1 H He CO NeO P RE -S UPER N OVA S TAGE O SiS H burning shell He burning shell T~4.0×10 9 K C burning shell Ne burning shell O burning shell Si burning shell Fe

2 P RE -S UPERNOVA S TAGE The Fe core is partially degenerate The pressure due to degenerate electrons dominate

3 C ORE C OLLAPSE S UPERNOVAE : E NERGETICS Basic idea: Fe core NS Energy liberated during collapse: Energy required for the conversion The minus sign means the energy content of the final state being lower than that of the initial one AMU AMU  erg 56 Fe Nuclei/g

4 C ORE C OLLAPSE S UPERNOVAE : E NERGETICS Energy required for the electron capture Energy lost by neutrino emission: Energy required to unbind the stellar envelope: Energy emitted through photons:

5 C ORE C OLLAPSE S UPERNOVAE : E NERGETICS 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!

6 C ORE C OLLAPSE S UPERNOVAE : T HE P ATH T O I NSTABILITY Following Si burning the core is mainly composed by Iron Peak NSE. Fe core 1.PhotodisintegrationsPhotodisintegrations 2.Electron capturesElectron captures - Contraction - Increase the fraction of Fe core highly degenerate Two physical processes rob the iron core of the energy it needs to maintain its pressure and avoid collapse - Loss of pressure support - Decrease the limiting mass for a highly degenerate star Highly degenerate zone Limiting Mass

7 Following Si burning the core is mainly composed by Iron Peak NSE. 1.PhotodisintegrationsPhotodisintegrations 2.Electron capturesElectron captures - Contraction - Increase the fraction of Fe core highly degenerate Two physical processes rob the iron core of the energy it needs to maintain its pressure and avoid collapse - Loss of pressure support - Decrease the limiting mass for a highly degenerate star Highly degenerate zone Fe core Limiting Mass When the highly degenerate mass approaches the limiting mass the core becomes unstable and collapses C ORE C OLLAPSE S UPERNOVAE : T HE P ATH T O I NSTABILITY

C ORE C OLLAPSE S UPERNOVAE : C OLLAPSE P HASE Analytic description of core collapse: general properties Equation of motion Mass conservation By means of some algebra the equation of motion can be written as some algebra If we assume an adiabatic collapse we have some algebra mass conservation adiabatic collapse 8

Using this last relation the equation of motion becomes Which, by means of some algebra, can be rewritten as Assuming which means we finally get C ORE C OLLAPSE S UPERNOVAE : C OLLAPSE P HASE 9 Sinc e must be conserved

the homologous solution Since the sound speed decreases with the radius, a radius must exist at which the infall velocity exceeds the sound velocity A fluid whose pressure is dominated by relativistic, degenerate electron pressure is expected to collapse homologously C ORE C OLLAPSE S UPERNOVAE : C OLLAPSE P HASE 10

Inner Core Outer Core homologous subsonic infall supersoni c infall Sonic point Maximum infall velocity 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 C ORE C OLLAPSE S UPERNOVAE : C OLLAPSE P HASE 11

depending on EOS and where (Goldreich & Weber 1980) During collapse, therefore, the Inner Core Mass decreases with decreasing the electron fraction due to electron captures down to about C ORE C OLLAPSE S UPERNOVAE : C OLLAPSE P HASE 12 Neutrinos are generated by electron capture on nuclei (dominate) and protons

13 C ORE C OLLAPSE S UPERNOVAE : N EUTRINO T RAPPING 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 Assumingwe get

14 C ORE C OLLAPSE S UPERNOVAE : N EUTRINO T RAPPING 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 (  -equilibirum)

15 C ORE C OLLAPSE S UPERNOVAE : S TIFFENNING OF THE EOS AND C ORE B OUNCE After neutrino trapping, the collapse proceeds until nuclear densities are reached The pressure in the inner core increases dramatically 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 The EOS stiffens Fermi effects and the repulsive nature of the nucleon-nucleon interaction potential at short distances The inner core becomes incompressible, decelerates and rebounds

16 C ORE C OLLAPSE S UPERNOVAE : F ORMATION OF THE P ROMPT S HOCK AND S HOCK P ROPAGATION Starting from the center an increasing number of infalling mass shells are stopped Pressure waves travel outward and steepen Waves 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:

17 C ORE C OLLAPSE S UPERNOVAE : P ROPAGATION AND S TALLING OF THE P ROMPT S HOCK 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:

18 C ORE C OLLAPSE S UPERNOVAE : P ROPAGATION AND S TALLING OF THE P ROMPT S HOCK (Limongi & Chieffi 2006, ApJ, 647, 483) 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 All state-of-art simulations of stellar core collapse show that: Prompt explosion fails!

