MYP Physics · topic MYP-16.04
Stellar life cycles
Connect the ideas, make your working visible, and test the result. Use the hints when you need a starting point; open the full solution after your attempt.
Extra challenging questions
Work through the linked stages and explain what each result means.
Two stars at the same temperature with very different luminosities
Optional enrichment: this challenge may extend beyond the usual syllabus depth and assumes confidence with algebra and graph interpretation. A main-sequence reference star and a red giant both have surface temperature 4000 K. The giant has luminosity 400 times the reference. A third star is a white dwarf with temperature 12000 K and luminosity 0.01 times the reference. Use L = 4πR²σT⁴. The supplied data place the three stars on temperature–luminosity axes; luminosities are relative to the reference star. Supplied data (Surface temperature / K; Relative luminosity): (4000, 1), (4000, 400), (12000, 0.01). (a) Determine the radius of the giant and dwarf relative to the reference. Explain why colour alone cannot determine luminosity. [3 marks] (b) Relate these observations to an H–R diagram and distinguish low-mass from high-mass stellar endpoints. [3 marks]
Three stellar observations
Supplied question data. Read the labelled axes and use the observations to test the physical model.
Vertical axis (y): Relative luminosity
Horizontal axis (x): Surface temperature / K
Read the exact data as a table
| Surface temperature / K | Relative luminosity |
|---|---|
| 4000 | 1 |
| 4000 | 400 |
| 12000 | 0.01 |
These are the supplied values, not a worked answer. No fitted trend is drawn.
Show a hint
Begin with part (a): Determine the radius of the giant and dwarf relative to the reference. Explain why colour alone cannot determine luminosity.
Reveal the worked solution
- At equal temperature, L∝R², so the giant radius ratio is √400 = 20.
- For the dwarf, Rw/Rref = √(Lw/Lref)(Tref/Tw)² = √0.01×(1/3)² = 1/90.
- Colour indicates a characteristic surface temperature, while luminosity also depends on emitting area. A hot small star may be less luminous than a cool large one.
- A standard H–R diagram places hotter temperatures toward the left and often uses logarithmic luminosity. The supplied linear data plot must be relabelled or transformed before being read as a standard H–R diagram.
- A Sun-like star can evolve into a red giant and leave a white dwarf after shedding outer layers. A white dwarf is not a newly formed small main-sequence star.
- Sufficiently massive stars can undergo core-collapse supernovae and leave neutron stars or black holes. Initial mass, mass loss and interactions matter; a single universal life-cycle chain is inadequate.
Answer (a) Giant radius = 20 times reference; dwarf radius = 1/90 of reference. (b) An H–R diagram compares intrinsic stellar properties, not spatial locations; stellar mass strongly influences evolution and endpoint.
Compare the assumptions, method and units with your attempt. Explain any correction before trying another question.