Nucleosynthesis Origins

The most intuitive production mechanism of positrons in space is the β⁺-decay of

"proton-rich" nuclei. It is experimentally proven in the lab, that positrons are emit-ted in this process. Also, radioactive decay gamma-rays have been observed in the Universe from a variety of isotopes. Astrophysical positron emitters are listed in Tab. 5.1. During their evolution, massive stars produce heavy nuclei. These are accumulated in the ISM, by the ejection of stellar winds or from core-collapse super-nova (CCSN) explosion. Among the most abundant isotopes which areβ⁺-unstable are²⁶Al and⁴⁴Ti. Also low-mass stars can be ecient positron producers, once they turned into a white dwarf (WD) after their main sequence phase. When a WD is disrupted in a thermonuclear type Ia supernova explosion (SN Ia), large amounts of

56Ni are created. In general, the environments in which those nuclei are produced need to have an excess number of protons, as positron emitters convert bound pro-tons into bound neutrons, and positron emission requires that the mass dierence between mother and daughter nucleus is greater than511 ^keV_c2 , Sec. 2.2.1. Radioact-ive decay of proton-rich nuclei has been one of the rst proposed explanations of the galactic 511 keV emission (Clayton 1973). For an over-abundance of protons, hy-drostatic equilibrium, like in the core of massive stars, or explosive nucleosynthesis, like in nova or supernova explosions, will lead to the production of such nuclei. In both cases, the requirement for the production is that the proton capture rate must be fast, i.e. it has to occur on shorter time scales than the decay of the correspond-ing β⁺-unstable nuclei. In a typical SN Ia, or in the innermost region of a CCSN, the explosion has a canonical time scale of ≈ 1 s. The strong nuclear force, being responsible for the creation of new nuclei, dominates over the weak nuclear force, destroying new nuclei by decay. The initial stellar composition, shortly before the explosion, has predominantly a neutron-to-proton ratio (N/Z) of 1.0, for example N =Z = 14in the case of²⁸Si for CCSN, orN =Z = 6 and N =Z = 8 in the case of¹²C and ¹⁶O, respectively, for WDs in a SN Ia. This ratio is essentially conserved during the explosion, but since the last stable nucleus with N = Z (= 20) is ⁴⁰Ca,

proton-rich nuclei which are created during such an explosion from α-capture then decay to stable nuclei, by either electron capture or the emission of positrons at dierent branching ratios, depending on the species (Thielemann et al. 2011).

Nuc. Decay EC β⁺ T_1/2 γ-rays hE_kini E_kin^max Source

13N ¹³N→¹³C 0.2 99.8 10 min - 493.2 1198.5 Novae

15O ¹⁵O→¹⁵N 0.1 99.9 2 min - 736.7 1735.0 Novae

18F ¹⁸F→¹⁸O 3.1 96.9 1.8 h - 249.5 633.9 Novae

22Na ²²Na→²²Ne^∗ 9.6 90.4 2.6 yr 1274.58 (1.00) 835.0 1821.0 Novae

26Al ²⁶Al→²⁶Mg^∗ 18.3 81.7 717 kyr 1808.63 (1.00) 543.3 1173.5 Winds / CCSNe

44Ti ⁴⁴Ti→⁴⁴Sc^∗ 100.0 0.0 60 yr 67.87 (1.01); 78.36 (1.00) - - CCSNe

44Sc→⁴⁴Ca^∗ 5.7 94.3 3.97 h 1157.02 (1.00) 632.0 1474.3 CCSNe

56Ni ⁵⁶Ni→⁵⁶Co^∗ 100.0 0.0 6.1 d 158.38 (0.99); 811.85 (0.86) - - CCSNe / SNe Ia

56Co→⁵⁶Fe^∗ 80.4 19.6 77.2 d 846.77 (1.00); 1238.29 (0.66) 631.2 1458.9 CCSNe / SNe Ia Table 5.1: Astrophysically important positron emitting nuclei. The most abundant nuclei from several source types

are illustrated, together with the decay chain and branching ratio of the EC andβ⁺ decay mode. If the decay is not proceeding into the ground state of the daughter nucleus, associated gamma-rays energies are given with number of photons per unit disintegration for the most important lines. If positron emission occurs in the decay chain, the average (hE_kini) and end point (E_kin^max) energy of theβ⁺-decay positron is given. Typical uncertainties on the line energies are of the order of 0.01 keV, and for the kinetic energies of the emitted positron of the order 0.1-1 keV. For additional gamma-ray lines, see Tab. A.1 in Appendix. A.

