EAPS 105 Notes: Solar System Origins and Stellar Evolution

About your instructor

• Prof. Andy Freed, Purdue Dept. of Earth, Atmospheric, and Planetary Sciences
• Education and background:
  • B.S. in Mechanical Engineering, Cornell University
  • M.S. in Applied Mechanics, Utah State University
  • 10 years as an aerospace engineer designing rockets, satellites, space stations, and amusement park rides
  • Ph.D. in Geophysics and Planetary Science, University of Arizona
  • Joined Purdue Faculty in 2003
• Research interests: numerical models for plate tectonics, earthquake triggering, asteroid impacts, and volcanic flows on terrestrial planets
• Teaching emphasis: currently teaching introductory science classes due to passion for foundational science

Course overview: topics covered this semester (EAPS 105)

• Unit 1: Solar System Origins
• Unit 2: Planet Formation
• Unit 3: Planetary Motions
• Unit 4: Heating and Cooling
• Unit 5: Volcanism
• Unit 6: Impact Cratering
• Unit 7: Atmospheres
• Unit 8: Minor Bodies
• Unit 9: Moons and Rings
• Unit 10: Exoplanets
• Unit 11: Robotic Spacecraft Missions
• Unit 12: Hazards of Space Travel

Unit 1 – Solar System Origins

• The Pillars of Creation in the Eagle Nebula: a stellar nursery where stars are born
• Part 1: Your Solar System, Galaxy, and Universe
• Part 2: It all started with a Big Bang
• Part 3: The fate of stars
• Part 4: The Nebula hypothesis

Part 1: Your Solar System, Galaxy, and Universe

• Our solar system is one of about 400 billion systems in the Milky Way

• The Milky Way is one of about 4 trillion galaxies in the visible universe

• Scale and distance reminders

• Our solar system location in the Milky Way:

  • The Milky Way is enormous; light takes about 100,000 years to cross the galaxy
  • We live in the “suburbs” roughly halfway between the center and the edge

• The Sun and the solar system contain almost all of the system’s mass

• Mass distribution in the Solar System:

  • The Sun has about $99.86\%$ of the Solar System’s mass
  • Jupiter contains about $70\%$ of the planetary mass
  • Earth’s mass is about $0.2\%$ of the planets’ total mass (not the Sun’s)

• Planet categories (for scale):

  • Terrestrial planets
  • Giant planets
  • Gas giants
  • Ice giants
  • Dwarf planets
  • Major planets

• Distances and astronomical units (AU):

  • 1 AU = distance from the Sun to the Earth ≈ $150\text{ million km}$
  • Distances to outer planets scale as: ~5 AU, ~1 AU, ~0.39 AU, ~1.5 AU, ~0.72 AU, ~19 AU, ~30 AU, ~10 AU, ~30–50 AU, ~2–3.5 AU (examples used to illustrate the scale; not all are exact planetary distances)

• Quiz reminders (sample questions):

  • 1) How much of the Solar System’s mass is contained in the Sun? Answer: Almost all; Sun ≈ $99.86\%$
  • 2) Which planet dominates the planetary mass fraction? Jupiter (~70% of planetary mass)

• Visual context (not to scale in distance or size): The Solar System is not drawn to scale; it’s for understanding relative positions and mass distribution

• Star Wars scene critique (cosmology mis-scale exercise):

  • Starkiller Base shown too close to its star; the star should be much larger in the sky
  • Scene would require Starkiller Base to have a stronger gravitational field than its star
  • Correct answer to the quiz: All of the above

• Starkiller Base distance in the scene: shown more than 25× closer to its sun than Mercury is to the Sun

• The relative size of the Earth and Moon:

  • The Earth–Moon size ratio is about 1:3.7 in diameter; Moon diameter ≈ 0.27 × Earth’s diameter

• The Moon’s distance and eclipse geometry:

  • The Moon is about 30 Earth diameters away from Earth
  • Our Moon is uniquely sized and at an appropriate distance to create a total solar eclipse
  • The Moon is moving away from Earth at about $4\ cm\,yr^{-1}$
  • We are in a cosmic “golden age” of eclipses; future eclipses will resemble what we observe from Mars’ Phobos

• Future eclipse scenario: billions of years from now the Moon will be too far to block the Sun completely

