E.5 · IB Physics
Stars and the HR diagram
Every star is a point on the luminosity–temperature plane. Drag the star around the diagram, or use the sliders: its radius follows from L = 4πR²σT⁴, and its neighbourhood tells you what kind of star it is.
Predict first
Choose The Sun in the Preset list. Keeping the temperature fixed, raise the luminosity from 1 L☉ to 100 L☉. How does the radius of the star change?
L = 4πR²σT⁴, so at fixed T the luminosity is proportional to R². A hundred times more luminosity needs only √100 = 10 times the radius.
Check it in the model: Pick The Sun, then move the Luminosity L slider until it reads 100 L☉ and compare the Radius R readout (1 R☉, then 10 R☉).
main sequence (approximate band) lines of constant radius
You can also drag the star on the diagram. Temperature increases to the left.
R ÷ R☉ = √(L ÷ L☉) × (T☉ ÷ T)²
T☉ = 5772 K, σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴
λmax T = 2.90 × 10⁻³ m K
Try this
- Choose the Sun preset. Raise L to 10⁴ L☉ without changing T. How does the radius change, and what type of star do you now have?
- Keep L = 1 L☉ and lower T from 5770 K to 2900 K. Which way does the radius move and by what factor? Check it against the R readout.
- Drag the star to the lower left, hot and faint. Which region is this and how small must the radius be? Compare the radius with the 0.01 R☉ line.
Common error: reading the temperature axis the usual way round. On an HR diagram T increases to the left, so a hot blue star is on the left and a cool red star on the right, while luminosity still increases upwards.