Evolutionary models
and their uncertainties
Achim Weiss
Max-Planck-Institute for Astrophysics
Overview
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Uncertainties from unknown parameters
–
solar abundance scale
–
helium content
–
evolutionary phase
... from ill-defined physical processes
–
diffusion (settling)
–
superadiabatic convection
–
overshooting
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... from numerics and physics implementation
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A comment on seismology
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Summary
Composition
Solar composition
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two competing "standard" sets
–
Grevesse & Sauval (1998):
(Z/X)S = 0.0229 → Zi = 0.0187
[Fe] = 7.50
–
Asplund et al. (2009):
(Z/X)S = 0.0178 → Zi = 0.0149
[Fe] = 7.46
–
given an [Fe/H], different choices of solar abundances result in
different (X,Y,Z)!
test calculations:
–
low-mass star with [Fe/H]=-1.5
–
intermediate-mass star with [Fe/H]=+0.2
TO-age effect due to solar element scaling
GS98
AGS09
compositions (Y=0.25)
X
Z
0.749457 0.000543
0.749608 0.000392
results:
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age difference between AGS09 and GS98 (at fixed mass) negligible
●
two stellar tracks matching (approximately) the same TO position differ by 0.6 Gyr
(8%) in age and 0.02 M⊙ (2%)
TO-age effect due to solar element scaling
GS98
AGS09
compositions (Y=0.25)
X
Z
0.749457 0.000543
0.749608 0.000392
results:
●
age difference between AGS09 and GS98 (at fixed mass) negligible
●
two stellar tracks matching (approximately) the same TO position differ by 0.6 Gyr
(8%) in age and 0.02 M⊙ (2%)
similar for intermediate-mass star:
M = 4.0 M⊙
Y=0.28, [Fe/H]=+0.2, GS98
main-sequence evolution
similar for M=3.9 M⊙
if AGS09 solar reference is used
lifetimes:
GS98 - 157.38 Myr
AGS09 - 166.93 Myr (+6%)
(at end of core He-burning +10 Myr (+5%))
generally:
unclear, what "[Fe/H]" implies for total metallicity Z for models?
what scale, relative to solar, absolute, other elements?
models need Z, and then [X/Fe]
Helium – the big unknown
0.45
0.4
0.35
0.3
0.25
0.2
0.15
what is wrong at
low metallicity?
is dY/dZ varying at
higher metallicities?
Helios and Helium – what's wrong with them? (EWASS14/SP2, Geneva, July 2&3, 2014)
Varying the helium content
reference:
M=4.0 M⊙, Y=0.30 (GS98)
ms-lifetime:
123.84 Myr
end of core He-brng.:
160.60
main-sequence evolution
mimicked at Y=0.28, if
M=4.15 M⊙
ms-lifetime:
143.09 Myr
end of core He-brng.:
187.25
( ≈ +15%)
Evolutionary phase
confusion of different evolutionary
phases at fixed, identical chemical
composition
example: (solar composition)
star 1: M = 1.0 M⊙ in core helium burn.
age: 12.2 Gyr
star 2: M = 1.7 M⊙ on first giant branch
age: 1.9 Gyr
pre-MS
of 1.0 M⊙
star
core He-burn.
("clump") of
1.7 M⊙ star
RGB (and bump)
of 1.0 M⊙ star
Evolutionary phase
confusion of different evolutionary
phases at fixed, identical chemical
composition
example: (solar composition)
star 1: M = 1.0 M⊙ in core helium burn.
age: 12.2 Gyr
star 2: M = 1.7 M⊙ on first giant branch
age: 1.9 Gyr
pre-MS
of 1.0 M⊙
star
core He-burn.
("clump") of
1.7 M⊙ star
RGB (and bump)
of 1.0 M⊙ star
Physics
Effect of diffusion
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If diffusion is at work, present surface abundances are not the initial ones!
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Any evolutionary model must take this into account!
–
"calibrated tracks/isochrones" (Salaris et al. 2000)
three different types of isochrones,
displayed for the lower main-sequence:
solid – no diffusion
dashed – with diffusion, with
initial [Fe/H] as observed
dotted – with diffusion, but
"calibrated", such that [Fe/H] as
observed all along isochrone
Effect of diffusion
on Teff:
upper/middle panel: calibrated isochrones
with two different [Fe/H]
lower panel: dotted: standard isochrones
on determined ages of subdwarfs
with Hipparcos parallaxes and
IFRM Teff :
Effect of diffusion (Jofre & Weiss 2011)
age determination of metal-poor
F and G dwarfs from TO-colour
(SEGUE; SDSS/DR7;
sample size of order 105 stars)
black lines: TO([Fe/H]) including
error range
upper panel: isochrones without
diffusion; age 14-16 Gyr
lower panel: isochrones
including diffusion ("calibrated")
age 11-12 Gyr
Restricted diffusion (Chaboyer et al. 2001)
Isochrones with
[Fe/H] = -1.9
to take into account the lack
of observations that confirm
the full effect of diffusion
(strong depletion of metals around
the TO), Chaboyer et al. constructed
models where diffusion is operating
in the deep interior, but not at the
surface (e.g. due to mass loss,
additional mixing processes, ...)