5.1.1 Positrons from Stars

During the majority of their evolution, stars produce He nuclei by the fusion of H in the so-called pp-cycles. In order to produce heavier nuclei, other, more energetic nuclear reactions have to take place, which is only possible if the initial mass of the star is large enough. For such massive stars (> 25M), stellar winds become signicant contributors to enrich the ISM with freshly produced nuclei. Also core-collapse supernovae play an important role to inject heavy nuclei into the Galaxy, once the star ran out of nuclear fuel. These nuclei will contribute to the galactic positron content, if they have the chance to escape from the star, and if they areβ⁺ -unstable. This then depends on the isotope abundances and life-times. Therefore, stellar evolution, i.e. the processing of an initial composition of a star during its evolution towards heavier nuclei, the ejection of new elements into the ISM by winds and supernovae, and the interplay between many of such stars in groups, is a crucial factor in the contribution of radioactivities to the positron puzzle.

5.1.1.1 Stellar Evolution

In general, a star can be considered a self-gravitating gas sphere in hydrostatic equilibrium,

dP

dr =−GM ρ

r² , (5.1)

where P is the star's pressure, M its mass, and ρ its density at a position r inside the stellar radiusR. The mass of a virialised star as a function of density and radius is given by

dM = 4πρr²dr. (5.2)

Assuming the equation of state of an ideal gas,

pV =N k_BT ⇔pµ =ρk_BT , (5.3)

a zero-order estimation of the central temperature in a star can be derived:

T ∝ M

R (5.4)

As dierent nuclear reactions, i.e. burning phases of a star, critically depend on the temperature in a way that higher-order nuclei are usually created at higher temperatures, massive stars are the main producers of heavy elements. Typically, the energy production rate per mass and time, ^nuc_it , for initial particles i towards target particles t, is expressed as

^nuc_it =^nuc₀ X_iX_tρT^β. (5.5) Here, ^nuc₀ is a process-specic constant, Xi/t = ^M_M^i/t

tot are the relative mass-fractions of the incident and target nucleus with respect to the total mass of nuclei particip-ating in that particular reaction, M_tot, and β = β(T) ranges between 1 and ≈ 49, depending on the process.

Once a star exceeds a mass of 0.08 M, the temperature in the centre can reach

≈10 MK, enough to start hydrogen burning via the PP-chain. The basic reaction is a conversion of four protons into one helium nucleus (α particle), which can be subdivided into three dierent branches, as shown in Tab. 5.2. The energy production rate of the PP-chain is proportional to T⁴, and is the main indicator of a star being on the main-sequence of stellar evolution. This main-sequence is dened as the time in which a star burns 10% of its initial hydrogen. In general, the evolutionary time scale of a star, t_E ≈ 7.3×10^9M/M_L/L

yr, describes that the more massive a star is, the higher is its burning rate, and thus its luminosityL∝∝T^β. In consequence, massive stars have a shorter main-sequence life-time, and can be considered ecient producers of positrons in the Galaxy. In fact, already in the PPI-and PPIII-chain, positrons are produced which, however, cannot escape the star's interior. These annihilate with electrons inside the star, and support the radiation pressure. At temperatures above≈23 MK, the CNO cycle starts to provide nuclear energy with a production rate, _{CN O} ∝ T¹⁷. In this burning phase, C, N, and O nuclei, predominantly built from earlier generations of stars, function as catalysts to produce further α particles, cf. Tab. 5.2.

When a star is massive enough to reach a temperature of40−50 MK, another CNO sub-branch, the NeNa-cycle, involving²⁰Ne,²¹Ne,²²Ne, and ²³Na, opens to produce even heavier nuclei. Around ≈ 60 MK, the equilibrium abundances of all nuclei between ²⁰Ne and ²⁷Al are reached, so that also the long-lived β⁺-unstable isotope

26Al is produced. This happens during the NeNaMgAl-cycle, see Fig. 5.1. The ²⁶Al nuclei are then either dredged up to the stellar surface and ejected by winds, for example in Wolf-Rayet stars, or injected into the ISM at the supernova explosion.

ppI, main sequence, all stars: 0.08 ≤ M/M ≤Mmax;10 MK≤T .14 MK

He burning, triple-α-process: T & 100 MK, He core massesMC≈0.2−0.45M

p + p→d + e⁺+νe (1.442) α+α→⁸Be(-0.092) d + p→³He(1.442) ⁸Be +α→¹²C(7.367)

