The Life of Stars

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Lecture 4: The Life of Stars

Lecture 4 The Life of StarsDownload

Last lecture, we explored the structure of our solar system. Now we turn to the true protagonists of cosmic evolution: stars.

What is a Star?

A star is a giant ball of gas undergoing nuclear fusion, primarily converting hydrogen into helium at its core. The Sun, our local star, is just one among an estimated 100 billion in the Milky Way galaxy, and there are likely 100 billion galaxies in the observable universe.

Nuclear Fusion

  • Core fusion happens in the central 15% of the star’s volume.
  • The dominant fusion process in stars like the Sun is the proton-proton chain:
  1. Two protons fuse to form deuterium (one proton, one neutron).
  2. Deuterium fuses with another proton to create helium-3.
  3. Two helium-3 nuclei fuse to create helium-4, releasing energy.

This process releases energy because of mass conversion: $E = mc^2$. The amount of mass lost in each reaction is tiny but, multiplied by the number of reactions in the Sun, becomes vast.

Energy Output

  • Fusion of 1 kg of hydrogen yields $~620 \text{ trillion joules}$, millions of times more than chemical combustion.
  • The Sun outputs the energy equivalent of millions of nuclear bombs every second.
  • Its fuel supply is sufficient for a 10-billion-year lifespan.

Stellar Lifespan

How Do We Know the Sun’s Age?

  • The Sun formed from remnants of a Population II star that underwent a supernova.
  • Radioactive dating of elements like uranium and lead in meteorites and zircons tells us the age of the solar system: 4.5 billion years.
  • The Sun is middle-aged.

Life Cycle of Stars

  1. Protostar: gravity pulls gas together.
  2. Main sequence: hydrogen fusion balances gravity.
  3. Red giant (for low-mass stars) or supergiant (for high-mass stars).
  4. Final stages:
  • Low-mass stars: become white dwarfs.
  • High-mass stars: undergo core-collapse supernova, leaving behind neutron stars or black holes.

You Are Made of Stars

Elements heavier than helium—carbon, oxygen, iron—were produced in ancient stars and spread by supernovae. This is why Carl Sagan said:

“We are made of star stuff.”

Classifying Stars

Stars are classified via:

Hertzsprung-Russell (H-R) Diagram

  • Main sequence: stars fusing hydrogen to helium.
  • Giants: cooler, larger stars.
  • White dwarfs: hot, dense remnants of low-mass stars.

Spectroscopy

  • Reveals chemical composition, temperature, and radial velocity.
  • Used in Doppler shift calculations.

Motions and Orbits

  • Planets orbit stars; stars orbit galaxy centers.
  • The Earth orbits the Sun at ~30 km/s.
  • The Sun orbits the Milky Way center at ~220 km/s.

Proper Motion

  • Barnard’s Star has the highest known proper motion: shifts by 1 degree every 350 years.

Kepler and Newton

Kepler’s Laws

  1. Planets move in elliptical orbits.
  2. Equal areas swept out in equal times.
  3. $T^2 \propto r^3$ (orbital period squared proportional to radius cubed).

Newton’s Universal Law of Gravitation

  • Gravity explains Kepler’s laws.
  • Distant planets move slower in their orbits.

Stellar Dynamics in the Galaxy

  • The Sun takes hundreds of millions of years to orbit the Milky Way center.
  • All stars experience motion: radial (toward/away) and tangential.
  • These motions combine to give the star’s proper motion.

Observational Tools

  • Doppler Shift: measures motion via frequency change.
  • Parallax: measures distance via geometric triangulation.
  • Luminosity & Flux: measures intrinsic and observed brightness.

Final Concepts

  • Globular clusters: tight, spherical groups of ~1 million stars orbiting the galaxy.
  • These structures helped prove we are not the center of the galaxy.

In the next lecture, we explore how stars aggregate into galaxies and uncover the mysterious dark matter that governs large-scale cosmic structure.

Stay curious.

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