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Pre-SuperNova Stage. H burning shell. H. He. He burning shell. CO. NeO. O. C burning shell. SiS. Fe. Ne burning shell. O burning shell. T~4.0 × 10 9 K. Si burning shell. Pre- Supernova Stage. The pressure due to degenerate electrons dominate. The Fe core is partially degenerate.
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Pre-SuperNova Stage Hburningshell H He He burning shell CO NeO O C burning shell SiS Fe Ne burning shell O burning shell T~4.0×109 K Si burning shell
Pre-SupernovaStage The pressure due to degenerate electrons dominate The Fe core is partially degenerate
Core Collapse Supernovae: Energetics Basic idea: Energy liberated during collapse: Fe core NS The minus sign means the energy content of the final state being lower than that of the initial one Energy required for the conversion 56Fe Nuclei/g AMUerg AMU
Core Collapse Supernovae: Energetics Energy required for the electron capture Energy lost by neutrino emission: Energy required to unbind the stellar envelope: Energy emitted through photons:
Core Collapse Supernovae: Energetics Kinetic Energy of the ejecta: derived from the observed spectra: Combining all the energy required to explain the SN display with all the energy lossess we get There is still a lot of energy that must be liberated Whichever is the process responsible for such an emission, getting a core collapse supernova to explode seems easy!
CoreCollapseSupernovae: The PathToInstability Following Si burning the core is mainly composed by Iron Peak nuclei @ NSE. Two physical processes rob the iron core of the energy it needs to maintain its pressure and avoid collapse Highly degenerate zone Photodisintegrations • - Contraction • - Increase the fraction of Fe core highly degenerate Electron captures • - Loss of pressure support • - Decrease the limiting mass for a highly degenerate star Fe core Limiting Mass
CoreCollapseSupernovae: The PathToInstability Following Si burning the core is mainly composed by Iron Peak nuclei @ NSE. Two physical processes rob the iron core of the energy it needs to maintain its pressure and avoid collapse Highly degenerate zone Photodisintegrations • - Contraction • - Increase the fraction of Fe core highly degenerate Electron captures • - Loss of pressure support • - Decrease the limiting mass for a highly degenerate star Fe core Limiting Mass When the highly degenerate mass approaches the limiting mass the core becomes unstable and collapses
CoreCollapseSupernovae: CollapsePhase Analyticdescriptionofcorecollapse: generalproperties Equationofmotion Mass conservation Bymeansof some algebra the equationofmotion can bewrittenas some algebra Ifwe assume anadiabaticcollapsewehave some algebra mass conservation adiabaticcollapse
CoreCollapseSupernovae: CollapsePhase Usingthis last relation the equationofmotionbecomes Which, bymeansof some algebra, can berewrittenas Assuming whichmeans wefinallyget Since mustbeconserved
CoreCollapseSupernovae: CollapsePhase the homologoussolution A fluid whose pressure is dominated by relativistic, degenerate electron pressure is expected to collapse homologously Since the sound speeddecreaseswith the radius, a radiusmustexist at which the infallvelocityexceeds the sound velocity
CoreCollapseSupernovae: CollapsePhase OuterCore InnerCore Maximum infall velocity Sonic point homologoussubsonicinfall supersonicinfall Sonic point: the radius at which the infall velocity exceeds the sound speed Outside the sonic point a free fall solution is approximately valid During collapse the core naturally splits into an Inner Core and an Outer Core
CoreCollapseSupernovae: CollapsePhase (Goldreich & Weber 1980) where depending on EOS and Neutrinos are generated by electron capture on nuclei (dominate) and protons Duringcollapse, therefore, the InnerCore Mass decreaseswithdecreasing the electron fraction due to electron captures down toabout
CoreCollapseSupernovae: Neutrino Trapping Neutrino opacities are dominated by neutral-current coherent scattering off heavy nuclei for which the cross section is approximately given by: (Freedman, 1974, PRD, 9, 1389) the mean free path is given by: being Assuming we get
