AST 300 Study Notes: Planet + Star Formation

AST 300 Study Notes: Planet + Star Formation

Overview of Solar System Formation

  • The formation of the Solar System involves several key processes and events.

  • Sun Ignition: The Sun ignites when nuclear fusion begins, clearing the protoplanetary disk of gas and dust.

  • Inner Planets: Despite the Sun igniting, objects in the Solar System were still in motion, leading to gravitational instability.

  • Late Heavy Bombardment (LHB): Occurred approximately 4 billion years ago, characterized by:
      - A significant number of impact events on inner planets.
      - Possible effects include:
        - Delivery of water to Earth.
        - Causing Venus to rotate retrograde.
        - Displacing Uranus, resulting in an axial tilt.
        - General chaos in the inner solar system.

Systems with Hot Jupiters

  • Migration Inward: Pertains to the movement of large gas giants towards their stars, influenced by several factors:
      - Disk: The presence of a protoplanetary disk affects migration.
      - Eccentricity: Planets can have varying eccentric orbits during and after migration.
      - Ex Situ Formation: Planets that form beyond the frost line are later drawn in.
      - In Situ Formation: Direct formation takes place in their current positions.
      - Tidal Migration: Gravitational interactions with the disk can influence planetary orbits.
      - Disk Disappearance: The phase when the protoplanetary disk dissipates.

Class Assignment: Star and Planet Formation Summary

  • Task: Write a narrative detailing the formation of the Sun and planets, using specified key terms:
      - Key Terms: protostar, angular momentum, ices, optically thin, gravity, rocky planet, accretion, hydrogen, Jeans Mass, protoplanetary disk, condensation, Main-Sequence, metals, fragmentation, moons, density, fusion, gas giant, optically thick, pressure, Zero-Age Main Sequence (ZAMS), Giant Molecular Cloud (GMC), rocks, helium, free-fall.

  • Hertzsprung-Russell (HR) Diagram Plot: Include a sketch representing the Sun's evolutionary track.

High Mass Stars and Star Formation

  • High Mass Stars: These stars reach the Main Sequence (MS) first, affecting the formation of other stars:
      - Pros:
        - Influence on surrounding gas dynamics, promoting more star formation.
        - Create stellar winds that may help clear the region for cleaner stellar formations.
      - Cons:
        - Their strong radiation can inhibit the formation of new stars in their vicinity.
        - They may disrupt forming systems with their supernova explosions.

Study of Stromgren Spheres

  • Definition: Regions around O-type stars where hydrogen gas is ionized, creating an optically thin area.

  • Key Parameters:
      - Stromgren Radius (R_S): The size of the ionized region.
      - Photon Production Rate (Q*): The rate at which the star produces ionizing photons, measured in photons/sec.
      - Recombination Coefficient (α(T_e)): Determines how easily electrons and protons recombine to form neutral hydrogen.
      - Electron Density (n_e): Represents the number of free electrons per unit volume.

In-Class Math Problem: Size of Stromgren Sphere

  • Given Data:
      - Nebular Temperature: T_e = 10^4 K (104 K).
      - Recombination Coefficient: α = 2.6 x 10^{-19} m³ s^{-1}.
      - Rate of Ionizing Photons from O star: Q* = 5 x 10^{48} s^{-1}.
      - Typical Nebular Density: n_e = 10^7 m^{-3}.

  • Calculation: Solve for R_S using the Stromgren sphere formula:

Stellar Evolution

Stellar Evolution Tracks

  • As stars go through their life cycles, observable properties such as luminosity and temperature change, which are plotted in HR Diagrams.

  • Main Sequence Life:
      - Stability: A star remains on the main sequence for about 80-90% of its life.
      - Evolutionary Changes: Stars do not remain identical; core composition changes significantly during this phase.
      - Core Fusion Process:
        - Hydrogen converts to helium, raising mean molecular mass, leading to increased core pressure.
        - The relationship described by the ideal gas law requires that either central temperature (T_c) or central density (ρ_c) must increase.
        

Main Sequence Characteristics

  • Stars increase in luminosity and radius during their main sequence lifetime while effective temperature decreases due to the core's heating dynamics.

