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Grade 11-12 (age 16-18)

high school Stellar Evolution

At a star's core, four hydrogen nuclei fuse into one helium nucleus, the lost mass comes out as energy, and that energy makes the star shine. Plot stars on an H-R diagram by surface temperature and luminosity and most of them gather on the main sequence, running from upper left to lower right; the heavier the star, the farther up and left it sits, so it is brighter but burns its fuel faster and lives a shorter life. A star that starts with less than about 8 times the Sun's mass ends as a white dwarf after a red-giant phase, while a heavier one becomes a supergiant, explodes as a supernova, and leaves a neutron star or a black hole. Changing the star's mass in the diagram moves its place on the main sequence and changes the path it takes afterward, along with its main-sequence lifetime and its fate.

What powers a star: hydrogen fusion

💡 Why do stars shine?
①The Sun's core is at about 15 million K, with a pressure hundreds of billions of times that of Earth's atmosphere
②Under these conditions, four hydrogen nuclei become one helium nucleus through several steps
③About 0.7% of the mass disappears in the process, and that mass turns into energy according to E = mc²
④Every second the Sun turns about 600 million tonnes of hydrogen into helium, and about 4 million tonnes of that leaves as energy

The H-R diagram: a map of stars

1 M⊙
📊 How to read an H-R diagram
①The horizontal axis is surface temperature, hotter to the left (spectral types O B A F G K M in order)
②The vertical axis is luminosity on a logarithmic scale, each grid step 100 times brighter
③About 90% of stars lie on the main sequence, from upper left to lower right
④The upper right holds red giants and supergiants, cool but bright because they are huge; the lower left holds white dwarfs, hot but dim because they are tiny

Mass decides a star's life

Mass–luminosity relation
L ∝ M3.5
Doubling the mass makes a star about 11 times as luminous (23.5 ≈ 11.3).
Main-sequence lifetime
t ∝ ML ≈ 1M2.5
A heavy star has more fuel but burns it far faster, so it lives a shorter life.

Comparison

How stars evolve by mass
ItemUnder about 8 solar massesAbout 8 solar masses or more
Main-sequence lifetimeabout 10 billion years for the Suna few million to tens of millions of years
Core fusionhydrogen → helium → carbon, oxygenhydrogen → helium → carbon → oxygen → … → iron
After the main sequencered giantsupergiant
Final stageplanetary nebula → white dwarfsupernova explosion
Remnantwhite dwarf (Earth-sized)neutron star or black hole
📐 Why heavy stars die first
①The greater the mass, the higher the temperature and pressure at the core, so fusion runs much faster
②Fuel grows in proportion to mass, but luminosity grows as mass to the 3.5 power, so the fuel runs out sooner
③That is why main-sequence lifetime is roughly inversely proportional to mass to the 2.5 power
④If the Sun lasts about 10 billion years, a star of 10 solar masses lasts about 30 million years, and a star of half a solar mass about 57 billion years, longer than the present age of the universe

How stars end

💫 The ends of light and heavy stars
①When a light star uses up the hydrogen in its core, its outer layers swell into a red giant while helium in the core turns into carbon and oxygen
②The outer layers drift away as a planetary nebula, and the remaining core becomes an Earth-sized white dwarf that slowly cools
③A heavy star makes elements up to iron in its core and then can release no more energy, so the core collapses in an instant and the outer layers blow apart as a supernova
④If the leftover core has less than about 3 solar masses it becomes a neutron star; if more, a black hole
⑤Elements in our bodies such as carbon, oxygen, and iron were made long ago by fusion in stars and by supernova explosions

Worked Examples and Exam Practice

Example 1
Using the mass-luminosity relation L ∝ M3.5, about how many times the Sun's luminosity is a main-sequence star with twice the Sun's mass?
1
Since L ∝ M3.5, doubling the mass makes the luminosity 23.5 times.
2
23.5 ≈ 11.3, i.e., about 11 times.
▸ About 11 times
A small increase in mass raises luminosity a great deal, and the star uses its fuel that much faster, so its life is shorter.
Example 2
What object remains at the end of a Sun-like star's life, and at the end of a much more massive (about 10x or more) star's life?
1
A Sun-like star passes through a red giant, sheds its outer layers as a planetary nebula, and leaves only its core as a white dwarf.
2
A massive star passes through a supergiant, explodes as a supernova, and becomes a neutron star or a black hole depending on the remnant mass.
▸ Sun-like → white dwarf / massive → neutron star or black hole
Mass decides how a star ends, and the heavier it is, the more violent the end, as in a supernova.
CSAT-style problem
Which statement about stellar evolution is correct?
①On the H-R diagram, surface temperature increases toward the right
②A more massive main-sequence star is more luminous and shorter-lived
③The Sun will end by exploding as a supernova
④A star's energy source is fission that splits helium into hydrogen
⑤A lower-mass star has a shorter main-sequence lifetime
▸ ② A more massive main-sequence star is more luminous and shorter-lived
1
Higher mass means a hotter, denser core and faster fusion, so the star is luminous but burns its fuel quickly and is short-lived.
2
Temperature increases toward the left (①), the Sun ends as a white dwarf (③), the energy source is hydrogen-to-helium fusion (④), and heavier stars are shorter-lived (⑤).

Summary

Key relations
L ∝ M3.5, lifetime ∝ 1M2.5
The more massive a star, the brighter and hotter it is, the shorter its life, and the more violent its end.
🎯 Exam Points
①On an H-R diagram the horizontal axis is surface temperature, hotter to the left, and the vertical axis is luminosity, brighter upward
②On the main sequence, more massive stars sit farther up and left (hotter and brighter)
③Light stars: main sequence → red giant → planetary nebula → white dwarf
④Heavy stars: main sequence → supergiant → supernova → neutron star or black hole
⑤Main-sequence lifetime is inversely proportional to mass to the 2.5 power, so heavier stars live shorter lives
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