3He +³He→⁴He + 2p(12.860) C burning, massive stars: M & 8M, T &

500 MK

ppII:14 MK.T .23 MK ¹²C +¹²C→²⁰Ne +α

3He +⁴He→⁷Be (1.587) ¹²C +¹²C→²³Na + p

7Be + e⁻→⁷Li +νe (0.862) ²³Na + p→²⁰Ne +α

7Li + p→⁸Be→α+α(17.347) ²³Na + p→²⁴Mg

ppIII:T &23 MK ¹²C +α→¹⁶O

3He +⁴He→⁷Be (1.587) Ne burning: T &120 MK

7Be + p→⁸B(0.14) ²⁰Ne +γ→¹⁶O +α

8B→⁸Be + e⁺+νe→α+α(18.069) ²⁰Ne +α→²⁴Mg CNO main cycle: dominant for stars with

M &1.3M,T &23 MK

24Mg +α→²⁸Si

12C + p→¹³N(1.944) O burning: M &9M,T &(150..260) MK

13N→¹³C + e⁺+νe (2.220) ¹⁶O +¹⁶O→²⁸Si +α

13C + p→¹⁴N(7.551) ¹⁶O +¹⁶O→³¹P + p

14N + p→¹⁵O(7.297) ¹⁶O +¹⁶O→³¹S + n

15O→¹⁵N + e⁺+νe (2.754) ³¹S→³¹P + e⁺+νe

15N + p→¹²C +α(4.966) Si burning: M &8..11M,T &(2.7..3.5) GK CNO sub-cycle: 25 MK.T .30 MK ²⁸Si +²⁸Si→⁵⁶Ni

15N + p→¹⁶O(12.127) ²⁸Si + (1..7)α→³²S..⁵⁶Ni

16O + p→¹⁷F(0.600)

17F→¹⁷O + e⁺+νe (2.761)

17O + p→¹⁴N +α(1.192)

17O + p→¹⁸F(5.607)

18F→¹⁸O + e⁺+νe (1.656)

18O + p→¹⁵N +α(3.981)

18O + p→¹⁹F(7.994)

NeNaMgAl sequence, also AGB stars:

40 MK.T .60 MK

20Ne + p→²¹Na(5.979)

21Na→²¹Ne + e⁺+νe (3.548)

21Ne + p→²²Na(6.739)

22Na→²²Ne + e⁺+ν_e (2.842)

22Ne + p→²³Na(8.794)

23Na + p→²⁰Ne +α(2.377)

23Na + p→²⁴Mg(11.693)

24Mg + p→²⁵Al (6.548)

25Al→²⁵Mg + e⁺+νe (4.277)

25Mg + p→²⁶Al (6.307)

26Al→²⁶Mg + e⁺+νe (4.004)

26Al + p→²⁷Si(12.275)

26Mg + p→²⁷Al (8.271)

27Si→²⁷Al + e⁺+νe (4.812)

27Al + p→²⁸Si(11.585)

27Al + p→²⁴Mg(1.601)

Table 5.2: Excerpt of nuclear reactions inside stars. The PP-chains I, II, and III are representing the main-sequence phase of a star, i.e. also for low-mass stars. For each reaction,Qtotis the released energy due to the mass defect in units of MeV, given in brackets if available. In addition, the mass ranges, star types, reaction rates, and temperatures at which the processes are dominant are listed for which these reactions can occur. After Lugaro & Chie (2011), Thielemann et al. (2011), and Karakas & Lattanzio (2014).

Figure 5.1: Main paths of the NeNaMgAl sequence from José et al. (2006). Shown are the participating isotopes towards the production of²⁶Al, where dashed circles denote unstable and closed circles stable isotopes.

The half life time of the intermediate nuclei and characteristic gamma-ray energies are also given.

When a star burns towards heavier elements, its central density is increasing, and thus will also be hotter in its interior. The star does not cool eciently by the emission of electromagnetic radiation then, which makes the emission of neutrinos an important process of cooling, as they can leave the surface nearly unhindered. The model paths of massive stars with15 M and 25M are illustrated in Fig. 5.2. In general, theρ∝T³behaviour expected from fundamental stellar evolution equations is evident. Deviations from such an idealised path come from the ignition points of dierent burning stages. The triple-α reaction, burning three α-particles to one carbon nucleus, then already proceeds at an energy production rate, ∝ T⁴⁰. Its ignition is accompanied by a large jump in luminosity and radius of the star. Stars have to be massive enough that, when they run out of hydrogen in their cores, they contract (i.e. they begin to collapse) until the central temperature rises up to 10⁸ K. Then, also the density is high enough for α-particles to fuse and to produce signicant amounts of carbon directly. In addition, matter is ejected into the ISM, and the star can peel o itself, and may shorten its life as a burning star further.

