Our Place in the Cosmos Lecture 12 Stellar Evolution

We saw in the last lecture that all main sequence stars generate their energy by fusing hydrogen into helium in their cores The Sun, a typical main sequence star, fuses over 4 billion kg of hydrogen to helium each second Eventually (in about 5 billion years time) that hydrogen will be exhausted, and the Sun will evolve off the main sequence The same will happen to all main sequence stars

Stellar Evolution Just as mass determines the other properties of a main sequence star (luminosity, size, temperature), the eventual fate of a star is also pre-ordained by its mass, which is locked in place when the star forms Chemical composition also plays a secondary role in a star’s properties and fate Each star is thus unique - minor differences in mass and composition can result in significant differences in fate Low and high mass stars evolve differently

Main Sequence Lifetime If one were to add mass to the Sun, the extra weight of material pushing down would compress its core, driving up temperature and density Nuclear reaction rate would increase as nuclei collide more frequently and with higher energy A modest increase in pressure can lead to a dramatic increase in energy production and hence luminosity

Main Sequence Lifetime This is why main sequence is primarily a sequence of masses More mass  stronger gravity  higher temperature and pressure  faster nuclear reaction rates  higher luminosity Hence more massive stars lie further up and to the left on the main sequence

Main Sequence Lifetime The length of time a star can continue fusing hydrogen to helium, its main sequence lifetime, depends on The amount of hydrogen available The rate at which hydrogen is fused into helium More massive stars contain more fuel, but the rate at which the fuel is used up, as measured by the luminosity, is also higher

Main Sequence Lifetime The main sequence lifetime is equal to the amount of fuel available (proportional to mass) divided by rate at which fuel is used (proportional to luminosity) The Sun has an estimated MS lifetime of ten billion years For other MS stars, lifetime is given by

Main Sequence Lifetime Luminosity increases very rapidly with mass The most massive stars (about 60 times more massive than the Sun) have luminosities 794,000 times greater and lifetimes below 1 million years In general, more massive stars are shorter-lived than less massive stars

Main Sequence Evolution As the hydrogen within a main sequence star is fused into helium, its composition gradually changes and it evolves slowly up the main sequence, gaining in luminosity The Sun’s luminosity will roughly double between first joining and leaving the main sequence Helium cannot be fused into heavier nuclei in a main sequence star due to four times stronger electrostatic repulsion between helium nuclei compared with hydrogen nuclei Helium simply accumulates within the core of a star, like the ash in a fireplace

Helium “ash” accumulates most rapidly in the centre of a star where reaction rates are highest Sun was initially 30% helium throughout Today, the Sun’s centre consists of 65% helium, 35% hydrogen In about 5 billion years time no hydrogen will remain at the centre

Farewell Main Sequence Once all hydrogen is exhausted in the core of a star, no more energy is generated and the star is no longer in equilibrium and is no longer on the main sequence How a star subsequently evolves depends on its mass The rest of this lecture will discuss the evolution of low mass stars, those less massive than about 3 M  The evolution of massive stars will be discussed in the next lecture

Degenerate Helium Core No hydrogen burning  lower pressure  gravity wins Core becomes extremely dense until it becomes electron degenerate (around 1000 kg per cubic centimetre) Although core is “dead”, hydrogen can still burn in a shell around the core - shell burning As shell deposits more helium “ash” on the core the core shrinks due to extra weight of material

Post-Main Sequence Evolution Just outside helium core the gravitational acceleration is given by g core = G M core /r 2 core As more helium “ash” is deposited onto core it both increases in mass M core and decreases in radius r core Both cause gravity at core’s surface to increase Stronger gravity increases pressure within hydrogen-burning shell thus increasing shell burning rate and hence luminosity of star As a star runs out of nuclear fuel it becomes more luminous!

Subgiant Stage As the degenerate core grows and the shell- burning rate increases, the surrounding layers of the star are heated and expand As the star’s surface expands it becomes more luminous but also cooler The star becomes a subgiant - luminous but red in colour The star moves above and to the right of the main sequence on the H-R diagram until its surface temperature has dropped by about 1000K

Red Giant At this point the formation of H - ions (hydrogen atoms with 2 electrons) regulates how much radiation can escape - just as greenhouse gases in the Earth’s atmosphere trap in heat The star is now a red giant - it can no longer cool and moves almost vertically up the red giant branch on the H-R diagram as it grows larger and more luminous but remains at the same surface temperature

Giant Evolution It takes around 200 million years for a star like the Sun to evolve from the main sequence to the top of the red giant branch, starting slowly, then evolving at a rapidly increasing rate In the first 100 million years the star’s luminosity increases to about 10 L  to become a subgiant In the remaining 100 million years the luminosity skyrockets to almost 1000 L  As mass accumulates on core hydrogen shell burning rate increases (positive feedback)

As core gains mass and shrinks, shell burning increases and the outer parts of the star swell up

Helium Burning As core shrinks it becomes hotter Eventually the helium nuclei are moving energetically enough to combine together to form carbon

Helium Flash The degenerate core behaves more like a solid than a gas so heat from helium burning rapidly spreads through core with no accompanying expansion Rapidly rising temperature within core leads to a chain reaction known as the helium flash Within just a few seconds the core explodes The energy released lifts the outer layers and core is no longer degenerate The expanded core now has a much weaker surface gravity  lower pressure  slower nuclear reactions  lower luminosity

Horizontal Branch Star The star is now stably burning helium to carbon in a non-degenerate core and burning hydrogen to helium in a surrounding shell Stars in this phase have a narrow range of luminosities, about one hundredth of their luminosity at the time of the helium flash, but still much more luminous than their main sequence stage They are know as horizontal branch stars from their locations on the H-R diagram, where they remain for about 50 million years

Asymptotic Giant Branch Star As helium is depleted in the core, gravity again wins over pressure and degenerate carbon core is surrounded by helium and hydrogen burning shells As before, star grows larger and redder, following a path close to the red giant branch known as the asymptotic giant branch (AGB) Core temperatures are too low for carbon fusion and AGB star starts to lose outer envelope This is heated by hot degenerate core and glows as a spectacular planetary nebula

Planetary nebulae are so-called because they look like planets when seen through small telescopes HST reveals their beautiful structure