# Outline

1. Stellar Structure
2. The Life of a Star
3. The Smallest Stars: Brown and Red Dwarfs
4. Sun-Like Stars Red Giants, then White Dwarfs
5. Stars with M>7 MSun: Main Sequence Supernova!
6. How stellar evolution looks on the H-R Diagram

# Terms to Know

brown dwarf
red dwarf
white dwarf
red giant
hydrogen shell burning
helium flash
degenerate matter
planetary nebula
Chandrasekhar limit (1.4 MSun)
neutron star
black hole
supernova

# 1. Stellar Structure

You can use simple equations that describe the mass, gas, and energy in stars to calculate their structure. For an average star like the Sun, you find that there is a
1. Core, with temperature 10,000,000 K -- the fusion "pressure cooker"
2. Radiative zone, in which photons bounce around and outwards towards the ...
3. Convective zone, so opaque that the gas starts to "boil," or turn over and rise up in big bubbles to let the heat escape. Extends about 30% of the way from the surface into the interior.

# 2. The Life of a Star

The mass of a star determines where on the Main Sequence it will spend most (typically 90%) of its life. High mass hot, bright, blue = upper left; low mass cool, dim, red = lower right.

As stars are born, evolve, and die, their luminosities and surface temperatures change -- so they move around on the H-R Diagram. NOTE: This does not mean that they move physically in space, just that their appearance changes with time.

Massive stars consume their fuel much faster than cool stars. Massive stars are like firecrackers, while low-mass stars are like slow-burning embers.

More precisely, since the Mass-Luminosity relation (L M3.5) is so steep (exponent = 3.5), the lifetime of a Main Sequence star is = (fuel available/rate of consumption) = M/L M/M3.5 or M-2.5. (Low mass long life, high mass short life.)

Example: A main sequence star with mass M=5 MSun has lifetime = 5-2.5 = 0.018 times as long as the Sun. It will burn itself out in about 180 million years, much less than it took for life to evolve on the Earth.

Stars with mass M=0.85 MSun have Main Sequence lifetimes about 15 billion years -- about the age of the entire Universe.

The combination of

• the brightness of a star,
• how common that kind of star is, and
• the length of time the star spends in each phase of its life
determines what the H-R diagram looks like.

# 3. Stellar Evolution in a Nutshell

Stars are born when huge clouds of gas and dust get nudged by a passing shock wave (from e.g., a nearby supernova) and collapse under their own gravity. Eventually, the collapse leads to temperatures and pressures high enough to ignite nuclear fusion in the core of the protostar. Leftover gas from the cloud either clumps together to form planets, or else gets blown away by the new star's intense radiation and stellar wind.

The star soon settles into a stable life converting H to He in its core, with gravity and pressure balanced by the "thermostat" of hydrostatic equilibrium. Stars in this long middle-age stage lie on the main sequence of the Hertzprung-Russell Diagram.

What happens when a star uses up its fuel, i.e., converts all the hydrogen in its core to helium? It all depends on the mass of the star:

1. If the mass is much lower than 1 MSun (red dwarfs), the star could live on the main sequence for hundreds of billions of years, much longer than the current age of the Universe! Eventually, it will either blow away its mass (mostly in the form of helium) or contract and turn into a small, hot, ember: a white dwarf.
2. If the mass is close to the Sun's mass, the star will turn into a red giant, and then blow away much of its atmosphere, becoming a planetary nebula and eventually turning into a white dwarf. This is the fate of the Sun.
3. If the mass is greater than about 7 MSun, the star will explode in a spectacular catastrophe: a supernova! The remains are either a tiny neutron star or an even tinier black hole, surrounded by an expanding shell of gas.

# 4. The Smallest Stars: Brown and Red Dwarfs

Some protostars don't even quite make it to star-hood: if its mass is less than about 0.08 MSun, a ball of H and He gas won't have enough gravity to produce the temperature and pressure necessary for nuclear fusion. These luke-warm failed stars are called brown dwarfs.

If the star is just massive enough to ignite nuclear fusion in its core, but not much more, what happens when it uses up its hydrogen? It will contract and heat up -- but not enough to fuse helium atoms together -- winding up as a small, hot, glowing helium ember, emitting black-body radiation and cooling over billions of years: a white dwarf.

Note that very low-mass stars like red dwarfs are fully convective: they mix up their insides constantly like boiling water. Therefore H gets used up throughout the star, not just in the core.

