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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 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 fixed by the Schwarzschild condition. Cured by introducing partial mixing in the border layers so that neutrality condition is achieved. Two possible criteria: Schwarzschild R A or Ledoux R A Inner structure & Loops in HRD: Schwarzschild or Ledoux? Schwarzschild: no loops Debate still with us !!! Ledoux: loops 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 • 25 Mo < M< 60 Mo • O BSG YSG RSG • M < 25 Mo • O (BSG) RSG WC (WO) SN Blue-Red-Blue WN (WC) SN High Ms |-------------- SN Low Ms 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 F FR FC MLT vr g vr r r r1 l l H P * ' ' ' dr r r1 r r T * T ' FC 2cP vr ' ' dr r r1 r r g 1 vr 3 1 g T FC 1 vr 2 T cP 3 r Integrate to get vr and vMax( 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. Artistic view of overshoot The Diffusion Coefficient Velocity Cascade, Intermittence & Stirring • Velocity cascade (energy conservation) v 30 v 3 d l0 ld • Intermittence (volume filling) 2 1 2 l ( d )1/ 2 lo v 30 v 3d l0 ld • Stirring (spoons & cups) Fs ( L lo 3 L ) ( 1)3 l0 l0 ld 3 / 2 Fi ( ) lo Results for Massive Stars: HRD & Lifetimes Diffusive Overshoot & WR Stars But WR…. & BSG Gap… 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 1 2 2 2 W r sin 2 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 ) F g eff 4 GM ( P ) W2 M ( P) M (1 ) 2 G Teff geff ( ) 1 4 L(P) is the luminosity of isobars For shellular rotation, the transport of AM along the vertical direction is d 2 1 1 4 4 W (r W) M r 2 ( r WU (r )) 2 ( Dr ) dt r 5r r r r 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 E suitable quantities functions of W and • 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 dM ( )[Vrot ] dt 1 dM ( )[Vrot 0] dt Vrot 1 V cri Mass loss rate increased by rotation! Evolution of Vrot & W/Wcrit HRD of Rotating Mass-losing Stars 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. Nuclear Reaction Rates C ( , ) O 12 16 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. Neutrinos in early stages • 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). C ( , ) O 12 16 • Coupled with much of the final history depends on these two physical ingredients. Final Structure of a Massive Star What does determine the size of 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 Hydrogen Helium Carbon Neon Oxygen Silicon Collapse Neutron Star Temperature Million K 37 180 720 1200 1800 3400 8300 < 8000 Density g/cm3 3.8 620 6.4 x 10^5 > 10^6 1.3 x 10^7 1.1 x 10^8 > 3.4 x 10^9 > 1.4 x 10^14 Lifetime 7.3x10^6 720 000 320 < 10 ~ 0.5 <1 0.45 – years years years years year day sec Structure of a massive star Up to the end of C-burning The chemical structure at the end of C-Burning The inner stratification The inner chemical structure at the onset of collapse Chemical and energy profiles at the onset of collapse A 25 Mo Mass cut Plane of central conditions Core collapse in a snapshot: 1 ne Ye NA 2 2 2 kT 2 M Ch 5.83Ye 1 2 F • 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 leading to total disintegration; without 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 r) and infalling region (v 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 N 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 -particles) • Captures of electrons via inverse -decay. Rules: continue • In the former, kinetic energy is used to unbind nuclei • In the latter, kinetic energy of degenerate electrons is converted to kinetic energy of ne which escape from the core 0.5 • P failure Collapse t ff ( 3 / 32G ) 1ms Nuclear photo-dissociation: Iron • Thermal photons are energetic enough to disintegrate Fe nuclei into less tightly bound nuclei and energy is absorbed. The process is schematically indicated as 56 Fe 13 4 He 4n Q ( 13m4 4m1 m56 ) 124.4 Mev • The fraction of Fe dissociated is derived in analogy to ionization 13 4 ( n4 )13 ( n1 )4 g 413 g14 nQ 4 nQ1 Q exp( ) n56 g 56 nQ 56 KT where 2 mA KT 3 / 2 ) quantum concentration 2 h statistical factor (depends on angular momentum), nQA ( gA g4 =1, g1 =2, g56 =1 • Implies treshold T and (10^9 g/cm^3 and 10^10 K, respectively) Photo-dissociation: Helium • At higher temperatures helium is