Modelling SN Type II: evolution up to collapse From Woosley et al. (2002) Woosley Lectures 11 and 12

Hydrogen Burning

Temperature sensitivity of nuclear reactions

The slowest reaction is 14 N(p,  ) 15 O. For temperatures near 2 x 10 7 K. (More on nucleosynthesis later) Nuclear Physics In a low mass star

The 4 CNO cycles

CNO tri-cycle neutron number C(6) N(7) O(8) F(9) Ne(10) CN cycle (99.9%) O Extension 1 (0.1%) O Extension 2 O Extension 3 All initial abundances within a cycle serve as catalysts and accumulate at largest  Extended cycles introduce outside material into CN cycle (Oxygen, …)

Energy production 4.2 £ erg/g for X 0 = 0.7

Helium Burning

Precursor reactions 14 N( ,  ) 18 F(e + ) 18 O

Helium Burning Helium burning is a two-stage nuclear process in which two alpha-particles temporarily form the ground state of unstable 8 Be *. Occasionally the 8 Be * captures a third alpha-particle before it flies apart. No weak interactions are involved.

Helium Burning ?

In a 15 solar mass star:

Energy production [ X( 16 O)] £ erg/g

Woosley et al. (2002; RMP 74, 1015)

Neutrino loss mechanisms Itoh et al. (1989; ApJ 339, 354)

Carbon Burning

Approximate initial conditions: As we shall see, the temperature at which carbon burns in a massive stars is determined by a state of balanced power between neutrino losses by the pair process and nuclear energy generation. This gives 8 x 10 8 K for carbon core burning. Burning in a shell is usually a little hotter at each step, about 1.0 x 10 9 K for carbon burning. Assuming that T 3 /  scaling persists at the center, and that helium burned at 2 x 10 8 K and 1000 gm cm -3, this implies a carbon burning density around 10 5 gm cm -3. The initial composition is the ashes of helium burning, chiefly C and O in an approximate 1 : 4 ratio (less carbon in more massive stars). There are also many other elements present in trace amounts: 22 Ne, 25,26 Mg from the processing of CNO elements in He-burning The s-process Traces of other heavy elements present in the star since birth Up to ~1% 20 Ne from 16 O(  ) 20 Ne during He-burning

Principal nuclear reaction

Many important secondary reactions: 20 Ne( a,g ) 24 Mg 23 Na( a,p) 26 Mg 26 Mg(p, g ) 27 Al 23 Na(p, g ) 24 Mg 23 Na(p, a ) 20 Ne 25 Mg(p, g ) 26 Al 22 Ne( a,n) 25 Mg 25 Mg( a,n) 28 Si 23 Mg(n,p) 23 Na 25 Mg(n, g ) 26 Mg and dozens (hundreds?) more

There are also some important weak interactions that can change the neutron excess h. The neutron branch of 12 C + 12 C itself makes 23 Mg. At lower temperature this decays by 23 Mg(e + n ) 23 Na. At higher temperature it is destroyed by 23 Mg(n,p) 23 Na. The former changes h ; the latter does not. 20 Ne(p, g ) 21 Na(e + n ) 21 Ne 21 Ne(p,  ) 22 Na(e + n ) 22 Ne Together these reactions can add to the neutron excess that was created in helium burning by 14 N( a,g ) 18 F(e + n ) 18 O or, in stars of low metallicity they can create a neutron excess where no existed before.

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Principal Nucleosynthesis in carbon burning: 20,21 Ne, 23 Na, 24,25,26 Mg, (26),27 Al, and to a lesser extent, 29,30 Si, 31 P The 16 O initially present at carbon ignition essentially survives unscathed. There are also residual products from helium burning – the s-process, and further out in the star H- and He-burning continue. A typical composition going into neon burning – major abundances only would be 70% 16 O, 20% 20 Ne, 5% 24 Mg

D. Energy Generation Suppose we make 20 Ne and 24 Mg in a 3:1 ratio (approximately solar) 12,12 /2 12,12 ' 3.9 £ T 9 28 cm 3 g -1 s -1 BE i : Binding energy (MeV)

The total energy released during carbon burning is Since D X 12 ~ 0.25 << 1, this is significantly less than helium burning

actually should use a smaller radius here  a longer lifetime.