# 5. Sun-Like Stars --> Red Giants, then White Dwarfs

If a star has a mass between about 0.4 MSun and 7 MSun, something different happens when the H runs out in a star's core:
• Now the star has a core of helium, surrounded by hydrogen too cool to fuse.
• No fusion? No pressure support! Gravity takes over again, and the core collapses under the weight of all the gas above it.
• Core heats up as it collapses.
• Eventually, temperature gets high enough to fuse the hydrogen outside the helium core: hydrogren shell burning.
• Surge of energy from the H shell burning makes star's outer parts blow up like a balloon. The star's atmosphere cools at the same time, producing a red giant. Size can be larger than Earth's orbit! Their huge surface area makes red giants bright even though they're not hot.
• Helium core continues to contract until it becomes degenerate (electrons are squeezed together as tightly as possible).
• Degenerate matter heats up without pressure increasing
• When core T finally reaches 100,000,000 K, helium can now fuse to form carbon -- there's a new burst of energy, the helium flash. Star enters new phase of relative stability (though much shorter than main sequence) converting helium to carbon and oxygen in core.

NOW what happens? After the helium is all used up, that's it. Core contracts to degenerate state again, and helium fuses into Carbon in a shell around the carbon core; another red giant phase. Eventually the rest of star blows away in stellar wind, forming a planetary nebula (so called because early astronomers thought they resembled planets; now we know they have nothing to do with each other). The Sun will die this way in about 5-6 billion years.

Note that the maximum mass allowed for white dwarfs is 1.4 MSun; this is the Chandrasekhar limit. If the white dwarf has more mass than that, it will collapse to a neutron star. So stars that begin with more than 1.4 MSun must lose all but that 1.4 MSun during their lifetime if they are going to finish up as white dwarfs.

# 6. Stars with M>7 MSun: Main Sequence --> Supernova!

Really massive stars, like firecrackers, are spectacular but short-lived, and they too go out in a blaze of glory.

When the hydrogen is used up in the core of a massive star (which takes only a few million years for a star with M=20MSun), the star goes through the same stages (core contraction, hydrogen shell burning, envelope expansion, core contraction, helium flash) as solar-type stars. But it keeps on going: the crushing force of gravity is so strong that it can heat up the core enough to fuse carbon into oxygen, oxygen into neon, followed by magnesium, silicon, sulfur, and finally iron, in multiple layers like an onion's.

But when the very interior fuses sulfur into iron, it has reached the end of the line . Further fusion will actually consume energy, not release it, because iron is the most strongly bound of all the elements. The iron core is a dead end.

When fusion in the core stops, pressure support disappears, and gravity takes over once again, crushing the core of the star in less than a second. This is too fast! The tremendous rush towards the center of the star results in a rebound, like a superball thrown against the floor, and most of the star is hurled out into space in a spectacular explosion, a supernova.

What is left behind?

1. a neutron star -- made up of degenerate matter, like a white dwarf, but so dense that protons and electrons are squeezed together to form a soup of neutrons. One sugar cube of neutron soup would weigh 100 million tons.

or

2. a black hole. If the remnant core has more mass than the Chandrasekhar limit (1.4 MSun), not even degenerate neutrons can stop the crush of gravity, and the whole core of the star winks out of sight as it collapses into a black hole. Not even light can escape from a black hole. A black hole with a mass of 1.4 MSun has a radius of only 4 km. Imagine a star more massive than our Sun compressed into a ball the size of the UMass campus.

What about the material that is blown away by the supernova? It drifts about between the stars, possibly collecting into clouds that eventually form new stars later on. This gas consists of lots of "heavy elements" such as carbon, oxygen, silicon, and iron. This is where we came from: every atom in your body has been processed by a massive star!

# 7. How stellar evolution looks on the H-R Diagram

Remember: the mass of a star determines almost everything in its life: its lifetime, luminosity, temperature, eventual composition, and ultimate fate.
• Stars start life as a dust and gas cloud, collapse, begin hydrogen fusion, and show up on the H-R Diagram on the main sequence.
• When the H fuel is exhausted, star puffs up and becomes red giant. Therefore, on H-R Diagram, star leaves main sequence and moves up and to the right (or, if mass is very low, star turns directly into white dwarf, left in H-R Diagram, bypassing red giant phase).
• Star may go through several additional phases (H shell burning, He flash, etc., depending on mass), which cause star to make small loops in H-R Diagram.
• Eventually, star explodes in supernova (luminosity way above ceiling on most H-R Diagrams!) or becomes planetary nebula and then white dwarf: in H-R Diagram, star moves hotter and bluer (to the left), then fainter (lower). White dwarfs cool slowly, moving to the bottom right in the H-R Diagram over time.