• Summary: scale models illustrate the limits of distance, size, and orbital geometry used in popular media vs. actual astrophysical constraints

Part 2: It all started with a Big Bang

• The universe began with a colossal explosion/expansion of matter from near nothing; details about why/how are not fully known

• Early universe (first 3 minutes) highlights:

  • A proton = hydrogen ion (H+): hydrogen atom missing its electron; positive charge
  • Hydrogen ions emit light when very hot; early universe was extremely bright

• Fusion in the early universe:

  • High pressures and temperatures fused hydrogen into helium
  • Fusion releases heat and light due to mass-to-energy conversion

• Key particles and reactions:

  • Isotopes: Deuterium (¹H with one neutron) and Tritium (³H) formed by adding neutrons to hydrogen
  • Reaction framework: H → He via fusion; mass decreases and energy is released

• Energy-mass relation (Einstein):

  • $E = mc^2$
  • The resulting helium and extra neutrons have slightly less total mass than the original hydrogen isotopes; the mass difference becomes energy

• The universe cooled and electrons + protons combined to form neutral hydrogen atoms (H) at a temperature of about $2{,}700\,\text{K}$, ending the hot, glow era and making the universe dark

• Emergence of the Cosmic Microwave Background (CMB):

  • About 380,000 years after the Big Bang, photons decoupled from matter and the CMB began to travel freely
  • The CMB is the remnant heat radiation from the early universe; now observed as a nearly uniform background with tiny temperature fluctuations that mark density seeds for structure

• Discovery of the CMB:

  • 1964: Arno Penzias and Robert Wilson detected the CMB's relic signal; Nobel Prize awarded

• Re-emergence of light and structure formation:

  • ~150 million years after the Big Bang, molecular hydrogen clouds clumped, reaching densities/pressures sufficient for hydrogen-to-helium fusion in new stars; light re-emerged in the cosmos

• Cosmological expansion and age estimates:

  • By tracing the expansion of the universe backwards, current estimates place the age at ~$13.8\text{ billion years}$
  • Expansion is accelerating; space itself is expanding everywhere, and distant objects recede faster than light due to the expansion of space

• The observable universe and causal history:

  • We can observe distant galaxies and extrapolate their history backward
  • The Hubble Deep Field demonstrates how long exposures reveal faint, distant galaxies and help reconstruct early cosmic history

• Distance is time: light travel time links observed distance to look-back time; the farther away an object is, the further back in time we see it

• The James Webb Space Telescope (JWST) Deep Field observations reveal a wealth of distant galaxies and gravitational lensing features; many distant galaxies appear stretched into arcs due to gravitational lensing

• Cosmic web and galaxy distribution:

  • The observable universe hosts an estimated ~2 trillion galaxies; their distribution forms a filamentary structure, reminiscent of brain networks (cosmic web)

• The Cosmic Microwave Background and the seeds of structure anchor our understanding of the early universe

• Key takeaways about the Big Bang timeline and evidence:

  • Early universe bright due to ionized hydrogen and fusion
  • CMB as a fossil of the hot, dense early universe
  • Expansion and subsequent structure formation leading to galaxies, stars, and planetary systems
  • Distance-time relation aids in inferring cosmic history

• Quiz-style reminders about cosmology (sample):

  • Stars and galaxies have been forming and dying for 13.8 billion years; how do we know this history? Through observations today and extrapolation back in time; direct observation of remnants and distant light provides the chain of evidence
  • Deep-field observations require long exposures to detect faint, far-away objects

• Stars, galaxies, and cosmic time visuals:

  • The JWST Deep Field image shows a universe rich with distant galaxies; many are stretched due to gravitational lensing
  • The deeper we look, the more galaxies and cosmic history we uncover

• Origin of the CMB visuals and cosmic seeds:

  • The CMB is a snapshot of the universe at ~380,000 years old; current fluctuations correspond to early density inhomogeneities that formed future structures

Part 3: The fate of stars

• Stars fuse hydrogen into helium (and some heavier elements) in their cores, powering their luminosity

• Photon travel times in the Sun:

  • From the Sun’s surface to Earth: ~8 minutes
  • From the core to the surface: can take up to ~100{,}000 years due to dense stellar material

• Stellar diversity:

  • Red dwarfs, Sun-like stars, red giants, etc.
  • Red dwarfs (M-type) are the most common star type; they are cooler and dimmer but extremely long-lived