CoreCollapseSupernovae: Neutrino Trapping This means that: Neutrinos escape freely and carry away a bit of energy From this point on the neutrinos will not freely stream but must diffuse At densities the weak interactions also approach an equilibrium (b-equilibirum)
CoreCollapseSupernovae: Stiffenningof the EOS and CoreBounce After neutrino trapping, the collapse proceeds until nuclear densities are reached At this point the inner core undergoes a phase transition from a two-phase system of nucleons and nuclei to a one-phase system of bulk nuclear matter: a GIANT NUCLEUS Fermi effects and the repulsive nature of the nucleon-nucleon interaction potential at short distances The EOS stiffens The pressure in the inner core increases dramatically The inner core becomes incompressible, decelerates and rebounds
CoreCollapseSupernovae: Formationof the Prompt Shock and Shock Propagation Starting from the center an increasing number of infalling mass shells are stopped Pressure waves travel outward and steepen Waves accumulate @ sonic point Prompt shock wave forms and propagates through the outer core As the shock propagates out, matter from the outer core continues to fall in supersonically Numerical simulations show that the initial energy of the shock wave is:
CoreCollapseSupernovae: Propagation and Stallingof the Prompt Shock As prompt shock propagates out: It dissociates Fe nuclei into free nucleons. Severe energy losses Neutrino burst at shock brackout Limiting mass that can be photodisintegrated:
CoreCollapseSupernovae: Propagation and Stallingof the Prompt Shock The shock consumes entire kinetic energy still within iron core Shock turns into an accretion shock at a radius between 100 and 200 km, i.e., the matter downstream of the shock has negative velocities and continues falling inward (Limongi & Chieffi 2006, ApJ, 647, 483) All state-of-art simulations of stellar core collapse show that: Prompt explosion fails!
CoreCollapseSupernovae: DelayedExplosionMechanism After the core bounce, a neutron star begins to form at the center The newly born neutron star is initially still proton-rich and contains a large number of degenerate electrons and neutrinos. The neutrinos are emitted from their respective neutrinospheres (surfaces of last scattering)
CoreCollapseSupernovae: DelayedExplosionMechanism Between the neutrinosphere and the shock, the material both heats and cools by electron neutrino and antineutrino emission and absorption. The neutrino heating and cooling have different radial profiles consequently, this region splits into a net cooling region and a net heating region, separated by a gain radius at which heating and cooling balance.
CoreCollapseSupernovae: DelayedExplosionMechanism The persistent neutrino energy deposition behind the shock keeps the pressure high in this region and drives the shock outwards again, eventually leading to a supernova explosion.
CoreCollapseSupernovae: DelayedExplosionMechanism This may take a few 100 ms and requires that during this time interval a few percent of the radiated neutrino energy (or 10–20% of the energy of electron neutrinos and antineutrinos) are converted to thermal energy of nucleons, leptons, and photons. Remember: The canonical explosion energy of a supernova is less than one percent of the total gravitational binding energy lost by the nascent neutron star in neutrinos. The success of the delayed supernova mechanism turned out to be sensitive to a complex interplay of neutrino heating, mass accretion through the shock, and mass accretion through the gain radius. After two decades of research the paradigm of the neutrino driven wind explosion mechanism is widely accepted BUT
The Supernova Problem The most recent and detailed simulations of core collapse SN explosions show that: • the shock still stalls No explosion is obtained • the energyof the explosionis a factorof3to 10 lowerthanusuallyobserved Work isunderwaybyall the theoreticalgroupstobetterunderstand the problem and wemayexpectprogresses in the next future The simulationof the explosionof the envelopeisneededtohave information on: • the chemical yields (propagation of the shock wave compression and heating explosive nucleosynthesis) • the initialmass-remnant mass relation
