EVOLUTION AND INTERNAL STRUCTURE OF RED

GIANTS

Maurizio SalarisAstrophysics Research InstituteLiverpool John Moores University

Kallinger et al. (2010)

What stars am I going to talk about?

Adapted from Gallart (1999)

From McConnachie et al. (2006)

RGB stars as metallicity indicators

↓

RC stars as SFH diagnostics

←

Number of RGB stars above the HB level

reduced by a factor 2

10

14Gyr

[Fe/H]= −0.7 −0.35 +0.06 +0.40

Blue circles Teff + 100 K (only RGB)

8

6

3

OUTLINE

• The three classes of red giant stars• Behaviour in the CMD (or HRD)• Internal structure• Some long-standing uncertainties• Examples of applications to more

general astrophysical problems

Solar initial chemical composition

1.0 Mo

2.4 Mo

RGB

RC

EAGB

Representative evolutionary tracks

RGB stars

• Objects with (initial) mass lower than ~2.0Mo

• Electron degenerate (nearly) isothermal He-core surrounded by a thin (~0.001-0.0001 Mo thickness) H-burning shell that is, in turn, surrounded by an extended convective envelope

• Evolution towards increasing luminosity and moderately decreasing Teff due to the steady increase of the He-core mass

• Efficient mass loss from the convective envelope• He-flash terminates RGB evolution when Mc

He~0.47 - 0.50Mo

LIFETIMES

RGB in the CMD (or HRD) metallicity age initial helium

One has to be careful with the intermediate ages

LLbol bol of the TRGB of the TRGB increases with increases with increasing Z, but increasing Z, but the behaviour in the behaviour in the CMD the CMD depends on the depends on the passbandpassband

First dredge-up

After the 1st dredge up

12C/13C to ~ 25 from ~90

14N by a factor ~ 2 12C by ~ 30

%

7Li by a factor ≈ 20

16O

Y by 0.01 0.02

RGB bump

1Mo solar composition

The size of the H-abundance discontinuity determines the ‘area’ of the bump region in the LF.

The shape of the H-profile discontinuity affects the shape of the bump region

13 Gyr

Z=0.008

Z=0.0004

10 – 13 Gyr

Z=0.008

Dependence of the bump luminosity on age and metallicity

Zoccali et al. (1999)

RGB bump detection in stellar populations

Chemical profiles and energy generation

grad(T)=grad(T)=ln(T)/ln(T)/ln(P)ln(P)

He-core Superadiabatic region

surface

Difficulties with the parametrization of the RGB mass loss

13RGB 4 10 R

dM L

dt gR

He WD He WD limitlimit

red red HBHB

EHB EHB limitlimit

10,00010,000 KK

RR RR LyraeLyrae

The Reimers’ law

free parameter

From Castellani & Castellani (1993)

Only extreme values of η affect appreciably the HRD of RGB stars

!

Different parametrizationsDifferent parametrizations

dMR

dt 3.2

“Goldberg formula”

“Mullan’s formula”

32

dM g

dt R

-0.9

“Judge & Stencel formula”

dMg

dt -1.6

Catelan (2009)

dM L

dt gR

1.4

“modified Reimersformula”

Uncertain dependence Uncertain dependence on the metallicityon the metallicity

Origlia et al. 2007

From Salaris et al (1993)

Difficulties with the Teff scale of RGB models

The Teff scale of RGB models depends on:

i) Low-T opacities

ii) Treatment of superadiabatic gradient

iii)Boundary conditions

Superadiabatic convection: The mixing length theory (Böhm-Vitense 1958)

a b c α

BV58 ⅛ ½ 24 calibration

HVB65 ⅛ ½ modified

calibration

ML1 ⅛ ½ 24 1.0ML2 1 2 16 0.6 -

1.0

ML3 1 2 16 2.0 ML2 and ML3 increase the convective efficiency compared to ML1

ll==αα HHp mixing lengthp mixing length

Widely used in stellar evolution codesWidely used in stellar evolution codes

Simple, local, time independent model, that assumes convective Simple, local, time independent model, that assumes convective

elements with mean size l,elements with mean size l, of the order of their mean free pathof the order of their mean free path

The value of The value of αα affects strongly the effective affects strongly the effective temperature of stars with convective temperature of stars with convective envelopes envelopes

The’canonical’ The’canonical’ calibration is based on calibration is based on reproducing the solar reproducing the solar radius with a radius with a theoretical solar theoretical solar models (Gough & models (Gough & Weiss 1976)Weiss 1976)

We should always keep We should always keep in mind that there is a in mind that there is a priori no reason why priori no reason why αα should stay constant should stay constant within a stellar within a stellar envelope, and when envelope, and when considering stars of considering stars of different masses different masses and/or at different and/or at different evolutionary stagesevolutionary stages

Are different formulations of the MLT Are different formulations of the MLT equivalent ?equivalent ?