19 C ORE C OLLAPSE S UPERNOVAE : D ELAYED E XPLOSION M ECHANISM 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)

20 C ORE C OLLAPSE S UPERNOVAE : D ELAYED E XPLOSION M ECHANISM 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.

21 C ORE C OLLAPSE S UPERNOVAE : D ELAYED E XPLOSION M ECHANISM 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.

22 C ORE C OLLAPSE S UPERNOVAE : D ELAYED E XPLOSION M ECHANISM 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

23 The most recent and detailed simulations of core collapse SN explosions show that: the shock still stalls  No explosion is obtained the energy of the explosion is a factor of 3 to 10 lower than usually observed Work is underway by all the theoretical groups to better understand the problem and we may expect progresses in the next future The simulation of the explosion of the envelope is needed to have information on: the chemical yields (propagation of the shock wave  compression and heating  explosive nucleosynthesis) the initial mass-remnant mass relation T HE S UPERNOVA P ROBLEM

24 Propagation of the shock wave through the envelope Compression and Heating Explosive Nucleosynthesis 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 presupernova model and then following the development of the blast wave by means of an hydro code. Piston Thermal Bomb Kinetic Bomb E XPLOSIVE N UCLEOSYNTHESIS

25 E XPLOSION AND F ALLBACK Matter Falling Back Mass Cut Initial Remna nt Final Remnant Matter Ejected into the ISM E kin  erg Piston (Woosley & Weaver) Thermal Bomb (Nomoto & Umeda) Kinetic Bomb (Chieffi & Limongi) Different ways of inducing the explosion FB depends on the binding energy: the higher is the initial mass the higher is the binding energy Fe core Shock Wave Compression and Heating Induced Expansion and Explosion Initial Remna nt Injected Energy

26 T HE H YDRODYNAMICS Sets the details of the physical conditions (temporal evolution of Temperature and Density) for each explosive burning  the detailed products of each explosive burning

27 Since nuclear reactions are very temperature sensitive, this cause nucleosynthesis to occur within few seconds that might otherwise have taken days or years in the presupernova evolution. C HARACTERISTIC E XPLOSIVE B URNING T EMPERATURES Where in general: The typical burning timescale for destruction of any given fuel is:

28 C HARACTERISTIC E XPLOSIVE B URNING T EMPERATURES These timescales for the fuels H, He, C, Ne, O, Si are determined by the major destruction reaction: and in general are function of temperature and density: He burning: C burning: Ne burning: O burning: Si burning:

29 C HARACTERISTIC E XPLOSIVE B URNING T EMPERATURES If we take typical explosive burning timescales of the order of 1s Explosive C burning Explosive Ne burning Explosive O burning Explosive Si burning

30 B ASIC P ROPERTIES OF THE E XPLOSION Behind the shock, the pressure is dominated by radiation The shock propagates adiabatically r T1T1 Fe core r2r2 T2T2 r1r1 Shock The peak temperature does not depend on the stellar structure

31 Complete Si burning 3700 NSE Ti Fe Co Ni 5000 Incomplete Si burning NSE Ti Cr V Mn Explosive O burning 6400 QSE 2 Clusters Si S Ar K Ca Explosive Ne burning Si P Cl K Sc Explosive C burning P Sc RADIUS (Km) No Modification By combining the properties of the matter at high temperature and the basic properties of the explosion

32 R OLE OF THE P ROGENITOR S TAR Mass-Radius Presupernova Stage: determines the amount of mass contained in each volume  determines the amount of mass processed by each explosive burning. Complete Si burning NSE Sc Ti Fe Co Ni Incomplete Si burning QSE 2 Clusters Cr V Mn Explosive O burning QSE 1 Cluster Si S Ar K Ca Explosive Ne burning Mg Al P Cl Explosive C burning Ne Na No Modification INTERIOR MASS