ExplosiveNucleosynthesis Propagationof the shock wavethrough the envelope Compression and Heating ExplosiveNucleosynthesis The explosive nucleosynthesis calculations for core collapse supernovae are still based on explosions induced by injecting an arbitrary amount of energy in a (also arbitrary) mass location of the presupernovamodeland thenfollowing the development of the blast wavebymeansofanhydro code. • Piston • Thermal Bomb • Kinetic Bomb
Explosion and Fallback Matter Falling Back Matter Ejected into the ISM Ekin1051 erg Shock Wave Compression and Heating Induced Expansion and Explosion Mass Cut Final Remnant Initial Remnant Initial Remnant Injected Energy Fe core • Piston (Woosley & Weaver) • ThermalBomb (Nomoto & Umeda) • KineticBomb (Chieffi & Limongi) Differentwaysofinducing the explosion FB depends on the bindingenergy: the higheris the initial mass the higheris the bindingenergy
The Hydrodynamics Sets the details of the physical conditions (temporal evolution of Temperature and Density) for each explosive burning the detailed products of each explosive burning
CharacteristicExplosiveBurningTemperatures Sincenuclearreactions are very temperature sensitive, this cause nucleosynthesistooccurwithinfewsecondsthatmightotherwisehavetakendays or years in the presupernovaevolution. The typicalburningtimescalefordestructionofanygivenfuelis: Where in general:
CharacteristicExplosiveBurningTemperatures Thesetimescalesfor the fuelsH, He, C, Ne, O, Si are determinedby the major destructionreaction: Heburning: Cburning: Ne burning: O burning: Si burning: and in general are functionof temperature and density:
CharacteristicExplosiveBurningTemperatures Ifwe take typicalexplosiveburningtimescalesof the orderof 1s Explosive C burning Explosive Ne burning Explosive O burning Explosive Si burning
BasicPropertiesof the Explosion • Behind the shock, the pressure is dominated by radiation • The shock propagates adiabatically Shock Fe core T1 T2 r1 r r2 The peak temperature doesnotdepend on the stellar structure
Bycombining the propertiesof the matter at high temperature and the basicpropertiesof the explosion Complete Si burning Incomplete Si burning Explosive O burning Explosive Ne burning ExplosiveCburning NSE NSE QSE 2Clusters No Modification P Sc Ti Fe Co Ni Si S Ar K Ca Si P Cl K Sc Ti Cr V Mn 3700 5000 6400 11750 13400 RADIUS (Km)
Role of the Progenitor Star • Mass-Radius relation @ Presupernova Stage: determines the amount of mass contained in each volume determines the amount of mass processed by each explosive burning. Complete Si burning Incomplete Si burning Explosive O burning Explosive Ne burning Explosive C burning NSE QSE 2 Clusters QSE 1 Cluster No Modification Ne Na Sc Ti Fe Co Ni Si S Ar K Ca Mg Al P Cl Cr V Mn INTERIOR MASS
Roleof the Progenitor Star • The Ye profile at Presupernova Stage: it is one of the quantities that determine the chemical composition of the more internal zones that reach the NSE/QSE stage r=108g/cm3 T=5∙109 K Ye=0.50 56Ni=0.63 – 55Co=0.11 – 52Fe=0.07 – 57Ni=0.06 – 54Fe=0.05 Ye=0.49 54Fe=0.28 – 56Ni=0.24 – 55Co=0.16 – 58Ni=0.11 – 57Ni=0.08 • The Chemical Composition at Presupernova Stage: it determines the final composition of all the more external regions undergoing explosive (in non NSE/QSE regine)/hydrostatic burnings
TheChemicalCompositionOf A Massive Star After The Explosion EXPLOSIVE BURNINGS Complete Si burning Incomplete Si burning Explosive O burning Explosive Ne burning Explosive C burning NSE QSE 2 Clusters QSE 1 Cluster No Modification Sc,Ti,Fe Co,Ni Ne,Na Mg,Al,P,Cl Si,S,Ar K,Ca Cr,V,Mn INTERIOR MASS
Fallback And FinalRemnant During the propagationof the shock wavethrough the mantle some amountofmattermayfall back onto the compact remnant Itdepends on the bindingenergyof the star and on the finalkineticenergy
CompositionOf The Ejecta The IronPeakelements are thosemostlyaffectedby the propertiesof the explosion, in particular the amountofFallback.