  • For the Sun, this phase lasts roughly 9.8 Gyr after reaching ZAMS.

Evolution on the HR Diagram

  • Once the hydrogen core is depleted, hydrogen fusion transitions to occur in a shell around the core, leading to changes in luminosity and radius affecting the star's position on the HR diagram.

Shell Hydrogen Fusion Period

  • After the core depletes its hydrogen reserves, it becomes isothermal:
      - Isothermal Region: The temperature remains constant for inner parts; density must increase towards the core to support material above in hydrostatic equilibrium.
      - Schönberg-Chandrasekhar Limit: Defines the maximum mass fraction for an isothermal core.

Transition to Red Giant Branch

  • Key Changes:
      - The core collapses if it exceeds the Schönberg-Chandrasekhar limit, leading to rapid stellar evolution.
      - Characteristics of a 1 M¤ star on the Red Giant Branch:
        - Radius: Approximately 170 R¤.
        - Temperature of Photosphere: Approximately 3000 K.
        - Luminosity: Approximately 2300 L¤.

Degeneracy in the Core

  • As the density in the core continues to rise, electrons become degenerate, influencing stellar behavior:
      - Electron Degeneracy: Governed by the Pauli Exclusion Principle, restricting electron states.
      - Pressure Dynamics: In degenerate gases, pressure does not depend on temperature; electron degeneracy pressure stabilizes the core as temperature rises.

Helium Flash

  • When temperature reaches about 10^8 K, helium fusion commences, initiating a helium flash:
      - Rapid energy generation changes core dynamics significantly—heat spreads rapidly through conduction.

Horizontal Branch Star Phase

  • After beginning helium fusion, the Red Giant transitions to a Horizontal Branch status:
      - Characteristics of a Horizontal Branch Star (1 M¤):
        - Radius: Approximately 10 R¤.
        - Temperature of Photosphere: Approximately 5000 K.
        - Luminosity: Approximately 100 L¤.

Stellar Fusion Requirements

Fusion Minimum Conditions

Fusion Type

Fusion By-Product

Minimum Core Temp (K)

Min Core Density (g/cm³)

Minimum Stellar Mass (M¤)

Hydrogen

Helium

13 million K

100

0.08

Helium

Carbon, Oxygen

100 million K

100,000

0.5

Carbon

Oxygen, Ne, Mg, Na

500 million K

200,000

4

Neon

Oxygen, Mg

1.2 billion K

4,000,000

~8

Oxygen

Mg, Si, S, P

1.5 billion K

10,000,000

~8

Silicon

Si, S, Ar, Ca, Ti, Cr, Fe, Ni

~3 billion K

30,000,000

~8

Russell-Vogt Theorem

  • It states that "A star’s properties are determined primarily by its mass." If the initial mass of a star is known, its evolution can be broadly predicted.

Stellar Fate Based on Mass Range


  • Different mass ranges dictate the series of fusion processes and the eventual fate of a star:

    Mass Range

    Fusion Process

    Final Fate


    M < 0.08 M¤ | NO FUSION | Brown Dwarf (failed star) | | 0.08 M¤ < M < 0.5 M¤ | H -> He only (Helium)

    White Dwarf


    0.5 M¤ < M < 5 M¤ | H -> He AND He -> C/O (Carbon/Oxygen)

    White Dwarf


    5 M¤ < M < 8 M¤ | H -> He, He -> C/O, C/O -> Ne/Mg

    White Dwarf


    M > 8 M¤

    H -> He, He -> C/O, C/O -> Ne/Mg, Ne/Mg -> Si, Si -> Fe

    Neutron Star; Black Hole

    Stellar Evolution Timescales

    • Duration for Key Fusion Processes:
        - Hydrogen burning: 7 million years
        - Helium burning: 700,000 years
        - Carbon burning: 600 years
        - Neon burning: 1 year
        - Oxygen burning: 6 months
        - Silicon burning: 1 day

    • Nuclear Reactions: Govern the evolution timescale of main sequence stars and post-main sequence stars, influenced by gravity and the Kelvin-Helmholtz timescale as fusion stops and the core contracts.