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Stellar Evolution in General and in Special Effects: Core Collapse, C-Deflagration, Dredge-up Episodes. Cesare Chiosi Department of Astronomy University of Padova, Italy. Part B: Massive stars and core collapse supernovae.
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Stellar Evolution in General and in Special Effects:Core Collapse, C-Deflagration, Dredge-up Episodes Cesare Chiosi Department of Astronomy University of Padova, Italy
History of Pre-Supernova Evolution of Massive Stars (Type II SN) • Semiconvection • Semiconvection & Mass Loss • Convective Overshoot • Convective Overshoot & Mass Loss • Rotation & Mixing • Rotation, Mixing & Mass Loss
Semiconvection Electron scattering and radiation pressure cause physical inconsistency at the border of the formal convective core fixedby the Schwarzschild condition. Cured by introducing partial mixing in the border layers so that neutrality condition is achieved. Two possible criteria: Schwarzschildor Ledoux
Inner structure & Loops in HRD: Schwarzschild or Ledoux? Ledoux: loops Schwarzschild: no loops Debate still with us !!!
Mass Loss by Stellar Wind: in the blue In the blue Radiation Pressure on ions Massive, blue stars lose lots of mass at the observed rates!!
Mass Loss by Stellar Wind: in the red • RSG lose mass at rates as high as those of O, BSG. • Two components: gas + dust interacting thermally and dynamically. • Radiation pressure on dust (atoms and/or molecules). However other mechanisms are also proposed. In massive stars, mass loss cannot be ignored !!!
An old interpretation of the HRD… Mass loss and semiconvection The blue-red connection
……….The Family Tree • M > 60 Mo Always Blue O OF BSG (+LBV) WN WC (WO) SN • 25 Mo < M< 60 Mo Blue-Red-Blue • O BSG YSG RSG WN (WC) SN High Ms |-------------- SN Low Ms • M < 25 Mo • O (BSG) RSG YSG + Cepheids RSG SN BSG SN (Z)
Overshoot: Generalities • Convective elements must cross the Schwarzchild border to dissipation their Kinetic Energy • How far can they go ? Controversial, likely l=LHp with L = 0.5 • Is mixing complete & instantaneous (as in MLT) or partial & slow? • How does energy transport occur? • What is the temperature profile in the overshoot region? Adiabatic or radiative? OVERSHOOT ……..
Two current models for overshoot • The ballistic description • The diffusive description
The ballistic model Integrate to getvr andvMax( r )
The diffusive model Looking for better overshoot models diffusion • Split the problem in three parts: • A) size of the unstable region (fully unstable + overshooting) Lov= lo/(1-f) with lo = Hp and f breaking exponent in turbulent cascade (0.5). • B) Energy transport: in overshoot region both radiative and adiabatic thermal structures yield akin results (Xiong 90). • C) Mixing mechanism.
Velocity Cascade, Intermittence & Stirring • Velocity cascade (energy conservation) • Intermittence (volume filling) • Stirring (spoons & cups)
Diffusive Overshoot & WR Stars But WR…. & BSGGap…
Diffusion & New Mass Loss Rates from RSG WR and Blue Gap perhaps simultaneously explained!!
Overshoot in Intermediate Mass Stars Brigther and longer lived on the MS. Brighter and shorter lived on PMS. Changes the ratio NPMS/NMS.
The HRD of intermediate mass stars Shorter Loops
Central Conditions Mup goes down to about 6.5 Mo (in these models).
Fate of Intermediate Mass Stars Overhoot increases both MHe and Mco and therefore shifts to lower initial masses the regime for Type II SN and for those stars they may end up as SN or WDs.
Overshoot and Late Evolutionary Stages • Most important consequence of convective overshoot are the larger He and C-O cores built up during the H- and He-burning phases. • In intermediate mass stars, it will lower the mass Mup (to about 5-6 Mo) so-called Type I+1/2 SN are ruled out, will decrease the minimum mass for Type II SN. • In massive stars it will decrease the transition mass for them to end up as a Neutron Star or a Black Hole.
Rotation • Among the most important achievements of the past ten years are the stellar models with rotation (and mass loss) From Maeder & Meynet
A bit of formalism • Replace spherical eulerian (lagrangian) coordinates with a new system characterized by equipotentials gravitational potential If W constant on isobars “shellular” rotation (it results from turbulence being highly anisotropic, much stronger transport horizontally than vertically).
von Zeipel Theorem & Transport of Angular Momentum (AM) L(P) is the luminosity of isobars For shellular rotation, the transport of AM along the vertical direction is
Continued 1 • W(r) angular velocity, U(r) vertical component of the meridional circulation velocity, D diffusion coefficient. • Rotation law allowed to evolve with time as a result of transport of AM by convection, diffusion, meridional circulation. Differential rotation caused by these processes further turbulence & meridional circulation coupling & feed-back solution for W(r). • Timescales
Transport of Chemical Elements U( r) vertical component of velocity; Dh coefficient of horizontal turbulence (vertical advection is inhibited by strong horizontal turbulence); Deff combined effect of advection and horizontal turbulence.
