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EVOLUTION AND INTERNAL STRUCTURE OF RED GIANTS Maurizio Salaris Astrophysics Research Institute Liverpool John Moores University Slide 2 Kallinger et al. (2010) What stars am I going to talk about? Adapted from Gallart (1999) Slide 3 From McConnachie et al. (2006) RGB stars as metallicity indicators RC stars as SFH diagnostics Slide 4 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 T eff + 100 K (only RGB) 8 6 3 Slide 5 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 Slide 6 Solar initial chemical composition 1.0 M o 2.4 M o RGB RC EAGB Representative evolutionary tracks Slide 7 RGB stars Objects with (initial) mass lower than ~2.0M o Electron degenerate (nearly) isothermal He-core surrounded by a thin (~0.001-0.0001 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 ~0.47 - 0.50M o Slide 8 LIFETIMES Slide 9 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 Slide 10 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 20 16 O Y by 0.01 0.02 Slide 11 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 Slide 12 13 Gyr Z=0.008 Z=0.0004 10 13 Gyr Z=0.008 Dependence of the bump luminosity on age and metallicity Slide 13 Zoccali et al. (1999) RGB bump detection in stellar populations Slide 14 Chemical profiles and energy generation grad(T)= ln(T)/ ln(P) Slide 15 He-core Superadiabatic region surface Slide 16 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 Slide 17 From Castellani & Castellani (1993) Only extreme values of affect appreciably the HRD of RGB stars Slide 18 ! Different parametrizations Goldberg formula Mullans formula Judge & Stencel formula Catelan (2009) modified Reimers formula Slide 19 Uncertain dependence on the metallicity Origlia et al. 2007 Slide 20 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 Slide 21 Superadiabatic convection: The mixing length theory (Bhm-Vitense 1958) a b c BV58 24 calibration HVB65 modified calibration ML1 24 1.0 ML2 1 2 16 0.6 - 1.0 ML3 1 2 16 2.0 ML2 and ML3 increase the convective efficiency compared to ML1 l= 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 Slide 22 The value of affects strongly the effective temperature of stars with convective envelopes Thecanonical 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 should stay constant within a stellar envelope, and when considering stars of different masses and/or at different evolutionary stages Slide 23 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 =0.6 Salaris & Cassisi (2008) ML2, =0.63 (solid - solar calibration) ML1, =2.01 (dashed solar calibration ) ML2 models at most ~50 K hotter Slide 24 Hydro-calibration Extended grid of 2D hydro-models by Ludwig, Steffen & Freytag Static envelope models based on the mixing length theory calibrate by reproducing the entropy of the adiabatic layers below the superadiabatic region from the hydro-models. A relationship =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) Slide 25 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 Slide 26 Solar calibrated models with different boundary conditions predict different RGB temperatures Salaris et al. (2002) Montalban et al. (2004) Boundary conditions Boundary conditions Slide 27 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 Slide 28 The need for additional element transport mechanisms Mucciarelli, Salaris et al. (2010) Gratton et al. (2000) Field halo stars Globular cluster M4 Slide 29 From Salaris, Cassisi & Weiss (2002) 0.8 M o metal poor RGB model Slide 30 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 () 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 gradient. Eggleton et al. (2006) ADDITIONAL TRANSPORT MECHANISMS 1M o solar composition See Corinne talk for more details Slide 31 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=0.0001 ATOMIC DIFFUSION Slide 32 Effect of smoothing the H-profile discontinuity Cassisi, Salaris & Bono (2002) Slide 33 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 Slide 34 Salaris et al. (2002) Bellazzini et al. (2001) 8,10,12,14 Gyr Z=0.0004 Z=0.0002 0.008 10 Gyr TRGB as distance indicator Slide 35 Holtzman et al. (1999) RGB stars in composite stellar populations, an example Slide 36 Synthetic M I -(VI) 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) Slide 37 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 Slide 38 He core mass at He ignition Salaris & Cassisi (2005) Slide 39 INSIDE A RC STAR Log(L/L o )=1.7 Slide 40 COMPARISON WITH RGB STARS Log(L/L o )=1.7 Slide 41 log( c 2) -15 Comparison of sound speed profiles Slide 42 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) Slide 43 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 Slide 44 Typical evolution of temperature gradients and He abundances in the core of RC stars Slide 45 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 Slide 46 DIFFERENT SFHs PRODUCE VERY DIFFERENT RC MORPHOLOGIES Girardi & Salaris (2001) Solar neighbourhood LMC fields Slide 47 M RC =M RC (local)-M RC (pop) Slide 48 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 Slide 49 Internal stratification Slide 50 Development of CO-core degeneracy Slide 51 Log(L/L o )=2.1 Comparison with RGB stars Slide 52 log( c 2) -15 Comparison of sound speed profiles Slide 53 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 Slide 54 Slide 55 Slide 56 The role of red giants in population synthesis Slide 57 Slide 58 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) Slide 59 Michaud et al. (2010) ATOMIC DIFFUSION AND INTERNAL PROFILES Slide 60 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) Slide 61 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 Slide 62 Semiconvection and HRD evolution Semiconvection increases central He-burning lifetime by a factor ~1.5 - 2 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 Slide 63 Too large overshooting erases the partial mixing profile Semiconvection Overshooting 1Hp Overshooting 1Hp Slide 64 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. Slide 65