1  Nukleosynthesis & Stars

Part 1: Nucleosynthesis (1.1 - 1.5)
The chemical elements are in fact the sum of certain isotopes. The latter are formed by a range of processes, of which most still occur. These processes are called ›nucleosynthesis‹. Describe these various processes of nucleosynthesis and where these occur.
Learning Goals
Die chemischen Elemente sind tatsächlich die Summe bestimmter Isotope. Letztere bilden sich in einer Reihe von Prozessen, von denen die meisten noch heute ablaufen. Diese Prozesse werden ›Nukleosynthese‹ genannt. Beschreibe diese verschiedenen Nukleosynthese-Prozesse, und wo diese stattfinden.

Part 2: Presolar Grains (1.6 - 1.10)
Presolar grains are a trace component in meteorite. They originate from other stars and are characterised by massively different isotope compositions than all other meteorite components. Learn about the formation, origin, transport, types and classification of presolar grains.
Learning Goals
Describe the various types of presolar grains and how these are classified. Compare the isotope variations of presolar grains to solar system materials. Explain how presolar grains can be found and identified.

Part 3: Stars and their Evolution (1.11 - 1.12)
The about 100.000 stars in our galaxy, as well as the billions others in our universe are highly diverse. Stars reach different ages and undergo various evolutions. Most importantly, they are a main source of element production (=nucleosynthesis). Describe the various stars, how these evolve, and how and when elements are formed in and around stars. Learning Goals
Recall and describe the formation environment of stars in general and our Sun in particular. Explain how stars evolve. Illustrate the nucleosynthesis in the various stars. Relate the various nucleosynthetic processes (these need to be known) to the nuclide binding energies, as well as to the various types of stars.

1.1 Nucleosynthesis – Big Bang

Space and time came into existence with the big bang about 13.8 Ga ago. In the first seconds, space was exclusively filled with radiation and expanded at super-light speed. Space cooled during this stage and the first elementary particles such as quarks and later electrons, protons and neutrons condensed. After a few minutes the temperature fell sufficiently for protons to capture electrons, thereby forming Hydrogen as the first chemical element. Then, protons and neutrons collided with each other, thereby forming Helium as the second chemical element, and in tiny traces Lithium. Space quickly expanded, and the moment of the elements and elementary particles became insufficient to produce any heavier element. The electron capture by a proton is about five times faster than the fusion of protons and neutrons to Helium, which is why the chemical composition of the early universe consisted of about 80% Hydrogen and 20% Helium.

H, He, and traces of Li

Elementary particles such as quarks and electrons condensed from the extremely hot and young universe. These then converted into protons and neutrons, and protons together with electrons to H. For a certain time the high density led to frequent collisions of H-nuclei, thereby producing He-nuclei and traces of Li. These then also combined with electrons to form the according atoms

✗… ca. 13.3 Ga

✓… ca. 13.8 Ga

✗… ca. 18.3 Ga

✗… ca. 18.8 Ga

✓It entirely consisted of radiation

✗It consisted of radiation and quarks

✗It entirely consisted of quarks

✗It entirely consisted of H and He

✓80% H

✓20% He

✗80% He

✗20% H

1.2 Nucleosynthesis – Spallation

The three lightweights Be, Li and B can neither be produced in a star by fusion, nor subsequently during the r-, s-, or p-process. Only tiny traces of Li were produced during the big bang nucleosynthesis. The three elements Be, Li and B form in spallation reactions in the interstellar medium. This process is sometimes also called l-process for light elements. Spallation means, e.g., a proton hits a nucleus and destroys it, thereby a new element is produced. Two examples of spallation reactions are: (i) one proton hits a 12C nucleus, the proton remains in the nucleus, but two others are ejected. This produces 11B, or in short: 12C(p,2p)11B. (ii) again, one proton hits a 12C nucleus, the proton remains in the nucleus, but four protons and two neutrons are ejected. This produces 7Li, or in short: 12C(p,4p2n)7Li.

Li, Be, B – however, traces of Li are also produced in the Big Bang nucleosynthesis.

Li, Be, and B are primarily produced by spallation (traces of Li are also produced in the Big Bang nucleosynthesis). This means, a nucleus – e.g., 12C – is hit by one proton and knocks 2 protons out of the nucleus, thereby producing a 11B nucleus. These spallation processes primarily occur in the ISM, which therefore is the primary formation site of the three light elements Li, Be, and B.

