10. NUCLEAR PROCESSES IN THE LATE STAGES OF THE EVOLUTION OF MASSIVE STARS

1. } Na23 + p Ne20 + a Mg23 + n 10. NUCLEAR PROCESSES IN THE LATE STAGES OF THE EVOLUTION OF MASSIVE STARS 10.1 THE EFFECT OF MASS As massive stars evolve they build up ash from the previous burning stage, and this material becomes the fuel for the next phase - that is if the star is massive enough to be able to create a suitably high temperature to overcome the progressively higher Coulomb barrier. We also know that supernovae explosions take place and that they are associated with individual stars. The energy release in these events is typically 1045 Joules which is equivalent to about 10-2 M0c2, i.e. a significant fraction of the available stellar mass energy. This is clearly a truly catastrophic event for the star. In the next sections we try to understand how this comes about. 10.2 CARBON BURNING We have seen how lower mass stars M < 4 M0 can build up a carbon core and create white dwarfs. We also know that more massive stars will have a hotter core since Clearly if the temperature (i.e the mass) of the star is high enough then carbon burning may take place DE (MeV) Na23 + p 2.3 Ne20 + a 4.6 Mg23 + n -2.6 O16 + 2 a 0.114 Since there are substantial fluxes of energetic particles within the plasma near to the centre of the star, the following reactions occur with high probability These reactions require the temperature to be typically 7 108 K PHYS3010 - STELLAR EVOLUTION

2. 10.3 OXYGEN BURNING At temperatures of typically 1.5 109 K oxygen burning can take place } Si31 + n P31 + p Si28 + a Si30 + 2p Mg24 + 2a (16.5 MeV) At higher temperatures (kT ~ 300 keV) there will be enough g-ray thermal photons around to cause photodisintegration of significant numbers of nuclei The result will be to produce copious alphas 10.4 SILICON BURNING Si28 is in fact a much more tightly bound nucleus than S32, and when the temperature is around 2.5 109 K then S32 rapidly photodisintegrates to form Si28 In fact the core becomes predominantly Si28 since the a particles at the end of the O burning also tend to build up the Si28 via At this stage Si28 + Si28 --> X56 does not happen since at temperatures around 3 109 K the photodisintegration means that there will be a more complex statistical balance between the photodisintegration and the build-up by a‘s (Note the a build-up is an easier way to effect thermonuclear fusion due to the comparatively lower alpha/nucleus Coulomb barrier). PHYS3010 - STELLAR EVOLUTION

3. Photodisintegration rate Reaction rate Binding Energy/Nucleon Fission Fusion Iron Group A = 56 A The statistical equilibrium may be expressed as follows Decay Build-up During the silicon burning there will be a general build up of the iron group i.e. Ni, Fe, Cr etc… The binding energy per nucleus reaches a maximum for Fe56, so that energy must be absorbed from the gas whenever particles are added to a nucleus with A>56. Hence elements above the iron group are not formed during this quasiequilibrium silicon burning. If the temperature (stellar mass) is high enough then there will be an iron group nuclei core to the star, but if the burning terminates before the Si28 is depleted then the core will contain a mixture of intermediate mass elements. (30 < A < 50) At the point of forming an iron group core the star is heading for a catastrophe. It has exhausted it supply of nuclear fuel. Contraction is the only other source of heat energy to fight against gravity. PHYS3010 - STELLAR EVOLUTION

4. 10.5 THE ROLE OF NEUTRINOS Unlike photons which couple to matter through the electromagnetic forces with a cross-section of typically 10-20 to 10-28 m2, neutrino processes involve cross-sections the order of 10-48 (En /mec2)2 m2 per particle. (En is the energy of the neutrino). This means that matter under most conditions is essentially transparent to neutrinos. The mean free path for neutrinos in matter with a baryon number density n is The mean free path in the core of the Sun will be typically 10 pc, so that the neutrinos escape and take their energy with them. In the PP and CNO hydrogen burning phases the neutrinos carry away between 2 and 5 % of the energy generated, making the lifetime of stars on the main sequence 2 - 5 % shorter. • For massive stars at the end of their lifetime the situation is much more dramatic • They have no replenishment of energy from nuclear sources • With a central temperature of T ~ 109 K i.e. (kT ~ mec2) many other processes generate immense fluxes of neutrinos • The result is catastrophic THE PRODUCTION OF NEUTRINOS IN STELLAR EVOLUTION BY WEAK INTERACTIONS Neutrino Pair Production Since kT ~ mec2 (T ~ 109 K) in massive stars, much of the thermal spectrum will be in the form of g-rays with energies Eg > 2mec2. We therefore expect large numbers of electron-positron pairs to be produced and subsequently annihilate. PHYS3010 - STELLAR EVOLUTION