Once the star ignites silicon burning towards iron, its fate has come, now containing all elements up to ⁵⁶Fe. The iron-peak elements have the highest binding energy per nucleon of all isotopes, and the star cannot gain more energy by nuclear fusion.

The pressure source from the interior runs dry and gravity wins - the star collapses.

In 1D supernova models¹, the interior, just before the collapse, is found as an onion like structure with layers of ¹H, ⁴He (with shares of ¹²C, ¹⁶O, and ²²Ne), several

16O layers, also containing ¹²C, ²⁰Ne, ²⁴Mg, ²⁸Si and ³²S, a Si-S-Ar layer, and the

"iron"-core (Woosley et al. 2002). When the iron core reaches its Chandrasekhar mass-limit, it collapses by free-fall until the density reaches & 2×10¹⁶ _cm^g3 in the case of a 25 M star, for example. This will heat its interior up to temperatures of5-10 GK. Thermal gamma-rays will photodisintegrate the iron-core nuclei, and a neutron star of≈10 km size has emerged within typically one second. At that time,

1The onion like structure with heavy elements inside and lighter elements near the surface is not appropriate as 3D eects, rotation, and convection will lead to a more complicated scheme (Woosley et al. 2002).

Figure 5.2: Evolution of massive stars as a function of density and temperature for a15Mand 25Mstar from hydrogen burning towards iron-core collapse; from Woosley et al. (2002). The zero-order ideal trajectory ρ∝T³ is clearly seen as the star contracts to fuse heavier nuclei and thereby heats. Nonmonotonic behaviour is due to ignitions of higher burning phases.

the upper layers have not noticed that the core shrank to a compact object, which is sending out a shock-wave after the innermost layers bounced o the core. The ingoing layers are being photo-dissociated, and, if the shock-wave is strong enough, the remaining layers are peeled o, enriching the ISM with stellar produced nuclei.

More details about CCSNe and nuclei produced and ejected will be discussed in Sec. 5.1.2. In the following Sec. 5.1.1.2, the contribution of ²⁶Al to the galactic positron content will be discussed.

5.1.1.2 Beta-Unstable Al-26 as Natural Positron Producer

The long-lived isotope ²⁶Al is produced during the NeNaAlMg cycle, by not only massive stars but also AGB stars. The abundances of Mg and Al are altered in an H-burning shell via the activation of the MgAl-chain (upper right part of Fig. 5.1) at around 60 MK, rather than in the core of a massive star or at the bottom of convective envelopes in AGB stars. It is created by the proton-capture reaction

25Mg(p, γ)²⁶Al, which is very sensitive to temperature. ²⁶Al can be easily destroyed again by neutron-capture reactions, such as ²⁶Al(n,p)²⁶Mg or ²⁶Al(n, α)²³Na. In bottom layers of the H-burning shell, and during convective pulses, the temperatures can easily reach 90 MK and 200 MK, respectively, high enough for the neutron donating process¹³C(α,n)¹⁶Oto become very ecient. If the temperature increases beyond250 MKin convective pulses, also the process²²Ne(α,n)²⁵Mgoriginates more neutrons, which destroy even more of the ²⁶Al-abundance. In general, the yield of

26Al, i.e. the amount of²⁶Al which is ejected into the ISM by winds and supernovae, depends on three factors. These are the reaction rate of converting²⁵Mg into²⁶Al, the amount of ²⁵Mg initially available, and the amount of ²⁶Al destruction. ²⁶Al has to be dredged up into the stellar surface, and will eventually be ejected in the stellar winds during the Wolf-Rayet phase of a massive star, or during the supernova explosion. Calculated²⁶Al yields range from10⁻⁷M for 1-4M AGB stars, and up to 10⁻⁴M for larger initial star masses. The contribution from AGB stars to the total galactic ²⁶Al abundance is probably low compared to supernova yields. But

AGB stars have been undoubtedly identied as ²⁶Al producers by the discovery of

26Al in meteorite grains and presolar dust. After stellar evolution, also a fraction

26Al is destroyed again, as a shock front, released by the core-collapse supernova explosion, will propagate through the stellar envelope. However, it might also be formed during explosive nucleosynthesis again (Thielemann et al. 2011).