Gough & Weiss (1976), Pedersen Gough & Weiss (1976), Pedersen et al. (1991)et al. (1991)

A simple testA simple test

The mixing length The mixing length calibration preferred in calibration preferred in White Dwarf model White Dwarf model atmospheres and atmospheres and envelopes (e.g. Bergeron envelopes (e.g. Bergeron et al. 1995) is the ML2 et al. 1995) is the ML2 with with αα=0.6=0.6

Salaris & Cassisi (2008)

ML2, ML2, αα=0.63 (solid - solar calibration)=0.63 (solid - solar calibration)ML1, ML1, αα=2.01 (dashed – solar calibration=2.01 (dashed – solar calibration))

ML2 models at most ~50 K hotter

Hydro-calibration Extended grid of 2D

hydro-models by Ludwig, Steffen & Freytag

Static envelope models based on the mixing length theory calibrate α by reproducing the entropy of the adiabatic layers below the superadiabatic region from the hydro-models.

A relationship α=f(Teff,g) is produced, to be employed in stellar evolution modelling

(Ludwig et al.1999)From Freytag & Salaris (1999)

Previous attempts by Deupree & Previous attempts by Deupree & Varner (1980) Lydon et al (1992, Varner (1980) Lydon et al (1992, 1993)1993)

Calibration of the mixing Calibration of the mixing length parameter using length parameter using RGB starsRGB stars

Effective Effective temperaturestemperatures

Prone to uncertainties in Prone to uncertainties in the temperature scale, the temperature scale, metallicity scale, colour metallicity scale, colour transformationstransformations

ColoursColours

CALIBRATION OF THE MIXING LENGTH CALIBRATION OF THE MIXING LENGTH ON RGB STARSON RGB STARS

See Paolo talk for more

Solar calibrated models with different boundary conditions predict different RGB temperatures

Salaris et al. (2002)Salaris et al. (2002)

Montalban et al. (2004)Montalban et al. (2004)

Boundary Boundary conditionsconditions

Calculations with empirical solar T() and same opacities as in model atmosphere (solid line) , compared with the case of

boundary conditions from detailed model atmospheres (ATLAS 9 – dashed line)

From Pietrinferni et al. From Pietrinferni et al. (2004)(2004)

Boundary Boundary conditions conditions taken at taken at =56=56

The need for additional element transport mechanisms

Mucciarelli, Salaris et al. (2010)

Gratton et al. (2000)

Field halo starsField halo stars

Globular cluster M4Globular cluster M4

From Salaris, Cassisi & Weiss From Salaris, Cassisi & Weiss (2002)(2002)

0.8 M0.8 Moo metal poor RGB metal poor RGB model model

“The H-burning front moves outward into the stable region, but preceding the H-burning region proper is a narrow region, usually thought unimportant, in which 3He burns.

The main reaction is 3He (3He, 2p)4He: two nuclei become three nuclei, and the mean mass per nucleus decreases from 3 to 2. Because the molecular weight (µ) is the mean mass per nucleus, but including also the much larger abundances of H and 4He that are already there and not taking part in this reaction, this leads to a small inversion in the µ gradient. “

Eggleton et al. (2006)

ADDITIONAL TRANSPORT MECHANISMS

1Mo solar composition

See Corinne talk for more details

Surface abundance variations on the RGB for the model with diffusion (red line) and the model without diffusion (blue line).

From Michaud et al. (2007)

0.8Mo Z=0.0001

ATOMIC DIFFUSION

Effect of smoothing the H-profile discontinuity Cassisi, Salaris & Bono

(2002)

Needs more than ~ 120 stars within ±0.20 mag of the bump peak, and photometric errors not larger than 0.03 mag to reveal the effect of smoothing lengths ≥ 0.5 Hp

Salaris et al. (2002)

Bellazzini et al. (2001)

8,10,12,14 Gyr

Z=0.0004

Z=0.0002 0.00810 Gyr

TRGB as distance indicator

Holtzman et al. (1999)

RGB stars in composite stellar populations, an example

Synthetic MI -(V–I) CMD detailing the upper part of the RGB, and two globular cluster isochrones for [Fe/H] equal to −1.5 and −0.9, respectively

Metallicity distribution of the synthetic upper RGB CMD.

Salaris & Girardi (2005)

Z=0.019

Girardi (1999)Solid lines end when 70  of tHe is reached. Short-dashed lines denote the evolution from 70  up to 85  of tHe, whereas the dotted ones go from 85 to 99  of

tHe.

RED CLUMP STARSRC stars are objects in the central He-burning phase.

A convective He-burning core is surrounded by a H-burning shell.