• Stellar lifetimes and end states:

  • Low-mass stars (like the Sun) eventually exhaust core hydrogen and evolve through helium burning to form carbon and oxygen; heavier elements require higher core pressures
  • Typical fusion pathways in low-mass stars progress to oxygen as the heaviest element fused in their cores

• Red giants and stellar expansion:

  • As fusion wanes, outer layers expand and cool; star becomes redder and larger
  • Our Sun is expected to become a red giant with a diameter ~500× its current; Earth’s fate is tied to this expansion

• Final stages of low-mass stars:

  • Core collapses to a white dwarf (roughly the size of Earth)
  • Outer layers are ejected, forming a planetary nebula (glowing hydrogen gas)

• Planetary nebulae:

  • The term is historical and not directly related to planets; coined by William Herschel due to visual similarity to gas giants

• White dwarfs and their evolution:

  • White dwarfs are dense cores of carbon and oxygen; remnants emit residual heat and glow; over extremely long timescales they cool to become black dwarfs (whether they exist yet is uncertain due to universe’s age)

• Neutron stars and pulsars:

  • Extremely dense neutron-rich matter; pulsars emit beams of radiation from magnetic poles and appear to pulse as the star rotates
  • Densities ~$10^{14}$–$10^{15}$ times that of Earth

• Black holes and their signatures:

  • Densities and gravitational effects are extreme; light cannot escape from within the event horizon
  • Evidence via gravitational lensing, accretion disks, and X-ray emissions from heated matter around the hole

• Massive-star evolution and iron core:

  • In very massive stars, fusion proceeds to heavier elements up to iron; iron fusion is not energetically favorable, leading to core collapse and dramatic supernova explosions

• Supernovae and heavy-element production:

  • Core-collapse supernovae perfume the universe with heavy elements; the Crab Nebula is a remnant example
  • Type II (massive stars) and Type Ia (white dwarfs accreting from companions) supernovae contribute to chemical enrichment

• Types of supernovae and their roles:

  • Core-collapse (massive stars) produce neutron-rich elements; some proceed to black holes
  • White dwarf accretion-driven (Type Ia) supernovae create heavy elements and standardizable luminosities for cosmology

• Neutron star mergers (kilonovas):

  • Collisions of neutron stars emit heavy elements and often form black holes; significant sources of elements heavier than iron

• Cosmic alchemy and the phrase "We are made of star stuff":

  • Elements in our bodies and planets originate from stellar fusion and explosive processes

• Key figures and data:

  • Supernova rate in a typical galaxy: about one supernova every ~50 years
  • In the observable universe (≈2 trillion galaxies), supernovae occur frequently enough that their cumulative rate is enormous; a rough statement is that a supernova occurs roughly every second somewhere in the observable universe

• Quick reference: life cycles and end states in a schematic flow:

  • Low-mass stars: Hydrogen core fusion → Helium → Carbon/Oxygen → White Dwarf → (possible Planetary Nebula outflow) → Black Dwarf (hypothetical)
  • Massive stars: Fusion up to iron → Core collapse → Core-collapse supernova → Neutron star or black hole

• “Origin of elements” diagram (origin story for Solar System elements):

  • Big Bang produced H and He; subsequent stellar processes and supernovae produced heavier elements (Li, Be, B formed by cosmic ray spallation and other pathways)
  • Heavier elements (C, N, O, etc.) formed in stars and exploded into the interstellar medium, becoming part of new star systems and planets

• Notable quotes:

