Stars: Properties and Evolution

Introduction to the topic

Nearly everything you see around you was manufactured in stars. Stars assemble hydrogen atoms into heavier atoms, a process called "stellar nucleosynthesis". In cool environments, atoms connect up to form molecules. Molecular-based life (the only type we know) seems to require complex carbon-based molecules. Life as we know it could not have started before a generation of stars had expired and ejected its heavy elements into space. Due to the importance of atoms in the scheme of our existence, this unit on stars will concentrate on how stars evolve and manufacture elements heavier than hydrogen.

A few notes on jargon

In astrophysics, the terms "heavy elements" and "metals" are not well-defined. Usually they apply to all elements apart from hydrogen. Lithium is a tricky one because it was synthesized in the early universe shortly after the Big Bang, but is destroyed in stars.

We attach an adjective to the word "nucleosynthesis" to differentiate between different environments. Therefore, Big Bang nucleosynthesis is different from stellar nuclesynthesis, is different from explosive nucleosynthesis. The actual physical mechanism, collisional reactions (aka "fusion"), is the same in all cases, but the host environments are different.

The exception to the collision mechanism is hydrogen. Hydrogen was probably formed as a result of an asymmetry in a particular creation-annihilation quantum fluctuation process during the first minute or so of the lifetime of the universe.

Star Formation

During cloud collapse, once the temperature gets high enough for hydrogen to be fused into helium, we say that a star is born.

The fusion reaction is:

    4 H -> 4 He + energy
or in words, four hydrogen nuclei collide to produce a single nucleus of helium-4. Helium-4 consists of 2 protons and 2 neutrons in a nucleus. This fusion reaction produces energy. The released energy becomes heat inside the star, which allows further fusion reactions to occur. In other words, fusion is a self-sustaining reaction.

At the onset of fusion, this new source of energy inside the star will completely halt the collapse. At this moment, the star balances itself, so that gravity pulling inwards exactly balances pressure pushing outwards. The star is in equilibrium, and its mass will remain constant or perhaps decrease a little.

Fusion reactions only take place in the central portion of the star, a region called the core. The rest of the star is called the atmosphere. At the start of a star's life, the core is quite small, occupying only a few percent of the size of the star. As heavy elements accumulate, fusion moves outwards, so that by the end of the star's life, more than half can be the host of fusion reactions.

Stellar Evolution

Stellar evolution is most easily seen on a diagram that plots the brightnesses of stars against thier temperatures. Such a diagram is called a Hertzsprung-Russell Diagram, or HR diagram. We will return to this diagram later.

Stars are distinguished by their mass - other properties can be determined or derived based on a star's mass. Stellar masses range from 80 MSun to 0.01 MSun. We noted earlier that stars "burn" hydrogen into helium to release energy (here, I use the word "burn" to refer to fusion, although the usage is not strictly correct). This burning occurs in the core of the star. The hydrogen core-burning stage of a star's life is called the main sequence stage. During the main sequence stage, helium will collect in the stellar core over time. It is the changing chemical composition of the star drives stellar evolution. The main sequence stage is by far the longest stage of a star's life, occupying more than 90% of a star's total lifetime.

When about 10% of the hydrogen is burned, then hydrogen burning moves to a shell outside the core. The star's atmosphere expands and cools and the star becomes a red giant - we say that the star is ascending the asymptotic giant branch (AGB) and is an AGB star. We can chart the changing brightness and surface temperature of the star on the HR diagram.

During the AGB phase the core continues to heat up until helium ignites. Helium can be burned in the core to produce carbon. During the core He-burning stage the star settles onto the horizontal giant branch of the HR diagram.

Carbon itself can be burned, and in fact there is a series of fusion products that can be burned to produce a heavier species. The basic fusion ladder looks like this (the other elements lighter than iron (Fe) are produced in secondary reactions):

    H -> He -> C (all stars) -> Ne -> O -> Si -> Fe (stop).

All stars will produce carbon. The production of heavier elements than carbon will depend upon the mass of the star, with more massive stars able to travel further along the fusion chain. Through other collisional or decay processes, all the elements up to iron are produced (with the exception of lithium which is destroyed in stars). Eventually, all stars will run out of fuel and then experience a mass-loss phase.

Stellar Mass Loss Phase

The mass-loss phase is important. So far we have seen how stars produce the heavy elements up to iron (Fe), but these atoms are still locked up inside the star. We need a way of getting these atoms out of the star and into interstellar gas clouds. These clouds, now enriched with heavy elements, will form the next generation of stars and planets which can use these elements in complex chemical reactions.

The mass-loss mechanisms depend upon the star's initial mass:

  • Stars with mass < 8 MSun will eject their atmospheres to form a planetary nebula, and the core will cool and contract to become a white dwarf (mostly C or O), core mass < 1.4 MSun. A planetary nebula occurs when the star gets so large that gravity can no longer hold onto the outer layers. Pressure will push them off and they expand outwards.
  • Stars with mass > 8 MSun will explode as a supernova. This explosion happens when the iron core collapses under its own weight. With no internal support, the outer layers of the star explode. The heat of this explosion is so intense that many, many new elements heavier than iron are formed, including nickel, gold and silver. This process is called explosive nucleosynthesis. There is also a remnant left behind, whose properties are based on the core mass:
    • core mass = 1.4-3 MSun yields a neutron star, basically a large ball of neutrons not unlike a giant atomic nucleus.
    • core mass = 3-5 MSun yields a quark star, a large ball of quarks with basically unknown properties. No one has ever discovered a quark star.
    • core > 5 MSun yields a black hole, a collapsed object whose gravity is so intense that light cannot escape.

Stellar (Main Sequence) Properties With Mass
MassTempRadiusLuminosity tMS
40 MSun35,000 K18 RSun 320,000 LSun106 yrs
1721,000813,000107
713,50046308 107
28,1002202 109
15,800111010
0.22,6000.320.0079 5 1011

Note on stellar lifetimes

See that large stars have very short lifetimes. Intuitively one would think that a larger has more fuel and therefore might live longer, but such is not true. Instead, massive stars are so much hotter that the fuel they have is burned much more rapidly. The result is that stellar lifetimes vary inversely with mass, in a proportion that is shown below. Note that small changes in stellar mass result in large changes in luminosities and lifetimes.

A few easy rules:
Main Sequence Luminosity: (L / LSun) = (M / M Sun)   3.45
Main Sequence Lifetime: (t MS / t Sun) ~ M / L ~ M / M   3.45 ~ M   -2.45
  t MS ~ (M / M Sun -2.45 10 10 years