Stars and astrophysics

IB Physics SL· Topic 7.3 (2025 IB Physics SL Guide)· 25 min read

1. Key Stellar Properties and Core Astrophysics Laws★★★☆☆⏱ 10 min

📘 Definition

Luminosity

L

Total electromagnetic energy output of a star per second, independent of observer distance

Example:

The Sun has a luminosity of ~3.9 × 10²⁶ W, written as 1 L☉

📘 Definition

Apparent Brightness

b

Power from a star that hits 1 square meter of a detector at the observer's location

b = \frac{L}{4\pi d^2}

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L = 4\pi R^2 \sigma T^4

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\lambda_{max} T = 2.9 \times 10^{-3} \text{ m K}

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📐 Worked Example

A star has surface temperature 5800 K and radius 7.0 × 10⁸ m. Calculate its peak wavelength and luminosity.

1
First apply Wien's displacement law to find peak wavelength:
2
$\lambda_{max} = \frac{2.9 \times 10^{-3}}{5800} = 5.0 \times 10^{-7} \text{ m}$
3
Substitute values into the Stefan-Boltzmann law for luminosity:
4
$L = 4\pi (7.0 \times 10^8)^2 \times 5.67 \times 10^{-8} \times (5800)^4 \approx 3.9 \times 10^{26} \text{ W}$

Exam tip:

IB mark schemes almost always award 1 separate mark for stating the full formula before substituting values, even if your final numerical result has a minor rounding error.

2. The Hertzsprung-Russell (HR) Diagram★★★☆☆⏱ 8 min

The HR diagram plots stellar luminosity (relative to the Sun's L☉) on the y-axis against surface temperature on the x-axis. Critically, temperature decreases from left to right, matching the standard O-B-A-F-G-K-M spectral class ordering. 90% of all known stars fall along the diagonal main sequence band.

📐 Worked Example

Star A has T=3000 K, L=1000 L☉. Star B has T=10000 K, L=0.01 L☉. Identify their HR diagram regions.

1
Star A has low cool temperature and very high luminosity, so it sits in the upper right red giant region, off the main sequence.
2
Star B has high hot temperature and very low luminosity, so it sits in the lower left white dwarf region, far below the main sequence.

3. Stellar Life Cycles for SL Syllabus★★★★☆⏱ 7 min

All stars form from collapsing interstellar gas clouds (nebulae) that heat up to form a protostar, before entering the main sequence where stable hydrogen fusion occurs in the core. Low mass stars (initial mass < 8 solar masses) expand to red giants after core hydrogen is exhausted, then shed their outer layers as a planetary nebula, leaving a dense white dwarf remnant. High mass stars (initial mass > 8 solar masses) expand to supergiants, end their life in a supernova explosion, leaving either a neutron star or black hole.

✓ Quick check

Test your basic understanding of stellar evolution:

What remnant does a 5 solar mass star leave at the end of its life?
- Neutron star
- White dwarf
- Black hole
- Protostar
Reveal answer
White dwarf —
Only stars below 8 solar masses end as white dwarfs; higher masses leave neutron stars or black holes.

Exam tip:

IB Physics SL does not require you to know detailed black hole formation physics beyond the basic final outcome for high mass stars.

4. Common Pitfalls

Wrong move:

Plotting HR diagram temperature increasing from left to right

Why:

Standard HR diagrams use temperature decreasing left to right, so you will misclassify all stellar positions and lose marks

Correct move:

Always confirm the x-axis direction printed on the exam diagram before answering classification questions

Wrong move:

Forgetting to square the distance term in the inverse square brightness law

Why:

This creates a linear 1/d relationship that gives a value d times larger than the correct result

Correct move:

Write the full formula $b = L / (4 π d^{2})$ before substituting any numerical values

Wrong move:

Stating main sequence stars fuse helium into hydrogen in their core

Why:

This reverses the fusion reaction, and you will lose all 3 marks for stellar life cycle descriptions

Correct move:

Explicitly state main sequence stars fuse hydrogen nuclei into helium to release energy

Wrong move:

Confusing apparent brightness and luminosity in calculation questions

Why:

These quantities have different units and physical meaning, leading to completely wrong final values

Correct move:

Label all given values clearly at the start of any calculation to separate L and b

Wrong move:

Claiming all stars end their life as a white dwarf

Why:

Only low mass stars below 8 solar masses follow this path; high mass stars end in a supernova event

Correct move:

Always reference the initial stellar mass when describing the final stage of stellar evolution

5. Quick Reference Cheatsheet

Law / Concept	Formula	Key Exam Notes
Inverse square brightness	$b = L / (4 π d^{2})$	b in W m⁻², d in m
Stefan-Boltzmann	$L = 4 π R^{2} σ T^{4}$	$σ = 5.67 \times 1 0^{- 8}$ W m⁻² K⁻⁴
Wien's Displacement	$λ_{ma x} T = 2.9 \times 1 0^{- 3}$ m K	T must be absolute Kelvin temperature
HR Diagram Regions	Main sequence, red giant, supergiant, white dwarf	T decreases left to right, L increases bottom to top
Low mass star end state	White dwarf	Initial mass < 8 solar masses
High mass star end state	Supernova → neutron star / black hole	Initial mass > 8 solar masses

When this came up on past exams

AI-estimated based on syllabus patterns — cross-check with official past papers for accuracy. Use only as revision-focus signals.

2024 · Paper 2
Stellar life cycle extended response
2023 · Paper 1
HR diagram multiple choice set
2022 · Paper 2
Combined stellar laws calculation

What's Next

Mastering stellar properties and the HR diagram is the critical foundation for the rest of IB Physics SL astrophysics, including standard candles, stellar parallax, and Big Bang cosmology topics that make up the rest of Unit 5. You will regularly combine the laws you learned here with nuclear fusion concepts to answer extended response Paper 2 questions worth 6-8 marks, which are some of the highest weight questions on the SL exam. Practice identifying HR diagram regions and completing full 3-step stellar property calculations to lock in easy marks. These concepts will also appear in your option topic if you select the Astrophysics option.