Determination of Stellar Radii
- The radius of a star can be estimated by combining Wien’s displacement law and the Stefan–Boltzmann law
- The procedure for this is as follows:
- Using Wien’s displacement law to find the surface temperature of the star
- Using the inverse square law of flux equation to find the luminosity of the star (if given the radiant flux and stellar distance)
- Then, using the Stefan-Boltzmann law, the stellar radius can be obtained
Worked example
Betelguese is our nearest red giant star. It has a luminosity of 4.49 × 1031 W and emits radiation with a peak wavelength of 850 nm.
Calculate the ratio of the radius of Betelgeuse rB to the radius of the Sun rs.
Radius of the Sun, rs = 6.95 × 108 m.
Answer:
Step 1: List the known quantities
- Luminosity of Betelgeuse, L = 4.49 × 1031 W
- Peak wavelength of Betelgeuse, λmax = 850 nm = 850 × 10−9 m
- Radius of the Sun, rs = 6.95 × 108 m
Step 2: Write down Wien’s displacement law
λmaxT = 2.9 × 10−3 m K
Step 3: Rearrange Wien’s displacement law to find the surface temperature of Betelguese
Step 4: Write down the Stefan-Boltzmann law
L = 4πr2σT4
Step 5: Rearrange for r and calculate the stellar radius of Betelguese
Step 6: Calculate the ratio rB / rs
- Therefore, the radius of Betelguese is about 1000 times larger than the Sun’s radius