33 The Y e 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 Y e =0.50  56 Ni=0.63 – 55 Co=0.11 – 52 Fe=0.07 – 57 Ni=0.06 – 54 Fe=0.05 Y e =0.49  54 Fe=0.28 – 56 Ni=0.24 – 55 Co=0.16 – 58 Ni=0.11 – 57 Ni=0.08 T=5∙10 9 K  =10 8 g/cm 3 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 R OLE OF THE P ROGENITOR S TAR

34 Complete Si burning NSE Sc,Ti,Fe Co,Ni Incomplete Si burning QSE 2 Clusters Cr,V,Mn Explosive O burning QSE 1 Cluster Si,S,Ar K,Ca Explosive Ne burning Mg,Al,P,Cl Explosive C burning Ne,Na No Modification INTERIOR MASS T HE C HEMICAL C OMPOSITION O F A M ASSIVE S TAR A FTER T HE E XPLOSION EXPLOSIVE BURNINGS

35 During the propagation of the shock wave through the mantle some amount of matter may fall back onto the compact remnant It depends on the binding energy of the star and on the final kinetic energy F ALLBACK A ND F INAL R EMNANT

36 The Iron Peak elements are those mostly affected by the properties of the explosion, in particular the amount of Fallback. C OMPOSITION O F T HE E JECTA

37 Si c Sc,Ti,Fe Co,Ni 56 Ni Si i Cr,V,Mn 56 Ni OxOx Si,S,Ar K,Ca Fe Core Initial Mass Cut Si c Sc,Ti,Fe Co,Ni 56 Ni Si i Cr,V,Mn 56 Ni Si,S,Ar K,Ca Fe Core OxOx Initial Mass Cut Si c Sc,Ti,Fe Co,Ni 56 Ni Si i Si,S,Ar K,Ca 56 Ni Cr,V,Mn OxOx Si c Sc,Ti,Fe Co,Ni 56 Ni Si i Cr,V,Mn 56 Ni Si,S,Ar K,Ca OxOx Final Mass Cut T HE E JECTION O F 56 N I A ND H EAVY E LEMENTS The amount of 56 Ni and heavy elements strongly depends on the Mass Cut Remnant

38 T HE E JECTED 56 N I In absence of mixing a high kinetic energy is required to eject even a small amount of 56 Ni

39 M IXING B EFORE F ALLBACK M ODEL 56 Ni and heavy elements can be ejected even with extended fallback Si c Sc,Ti,Fe Co,Ni 56 Ni Si i Cr,V,Mn 56 Ni OxOx Si,S,Ar K,Ca Fe Core Initial Mass Cut Si c Sc,Ti,Fe Co,Ni Si i Cr,V,Mn 56 Ni OxOx Si,S,Ar K,Ca Mixing Region Fe Core Initial Mass Cut Si c Sc,Ti,Fe Co,Ni Si i Cr,V,Mn 56 Ni OxOx Si,S,Ar K,Ca Mixing Region Final Mass Cut Isotopes produced in the innermost zones Remnant 56 Ni

40 No Mass Loss Final Mass He-Core Mass He-CC Mass CO-Core Mass Fe-Core Mass WNL WNE WC/WO Remnant Mass Neutron Star Black Hole SNIISNIb/c Fallback RSG Z=Z  E=10 51 erg NL00 WIND T HE F INAL F ATE O F A M ASSIVE S TAR

41 T HE Y IELDS OF M ASSIVE S TARS

42 T HE Y IELDS OF M ASSIVE S TARS

43 C HEMICAL E NRICHMENT DUE TO A S INGLE M ASSIVE S TAR The Production Factors (PFs) provide information on the global enrichment of the matter and its distribution Solar Metallicity Models

44 C HEMICAL E NRICHMENT DUE A G ENERATION OF M ASSIVE S TARS Yields averaged over a Salpeter IMF The integration of the yields provided by each star over an initial mass function provide the chemical composition of the ejecta due to a generation of massive stars Production Factors averaged over a Salpeter IMF

45 C HEMICAL E NRICHMENT DUE TO A G ENERATION OF M ASSIVE S TARS ~2 < PF( C < Z < As ) < ~11massive stars significantly contribute to the production of these elements

46 T HE R OLE OF THE M ORE M ASSIVE S TARS Large Fall Back Mass Loss Prevents Destruction Which is the contribution of stars with M ≥ 35 M  ? 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)

47 C HEMICAL E NRICHMENT DUE TO M ASSIVE S TARS 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

48 C HEMICAL E NRICHMENT DUE TO M ASSIVE S TARS Secondary Isotopes? No room for other sources (AGB) Remnant Masses? Type Ia AGB? process. Other sources uncertain Explosion?