Meridional Circulation • Velocity of meridional circulation • Important effects of horizontal turbulence and • At increasing the circulation velocity slows down. • EW and Em suitable quantities functions of W and m • Eddington-Sweet time scale tES.
Convective Instability • Schwarzschild or Ledoux stability criteria no longer apply and are replaced by Solberg-Hoiland condition above (it accounts for differences in centrifugal forces on adiabatically displaced elements) • is named the Brunt-Vaisala frequency • s is the distance from rotation axis.
Shear Instabilities: dynamical & secular • In radiative zones differential rotation efficient mixing on tdyn = trot & which is maintained if Richardson number obeys above condition (V horizontal velocity, z vertical coordinate). • In presence of thermal dissipation, the restoring force of buoyancy is reduced and instability can easily occur but on a longer timescale (secular). • Secular on MS phase and dynamical on advanced stages.
Evolution of Internal Rotation W • Passing from nearly rigid body on ZAMS to highly differential. • The core spins up and the outer layers slow down as the star expands.
Rotation & Mass Loss Mass loss rate increased by rotation!
Consequences in Relation to SNs • Masses of He cores are larger and less C is left over, shorter lifetimes of C-burning phase, less neutrino cooling, formation of BH favoured. • Masses of CO cores are larger, e.g. a 20 Mo Vrot =300 km/s has 5.7 Mo instead of 3.8 Mo for the nonrotating case.
This reaction is perhaps the most important one as far as the fate of a massive star is concerned. It controls the amount of Carbon left over at the end of the core He-burning phase and hence the duration (together with neutrinos) of the core C-burning phase and the entropy profile throughout a star. Nuclear Reaction Rates
Neutrinos are the starring actors of a star’s evolutionary history. • It was not so in the past. In the sixties there was a vivid debate among stellar evolutionists looking for astrophysical tests of neutrino emission. The lifetime of the C-burning phase in massive stars, the third long-lived phase before the end (blue to red supergiant number ratio NB/NR). • Coupled with much of the final history depends on these two physical ingredients. Neutrinos in early stages
Final Structure of a MassiveStar What does determine the sizeof the various regions? MHe, MCO, ….. Convective Cores & Shells…… The various processes we have discussed above. Fortunately the evolution of the core is decoupled from that of the envelope.
Characteristics of a massive star Burning Temperature Density Lifetime Million K g/cm3 Hydrogen 37 3.8 7.3x10^6 years Helium 180 620 720 000 years Carbon 720 6.4 x 10^5 320 years Neon 1200 > 10^6 < 10 years Oxygen 1800 1.3 x 10^7 ~ 0.5 year Silicon 3400 1.1 x 10^8 < 1 day Collapse 8300 > 3.4 x 10^9 0.45 sec Neutron Star < 8000 > 1.4 x 10^14 –
Structure of a massive star Up to the end of C-burning
Chemical and energy profiles at the onset of collapse A 25 Mo Mass cut
Iron core in excess of MCh collapses on a thermal timescale as neutrino emission carries away binding energy. • Collapse accelerated by two instabilities: 1. e-captures on Fe-group increase n-rich composition, decrease of ne & Pe, reduce MCh; 2. Photodisintegration increase number a-particles without leading to total disintegration; Core collapse in a snapshot: 1
Core collapse in a snapshot: 2 • Bounce relatively cold with heavy nuclei persisting until they merge just below nuclear density stellar mass nucleus which would bounce acting like a spring which stores energy at compression and rebound at the end. • Portions of neutronized hard core (v a r) and infalling region (va 1/r^2 ) nearly equal. • Bounce shock forms and moves outward and could explode the star. It does not because energy is consumed to disintegrate the infall staff (some 10e51 ergs per 0.1Mo) and to emit neutrinos behind the shock. The shock wave stalls and dies. • A succesful shock requires an additional source of energy: neutrino deposit. • The situation is however unclear and controversial.
Closer look at the physics of core collapse: rules • If contraction heats up matter and eN is activated, particle kinetic energy increases P and contraction is opposed (stellar boiler). • If energy absorbing processes are present the opposite occurs (stellar refrigerators). • Two possible refrigerators drive the Fe core into an uncontrolled collapse. • Photo disintegration of nuclei (Fe a-particles) • Captures of electrons via inverse b-decay.