✗Be, Li, B

✗Be, B, Li

✓Li, Be, B

✗Li, B, Be

✗B, Li, Be

✗B, Be, Li

✗H

✓He

✗Be

✗C

✗N

✓True

✗False

1.3 Nucleosynthesis – Stellar

A star forms inside a collapsing molecular cloud. The pressure inside jumps significantly, and H starts fusing to He, thereby releasing enormous amounts of energy. This fusion reaction is called ›H-burning‹. After this initial ignition a chain of fusion reaction starts, along which elements until Fe are produced. The individual burning stages and the associated fusion reactions are shown in the reaction equations. This chain of fusion reaction might stop earlier, depending on the mass of the star. Our Sun is comparatively small and of low mass, and will only reach He-burning.

Stellar nucleosynthesis primarily refers to fusion processes.

Fusion means that at least two nuclei collide and stick together, thereby forming a larger nucleus. This is, however, only possible if the binding energy (per nucleus) of the larger nucleus is larger than the combined binding energies (per nucleus) of the colliding nuclei. This is possible for elements up to Fe.

✗54Fe

✓56Fe

✗58Ni

✗62Ni

✓True

✗False

✓He-burning

✗CNO-burning

✗H,He-cycle

✓CNO-cycle

✓C-burning

✗P-burning

✓O-burning

✗Si-cycle

1.4 Nucleosynthesis – r-s-p-Processes

Elements with mass-numbers above Fe are produced in collisions of neutrons with an element’s nucleus. Supernova explosions, for example, free enormous amounts of neutrons. When many collisions occur, e.g., in an environment of high neutron density, individual nuclei can be hit by neutrons in rapid succession, which the nuclei can then capture. This produces nuclides of increasing mass. This is called the r-process (rapid). This process can produce super-heavy nuclides that are unstable and usually quickly decay via beta^- reaction. This decay results in nuclides of higher atomic numbers. If collisions are comparatively sparse, neutron capture is less frequent. This is called the s-process (slow). Super-heavy nuclides are not formed, as the first super-heavy radioactive nuclide in most cases decays more quickly than the next super-heavy nuclide is formed in the s-process. In cases stable nuclides cannot be formed by the s-process, as an unstable nuclide with short half-life is positioned directly before it. This so protected stable nuclide can then only be formed in the r-process. The r- and s-process nuclide abundances of each so-formed element is known from model calculations. A few nuclides cannot be formed by any of these two processes. These are always the lightest nuclides of an element, that cannot be reached by an r- or s-process reaction chain. Their formation is yet still not entirely clear, and is often collectively called p-process. This name refers to a possible process in which protons are added to the nucleus. Another possibility is the (gamma,xn)-reaction (gamma capture, loss of x neutrons) and subsequent beta^+ decay.

Primarily the elements heavier than Fe.

The r-process occurs in a region of relative high neutron density, so that existing nuclides can be hit by neutrons in rapid succession. It is thereby possibly to produce quite heavy nuclides of a specific element, which then – of course – rapidly decay towards stable nuclides of higher mass numbers. Contrary to this, the s-process occurs in a region of relative low neutron density, so that nuclides are hit by a neutron only from time to time. Therefore, high mass neutrons cannot be formed, as intermediate nuclides decay before a heavier one can be formed. The nature of the p-process is still unclear. It was initially thought that these form by the addition of a proton – which still is a considered possibility.

✓AGB stars

✗Big Bang

✗Spallation

✓Super-Nova

✓… beta^-

✗… beta^+

✗… r

✗… s

✓… p

1.5 Chart of Nuclides

Each chemical element represents a collection of numerous radioactive and/or stable isotopes. An isotope consists of a nucleus (= core) of protons and neutrons, surrounded by electrons. A nuclide designates the nucleus of a specific isotope. The number of protons (= atomic number, = Z) in a nucleus defines the chemical element. Isotopes of an element are defined by variable numbers of neutrons (= N) in their nucleus. The mass number (not mass!) is the sum of protons and neutrons (Z + N) in the nucleus. The various nuclides are displayed in the ›chart‹ or ›table of nuclides‹. In this chart, Z is on the y-axis and N on the x-axis. This means, the chemical elements change along the y-axis, and the isotopes along the x-axis. Isotopes with the same mass number plot along diagonal lines with a slope of -1. Stable isotopes fall into the ›valley of stability‹, in-between isotopes the decay towards this valley. The chart comes in various flavours, each containing various wealths of information regarding the various nuclide properties, such as stability, formation, radioactive decay, etc.

The Chart of Nuclides (CoN) displays the systematics of the core, i.e., the nucleus of the chemical elements. Just like the PSE displays the systematics of the electron shell of the chemical elements. Each chemical element is defined by the number of protons in its core, which is called the atomic number and abbreviated with ›Z‹. The atomic number is plotted along the y-axis in the CoN, i.e., the elements are getting heavier in the positive direction of the y-axis. Isotopes are defined by the number of neutrons in the nucleus of a chemical element. The number of neutrons are plotted along the x-axis in the CoN and abbreviated with ›N‹. This means, each nuclide is defined by a specific combination of Z and N, and the mass-number of a nuclei is the sum of Z+N. This mass number is always an integer, as it only designates the sum of protons and neutrons. The actual mass of a nuclei is close to, but not identical to the mass-number. Only a small number of nuclides of each chemical element are stable, in cases only one, and the most heavy elements even do not have a single stable nuclide.