Isochrones with restricted diffusion
show "half" of the effect of full
diffusion
Superadiabatic convection: αMLT
The mixing-length parameter αMLT is "calibrated" with the solar model and kept constant for
all other cases.
However, 3d-hydro stellar atmosphere calculations (Magic 2013) demonstrate that αMLT is
variable (with log g, Teff, metallicity) to reproduce entropy difference between adiabatic
interior and photosphere
"equivalent" αMLT for two different metallicities as function of log g and Teff (Magic et al. 2014)
(see also Ludwig et al. 1999)
Effect of varying αMLT
M=0.8 M⊙, Z=0.0162 (solar, GS98), "solar calibrated" (1.9) and RG-equivalent (2.2) αMLT
ΔTeff on MS: ca. 130 K, on RGB: ca. 160 K
TO-age of 0.8 M⊙star: 21 Gyr, of 0.7 M⊙ star: 35 Gyr
Overshooting
(Magic, dipl.LMU 2011)
Isochrone fit to NGC 1866 ([Fe/H]=-0.35, LMC)
left: without overshooting (for both GS and AGS solar composition)
right: including overshooting
without the information of the blue-loop stars, the age could be off
by 70%
Nuclear reaction: the 14N(p,γ)15O bottleneck reaction
new measurements (LUNA; Formicola 2004, Marta 2008) reduce rate by 50% compared
to NACRE or CF88 value
globular cluster age increase by up to 0.7-1 Gy
Codes
Code differences
"Aarhus workshops" on model comparisons (2013, 2014) for Kepler-seismology
- predefined physics
- comparison of 1.0, 1.5, 2.0 M⊙ models at given radius (on RGB and in "clump"):
interior structure, pulsation properties
- but also global evolution, such as t(Teff) or t(L)
MS and lower RGB for 1.0 M⊙ (Z=0.02)
2%
Code differences
same for a 2 M⊙ star
specific problem of
convective boundaries
and convective core
evolution
5%
note that also relative ages are not necessarily consistent!
agreement already improved from initial calculations, but only at some effort!
Help from seismology?
Seismology
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Scaling relations for "solar-type" oscillation patterns
used to determine mass and radius of stars (at known Teff)
Δν = M
Δ ν⊙ M ⊙
1/ 2
R
R⊙
−3/ 2
( ) ( )
( )( ) (
νmax
M R
=
νmax ,⊙ M R
⊙
⊙
●
−2
T eff
T eff ,⊙
−1/2
)
however, there are systematic effects, at least concerning the mass
determination
Seismic mass of stars in old open cluster NGC 6791
Mass of red giants in NGC 6791 as a
function of visual magnitude in the RGB
(left-hand panels) and in the Red Clump
(central panels).
(aimed at determining the integrated
mass loss on the RGB)
Note: RG mass is 1.23±0.02 M⊙
Miglio A et al. MNRAS 2012;419:2077-2088
Other mass determinations in NGC 6791
Brogaard et al. (2011)
mass (and Y) determination of
detached eclipsing binaries in
NGC 6791
most massive component
(M=1.1 M⊙) is at TO and
therefore mass on the RGB is
determined to 1.15±0.02 M⊙
also, the RGB mass as determined
from isochrone fitting of the TO,
is 1.15 M⊙
Therefore, there is a tendency for
"seismic masses" being too high
The very metal-poor stars "Rogue" and "K2"
(Jendreieck et al. 2014)
Spectroscopy: [Fe/H] for both stars < -2.20 (2 out of < 10 metal-poor Kepler-stars)
Teff < 5400 K
log g < 3
(red giant)
seismic mass: ≈ 1.1±0.2 M⊙ → age 3.5 – 5.7 Gyrs
Spectroscopy and evolutionary models favor stars of 0.7-0.9 M⊙ and age of > 10 Gyrs
Summary
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stellar models can predict neither Teff nor L accurately, because of
–
uncertainties in initial composition of observed star
–
effects of convection and diffusion
–
further mixing processes (rotation, levitation, gravity waves ...)
–
mass loss (for massive stars)
agreement between different stellar evolution codes neither perfect
uncertainties in age/mass determinations between a few percent to large
factors
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not clear, if relative ages/masses are much better
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help from seismology to be taken with care
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needed: appropriate calibration objects