  • "We are made of Star Stuff" — Carl Sagan

Part 4: The Nebula hypothesis

• The Solar Nebula hypothesis: solar systems form as part of the cycle of star birth and death
• Stellar remnants and nebula formation:
  • Supernova remnants spread gas and dust that coalesces into nebulas
  • Emission nebulas glow due to hot, ionized hydrogen (H+) gas
• Molecular clouds and dark, star-forming regions:
  • As nebulas cool, H2 forms and becomes molecular clouds that do not emit light but can reflect starlight
• Star-forming regions and clumping:
  • Gravity perturbs molecular clouds, causing clumps to contract and heat up to ignite hydrogen fusion in new stars
• Pillars of Creation (Eagle Nebula):
  • A prominent star-forming region with pillars approximately 4 light-years tall
• Other famous nebulas:
  • Horse Head Nebula
  • Statue of Liberty Nebula
• Galaxy context: the Whirlpool Galaxy contains a mix of emission nebulas and molecular clouds; star formation and death cycles occur within galaxies
• Gravity and angular momentum in star formation:
  • Newton’s law of gravity: $F<em>{grav} = \dfrac{G m</em>1 m_2}{r^2}$
  • Conservation of angular momentum: $L = m r \omega$
  • As a contracting nebula clump shrinks in radius, its rotation speeds up (like a figure skater)
• Why nebulas contract into stars:
  • Gravity pulls matter inward, overcoming internal pressure until fusion ignites
• Formation of accretion discs:
  • As a protostar forms, conservation of angular momentum and collisions between particles flatten the surrounding material into a disc
  • The disc is flattened due to collisional damping of vertical motions; this is not solely gravity or angular momentum but the combined effect of collisions and angular momentum transport
• Flattened accretion discs lead to planetary system formation; planets form within these discs
• End-of-unit quiz-style prompts (sample concepts):
  • What physical process causes nebula contraction into stars? (Gravity) + (Conservation of angular momentum) + (Perpendicular collisions) → All above
  • Why do accretion discs spin rapidly? (Conservation of angular momentum)
  • Why are accretion discs flat? (Gravity + angular momentum + collisional damping)
• Visuals:
  • Fly-through of Orion Nebula (3-D model from telescope data) illustrating star-forming activity

Additional cross-cutting concepts and connections

• Scale and perspective:
  • The universe operates on scales from planetary orbits (AU) to galaxy clusters (light-years, billions of years)
• Evidence-based science:
  • Observations (spectra, redshifts, CMB, deep field images) underpin cosmological models and solar system formation theories
• Interdisciplinary links:
  • Physics: gravity, thermodynamics, quantum processes in stellar cores
  • Chemistry: nucleosynthesis and elemental abundances
  • Earth and planetary science: formation of terrestrial planets and volatile delivery
• Practical implications:
  • Understanding space weather, planetary habitability, and the potential for exoplanets with life-supporting conditions
  • Ethical and philosophical reflections on our place in the cosmos, informed by cosmic time scales and the interconnectedness of matter

Quick reference: key numerical and symbolic details (LaTeX)

• Sun’s share of Solar System mass: $99.86\%$
• Jupiter’s share of planetary mass: $\approx 70\%$
• Earth’s share of planetary mass: $\approx 0.2\%$
• 1 AU = $1.50\times 10^8\text{ km}$
• Light travel times: photons from the Sun reach Earth in about $8\text{ minutes}$; core-to-surface photon diffusion timescale in the Sun can be up to $10^5\text{ years}$
• Milky Way: ~$4\times 10^{4}\text{ ly}$ scale; light crossing time ~$10^5\text{ years}$ across galaxy
• Age of the universe: $13.8\times 10^9\text{ years}$
• Galaxy/Universe counts: ~2 trillion galaxies in the observable universe; Milky Way has ~4×10^11 stars (rough figures used in slides)
• CMB: relic radiation present at ~380{,}000 years after the Big Bang; current T ∼ 2.7 K
• Supernova rate: ~1 per galaxy per ~50 years; universe-wide rate implied by the number of galaxies in the observable universe
• Pillars of Creation height: ~4 light-years
• Nebula and accretion-disc mechanics: $F<em>{grav} = \dfrac{G m</em>1 m_2}{r^2}, \quad L = m r \omega$
• Notation recap: H, He, Li, Be, B as light elements; heavier elements formed in stars and dispersal events

Summary takeaways

• The Solar System’s origin is tied to the larger context of the Milky Way and the observable universe, with key mass distribution in the Sun and the planets
• The Big Bang provides the framework for cosmic evolution, with the CMB serving as a fossil signal of the early universe and current expansion driven by cosmic dynamics
• Stars live on a lifecycle governed by gravity, fusion, and nucleosynthesis; their deaths seed the cosmos with heavy elements, enabling planet formation and the potential for life
• Nebulae and accretion discs explain how stars form and how planetary systems emerge, including the physics of angular momentum and flattening
• The course weaves together observational evidence, physical laws, and cosmic timelines to build a comprehensive view of how the Solar System and universe came to be