broken γ + 4 He 2p + 2n Q = -28.3 Mev • Similar consideration apply as above Total amount of energy absorbed by these photo - dissociation processes for a Fe core of about 1.4 M Θ 4x1051 erg for Fe 13 He + 4 n 10x1051 erg for He 2 p + 2n or in a more practical form 1.5 x 1052 erg per 0.1 M Θ of Fe This energy nearly parallels the total energy radiated by the SUN over 10 Gyr Neutronization 1 • In normal circumstances n p + e + ne on a time scale of 15 min • Electrons and neutrinos have a combined energy of 1.3 Mev (the mass-energy difference between n and p) • When neutrons decay, electrons with energies up to 1.3 Mev are produced it follows that neutrons cannot decay if the electrons cannot be accepted by the medium. This is case when neutrons are in a dense degenerate gas of electrons where all energy states up to 1.3 Mev are filled. The density for this to occur can be estimated from the Fermi momentum – energy 3n e 1/3 PF h[ ] 8π and ε F p F c 2 me c4 2 2 • Furthermore, if the gas is denser, electrons with energies > 1.3 Mev exist and they may be captured by protons to form neutrons e + p n + ne . The new formed neutrons cannot decay: the nuclei becomes richer in neutrons. NEUTRONIZATION Neutronization: continue • Neutronization begins when 56 Fe e 56 Mn ν e at ρ 1.1 x 109 g/cm 3 ε F (e ) me c 2 3.7 Mev • Normally a nucleus of Mn Fe with a half-life of 2.4 h, but in the dense stellar cores it captures an electron to form Cr which in turn captures another electron. Many other captures are possible with many other nuclei. Very soon e-captures get very fast. The neutrinos carry away the energy originally stored in the electrons. • THE NUMBER DENSITY OF ELECTRONS and Pe IN TURN FALL DOWN THE COLLAPSE IS STARTED. Mn by Fee-captures? • How much energy is subtracted 56 56 Energy removed by e-captures • A core of about 1.4 Mo has about 10^57 electrons and can produce an equal number of neutrinos. Assume that the typical energy of a captured electron is about 10 Mev (roughly the mean energy of a degenerate electron at densities of 2x10^10 g/cm^3 ) we have 13 Ecap 10 (10 10 1.6 10 ) 1.6 10 57 Number of electrons 6 Energy per electron 52 erg Conversion factor Energy budget in the collapse • Pressure removal by e-captures & photo-dissociations induce collapse: very rapid and almost unopposed until the matter reaches nearly nuclear densities ρNuc 3 Amn 14 -3 2 . 3 10 g/cm 3 4RN • At these densities neutron degeneracy and nuclear forces oppose to compression 3Am ρ 2.3 10 g/cm 4ππ and bring collapse to a halt when = 2-3 nuc. Furthermore at these densities the mininum energy configuration requires the neutrons to drip out of nuclei, free neutrons appears and the final configuration is that all nuclei dissolve into a gas of free neutrons new EOS. • The mass and the radius of the newly formed object ( a neutron star) are about MNS = 1 Mo (or more) and RNS =10 km. Nuc n 3 N 14 -3 • How much energy has been liberated by gravitational contraction? Energy budget in the collapse: continue GM 2 M 2 10km 53 EΩ 3 10 [ ] [ ] erg RNS MΘ R Balance EΩ E photo Ecapt Ekin Eopt ? 3 10 53 1.5 10 52 1.6 10 52 1.0 10 51 1.0 10 49 ? erg There is a factor of 10 missing! NEUTRINOS Neutrinos from e e- annihilation, plasma, photo, bremsstrahlung. The real event of a SN explosion is the burst of neutrinos!!! Collapse: basic questions • Can the collapse of the inner core induce the ejection of the remaining mass (core plus mantle)? • The key problem is how to transfer even a small amount of the energy liberated by the collapsing nucleus to the rest of the star. Simple description of collapse • Onset of collapse with 1010 g / cm and T 1010 K • Electrons degenerate and relativistic 4/3 P K4/3 ( ) e • The collapse can be described as a politrope of index 3. • The collapsing core can be split in two regions whose velocity profile is • The homologous region is in sound communication. The peak position shifts outward with time v(r)max = 70000 km/s Elastic vs anelastic bounce • When the central part gets 5 1014 g / cm3 it becomes rigid and almost incompressible. • If the whole process were completely elastic, the kinetic energy of the collapsing matter would be sufficient to bring it back to the original state (bounce). The energy is simply 2 GM NS EW 31053 