stellar
physics in a wide range of situations
• detach (as far as possible) stellar
evolution and explosion (SEE library)
business from nucleosynthesis
business (PPN - post-processing
network code suite)
NIC_XI_255 Pignatari M. etal. Neutron capture processes in stars between the s process and the r process
NIC_XI_285 Pignatari M. etal. Nucleosynthesis in the He-burning shell in massive stars
NIC_XI_244 Bennett M. etal. The effect of 12C + 12C rate uncertainties on the weak s-process component
Evolution of low- & intermed. mass stars
Results: Set 1
•2 metallicities: Z=0.02, 0.01
•masses: 1.65, 2, 3, 5, 15, 20, 25 (32 and 60 for Z=0.02
only), massive star tracks with Geneva code, low-mass
tracks with MESA code
•all tracks to the end of the AGB or end of Si burning
•synthetic explosions for massive stars
•complete post-processing of all tracks with the NuGrid
ppn codes: all reactions and isotopes that could have
taken place are considered
Evolution of low- & intermed. mass stars
Results Set 1: 2Msun star
Z=0.01
Nucleosynthesis including s-process
in the He-shell flash thermal pulses
of AGB stars from the NuGrid
collaboration
Evolution of low- & intermed. mass stars
Results Set 1: 2Msun star
Z=0.01
Nucleosynthesis in the 13C-pocket
Evolution of low- & intermed. mass stars
Results Set 1: 20Msun star
Z=0.01
Nucleosynthesis in a massive star
Evolution of low- & intermed. mass stars
Availability of results
34
all data will be made available along with convenient tools to explore the data, e.g.
SEexplorer: interactive data exploration and visualization as well as Python tools
Evolution of low- & intermed. mass stars
Next steps: Set2
35
• 21 masses between 0.8 and
60Msun for 5 metallicities between
Z=0.04 and 1.e-4
• again non-rotating, no B-fields
• improved convective boundary
mixing, mass loss
• 1D and 3D explosions
• SN Ia contributions
• again complete post-processing
data sets of all tracks with the
NuGrid ppn codes with all
reactions and isotopes that could
have taken place
HRD of a subset of preliminary Set 2
calculations to the end of He-core burning
Evolution of low- & intermed. mass stars
Concluding remarks
36
•progress is being made in many areas now by
investigating multi-dimensional effects in the
stellar interior.
•many approaches needed - don’t expect the
golden bullet
•great opportunities for nuclear astrophysics: as we
push to simulate shorter timescales we need new
diagnostics sensitive on shorter time scales ->
branchings, radiaoctive beams, nuclear physics of
radioactive targets