No central convective carbon burning!

Burning Stages in the Life of a Massive Star 0

Neon Burning Following carbon burning, at a temperature of about 1.5 x 10 9 K, neon is the next abundant nucleus to burn. It does so in a novel “photodisintegration rearrangement” reaction which basically leads to The energy yield is not large, but is generally sufficient to power a brief period of convection. It was overlooked early on as a separate burning stage, but nowadays is acknowledged as such. The nucleosynthetic products resemble those of carbon burning but lack 23 Na and have more of the heavier nuclei, (26),27 Al, 29,30 Si, and 31 P.

The composition following carbon burning is chiefly 16 O, 20 Ne, 24 Mg but 16 O is not the next to burn (influence of Z = N = 8 = magic) Species S a (MeV) energy required to remove an a -particle. 16 O Ne Mg 9.32 Before the temperature becomes hot enough for oxygen to fuse (T 9 = 2.0 as we shall see), photons on the high energy tail of the Bose-Einstein distribution function begin to induce a new kind of reaction - 20 Ne( g,a ) 16 O The a -particle “photo-disintegrated out of 20 Ne usually just adds back onto 16 O creating an “equilibrated link” between 16 O and 20 Ne. Sometimes though an a captures on 20 Ne to make 24 Mg. When this happens the equilibrium between 16 O and 20 Ne quickly restores the a that was lost.

Other secondary reactions: 24 Mg( a,g ) 28 Si 27 Al( a,p) 30 Si 25 Mg( a.n) 29 Si 30 Si(p, g ) 31 P 26 Mg( a,n) 30 Si etc. Products: some more 16 O and 24 Mg, 29,30 Si, 31 P, 26 Al and a small amount of s-process.

B. Photodisintegration Reactions At high temperatures, the inverse reaction to radiative capture, [(n, g ),(p, g ),( a,g)] becomes important as there exists an appreciable abundance of  -rays out on the tail of the Bose-Einstein distribution that have energy in excess of several MeV. The reactions these energetic photons induce are called photodisintegration reactions – the major examples being ( g,n),( g,p), and ( g,  )

YIYI

Nucleosynthesis The principal nuclei with major abundances at the end of neon burning are 16 O and 24 Mg. Most of the neutron excess resides in 25,26 Mg. Most of the 16 O has in fact survived even since helium burning. In terms of major production of solar material, important contributions are made to [ 16 O], 24,25,26 Mg, (26),27 Al, 29,30 Si, and 31 P

Oxygen Burning: After neon burning the lightest nucleus remaining with appreciable abundance is 16 O. This not only has the lowest Coulomb barrier but because of its double magic nature, has a high  -particle separation energy. It is the next to burn. Because of its large abundance and the fact that it is a true fusion reaction, not just a rearrangement of light nuclei, oxygen burning releases a lot of energy and is a very important part of the late stages of stellar evolution in several contexts (e.g., pair-instability supernovae). It is also very productive nucleosynthetically. It’s chief products being most of the isotopes from 28 Si to 40 Ca as well as (part of) the p-process.

Initial composition: 16 O, 24 Mg, 28 Si Nuclear reactions: The deuteron, d, is quickly photodisintegrated into a free neutron and proton. proceeds through the 32 S compound nucleus with a high density of resonances. Very like carbon burning.

Nucleosynthesis 28 Si, 32,33,34 S, 35,37 Cl, 36,38 Ar, 39,41 K, 40,42 Ca, some p-process Element-wise: Si, S, Ar, Ca in roughly solar proportions. Destruction of the s-process Increasing neutronization, especially right after oxygen disappears from the center.

