Astronomy 100

Lectures

Table of Contents

Astro 100

Lecture 15
Power Sources: How do Stars Shine?

Outline

A Beautiful Balance: Gravity vs. Pressure
Stars are Nuclear Reactors
Stellar Structure
The Life of a Star

Terms to Know

fission
fusion
4 forces of Nature (gravity, electromagnetism, strong, weak)
binding energy
E=mc²
neutrino
convection
mass-lifetime relation

1. A Beautiful Balance: Gravity vs. Pressure

Stars are balanced! Two forces are exactly equal and opposite in most stars: Gravity pulls in (like the rubber of a balloon) while pressure pushes out (like the air inside the balloon).

The force of gravity at the center of a star is immense, billions of times greater than at the bottom of the deepest ocean trench on Earth. How can a star possibly support that weight?

Gravity compresses gas gas heats up star ignites nuclear fusion in core releases energy provides pressure support (and makes star shine!) stops gravitational collapse.

2. Stars are Nuclear Reactors

Nuclear fusion is the process of combining (or fusing) light nuclei (such as hydrogen nuclei, which are just single protons) into heavier nuclei (such as helium). It is the energy source of stars! Fusion is the opposite of fission, the process used in nuclear energy generators here on Earth; in fission, heavy elements are broken apart to form light elements.

The stars, including the Sun -- as well as most of the Universe -- are made up of around 75% H and 25% He.

The end product of fusion (e.g., a helium atom) is a tiny bit lighter than the ingredients that go into the process ( why? ). This miniscule mass is converted into pure energy according to Einstein's famous equation, E=mc². The energy escapes in the form of photons (light) and neutrinos, which are like light but which don't interact strongly with matter (and they also probably have a tiny bit of mass, which photons don't).

The amount of energy released per reaction is very small: 4.3 x 10^-5 ergs (1 erg = 1 mosquito hitting your forehead). But the huge number of fusion reactions taking place in a typical star every second makes the total luminosity very large.

The two common processes for converting H to He are the "pp chain" (proton-proton) and the "CNO cycle" (carbon, nitrogen, oxygen).

Note that fusion is totally different from chemical reactions such as combustion (fire), which are merely breaking electromagnetic bonds between molecules or between atoms in molecules. Fusion is much more powerful and requires much hotter temperatures -- millions of degrees K.

In fusion, the strong force of physics comes into play. Like charges -- such as two protons -- repel each other via the EM force, but if you can get them close enough together, the strong force will "latch on" like Velcro and bind them to each other.

How do you get them that close together? Heat them up so they fly around very fast and crash into each other! That's what the gravity of stars does, and that's why stars need to be hot to work.

3. 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

Core, with temperature 10,000,000 K -- the fusion "pressure cooker"
Radiative zone, in which photons bounce around and outwards towards the ...
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.

4. 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 (LM^3.5) is so steep (exponent = 3.5), the lifetime of a Main Sequence star is = (fuel available/rate of consumption) = M/L M/M^3.5 or M^-2.5. (Low mass long life, high mass short life.)

Example: A main sequence star with mass M=5 M_Sun 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 M_Sun 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.