The vast majority of nuclides are unstable, mostly with short half-lifes of days to hours to less than a milli-second. These radioactive isotopes are lighter and heavier as the stable isotopes and decay either by beta- or beta+ decays towards the stable isotopes with intermediate masses. These decays from lighter and heavier isotopes are the slopes of the valley, ending in the valley itself, which are the stable isotopes with intermediate masses. This is why it is called ›Valley of Stability‹.

✓Nuclide only designates an element core without the electron shell.

✗Isotope only designates the element core without the electron shell.

✓A chemical element is the sum of all isotopes with the same Z.

✓Isotope designates the element core plus its electron shell.

✓A nuclide is defined by its number of protons and neutrons.

✗A chemical element is the sum of all nuclides with the same Z.

✗The PSE is the systematic of the electron shell of elements, the CoN the systematic of the radioactive decay.

✗The PSE is the systematic of the electron shell of elements, the CoN the systematic of the isotopes of the elements.

✓The PSE is the systematic of the electron shell of elements, the CoN the systematic of the cores of the elements.

✗True

✓False

1.6 Modelling Star Formation from a Molecular Cloud

Stars – including our Sun – formed in clusters, not as individual stars. It is possible to model simulations of such star cluster formations within a collapsing molecular cloud. It can then for example be studied how many stars develop a protoplanetary disk and how stable and long-lived such disks are. However, this needs to be taken cautiously, as the models currently might still be too limited for quantitative studies of in particular protoplanetary disks.

So for more for star formation. The formation and abundances of protoplanetary disks can more qualitatively be understood from the simulations.

Smaller star forming regions are more likely to produce stars with protoplanetary disks, while in massive star clusters these are quickly destroyed by nearby stars – if protoplanetary disks form in these regains at all.

✗ca. 0.1 light year

✗ca. 0.5 light years

✓ca. 1 light year

✗ca. 10 light years

✗ca. 15 light years

✗True

✓False

✗… as a single star

✗… in massive star-clusters

✓… in the vicinity with other stars

1.7 Comparing Star Sizes

Stars change their size massively – by many orders of magnitude – during their life cycle. For example, the Sun will become a Red Giant and fit the Earth’s orbit within it.

Hertzsprung-Russell-Diagram. This is the most fundamental classification diagram for stars.

The main sequence/main sequence stars. Red Giant stars. Super-Giant sars. Neutron star. White Dwarfs. AGB (asymptotic giant branch) stars.

✗About the size of the Moon.

✗About the size of Mars.

✓About the size of Venus.

✓About the size of the Earth.

✗True

✓False

✗Up to the orbit of Earth

✗Up to the orbit of Mars

✓Up to the orbit of Jupiter

✗Up to the orbit of Neptune

1.8 Hertzsprung-Russell Diagram

The Hertzsprung-Russell Diagram (mostly only called ›HRD‹) describes the evolution of stars from their birth to death. It is one of the most fundamental diagrams in astronomy. And in fact, the HRD is not one diagram, but comes in various flavours depending on what is plotted on the x- and y-axis. This versatility underlines the fundamental character of the HRD. The Sun plots in the middle of the main sequence, is a G2V star and in the middle of its life cycle. Stars typically start their journey in the lower right (small & cold), travel through the main sequence to the somewhat upper left (hot & larger), then kink to the upper right and become a red giant, super-giant, AGB-star, … (cold & big) – depending on their initial mass. They finally end in the lower left as dwarf, neutron star or black hole, … (hot & small) – again depending on their initial mass.

The evolutionary path of stars from birth to death, i.e., their changes in e.g., size, temperature, luminosity, or colour.

The main sequence/main sequence stars. Red Giant stars. White Dwarfs. AGB (asymptotic giant branch) stars.