5. Most of the time this is what happens, however direct electron-neutrino coupling is also possible allowing the electron-positron pair to decay into neutrinos Although the probability of this happening is about 10-22 that of the electromagnetic process, the vast number of reactions which take place at the centre of stars results in a considerable rate of energy loss. Photoneutrino Process This process depends on the fact that an electron can absorb a photon and re-emit a neutrino-antineutrino pair : This is the (weak) equivalent of the Compton effect. Plasma Process Electromagnetic radiation is strongly affected by the dielectric properties of the electron gas when the stellar core density is high. The collective interaction of a photon with the plasma is called a plasmon. The plasmons can decay directly into neutrinos It is the plasma that enables both energy and momentum to be conserved. PHYS3010 - STELLAR EVOLUTION

6. Plasma process 10 Pair -annihilation process Log r (kg/m3) Photoneutrino process 5 8 9 10 Log T (K) URCA PROCESS During the course of the nuclear processing which takes place at the core of massive stars a great many b-decay processes will take place. Some of these are effectively cyclic such that the same nuclei are involved in the process many times and liberate vast amounts of energy in the form of neutrinos The material cycles and recycles itself with a constant drain of energy from the star. DEPENDENCE ON DENSITY AND TEMPERATURE Processes involving neutrinos are very dependent upon the density and temperature. This is illustrated in the figure, where the dominance of the various mechanisms are illustrated. The rate of energy loss by neutrino will have an important effect on the evolution of the star. For example for some (mass dependent) stars the neutrino losses can be comparable to or exceed the nuclear energy release during silicon burning. The general effect will be to shorten considerably the lifetime of a given burning stage. A typical carbon burning phase would last about 106 years in the absence of neutrino losses. With neutrino losses this stage can be shortened to typically 103 years. PHYS3010 - STELLAR EVOLUTION

7. 10.6 THE FINAL STAGES OF A MASSIVE STAR The neutrino losses greatly speed up the final stages of thermonuclear evolution for massive (M0³ 8 M0) stars. Below we see the computer description of the end of a 25 M0 star. The final stages of other massive stars will be similar, although many details will be different. This particular one leaves a 1 M0 neutron star behind. Under slightly different conditions the star might blow itself apart leaving no central object, alternatively a very massive burnout might undergo gravitational collapse to form a black hole. We will follow the central objects later in the course. During the latter stages the star will have to contract rapidly. The length of the various stages depends upon the temperature (and hence the mass) of the star’s interior. In any case the timescales are effectively determined by neutrino losses. for example silicon the burning timescale can typically vary between 10 seconds to 10 days. Clearly the star is heading for a catastrophe since as it builds up an iron core it has no nuclear fuel at the core. The high core density ensures that neutrinos are generated and the energy for support has to come from contraction which further increases the density and the temperature, leading to increased neutrino production…. PHYS3010 - STELLAR EVOLUTION

8. 10.7 EXPLOSION OF THE STAR 7 1011 m Hydrogen burning shell Helium burning shell Carbon burning shell Neon burning shell Oxygen burning shell Silicon burning shell Iron core Near the end of its life the star becomes a red supergiant and the energy comes from concentric nuclear burning shells at the centre. The rising temperature of the contracting iron core also means that the average photon energy of the thermal bath increases. These g-ray photons are energetic enough th cause PHOTODISINTEGRATION of the iron nuclei. and also These processes are ENDOTHERMIC with BANG and This loss of support energy results in a catastrophic collapse of the core (really a free-fall in seconds). The outer layers of the star will be blown off into the interstellar medium. (more ashes and dust for re-cycling) and the central region will collapse. We will follow the core region later in the course, next we will study the exploding material. PHYS3010 - STELLAR EVOLUTION