Production factors only in inner solar mass of 25 solar mass star near oxygen depletion (5%). s25a28 main products Si, S, Ar, Ca, Cl, K p-process

Whole star production factors near oxygen depletion (5%) in a 25 solar mass star. s25a28

Silicon Burning Silicon burning proceeds in a way different from any nuclear process discussed so far. It is analogous, in ways, to neon burning in that it proceeds by photodisintegration and rearrangement, but it involves many more nuclei and is quite complex. The reaction 28 Si + 28 Si  ( 56 Ni) * does not occur owing to the large Coulomb inhibition. Rather a portion of the silicon (and sulfur, argon, etc.) “melt” by photodisintegration reactions into a sea of neutrons, protons, and alpha-particles. These lighter constituents add onto the silicon and heavier elements, gradually increasing the mean atomic weight until species in the iron group are produced.

Initial Composition The initial composition depends on whether one is discussing the inner core or locations farther out in the star. It is quite different, e.g., for silicon core burning in a presupernova star and the explosive variety of silicon burning we will discuss later that goes on in the shock wave and gets ejected. In the center of the star, one typically has, after oxygen burning, and a phase of electron capture that goes on between oxygen depletion and silicon ignition: 30 Si, 34 S, 38 Ar and a lot of other less abundant nuclei Farther out one has: 28 Si, 32 S, 36 Ar, 40 Ca, etc. Historically, Si burning has been discussed for a 28 Si rich composition

Quasi-equilibrium This is a term used to describe a situation where groups of adjacent isotopes, but not all have come into equilibrium with respect to the exchange of n, p, , and .

Late during oxygen burning, many isolated clusters grow and merge until, at silicon ignition, there exist only two large QE groups Reactions below 24 Mg, e.g., 20 Ne( a,g ) 24 Mg and 12 C( a,g ) 16 O are, in general, not in equilibrium with their inverses (exception, 16 O( a,g ) 20 Ne which has been in equilibrium since neon burning). Within the groups heavier than A = 24, except at the boundaries, the abundance of any species is related to that of another by successive application of the Saha equation.

In the group that contains 28 Si, one can write any abundance Need 6 parameters: Y a, Y p, Y n and Y( 28 Si) plus T and r.

32 S 31 P 28 Si 29 Si 30 Si This reduces the number of independent variables to 5, but wait … Moreover there exist loops like: p p n a

The situation at the end of oxygen burning is that there are two large QE groups coupled by non-equilibrated links near A = 45. Early during silicon burning these two groups merge and the only remaining non-equilibrated reactions are for A < Mg The non-equilibrated link has to do with the double shell closure at Z = N = 20

28 Si 24 Mg+ a 20 Ne+ a 16 O+ a 12 C+ a 3a3a 7a7a The cluster evolves at a rate given by 24 Mg( g,a ) 20 Ne The photodisintegration of 24 Mg provides  ’s (and n’s and p’s since Y a =C a Y n 2 Y p 2 ) which add onto the QE group gradually increasing its mean atomic weight. As a result the intermediate mass group, Si-Ca gradually “melts” into the iron group.

The large QE cluster that includes nuclei from A = 24 through at least A = 60 contains most of the matter ( 20 Ne, 16 O, 12 C, and a are all small), so we have the additional two constraints The first equation can be used to eliminate one more unknown, say Y p, and the second can be used to replace Y n with an easier to use variable. Thus 4 variables now specify the abundances of all nuclei heavier than magnesium. These are r, T 9, h, and Y( 28 Si)

30 Si and 34 Si burning to 54 Fe and 56 Fe give more in the actual stellar environment.

This is very like neon burning except that 7 alpha-particles are involved instead of one.

Reaction rates governing the rate at which silicon burns: Generally speaking, the most critical reactions will be those connecting equilibrated nuclei with A > 24 (magnesium) with alpha-particles. The answer depends on temperature and neutron excess: Most frequently, for  small, the critical slow link is 24 Mg(  ) 20 Ne The reaction 20 Ne(  ) 16 O has been in equilibrium with 16 O(  ) 20 Ne ever since neon burning. At high temperatures and low Si-mass fractions, 20 Ne(  ) 24 Mg equilibrates with 24 Mg(  ) 20 Ne and 16 O(  ) 12 C becomes the critical link. However for the values of  actually appropriate to silicon burning in a massive stellar core, the critical rate is 26 Mg(p,  ) 23 Na(  20 Ne

Nucleosynthesis Basically, silicon burning turns the products of oxygen burning (Si, S, Ar, Ca, etc.) into the most tightly bound nuclei (in the iron group) for a given neutron excess,   The silicon-burning nucleosynthesis that is ejected by a super- nova is produced explosively, and has a different composition dominated by 56 Ni and will be discussed later. The products of silicon-core and shell burning in the core are both so neutron- rich (  so large) that they need to be left behind in a neutron star or black hole. However, even in that case, the composition and its evolution is critical to setting the stage for core collapse and the supernova explosion that follows.

