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Current uncertainties in
Red Giant Branch stellar models:
Basti & the “Others”
Santi Cassisi
INAF - Astronomical Observatory of Teramo, Italy
Stellar models & Asteroseismic analysis
Huber et al. (2010)
To assess the accuracy
and reliability of the
evolutionary scenario
is mandatory!
Kallinger et al. (2010)
based on
BaSTI models
2
Setting the (evolutionary) “scenario”
Mup
massive stars
Intermediate-mass stars
MHeF
low-mass stars
Intermediate-mass stars
Physical Properties:
Microscopical Mechanisms:
Macroscopical Mechanisms:
Low-mass stars
Input physics affecting models for RGB low-mass stars
Input
Evolutionary properties
•
Equation of State
•
Low Temperature Radiative Opacity
•
Efficiency of the convective energy
transport
•
Boundary conditions
•
Abundances (He, Fe & -elements)
•
Conductive Opacity
•
Neutrino energy losses
•
Atomic diffusion efficiency
Teff

RGB location & shape
 Max  f1(Teff )   f 2 (Teff )


He core mass@RGB Tip

RGB Tip brightness
He-burning stage luminosity
The effect of the EOS
solar-calibrated ml
Models computed by using some of the most commonly adopted EOS show:
•Different RGB slope
•Even if the ml is calibrated on the Sun, differences in the Teff of the order
of 100K exist
Low-temperature radiative opacity
Ferguson et al. 05
Current sets of stellar models employ
mainly the low-T opacity computations by
Ferguson et al. (2005)
The largest improvement in low-T opacity
has been the proper treatment of
molecular absorption… and grains…
Ferguson et al. 2005
RGB models predict the same location and shape for the RGB until the Teff is
larger than ~4000K;
For lower Teff, computations based on the most updated opacity, predict cooler
models (the difference is of the order of 100K);
Treatment of superadiabatic convection
The mixing length is usually calibrated on the Sun: is this approach
adequate for RGB stars?
The solar-calibration of the ml guarantes
that the models always predict the “right”
Teff of at least solar-type stars;
However, it is important to be sure that a
solar ml is also suitable for RGB stars of
various metallicities
Ferraro et al. (2006)
These results seem to point to the fact
that the solar-calibrated ml is a priori
adequate also for RGB stars
Basti models
7
Outer Boundary conditions
1/2
What is the most adequate approach for fixing the boundary conditions?
•The RGB based on model atmospheres shows a slightly different location with
respect the models computed by using the Krishna-Swamy solar T()
•The difference is of the order of 100K at solar metallicity
8
Outer Boundary conditions
2/2
What about at lower metallicities?
Kurucz
•The RGB based on model atmospheres shows
a slightly different slope, crossing over models
computed using the KS66 solar T()
…but…
•The difference is always within ~50K or less
9
Outer Boundary conditions
3/2
T(τ) versus “model atmosphere”: structural predictions
The trend of various thermodynamic
quantities, opacity, convective velocity
and the fraction of the total flux
carried
by
convection
in
the
subphotospheric layers of a solar model
Solid line – model atmosphere
Dashed line – evolutionary code integration but
fixing the outer boundary conditions from the
model atmosphere
Vandenberg et al. (2008)
Despite the significant differences in the two
approaches quite similar results are obtained…
10
Red Giant Branch models: the state-of-the-art
200K
Models from different libraries, based
on a solar-calibrated ml, can show
different RGB effective temperatures
The difference in the RGB location can
be also significantly larger (…up to 400
K…) when accounting from less updated
model libraries
This is probably due to some differences in the input physics, such EOS and/or
boundary conditions which is not compensated by the solar recalibration of the ml
11
Input physics affecting the RGB models
Input
Teff~100K
•
Equation of State
•
Low Temperature Radiative Opacity T ~150K
eff
•
Efficiency of the convective energy
transport
•
Boundary conditions
•
Abundances (He, Fe & -elements)
•
Conductive Opacity
•
Neutrino energy losses
•
Atomic diffusion efficiency
Solar
calibrated ml
Teff≤80K
Evolutionary properties
Teff