9. Rate µ d3 1.0 Rate Closer than d (yr-1) H0 = 50 km/s/Mpc 0.1 H0 = 100 km/s/Mpc 1.0 10 100 Distance d (Mpc) 11. SUPERNOVAE 11.1 GENERAL BACKGROUND INFORMATION Observational Data A supernova represents a very rapid brightening of a star. The luminosity increases to typically 1010 L0, such that it can be as bright as the rest of the galaxy in which it is situated. It clearly represents a catastrophic redistribution of the stellar material. The total energy output is typically of the order 1044-45 J i.e ~ 0.01 M0c2. Looking at the distribution of known supernovae remnants close to the Sun and the measured rate of occurrence in other galaxies it is possible to estimate a rate of ~1 per 30 years per galaxy. In this context it should be remembered that, because of dust etc in the planes of galaxies many supernovae events are missed. This shows up in two ways : Discovery Rate. The rate of discovery over the period 1954 - 1985 is shown in the figure. As the distance increases we can see that proportionally less supernovae are discovered than one would expect from a uniform space density distribution. Clearly many are missed. Galactic Supernovae. The table below gives the date of occurrence, distance from the Sun, type and height above the Galactic plane of all known galactic supernovae. Since only six have been observed in the last 1000 years, many have been missed. At a rate of 1 per 30 years we would expect to have had ~ 30 supernovae events reported over this time period. PHYS3010 - STELLAR EVOLUTION

10. Type Ia ~ 100 day exponential decay Magnitude Magnitude 200 400 600 200 400 600 Days Days 11.2 LIGHT CURVES The light curves may be used to divide the supernovae into two main classifications with the typically inspired and imaginative names, : type I and type II. There are however a number of subdivisions. Type II Type Ia The light curves show a rapid rise to the maximum luminosity which is followed by a steep drop over a period of about 30 days. The subsequent light curve is very regular showing a straight exponential (remember magnitude is a logarithmic scale) decay with a time constanttof about 100 days. which is thought to correspond to the light curve being driven by the energy release from radioactive decay process for which the decay constant t ~110 d (t1/2 ~ 70 d) PHYS3010 - STELLAR EVOLUTION

11. Type II (and Ib) Type II supernovae are about 1 - 2 magnitudes more luminous than type Is which suggests more massive progenitor stars. Instead of the regular L ~ L0 e -t/t seen in type I events type II SN vary from one event to another, although the exponential decay often eventually appears. This variation indicates a more varied scenario. 11.3 OCCURRENCE Type Ia occur in both spiral and elliptical galaxies. Since elliptical galaxies do not contain interstellar dust and thus have no on-going star formation we can conclude that type Ia SN are related to older (and less massive) stars. Type II (and Ib) occur only in the galaxies with on-going star formation and thus probably relate to younger (and more massive) stars 11.4 SPECTRA During the early stages the spectra exhibit near black-body spectra with emission and absorption features which are broadened and blue-shifted byDl/l corresponding to velocities of typically 104 km/s. However the main reason for the type I/II classification is the absence of hydrogen lines in type Is as opposed to their presence in type IIs. The Ia/Ib classification comes about because the both have a lack of hydrogen line emission, but type Ib events are clearly derived from different parent stellar types and have many features which relate them to the type II events. In the initial phases an intense uv continuum appears before maximum and fades away. After the maximum the broadened emission and absorption lines appear. Forbidden line appear later as the system expands, and since their onset is density dependent it is possible to estimate the mass of gas ejected using the expansion velocity. Masses in excess of 1M0 are normal, with type II events characteristically ejecting considerably more than 1 M0. The original classifications have been made on the basis of the historical optical observations. Supernovae also emit across the electromagnetic spectrum, embracing radio, ir, uv, X-rays and g-rays, and as these wavebands accumulate more diagnostic information on an improved statistical basis our understanding of the phenomenon will improve. PHYS3010 - STELLAR EVOLUTION

