UPSC Prelims 2024 Q32: Giant vs Dwarf Stars, Lifespan — Explained
Consider the following statements:
Statement-I:
Giant stars live much longer than dwarf stars.
Statement-II:
Compared to dwarf stars, giant stars have a greater rate of nuclear reactions.
Which one of the following is correct in respect of the above statements?
- Both Statement-I and Statement-II are correct and Statement-II explains Statement-I
- Both Statement-I and Statement-II are correct, but Statement-II does not explain Statement-I
- Statement-I is correct, but Statement-II is incorrect
- Statement-I is incorrect, but Statement-II is correct
Answer: (d) Statement-I is incorrect, but Statement-II is correct
Statement-wise explanation
- Statement-I: incorrect — It is the other way round: the more massive a star, the shorter its life. NASA notes that some massive stars live only a few million years, while some low-mass stars will shine for trillions of years. That is longer than the universe has existed so far. The Sun is a yellow dwarf and will spend about 10 billion years on the main sequence.
- Statement-II: correct — A massive star needs a high outward pressure to hold up against its own strong gravity. To make that pressure its core is hotter and denser, so it fuses hydrogen into helium much faster than a dwarf star. Its luminosity rises roughly as mass to the power 3.5, so a star 10 times the Sun's mass burns fuel thousands of times faster. Statement-II cannot explain Statement-I because Statement-I is false. The faster burning is actually the reason giants die young.
How to eliminate
Statement-II gives the clue. If giant stars burn nuclear fuel faster, they should run out sooner, not live longer. Think of a big fire that burns through its wood quickly. So both statements cannot be true together, and Statement-II cannot explain Statement-I. That rules out the two options where both statements are correct. You are left choosing between 'I correct, II incorrect' and 'I incorrect, II correct'. To settle it, remember one fact: a star's mass decides its fate. Massive stars live hot, bright and short (a few million years). Small stars live cool, dim and long (billions to trillions of years). Only the second pairing fits that fact.
Know more
Mass decides a star's life. A star is a balance between gravity pulling inward and pressure from nuclear fusion pushing outward. A heavier star has stronger gravity. To stay stable, its core must be hotter and denser, so fusion runs much faster.
Fuel vs burn rate. A massive star has more hydrogen, but its burn rate rises far faster than its fuel supply. Roughly, luminosity ∝ M^3.5, so main-sequence lifetime ∝ M/L ≈ M^-2.5. If you double the mass, the life becomes about 5–6 times shorter.
| Star type | Approx. mass (Sun = 1) | Main-sequence life | End state |
|---|---|---|---|
| Red dwarf | 0.1–0.5 | Hundreds of billions to trillions of years | White dwarf (in theory; none has yet died) |
| Sun (yellow dwarf, G2V) | 1 | ~10 billion years | Red giant, then white dwarf |
| Massive star | 8 or more | A few million to tens of millions of years | Red supergiant, supernova, then neutron star or black hole |
Terminology trap. Astronomers call ordinary main-sequence stars, like the Sun, 'dwarfs'. A white dwarf is a different thing: the dead core left behind by a Sun-like star. A brown dwarf is a 'failed star' that is too light to fuse hydrogen at all. 'Giant' can mean a high-mass star, or a star that has swollen up after using the hydrogen in its core. Either way, the giant stage is short-lived.
Fate after death (NASA): if the leftover core is about 1.4–3 times the Sun's mass, it becomes a neutron star. If it is more than about 3 times the Sun's mass, it collapses into a black hole. Sun-like stars shed their outer layers as a planetary nebula and leave a white dwarf, which slowly cools.