erg RNS The energy required to expell the remaining part of the star would be Eesc G( M M NS ) 2 3 1052 erg RW D For a 10 Mo star. Only a small fraction of EW. • What happens next depends on understanding what fraction of the collapse energy goes into kinetic energy of the outward motion Schock Wave • Suppose that by inertia the central sphere is compressed beyond its equilibrium state and like a spring it expands, pushing back the infalling material above. • This creates a pressure wave that steepens while travelling into regions of lower density. A rough estimate of the kinetic energy of the SW is ESW 0.1 E Ω comparable to the potential energy of the nucleus and thus fully sufficient to expell the mantle (rest of the star). • However the SW must find its way out through layers of still undissociated Fe • and dissipate (or may) the whole energy in doing this. The SW dies inside the collapsing Fe core. • This depends on where the SW is formed: if too inside very little hope, if very external it may be succesful (this depends in turn on the original size of the Fe core). Neutrino Cavalry • The typical energy of neutrinos emitted during collapse is of the order of that of relativistic electrons n me c 2 F me c 2 pF 10 2 ( )1/ 3 me c e • If heavy nuclei are present neutrino interact via cherent scattering rather than scattering by free nucleons n ( Z , A) n ( Z , A) n process En A2 10 45 A 2 ( ) 2/3 cm 2 cross section 2 mec e mean free path ln 1 n n 1 5 / 3 ( ) 10 49 cm 2 e A e for 2, A 100, 109 g/cm -3 , ln 10 km R NS • Neutrinos may be trapped and release their energy to the SW, to the star. Even 0.01 of their energy is enough. SW does not die and SN explosion may occur. Schematic view Radius 10 14 Static dense core Neutrino sphere 1011 108 Slow infalling matter Rapidly infalling cool matter Shock Front U N B U R N E D S T A F F Border Fe nucleus Seven years to explosion Oxygen and Magnesium Nucleus One year to explosion Hydrogen/ Helium Carbon Neon / Magnesium Magnesium / Oxygen Iron Ten seconds to explosion High density Iron Nucleus Millisecs after collapse A few seconds after collapse Neutron Star Hours after collapse Ejection of outer layers Neutron Star Collapse & Bounce of the Iron Core of a 13 Mo SN • One is left 10ms after the core has bounced with a hot, dense protoneutron star accreting matter at the high rate of 1-10 Mo /s Shock Waves • SW revived for 0.1s, long compared to tdyn (ms) bur short compared to the 3-10 s of the tKH time scale for NS to emit the binding energy • Convective flows of neutrinos (increase neutrino absorption) • Problems: Too much n-rich nucleosynthesis because neutrinos interact with nucleons in the convective bubble decrease Ye; Remnant masses too small Neutrino-driven convection after core bounce in a 13 Mo Mixing in the explosion of a 15 Mo Failure of Supernova Explosion Remnants: NS & BH • NS will have masses comprised between the Fe-core and the O-shell: for 1-20 Mo stars 1.3-1.6 Mo. • At higher initial masses either larger NS or eventually BH. Final vs initial mass SN Types: metallicity & mass M E T A L L I C I T Y INITIAL MASS SN Types : metallicity & mass SN and Remnants of Massive Stars with Solar Metallicity Summary 1 Summary 2 25 Mo 25 Mo Summary 3 Summary 4 Radiactive decay in ejecta Light Curves SN 1987A in LMC SN1087A in the LMC: main facts • Sn1987a brightened very rapidly compact progenitor: SK69202, B3I, logL/Lo=5.1, logTeff=4.2 • Core mass 6 1 Mo, total mass 16-22 Mo. • With distance to LMC of 50 5 kpc (1.5 0.15) x1023 cm event took place 160,000 years ago. • Detected Neutrinos (20) 53 E (2.5 1) x 10 estimate of gravitational energy G ergs 53 or from their temperature EG (3.7 2) x 10 ergs Baryon mass inside neutron star (1.6 0.4) Mo. Main facts: continued • Prominent H lines (Type II) • Chemical Abundances: [O] & [N] much larger than solar CNO-cycle material exposed; expansion velocities of about 30 km/s progenitor was in the past a RSG, lost part of the envelope, and subsequently contracted to the size of a BSG • Relatively small mass in the original envelope • Observational evidence of mixing and mass loss in progenitor: both stronger than expected • Evidence of mixing in the ejecta Possible evolutionary history of progenitor New Family Tree after SN1987A