12. N(p) 105 K 0o K p White T, p Nuclear burning Dwarf 11.5 THE PHYSICS OF SUPERNOVA EXPLOSIONS TYPE Ia The low (~ 1M0) mass , lack of hydrogen (i.e. no stellar envelope) and the fact that they are related to very old stars has led to an association of Type Ia events with white dwarfs. Furthermore the extreme consistency of the explosion characteristics is a natural consequence of a uniform starting condition. Mechanisms for Type Ia Explosions The most likely scenario for a type Ia explosion is that an accreting white dwarf in a binary system is provoked into thermonuclear instability by the accumulation of a critical mass. Ignition then takes place under degenerate conditions such that a substantial fraction of the mass undergoes nuclear burning. This is readily understood from our previous discussion relating to white dwarfs. The degeneracy pressure ð K r 5/3 (non relativistic case) ð K1r 4/3 (relativistic case) pF Whatever Thus if nuclear burning commences within a white dwarf the pressure changes negligibly but the temperature will increase dramatically because of the excellent conductivity. The thermonuclear reaction rates rise even faster since The resultant nuclear burning will be very rapid (either sub-sonic deflagration or super-sonic detonation) and because of the homogeneity of the system will burn through to the logical conclusion of products in the iron group. In fact we may expect a 1.4 M0 white dwarf to produce about 0.5 to 1.0 M0 of the radioactive isotope 56Ni. PHYS3010 - STELLAR EVOLUTION

13. Type Ia ~ 100 day exponential light decay Magnitude 200 400 600 Days The Production of Radioactive Isotopes and an Explanation of the Light Curve A model 1.4 M0 white dwarf produces typically 0.86 M0 of the iron group, 0.58 M0 of which is the radioactive isotope 56Ni. The decay scheme of this isotope is as follows t ~ 9 d t ~ 110 d key Eg are 0.847, 1.238, and 2.599 MeV Such a large mass in the form of a radioactive isotope has a considerable amount of stored energy which is liberated exponentially in time later through the g-rays and positrons. (Some MeV per disintegration). This has to be the mechanism which causes the exponential light curve seen in type Ia SN. It probably operates as follows The radioactive decay of the 56Ni isotopes liberates energy at the centre of the explosion in the form of energetic g-rays over an e-folding timescale of ~ 110 days. The surrounding material is opaque to the g-rays and they cannot escape the expanding envelope. They degrade their energies into lower energy photons by interactions with the material of the expanding shell which eventually emerge to be radiated away. A large fraction of the g-ray energy also pushes the expansion along. Note neutron star production is unlikely in type Ia SN Optical/ir/uv emission g-rays PHYS3010 - STELLAR EVOLUTION

14. BE/Nucleon Fusion Fission Iron Group A = 56 A TYPE II. The association with massive > 10M0 stars implies that type II SN are the result of the collapse of the iron core associated with stars which have evolved through the various burning stages to the onion model shown earlier. Let us look at this a little more closely. Mechanisms for Type II Supernovae Hydrogen burning shell Helium burning shell Carbon burning shell Neon burning shell Oxygen burning shell Silicon burning shell Iron core The core of a massive star When the iron core is formed the only means it has to support its increasing mass is to contract adiabatically, raise the temperature and hence the pressure. This has the unfortunate effect of causing endothermic photodisintegration The result is frantic collapse and ensures a free fall of the core. Gravitational Potential Energy of the Core. The gravitational potential energy liberated by the collapsing core is i.e just about right PHYS3010 - STELLAR EVOLUTION

15. The collapsing core will cause neutronization to take place as the force of the collapse pushes the density beyond the level which electron degeneracy can support. NEUTRONIZATION AND THE FORMATION OF A COMPACT OBJECT This process will generate a pulse (few seconds) of about 1057 neutrinos which should be emitted from the star. The falling neutrons will feel the effects of degeneracy pressure at about 1017 kg m-3, the sudden stiffening can cause the so-called core bounce phenomenon. A shock wave will propagate outwards and transfer energy to the outer layers of the star. If the neutron degeneracy is capable of stopping the infall then a neutron star will be formed. i.e neutron degeneracy has found a means to compete with gravity to form a stable object - the neutron star. If the neutron degeneracy is incapable of stopping the infall, no known physical forces left to halt the attraction of gravity and, presumably, a black hole is created. The onion-like distribution of the nuclear species above the central core is subjected to intense neutron fluxes and rapid heating. Under these conditions it is easy to understand the variety of different light curves which are seen from type II SN. It is thought that Wolf-Rayet stars (massive stars which have shed their hydrogen mantles in a similar way to red giants, but retain the evolving onion core) are the progenitors of type Ib SN. As for the case of planetary nebulae supernovae both eject material into the interstellar medium for recycling and leave cinders behind. PHYS3010 - STELLAR EVOLUTION