Following Si-burning at the middle of a 25 solar mass star: 54 Fe Ni Fe Fe Co Neutron-rich nuclei in the iron peak. Y e = Following explosive Si-burning in a 25 solar mass supernova, interesting species produced at Y e = to Ca 44 Ti 47,48,49 Ti 48,49 Cr 51 V 51 Cr 55 Mn 55 Co 50,52,53 Cr 52,53 Fe 54,56,57 Fe 56,57 Ni 59 Co 59 Cu 58,60,61,62 Ni 60,61,62 Zn product parent Silicon burning nucleosynthesis 44 Ti and Ni are important targets of  -ray astronomy

Nuclear Statistical Equilibrium As the silicon abundance tends towards zero (though it never becomes microscopically small), the unequilibrated reactions below A = 24 finally come into equilibrium Then every isotope is in equilibrium with every other isotope by strong, weak, and electromagnetic reactions (but not by weak interactions)

The resultant nucleosynthesis is most sensitive to 

True Equilibrium If the weak interactions were also to be balanced, (e.g., neutrino capture occurring as frequently on the daughter nucleus as electron capture on the parent), one would have a state of true equilibrium. Only two parameters,  and T, would specify the abundances of everything. The last time this occurred in the universe was for temperatures above 10 billion K in the Big Bang. However, one can also have a dynamic weak equilibrium where neutrino emission balances anti-neutrino emission, i.e., when This could occur, and for some stars now seemingly does, when electron-capture balances beta-decay globally, but not on individual nuclei. The abundances would be set by  and T, but would also depend on the weak interaction rate set employed.

Weak Interactions Electron capture, and at late times beta-decay, occur for a variety of isotopes whose identity depends on the star, the weak reaction rates employed, and the stage of evolution examined. During the late stages it is most sensitive to eta, the neutron excess. Aside from their nucleosynthetic implications, the weak interactions determine Y e, which in turn affects the structure of the star. The most important isotopes are not generally the most abundant, but those that have some combination of significant abundance and favorable nuclear structure (especially Q-value) for weak decay. From silicon burning onwards these weak decays provide neutrino emission that competes with and ultimately dominates that from thermal processes (i.e., pair annihilation).

He – depletion O – depletion PreSN He – depletion O – depletion PreSN The distribution of neutron excess, h, within two stars of 25 solar masses (8 solar mass helium cores) is remarkably different. In the Pop I star, h is approximately 1.5 x everywhere except in the inner core (destined to become a collapsed remnant) In the Pop III (Z = 0) star the neutron excess is essentially zero at the end of helium burning (some primordial nitrogen was created) Outside of the core h is a few x 10 -4, chiefly from weak interactions during carbon burning. Note some primary nitrogen production at the outer edge where convection has mixed 12 C and protons.

Si-depletion Si-shell burn Core contraction PreSN T(10 9 K)  (c cm -3 ) 5.9 x x x x 10 9 Y e e-capture 54,55 Fe 57 Fe, 61 Ni 57 Fe, 55 Mn 65 Ni, 59 Fe b-decay 54 Mn, 53 Cr 56 Mn, 52 V 62 Co, 58 Mn 64 Co, 58 Mn O-depletion O-shell Si-ignition Si-shell T(10 9 K)  (g cm -3 ) 1.2 x x x x 10 7 Y e e-capture 35 Cl, 37 Ar 35 Cl, 33 S 33 S, 35 Cl 54,55 Fe b-decay 32 P, 36 Cl 32 P, 36 Cl 32 P, 28 Al 54,55 Mn 15 solar mass star (Heger et al 2001)

Woosley et al. (2002)