The third dredge-up brings most of the newly produced nuclei to the stellar surface, where they are carried away by strong stellar winds. The origin of these winds are radiation pressure acting on large amounts of dust and gas that have been formed around AGB stars. Another origin is the luminosity variability of AGB stars, which is caused by stellar pulsation. During pulsations, the star contracts and expands, i.e. a de- and increase of the radius, and thus an in- and decrease of the temperature, will be followed by a change in luminosity. Stellar winds have dierent velocities depending on the origins; while strong and dense winds (called superwinds) have relatively low velocities of 5-30 km/s, with a huge mass loss rate of 10⁻⁴ M/yr, normal hydrogen burning main sequence stars like the Sun show terminal velocities of a few 100 km/s, and a mass loss rate of 10⁻¹¹ M/yr (Lugaro

& Chie 2011). Wolf-Rayet stars eject nuclei with even higher speeds of up to 4000 km/s, losing ∼ 0.1% of their mass per year (Kippenhahn & Weigert 1990).

Due to the combined forces of radiation pressure and pulsation at the end of the AGB phase, the extended stellar envelopes where molecules like CO, TiO or ZrO found good conditions (temperatures∼1000 K) to form, can be completely eroded (Willson 2000). An AGB star might also illuminate its own shell, which is then called a planetary nebula. At the end of a star's evolution, when no more fuel is available, the planetary nebula nucleus turns into a WD. However, the ²⁶Al output of stellar winds is dominated by Wolf-Rayet stars, since they have by far the most intense winds.

Wolf-Rayet stars evolve very quickly as they are part of the normal evolutional stages of O stars. For example, a typical 25 M Wolf-Rayet star has a life-time around a few million years. Their strong stellar winds blow out the material into their surroundings, also including freshly produced ²⁶Al. Depending on the initial mass, dierent evolution models are proposed: In the mass-range above ∼ 30 M, every evolutional sequence is starting with an O-type main-sequence star. Its next stage is either a red or blue supergiant (R/BSG), or a luminous blue variable (LBV) (Meynet et al. 2011). The extreme stellar winds in those phases are ejecting the unprocessed outer H-rich layer, for which reason the nitrogen-rich products of the CNO-cycle are uncovered (WN stars). Later, also the carbon-rich layers which originated from He-burning are uncovered (WC and WO stars), resulting in a complex internal structure. Whole layers can be repelled, which afterwards mix with the ISM, and make Wolf-Rayet stars to the main contributors to galactic ²⁶Al. If the radiation pressure cannot prevent the remaining layers to fall into the centre (core-collapse supernova, see also Sec. 5.1.2), the supernova of the Wolf-Rayet star again ejects

26Al into the ISM.

Once²⁶Alis created and ejected, it accumulates inside large cavities ("superbubbles") which have been blown by previous supernova explosions and winds. These cavit-ies are surrounded by shells of neutral hydrogen (HI). Usually, massive stars do not evolve separated from each other, but are created simultaneously in OB associations.

With typical ages between ≈ 1 and 20 Myr, these regions are young, compared to

S.Plüschke

30 0 90 60

150 120

180 330 300 270 240 210

−60

−30 0 30 60

−Intensität [ph cm⁻² sr⁻¹ s⁻¹] x 10⁻³

Perseus Cygnus

Cepheus

Aquila

"innere Galaxie"

Carina Vela

Centaurus-Circinus Orion

Figure 5.3: COMPTEL sky survey²⁶Almaximum entropy map iteration 7. The map shows the galactic 1809 keV emission (17 contour-lines) together with important, also probable foreground, emission regions, based on all COMPTEL observations. From Plüschke (2001).

the age of the Milky Way (>10 Gyr), and thus suitable to investigate and observe stellar formation and nucleosynthesis. Stars belonging to such an OB association have formed out of the same volume inside a molecular cloud, and at nearly the same time, with a distribution width of a million years. As O- and B-type stars are short-lived and will explode in a CCSN only a few million years after formation, OB associations are limited to tens of million years. O and B stars hence dominate the enrichment of the ISM, at least in the case of²⁶Al, albeit this short time scale.

Supernovae may then trigger new star formation in neighbouring molecular clouds, if the gas pressure cannot counteract its own gravity any more. This situation can be estimated by the Jeans mass, M_J =

3 4πρ

1/2

5kBT Gµ

3/2

, i.e. the mass at which gravity wins against radiation pressure. Such a compression can either happen due to the accumulation of enough mass in the cloud (self-acting star formation), or by shock-waves, which are sent out by preceding supernova explosions (triggered star formation). The stellar content of an OB association can be described empirically by an initial mass function,

dN

dM ∝M^−(Γ+1), (5.6)

counting the number of stars in a given mass interval[M, M+dM]. The indexΓin

counting the number of stars in a given mass interval[M, M+dM]. The indexΓin

Im Dokument Positron-Annihilation Spectroscopy throughout the Milky Way  (Seite 169-200)