Lecture Notes: Stellar Sizes

Introduction

• Stellar sizes are difficult to measure.
• Stars appear as points of light due to distance.
• Only the largest and nearest stars (e.g., Betelgeuse) can have their angular size measured.
• Technique Used: Speckle interferometry helps deduce angular size.

Measuring Stellar Sizes

• Challenges: Most stars can't be directly imaged for size.
• Methods: Use physics and mathematical formulas.
• Key Relationships:
  • Luminosity proportional to radius squared.
  • Luminosity proportional to surface temperature to the fourth power.

Types of Stars by Size

• Giant Stars: Radii 10-100 times the Sun's.
• Dwarf Stars: Smaller than or equal to the Sun's size.
• Supergiant Stars: Even larger, more rare.
  • Make up a significant portion of the brightest stars due to size and proximity.

Examples of Stellar Sizes

• Antares: 500 solar radii, beyond Mars' orbit if placed in our solar system.
• Aldebaran: 40 solar radii.
• Capella: 15 solar radii.
• Spica: 7 solar radii.
• Sirius: 2 solar radii.
• Jupiter: About 0.1 solar radii.
• Barnard's Star: 0.2 solar radii.
• Proxima Centauri: 0.08 solar radii.
• Sirius B: 0.01 solar radii (white dwarf).

Calculating Stellar Radii

• Stefan-Boltzmann Law: Surface flux relates to temperature raised to the fourth power.
• Inverse Square Law for Light: Luminosity relates to distance squared and flux.
• Steps to Calculate Radius:
  1. Determine surface temperature from stellar spectrum.
  2. Estimate true luminosity.
  3. Calculate radius using measured flux and distance.
  4. Acknowledge uncertainties in measurements.

Implications of Stellar Size

• Brightness and Power: Larger and hotter stars are significantly more luminous.
• Lifetime: Bigger stars burn fuel faster, leading to shorter lifespans.

Conclusion

• Stellar sizes vary vastly; methods exist to estimate sizes despite challenges.
• Larger stars have greater luminosity but shorter life spans due to rapid fuel consumption.