RGB location & shape
He core mass@RGB Tip

RGB Tip brightness
He-burning stage luminosity
A crucial issue: the color – Teff relations
Eclipsing binaries can represent an important benchmark for model libraries
The case of V20 in the Galactic
Open Cluster NGC6791
(Grundahl et al. 2008)
(m-M)V=13.46 ± 0.10
E(B-V)=0.15 ± 0.02
Victoria-Regina (t=8.5Gyr)
Photometry by Stetson et al. (2003)
The RGB luminosity function: the state-of-the-art
Bertelli et al. 08 (Padua)
Theoretical predictions about the
RGB star counts appear a quite
robust result!
M13: Sandquist et al. (2010)
Evolutionary lifetimes for the RGB stage are properly predicted;
There is no “missing physics” in the model computations;
What is present situation about the level of agreement between
between theory and observations concerning the RGB bump
brightness?
The RGB bump brightness
To overcome problems related to still-present indetermination on GC distance
modulus and reddening, it is a common procedure to compare theory with
observations by using the ΔV(Bump-HB) parameter
Monelli et al. (2010)
Does it exist a real problem in RGB
stellar models or is there a problem in
the data analysis?
The RGB bump brightness: an independent check
In order to avoid any problem associated to the estimate of the HB luminosity
level from both the theoretical and observational point of view, we decided to
use the ΔV(Bump-Turn Off) parameter (see also Meissner & Weiss 06)
BaSTI models
Cassisi et al. (2010)
a clear discrepancy between theory and observations is present, the
theoretical RGB bump magnitudes being too bright by on average ~0.2 mag
…any hint from asteroseismology…?
Input physics affecting the RGB models
Input
•
Equation of State
•
Low Temperature Radiative Opacity
•
Efficiency of the convective energy
transport
•
Boundary conditions
•
Abundances (He, Fe & -elements)
•
Conductive Opacity
•
Neutrino energy losses
•
Atomic diffusion efficiency
Evolutionary properties
Teff

RGB location & shape
He core mass@RGB Tip

RGB Tip brightness
He-burning stage luminosity
The brightness of the Red Giant Branch Tip
RGB tip
The I-Cousin band TRGB magnitude
is one of the most important
primary distance indicators:
• age independent for t>2-3Gyrs;
• metallicity independent for [M/H]<−0.9
The TRGB brightness is a strong
function of the He core mass at
the He-burning ignition
Being McHe@TRGB strongly dependent on the adopted “physical framework”,
it has been often used as benchmark for testing “fundamental theory”
TRGB: He core mass – luminosity
log L(TRGB)
 4.7
M cHe

≈ 0.03M
Salaris, Cassisi & Weiss (2001)
These differences are – often but not always…- those expected when
considering the different physical inputs adopted in the model computations
The He core mass@TRGB
Who is really governing the uncertainty in the McHe predictions?
0.8M
Z=0.0002 – Y=0.23
McHe
McHe
No diffusion
0.5110
-0.0043
Stand. diffusion
0.5153
//
Plasma  +5%
0.5166
+0.0013
Plasma  -5%
0.5141
-0.0012
3 +15%
0.5143
-0.0010
3 -15%
0.5166
+0.0013
 +5%
0.5158
+0.0005
 -5%
0.5147
-0.0006
 cond (HL)
0.5148
-0.0050
Diffusion 1/2
0.5136
-0.0017
Diffusion 2
0.5187
+0.0034
42%
conductive
opacity
4%
radiative
opacity
36%
diffusion
efficiency
8%
3α reaction
rate
MAXMcHe ≈ 0.01M
Mbol~0.1 mag
Cassisi et al. (1998) – Michaud et al. (2010)
10%
plasma
neutrinos
@TRGB
@ZAHB
TRGB: He core mass & luminosity
• last generations of stellar models agree – almost all – within ≈ 0.003M
• a fraction of the difference in McHe is due to the various initial He
contents – but in the case of the Padua models…
• the difference in Mbol(TRGB) is of the order of 0.15 mag when excluding
the Padua models…
The TRGB brightness: theory versus observations (an update)
Updated RGB models are now in
agreement with empirical data at
the level of better than 0.5σ
In the near-IR bands, the same calibration
seems to be in fine agreement with
empirical constraints (but in the J-band…)
The reliability of this comparison would be largely improved by:
• increasing the GC sample…;
• reducing the still-existing uncertainties in the color-Teff transformations
McHe & ZAHB brightness
De Santis & Cassisi (1999)
• The difference among the most recent models is about 0.15 mag
• All models but the Dotter’s ones, predict the same dependence on [M/H]
Future perspectives for the BaSTI archive
• to update the database, taking into account all the improvements in
the physical framework;
• to improve the parameter-space coverage…;
• to check the accuracy & reliability by comparing the models with
suitable empirical constraints such as eclipsing binaries, star clusters…;
• collaborations with reseachers working in the asteroseismology field
are very welcomed!;
The BaSTI archive is available @
http://www.oa-teramo.inaf.it/BASTI