Above the H-burning shell lies a convective envelope

The path in the HRD is determined by the relative contribution of the central and shell burning to the total energy output

He core mass at He ignition

Salaris & Cassisi (2005)Salaris & Cassisi (2005)

INSIDE A RC STAR

Log(L/Lo)=1.7

COMPARISON WITH RGB STARS

Log(L/Lo)=1.7

log

( clo

g( c 2

)2)-1

5-1

5

Comparison of sound speed profilesComparison of sound speed profiles

Treatment of Core ConvectionTreatment of Core Convection

C produced by He-burningC produced by He-burning

Opacity increasesOpacity increases

Radiative gradient discontinuity atRadiative gradient discontinuity at

the convective core boundarythe convective core boundary

Mass of Mass of convective convective core core increasesincreases

See, e.g. Castellani et al. (1971)See, e.g. Castellani et al. (1971)

Michaud et al. (2008) have shown that the phase of core expansion can be also produced by atomic diffusion

What happens next ?

See Achim talk

Typical evolution of temperature gradients and He abundances in the core of RC stars

The RC age-magnitude-colour distribution for a given SFH depends on the trend of the TO lifetime with mass, and the He-burning/TO lifetime ratio with mass

Solar neighbourhood RC simulation (Girardi & Salaris 2001)

INPUT (Rocha-Pinto et al. (2000)

OUTPUT

DIFFERENT SFHs PRODUCE VERY DIFFERENT RC MORPHOLOGIES

Girardi & Salaris (2001)

Solar neighbourhood

LMC fields

ΔMλRC=ΔMλ

RC (local)-ΔMλRC (pop)

Early AGB

Early-AGB stars are objects with an electron degenerate CO-core embedded within the original He-core at He-ignition.

An H-burning shell is efficient above the He-core boundary, surrounded by a convective envelope.

The evolution is similar to RGB stars. The early-AGB ends with the ignition of the He-burning shell (AGB clump). Timescales ≈107 yr

EARLY-AGB

Internal stratification

Development of CO-core degeneracy

Log(L/Lo)=2.1

Comparison with RGB stars

log

( clo

g( c 2

)2)-1

5-1

5

Comparison of sound speed profilesComparison of sound speed profiles

Open questions:

• Accuracy of model Teff (superadiabatic convection + boundary conditions)

• RGB mass loss• Element transport mechanisms during

the RGB• Mixing in the core during the central

He-burning phase

The role of red giants in population synthesis

Difference between the theoretical I(TRGB) for t= 12.5 Gyr, scaled solar [Fe/H]=−1.38 and the theoretical values predicted for the ages and scaled solar [Fe/H] values displayed.

The underlying theoretical models are from Girardi et al. (2000). Panels (a), (b), (c) and (d) show, respectively, the results using the Yale transformations, Westera et al. (2002) transformations, Girardi et al. (2002) transformations, and the transformations used in Girardi et al. (2000).

Michaud et al. (2010)

ATOMIC DIFFUSION AND INTERNAL PROFILES

The properties of H-burning shell, hence the luminosity of the RGB star are mainly determined by the mass (Mc

He) and radius (Rc

He) of the He-core.

Using the M-R relation of cold WDs, the CNO-cycle energy generation mechanism and electron scattering opacity in the shell, homology considerations give:

dln(L)/dln(McHe) ≈ 8 – 10

And for the temperature at the base of the H-shell

dln(T)/dln(McHe)>1

Kippenhahn & Weigert (1991)

Caloi & Mazzitelli (1990) Sweigart (1990)

Mimicking semiconvection with Mimicking semiconvection with overshootingovershooting

Breathing pulses Breathing pulses are still found to are still found to occuroccur

Extension of mixing (by Extension of mixing (by ~0.1Hp) ~0.1Hp) in regions beyond the boundary in regions beyond the boundary of all convective regions (core of all convective regions (core and shells) forming within the and shells) forming within the He-rich core (He-rich core (~0.1Hp)~0.1Hp)

The edge of the convective core The edge of the convective core is let is let

propagate with velocitypropagate with velocity

‹‹‹‹‹‹‹‹ ‹‹‹‹‹‹‹‹ Semiconvection Semiconvection and HRD evolutionand HRD evolution

Semiconvection Semiconvection increases central He-increases central He-burning lifetime by a burning lifetime by a factor factor ~1.5 - 2~1.5 - 2

Breathing Pulses Breathing Pulses ››››››››››››››››

(Start when Y(Start when Ycc~0.10)~0.10)

Numerical artifact ??Numerical artifact ??Parameter R2=Nagb/NhbParameter R2=Nagb/Nhb

Observations R2Observations R2~~0.140.14

Semiconv +BPs R2=0.08Semiconv +BPs R2=0.08

Semiconv noSemiconv no BPs R2=0.12 BPs R2=0.12

Too large overshooting erases the partial mixing Too large overshooting erases the partial mixing profileprofile

SemiconvectionSemiconvection Overshooting Overshooting 1Hp1Hp

II phase: Development of a II phase: Development of a ‘partial mixing zone’ ‘partial mixing zone’

When YWhen Yc c decreases below decreases below ~~0.7, 0.7, a ‘partial mixing’ a ‘partial mixing’ (semiconvective) zone develops (semiconvective) zone develops beyond the boundary of the beyond the boundary of the convective core.convective core.