EVOLUTION AND INTERNAL STRUCTURE OF RED GIANTS Maurizio Salaris Astrophysics Research Institute Liverpool 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 Gyr [Fe/H]= −0.7 − Blue circles  T eff 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 M o 2.4 M o RGB RC EAGB Representative evolutionary tracks

RGB stars Objects with (initial) mass lower than ~2.0M o Electron degenerate (nearly) isothermal He-core surrounded by a thin (~ M o thickness) H- burning shell that is, in turn, surrounded by an extended convective envelope Evolution towards increasing luminosity and moderately decreasing T eff due to the steady increase of the He-core mass Efficient mass loss from the convective envelope He-flash terminates RGB evolution when M c He ~ M o

LIFETIMES

RGB in the CMD (or HRD) metallicity age initial helium  One has to be careful with the intermediate ages L bol of the TRGB increases with increasing Z, but the behaviour in the CMD depends on the passband

First dredge-up After the 1 st dredge up 12 C/ 13 C  to ~ 25 from ~90 14 N  by a factor ~ 2 12 C  by ~ 30 % 7 Li  by a factor ≈ O  Y  by 0.01  0.02

RGB bump 1M o 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= – 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)=  ln(T)/  ln(P)

He-core Superadiabatic region  surface

Difficulties with the parametrization of the RGB mass loss He WD limit red HB EHB limit 10,000 K RR Lyrae The Reimers’ law free parameter

From Castellani & Castellani (1993) Only extreme values of η affect appreciably the HRD of RGB stars

! Different parametrizations “Goldberg formula” “Mullan’s formula” “Judge & Stencel formula” Catelan (2009) “modified Reimers formula”

Uncertain dependence on the metallicity Origlia et al. 2007

From Salaris et al (1993) Difficulties with the T eff scale of RGB models The T eff scale of RGB models depends on: i) i)Low-T opacities ii) ii)Treatment of superadiabatic gradient iii) 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 ML ML ML2 and ML3 increase the convective efficiency compared to ML1 l=α H p mixing length Widely used in stellar evolution codes Simple, local, time independent model, that assumes convective elements with mean size l, of the order of their mean free path

The value of α affects strongly the effective temperature of stars with convective envelopes The’canonical’ calibration is based on reproducing the solar radius with a theoretical solar models (Gough & Weiss 1976) We should always keep in mind that there is a priori no reason why α should stay constant within a stellar envelope, and when considering stars of different masses and/or at different evolutionary stages

Are different formulations of the MLT equivalent ? Gough & Weiss (1976), Pedersen et al. (1991) A simple test The mixing length calibration preferred in White Dwarf model atmospheres and envelopes (e.g. Bergeron et al. 1995) is the ML2 with α=0.6 Salaris & Cassisi (2008) ML2, α=0.63 (solid - solar calibration) ML1, α=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(T eff,g) is produced, to be employed in stellar evolution modelling (Ludwig et al.1999) From Freytag & Salaris (1999) Previous attempts by Deupree & Varner (1980) Lydon et al (1992, 1993)

Calibration of the mixing length parameter using RGB stars Effective temperatures Effective temperatures Prone to uncertainties in the temperature scale, metallicity scale, colour transformations Colours Colours CALIBRATION OF THE MIXING LENGTH ON RGB STARS See Paolo talk for more

Solar calibrated models with different boundary conditions predict different RGB temperatures Salaris et al. (2002) Montalban et al. (2004) Boundary conditions Boundary conditions

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. (2004) Boundary conditions taken at  =56

The need for additional element transport mechanisms Mucciarelli, Salaris et al. (2010) Gratton et al. (2000) Field halo stars Globular cluster M4

From Salaris, Cassisi & Weiss (2002) 0.8 M o metal poor RGB 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 3 He burns. The main reaction is 3 He ( 3 He, 2p) 4 He: 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 4 He 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 1M o 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) 0.8M o Z= 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 H p

Salaris et al. (2002) Bellazzini et al. (2001) 8,10,12,14 Gyr Z= Z= Gyr TRGB as distance indicator

Holtzman et al. (1999) RGB stars in composite stellar populations, an example

Synthetic M I -(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 t He is reached. Short-dashed lines denote the evolution from 70  up to 85  of t He, whereas the dotted ones go from 85 to 99  of t He. RED CLUMP STARS RC 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)

INSIDE A RC STAR Log(L/L o )=1.7

COMPARISON WITH RGB STARS Log(L/L o )=1.7

log( c 2) -15 Comparison of sound speed profiles

Treatment of Core Convection C produced by He-burning Opacity increases Radiative gradient discontinuity at the convective core boundary Mass of convective core increases 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

ΔM λ RC =ΔM λ RC (local)-ΔM λ RC (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 ≈10 7 yr EARLY-AGB

Internal stratification

Development of CO-core degeneracy

Log(L/L o )=2.1 Comparison with RGB stars

log( c 2) -15 Comparison of sound speed profiles

Open questions: Accuracy of model T eff (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).Girardi et al. (2000)Westera et al. (2002)Girardi et al. (2002)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 (M c He ) and radius (R c 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(M c He ) ≈ 8 – 10 And for the temperature at the base of the H- shell dln(T)/dln(M c He )>1 Kippenhahn & Weigert (1991)

Caloi & Mazzitelli (1990)Sweigart (1990) Mimicking semiconvection with overshooting Breathing pulses are still found to occur Extension of mixing (by ~0.1Hp) in regions beyond the boundary of all convective regions (core and shells) forming within the He-rich core (~0.1Hp) The edge of the convective core is let propagate with velocity

‹‹‹‹‹‹‹‹ Semiconvection and HRD evolution Semiconvection increases central He-burning lifetime by a factor ~ Breathing Pulses ›››››››› (Start when Y c ~0.10) Numerical artifact ?? Parameter R2=Nagb/Nhb Observations R2~0.14 Semiconv +BPs R2=0.08 Semiconv no BPs R2=0.12

Too large overshooting erases the partial mixing profile Semiconvection Overshooting 1Hp Overshooting 1Hp

II phase: Development of a ‘partial mixing zone’ When Y c decreases below ~0.7, a ‘partial mixing’ (semiconvective) zone develops beyond the boundary of the convective core.