TheEjectionOf56Ni And HeavyElements Ox Ox Ox Ox Sii Sii Sii Sii 56Ni 56Ni 56Ni 56Ni Sic Sic Sic Sic 56Ni 56Ni 56Ni 56Ni Fe Core Fe Core Sc,Ti,Fe Co,Ni Sc,Ti,Fe Co,Ni Sc,Ti,Fe Co,Ni Sc,Ti,Fe Co,Ni Cr,V,Mn Cr,V,Mn Cr,V,Mn Cr,V,Mn Final Mass Cut Initial Mass Cut Initial Mass Cut Si,S,Ar K,Ca Si,S,Ar K,Ca Si,S,Ar K,Ca Si,S,Ar K,Ca Remnant The amountof56Ni and heavyelementsstronglydepends on the Mass Cut
TheEjected56Ni In absenceof mixing a high kineticenergyisrequiredtoejecteven a smallamountof56Ni
Mixing Before Fallback Model 56Ni Isotopes produced in the innermost zones Ox Ox Ox 56Ni 56Ni Sii Sii Sii Sic Sic 56Ni Sic Mixing Region 56Ni 56Ni 56Ni Fe Core Fe Core 56Ni Mixing Region Remnant 56Ni Sc,Ti,Fe Co,Ni Sc,Ti,Fe Co,Ni Sc,Ti,Fe Co,Ni Cr,V,Mn Cr,V,Mn Cr,V,Mn 56Ni Final Mass Cut Initial Mass Cut Initial Mass Cut 56Ni Si,S,Ar K,Ca Si,S,Ar K,Ca 56Ni Si,S,Ar K,Ca 56Ni and heavyelements can beejectedevenwithextendedfallback
Z=Z E=1051 erg NL00 No Mass Loss WIND SNII SNIb/c RSG WNL Final Mass WC/WO WNE He-Core Mass Fallback Remnant Mass He-CC Mass CO-Core Mass Black Hole Fe-Core Mass Neutron Star The Final Fate Of A Massive Star
ChemicalEnrichment due to a Single Massive Star The Production Factors (PFs) provide information on the global enrichmentof the matter and itsdistribution SolarMetallicity Models
ChemicalEnrichment due a Generation of Massive Stars The integrationof the yieldsprovidedbyeach star overaninitial mass functionprovide the chemicalcompositionof the ejecta due to a generation of massive stars Yieldsaveragedover a Salpeter IMF Production Factorsaveragedover a Salpeter IMF
ChemicalEnrichment due to a Generation of Massive Stars ~2 < PF( C < Z < As ) < ~11 massive stars significantly contribute to the production of these elements
The Role of the More Massive Stars Which is the contribution of stars with M ≥ 35 M? Mass Loss Prevents Destruction Large Fall Back They produce: • ~60% of the total C and N (mass loss) • ~40% of the total Sc and s-process elements (mass loss) • No intermediate and iron peak elements (fallback)
Chemical Enrichment due to Massive Stars The average metallicity Z grows slowly and continuously with respect to the evolutionary timescales of the stars that contribute to the environment enrichment Most of the solar system distribution is the result (as a first approximation) of the ejecta of ‘‘quasi ’’–solar-metallicity stars. The PFs of the chemical composition provided by a generation of solar metallicity stars should be almost flat
ChemicalEnrichment due to Massive Stars No roomforothersources (AGB) RemnantMasses? Secondary Isotopes? AGB? Type Ia n process. Other sources uncertain Explosion?
Complete Explosive Si Burning • ForT>5109 Kall the forward and the reverse strong reactions (withfewexceptions) come toanequilibrium and a NSE distributionisquicklyestablished In thiscondition the abundanceofeachnucleusisgivenby: Theseequationshave the propertiesoffavouring the more boundnucleuscorrespondingto the actualneutronsexcess.