Current uncertainties in Red Giant Branch stellar models:

Basti & the “Others”

Santi Cassisi

INAF - Astronomical Observatory of Teramo, Italy

Stellar models & Asteroseismic analysis

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Huber et al. (2010)

Kallinger et al. (2010)based on

BaSTI models

To assess the accuracy and

reliability of the evolutionary

scenariois mandatory!

Setting the (evolutionary) “scenario”

massive stars

Intermediate-mass stars

low-mass stars

Mup

MHeF

Intermediate-mass stars Low-mass stars

Physical Properties:

Microscopical Mechanisms:

Macroscopical Mechanisms:

Input physics affecting models for RGB low-Input physics affecting models for RGB low-mass starsmass stars

• 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

Input Evolutionary properties

Teff

RGB location & shape

He core mass@RGB Tip

RGB Tip brightnessHe-burning stage

luminosity

€

νMax = f1(Teff )

€

Δν = f2(Teff )

The effect of the EOS

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

solar-calibrated ml

Low-temperature radiative opacity

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);

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

Ferguson et al. 05

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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

These results seem to point to the fact that the solar-calibrated ml is a priori adequate also for RGB stars

Basti models

Ferraro et al. (2006)

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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

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Outer Boundary conditions 2/2

What about at lower metallicities?

•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

Kurucz

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Outer Boundary conditions 3/2

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

Vandenberg et al. (2008)

T(τ) versus “model atmosphere”: structural predictions

Solid line – model atmosphere

Dashed line – evolutionary code integration but fixing the outer boundary conditions from the model atmosphere

Despite the significant differences in the two approaches quite similar results are obtained…

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Models from different libraries, based on a solar-calibrated ml, can show different RGB effective temperatures

This is probably due to some differences in the input physics, such EOS and/orboundary conditions which is not compensated by the solar recalibration of the ml

Red Giant Branch models: the state-of-the-art

200K

The difference in the RGB location can be also significantly larger (…up to 400 K…) when accounting from less updated model libraries

Input physics affecting the RGB modelsInput physics affecting the RGB models

• 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

Input Evolutionary properties

Teff

RGB location & shape

He core mass@RGB Tip

RGB Tip brightnessHe-burning stage

luminosity

ΔTeff~100K

ΔTeff~150K

ΔTeff≤80K

Solar calibrated

ml

Eclipsing binaries can represent an important benchmark for model libraries

The case of V20 in the Galactic Open Cluster

NGC6791(Grundahl et al. 2008)

Victoria-Regina (t=8.5Gyr)

Photometry by Stetson et al. (2003)

(m-M)V=13.46 ± 0.10

E(B-V)=0.15 ± 0.02

A crucial issue: the color – Teff relations

The RGB luminosity function: the state-of-the-art

Theoretical predictions about the RGB star counts appear a quite robust result!

Evolutionary lifetimes for the RGB stage are properly predicted;

There is no “missing physics” in the model computations;

M13: Sandquist et al. (2010)

What is present situation about the level of agreement between between theory and observations concerning the RGB bump brightness?

Bertelli et al. 08 (Padua)

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

Does it exist a real problem in RGB stellar models or is there a problem in the data analysis?Monelli et al. (2010)

The RGB bump brightness: an independent checkIn 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)

a clear discrepancy between theory and observations is present, the theoretical RGB bump magnitudes being too bright by on average ~0.2 mag

Cassisi et al. (2010)

BaSTI models

…any hint from asteroseismology…?

Input physics affecting the RGB modelsInput physics affecting the RGB models

• 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

Input Evolutionary properties

Teff

RGB location & shape

He core mass@RGB Tip

RGB Tip brightnessHe-burning stage luminosity

The brightness of the Red Giant Branch Tip

RGB tip

The I-Cousin band TRGB The I-Cousin band TRGB magnitude magnitude is one of the most is one of the most important primary distance important primary distance indicators:indicators:

• age independent for t>2-3Gyrs;

• metallicity independent for [M/H]<−0.9

Being McHe@TRGB strongly dependent on the adopted “physical framework”, it has been often used as benchmark for testing “fundamental theory”

The TRGB brightness is a strong function of the He core mass at the He-burning ignition

TRGB: He core mass – luminosity

Salaris, Cassisi & Weiss (2001)

≈ 0.03M

These differences are – often but not always…- those expected when considering the different physical inputs adopted in the

model computations

€

∂logL(TRGB)

∂McHe

≈ 4.7

The He core mass@TRGB

Who is really governing the uncertainty in the McHe predictions?

0.8M Z=0.0002 –

Y=0.23McHe ΔMcHe

No diffusion 0.5110 -0.0043

Stand. diffusion 0.5153 //

Plasma ν +5% 0.5166 +0.0013

Plasma ν -5% 0.5141 -0.0012

3 +15% 0.5143 -0.0010

3 -15% 0.5166 +0.0013

κ +5% 0.5158 +0.0005

κ -5% 0.5147 -0.0006

κcond (HL) 0.5148 -0.0050

Diffusion 1/2 0.5136 -0.0017

Diffusion 2 0.5187 +0.0034

42%conductive

opacity

36%diffusion efficiency

4%radiative opacity

8%3α reaction

rate

10%plasma

neutrinos

ΔMAXMcHe ≈ 0.01M

ΔMbol~0.1 mag@TRGB

@ZAHBCassisi et al. (1998) – Michaud et al. (2010)

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)

The reliability of this comparison would be largely improved by:• increasing the GC sample…;• reducing the still-existing uncertainties in the color-Teff transformations

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…)

McHe & ZAHB brightness

• 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]

De Santis & Cassisi (1999)

Future perspectives for the BaSTI archive

Pulsational models

• 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