Lecture Notes: Estimating the Luminosity of Regulus (α Leonis)

Introduction

• Discussion on estimating the luminosity of Regulus, the brightest star in the constellation Leo.
• Regulus has a mass approximately 5 times that of the Sun.
• The task is to use the mass-luminosity relationship for main sequence stars to estimate its luminosity.

Importance of Main Sequence Stars

• The mass-luminosity relationship is applicable only to main sequence stars.
• The Sun is also a main sequence star, making comparisons possible.

Mass-Luminosity Relationship

• States that the luminosity of a star compared to the Sun is proportional to the star's mass compared to the Sun's, raised to the power of 3.5.
  • Formula: ( \left( \frac{L_{star}}{L_{sun}} \right) = \left( \frac{M_{star}}{M_{sun}} \right)^{3.5} )
• The author prefers the exponent 3.5 for accuracy, though some texts use 4.

Calculation

• Given:
  • Regulus has 5 solar masses (5 times the mass of the Sun).
• Substitute into the formula:
  • ( \left( \frac{L_{star}}{L_{sun}} \right) = 5^{3.5} )
• Calculation steps:
  • Use a calculator to compute 5 raised to the power of 3.5.
  • Button sequence: input 5, use the power button ((^\wedge) or (x^y)), then input 3.5.
  • Result: Approximately 279.5.

Interpretation of Results

• The luminosity of Regulus is about 279.5 times that of the Sun's.
• Despite having only 5 times the mass, it outputs nearly 300 times more power.
• Implications:
  • Greater fuel consumption rate.
  • Shorter lifespan due to the rapid burning rate.

Conclusion

• Massive stars like Regulus have intense but short lifetimes due to their high luminosity and power output.
• They "burn brightly" and exhaust their fuel quickly compared to less massive stars.

These notes summarize the key points discussed about estimating the luminosity of Regulus using the mass-luminosity relationship for main sequence stars.