✓True

✗False

✗In about the middle of the white dwarfs

✗In about the middle of the AGB stars

✗In about the middle of the Red Giants

✓In about the middle of the main sequence

✗Black Holes

✗Neutron stars

✓AGB stars

✗Red Giant stars

✗main-sequence stars

1.9 Nuclide Binding Energies

The binding energy is a measure for how strong each nucleon (i.e., a proton or neutron) is bonded to another nucleon. The larger the binding energies, the stronger the bond between the nucleons. The difference in binding energies between two nuclides is the energy that is either released or required when one nuclide is formed from the other. One nuclide forms from another in collisions of nucleons or during radioactive decay. Massive amounts of energies are released when light nuclides form heavier nuclides (towards higher atomic numbers). This happens in stars. Still large amounts of energies are released during radioactive decay (towards smaller atomic numbers). The nuclide with the highest binding energy is 62Ni. Nuclides up to 62Ni release energy upon formation, e.g., in stars. Nuclides heavier than 62Ni require energy to form, e.g., in supernovas. The heaviest stable nuclide is 209Bi. The total binding energy of the isotopes increase continuously.

x-axis: all stable nuclides. y-axis: the binding energy of the nuclide, divided by the number of nucleons (= protons + neutrons) in the according nuclide.

Nuclides with increasing mass-numbers up to about Fe have increasing binding energies per nucleon. This means, nuclides fuse togehter as long as their combined mass-number is smaller than Fe. They fuse, because their combined binding energy per nucleon is higher than the binding energy of each of the colliding nucleons. Such fusion process occur ins stars. Nuclides with increasing mass-numbers from Fe on have deceasing binding energies per nucleon. This means, nuclides with a combined mass-number higher than Fe cannot fuse should they collide. This is the case, because the binding energy of the hypothetically forming nuclide is smaller than the binding energies of the colliding nuclides. Nuclides with a higher mass-number than Fe can only form if energy is added. This can happen in e.g., star-explosions, in which neutrons can be added to existing nuclides. Star-explosions are a formation site of many heavy nuclides.

✗208Pb

✓209Bi

✗232Th

✗235U

✗237Pu

✓Fe

✗Si

✓Ni

✓Ti

✗Al

✗56Fe

✗57Fe

✗58Fe

✓62Ni

✗63Ni

1.10 Onion Shell Model of Stellar Nucleosynthesis

All stars start in the same way – with H-burning, i.e., the fusion of H to He. The stars then pass through various lengths of fusion chains, depending on their initial mass. Stars with a mass >10 that of our Sun produce further elements in fusion reactions, up to max. Fe. Heavier elements are produced closer to the core of the star, as these require higher energies to overcome the Coulomb-barrier of the positively charged element cores. These reactions get their energy from the high pressures towards the inner regions of the stars. The change from one burning stage to the next, eg., from H- to He-burning, is continuous. H-, He-, … burning continuous in shells around the inner core. These shells migrate outwards, while the core of e.g., He-burning expands. Over time, an onion-like structure develops in the star with H-burning in the outermost shell and – in the extreme case – Si-burning in the core. Simultaneously, a temperature gradient develops with high temperatures in the core. Elements with higher atomic number than Fe cannot be produced by fusion. This means, once Fe formed, fusion ends. As at this point no more radiation is produced in the core from fusion, the ceasing radiation can no longer balance the hydrodynamical pressure from the inward-directed gravitation. The star collapses (›core-collapse‹) into a supernova.

The pressure inside a H-rich cloud becomes so dense that H atoms overcome their repulsive Coulomb-barrier (repulsion of the positively charged H nuclei (=protons)) and fuse together to He. This fusion marks the birth of a new star.

In the last stage of element fusion in the core of a star Fe is produced. No further element can be produced and fusion ceases. As no more radiation is produced by fusion to counter-balance the gravitational pressure, the core of the star collapses (core-collapse). The infalling material after the core collapse eventually bounce back and into space, which is then a super-nova.

✗0.25 x the mass of the Sun

✗2.5 x the mass of the Sun

✓25 x the mass of the Sun

✗250 x the mass of the Sun

✗True

✓False

✓A few million years.

✗A few hundred million years.

✗A few billion years.

1.11 Presolar Grains – Isotope Compositions

Presolar grains are characterised by their largely different isotope compositions. While solar system materials typically have isotope variations in the maximum permil range of the delta-notation, presolar grains have up to orders of magnitude variations of individual isotope ratios. Typical and large isotope variations are found in e.g., O, C, N, Si, Cr, Ti. The grains are classified according to their isotope composition in various groups that can then be assigned to their origin and formation in e.g., red giants, AGB stars, supernovae, etc. Presolar grains can be isolated after acid dissolution or found using in-situ techniques.

1.12 Presolar Grains – Types and Abundances

Presolar grains originate from other stars, e.g., from red giants, AGB stars, but also from (super)novaes. These grains are then expelled from such stars and added to the ISM. Reprocessing – evaporation & recondensation due to galactic cosmic rays – destroys presolar grains, but about 3% of the ISM survives as original presolar grains (=stardust). These grains can then become part or are being added to protoplanetary disks, where these may end up in meteorites. Presolar grains are sub-µm sized and e.g., SiC, TiC, graphite, nanodiamonds, corundum, etc. – but also silicates. Their abundances are highly variable, but always only in the ppm range.