Properties of Stars

Stellar Properties

Stars in the night sky differ in size, temperature, and brightness; hotter stars look blue and cooler ones red. On the H-R diagram of temperature versus luminosity, main-sequence stars, red giants, and white dwarfs sit in clear regions. Stellar luminosity follows L = 4πR²σT⁴ and depends on radius and temperature. Here you can use the star-type slider to see where main-sequence stars, red giants, and white dwarfs lie on the H-R diagram.

Are all stars in the night sky the same?

⭐ Each star has different properties

①Stars vary in size, temperature, and brightness

②Hotter stars emit blue light; cooler stars emit red light

③Plotting temperature vs luminosity reveals patterns → H-R diagram

H-R Diagram (Hertzsprung–Russell)

Star type0

💡 Key observations

①0: Main sequence — most stars on a top-left→bottom-right diagonal (hydrogen fusion phase)

②1: Red giant — low temperature but large radius → high luminosity (upper right)

③2: White dwarf — high temperature but small radius → low luminosity (lower left)

Physical quantities of stars

Stefan–Boltzmann law

L = 4πR²σT⁴

luminosity = 4π × radius² × σ × surface_temp⁴ — brightness depends on size and temperature

Wien's displacement law

λ_max = b / T

peak wavelength = constant(b) / surface temperature → higher T → shorter λ (bluer)

🔬 Star color and temperature

①Blue: surface T ~30,000 K+ (O, B type)

②White: ~10,000 K (A type)

③Yellow: ~6,000 K (G type, Sun)

④Red: ~3,000 K (M type)

Star brightness

Apparent vs absolute magnitude

m − M = 5 log(d/10)

m: apparent, M: absolute, d: distance (pc) — smaller magnitude = brighter

📏 Meaning of magnitudes

①Apparent magnitude (m): observed brightness (distance-dependent)

②Absolute magnitude (M): brightness if placed at 10 pc — true intrinsic brightness

③1 magnitude diff = ~2.5× brightness, 5 magnitudes = 100×

Worked Examples and Exam Practice

Example 1

Two stars differ by 5 magnitudes in brightness. How many times brighter is the brighter star?

Each step of 1 lower in magnitude is about 2.5 times brighter.

A 5-magnitude difference is about 2.5 to the fifth power, which is exactly 100 times in brightness.

▸ 100 times

Smaller magnitude numbers are brighter. Every 5 magnitudes is exactly a 100-fold brightness difference.

Example 2

A star has the same surface temperature as the Sun but 100 times the radius. About how many times the Sun's luminosity is it? (L = 4πR²σT⁴)

At equal temperature, the Stefan-Boltzmann law makes luminosity proportional to radius squared (L ∝ R²).

With 100 times the radius, luminosity is 100² = 10,000 times.

▸ About 10,000 times

A red giant has a low temperature but a huge radius, so its luminosity is large.

CSAT-style

Which statement about the H-R diagram and stellar quantities is correct?

①On the H-R diagram, surface temperature decreases toward the left

②Main-sequence stars run from upper-left to lower-right on the H-R diagram

③Red giants have high surface temperature and small radius

④Absolute magnitude is the brightness at a star's actual distance

⑤A larger magnitude number means a brighter star

▸ ② Main-sequence stars run from upper-left to lower-right on the H-R diagram

Main-sequence stars (hydrogen fusion) form a diagonal from hot, luminous (upper-left) to cool, faint (lower-right).

Temperature increases toward the left (①), red giants are cool with large radii (③), absolute magnitude is defined at 10 pc (④), and smaller magnitude numbers are brighter (⑤).

Summary

Stellar properties core

L = 4πR²σT⁴ / H-R diagram: temperature (x decreases) vs luminosity (y up)

luminosity depends on radius and temperature; H-R diagram identifies star type and evolutionary stage

🎯 Exam Points

①H-R diagram: x-axis is surface temperature (left = hotter), y-axis is luminosity

②Main sequence: top-left→bottom-right diagonal, ~90% of stars (H fusion)

③L = 4πR²σT⁴ — at same T, larger R → brighter

④Red giant: T↓, R↑↑ → high L / White dwarf: T↑, R↓↓ → low L

⑤Magnitudes: 1 mag = 2.5×, 5 mag = 100× brightness

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