4. universe formation

Properties of Stars

• Characterized by the following properties:

  • Surface Temperature

  • Color

  • Size

  • Mass

  • Brightness

  • Energy radiated (Luminosity)

  • Lifetime

• Many of these properties are interrelated.

• Astronomy, being a historical science, utilizes various classification schemes based on different attributes:

  • Brightness

  • Apparent Magnitude

  • Absolute Magnitude

  • Color

  • Temperature

• The Hertzsprung-Russell diagram provides critical insights into star classification and properties.

Hertzsprung-Russell Diagram

• Vertical axis represents Luminosity and Absolute Magnitude.

  • Luminosity: absolute electromagnetic power radiated by a star, usually normalized to solar output.

  • Absolute Magnitude: inversely related to luminosity (higher luminosity = lower absolute magnitude).

• Horizontal axis represents Stellar Temperature:

  • B-V Color Index indicates temperature, where higher values correlate with lower temperatures.

  • Stellar Class categorizes stars from O (hot) to M (cool).

Black Body Radiation and Temperature

• Peak height of black body radiation curves correlates with frequency; higher temperatures result in higher peak energy and frequencies:

  • Frequency (UV to Infrared) relates to the energy output.

Color Index and Temperature

• Color of stars indicates temperature:

  • Hot stars: appear bluer (B-V color index close to 0 or negative).

  • Cool stars: appear redder (B-V color index close to 2.0).

• Calculating B-V Color Index:

  • Measure apparent brightness using B and V filters.

  • Compute magnitude difference: B - V.

From B-V Index to Temperature

• Examples of spectral classes:

  • Class: BOV, Average B-V: -0.30, Temperature: 30,000 K

  • Class: GOV, Average B-V: 0.58, Temperature: 5,940 K

• Formula to find temperature from B-V index:

  • T = 4600 K + 0.92(B-V) + 1.7

Main Sequence Stars

• Sun's luminosity assigned to 1; 90% of stars found on the Main Sequence.

• Higher temperatures correlate to larger mass; stars on this sequence can expand into Red Giants or explode as Supernovae depending on evolutionary stage.

• Stars in the upper right (expanding) and lower left (end of life) of the H-R diagram.

Stages of Star Formation on HR Diagram

1. Protostar forms from a collapsing cloud fragment, hidden beneath gas and dust.

2. Gravitational energy is converted into thermal energy; surface temperature rises.

3. Fusion rate increases until it balances the energy radiated from the surface, marking main-sequence transition.

Main-Sequence Star Lifecycle

• Lifespan dependent on mass:

  • High-mass, Medium-mass, Low-mass, Very Low-mass (Brown dwarfs).

  • Stars <0.5 Msun may account for most stars in the galaxy.

• Those below 0.08 Msun are defined as brown dwarfs.

Evolution of Stars

• Evolution differs for low and high mass stars post-main sequence:

  • Higher mass resulting in shorter main sequence lifetimes.

  • Processes include burning heavier elements, evolution influenced by thermal/dynamical processes, and temperature changes.

Main Sequence Lifetime

• Comparisons made to vehicle fuel dependence:

  • Lifetime = (mass/usage rate)

• For stars, fuel availability is proportional to mass;

  • Larger stars consume fuel faster, affecting luminosity and lifespan.

Changes During Main Sequence Phase

• Hydrogen fuses into helium more rapidly as core depletes fuel.

Evolving from Main Sequence

• Main sequence phase (~10 billion years for solar mass stars).

• Transition occurs when hydrogen in the core runs out; core collapses leading to increased temperature and fueling further evolution.

The Red Giant Branch

• Helium core contraction causes temperature rise, initiating hydrogen fusion in surrounding layers.

• Transition to red giant phase leads to a significant increase in star size and luminosity (10 to 1000 times the Sun's).

Electron Degeneracy in Low Mass Stars

• Gravitational collapse leads to denser helium cores; electron degeneracy pressure prevents further collapse.

• Evolution of these stars post-main sequence triggers significant events over ~50 million years.

Helium Fusion and the Triple-Alpha Process

• Rising core temperatures lead to helium fusion initiation at about 100 million K.