49 THE END

50 For T> K all the forward and the reverse strong reactions (with few exceptions) come to an equilibrium and a NSE distribution is quickly established C OMPLETE E XPLOSIVE S I B URNING In this condition the abundance of each nucleus is given by: These equations have the properties of favouring the more bound nucleus corresponding to the actual neutrons excess.

51 i + k j + l No equilibrium Full equilibrium Since the matter exposed to the explosion has Y e >0.49 (  <0.02) Most abundant isotope 56 Ni Elements also produced: Ti ( 48 Cr), Co ( 59 Ni), Ni ( 58 Ni) C OMPLETE E XPLOSIVE S I B URNING

52 I NCOMPLETE E XPLOSIVE S I B URNING Temperatures between K < T < K are not high enough to allow a complete exhaustion of 28 Si, although the matter quickly reaches a NSE distribution Main products: Ti ( 48 Cr), V ( 51 Cr), Cr ( 52 Fe), Mn ( 55 Co)

53 E XPLOSIVE O B URNING Temperatures between K < T < K are not high enough to allow a full NSE Two equilibrium clusters form separted at the level of the A=44 Since the matter exposed to the explosion has A<44 and since there is a very small leackage through the A=44, the path to the heavier elements is severely inhibited

54 Temperatures between K < T < K are not high enough to allow a full NSE Two equilibrium clusters forms separted at the level of the A=44 Since the matter exposed to the explosion has A<44 and since there is a very small leackage through the A=44, the path to the heavier elements is severely inhibited Main products: Si ( 28 Si), S ( 32 S), Ar ( 36 Ar), Ca ( 40 Ca) E XPLOSIVE O B URNING

55 E XPLOSIVE C/N E BURNING If T < K the processes are far from the equilibrium and nuclear processing occur through a well defined sequence of nuclear reactions. Elements preferrentially synthesized in these conditions over the typical eplosion timescales: If T < K no nuclear processing occur over the typical explosion timescales. Si ( 28 Si), P ( 31 P), Cl ( 35 Cl), K ( 39 K), Sc ( 45 Sc)

56 H IGH T EMPERATURE NSE C OMPOSITION As the temperature is rised, an increasing fraction of the composition resides in lighther particles At core Si exhaustion the matter is at the Nuclear Statistical Equilibrium All the strong and electromagnetic interactions are balanced by their reverses and all the nuclei are in equilibrium with exchange of p,n The gas is described by the Maxwell-Boltzmann distribution for fixed T, , Y e (p/n) ratio  the abundance of each nucleus is given by:

57 H IGH T EMPERATURE NSE C OMPOSITION NSE 1NSE 2 An increasing fraction of gravitational energy is used to melt down heavy isotopes to ,p,n (photodisintegration) 10,10, Ca(0.48) 5,1, Ni(.9) 10,1,0.5  (0.9) erg/gr 10,10,0.5  (0.2) 54 Fe(0.18) erg/gr erg/gr Energy absorbed by the changing of the NSE abundances time T, ,Y e Comp. T 1 > T 2 tt B.E.=(Zm p +Nm n -M nuc )c 2 B.E./nucleon partially undoing in less than an hour the last million years or so of nuclear evolution!!!

58 (Chandrasekhar, S., 1935, MNRAS, 95, 207) Pure non relativistic solution Fraction of the star in relativistic regime Real solution taking into account relativistic effects T HE L IMITING C HANDRASEKHAR M ASS The maximum mass that can be supported by the degenerate electrons is: When the star is fully relativistic For a fully degenerate star the EOS is Non relativistic Relativistic As the total mass increases the relativistic effects become progressively important, the equation of state progressively change from P=k 1  5/3 to P=k 2  4/3 and the total radius of the star decreases