Exploring the Life Cycle of Stars: From Nebulas to Black Holes

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Introduction to Stars and Stellar Evolution
Stars are massive celestial bodies composed primarily of hydrogen and helium, undergoing nuclear fusion, which produces immense energy. The life cycle of a star depends on its initial mass and varies significantly for stars of different sizes. Stellar evolution describes the series of stages a star undergoes during its lifetime, from its formation to its death.

Life Cycle of Stars

The life cycle of stars can be divided into several stages, beginning with the birth of a star from a cloud of gas and dust and ending with its death, which can result in a white dwarf, neutron star, or black hole depending on the star’s initial mass.

Stage 1: Stellar Nebula

Stars are born in stellar nebulas, which are clouds of gas and dust. Gravitational forces cause these clouds to collapse, increasing pressure and temperature at the center. Once the temperature becomes high enough, nuclear fusion begins, marking the birth of a protostar.

Stage 2: Protostar

A protostar forms as the gas and dust collapse due to gravity. The core heats up, and when the temperature reaches a critical point, hydrogen fusion begins, converting hydrogen into helium. Once the star achieves hydrostatic equilibrium, it enters the next stage of its life cycle.

Stage 3: Main Sequence Star

In the main sequence stage, a star spends the majority of its life. It fuses hydrogen into helium in its core, and the energy produced creates an outward pressure that balances the inward pull of gravity. The star is stable during this phase.

Sun-like stars spend about 10 billion years in this stage.
Larger stars consume their fuel more rapidly and spend less time in the main sequence.

Stage 4: Red Giant

Once a star exhausts its hydrogen fuel, the core contracts and heats up, causing the outer layers to expand. The star becomes a red giant.

Example: The Sun will eventually become a red giant in about 5 billion years.

Stage 5: Planetary Nebula (for Sun-like Stars)

For stars with a mass similar to the Sun, the outer layers are ejected after the red giant phase, forming a planetary nebula. The core remains and becomes a white dwarf.

Stage 6: White Dwarf

A white dwarf is the remnant core of a star like the Sun. It no longer undergoes fusion and gradually cools over time.

High-Mass Stars: Supergiant and Supernova

For high-mass stars, the evolution is more dramatic:

Supergiant: These stars evolve into supergiants after the main sequence phase, continuing to fuse heavier elements like carbon and oxygen.
Supernova: When the core collapses, the star explodes in a supernova, releasing an immense amount of energy.

Stage 7: Neutron Star or Black Hole

Depending on the mass of the core after a supernova, the remnant becomes either a neutron star or a black hole.

Neutron Star: If the remaining mass is between 1.4 and 3 times the mass of the Sun, a neutron star forms.
Black Hole: If the remaining mass is greater than 3 solar masses, gravity causes the core to collapse into a black hole.

Example: The Lifecycle of a Sun-like Star

Question: What are the stages in the life cycle of a Sun-like star?

Answer:

Step 1: Given Data:

The star has a mass similar to the Sun.

Step 2: Solution:

The star begins its life in a stellar nebula.
It evolves into a protostar.
It enters the main sequence phase, where it spends most of its life.
After using up its hydrogen, it becomes a red giant.
The outer layers are ejected to form a planetary nebula.
The remaining core becomes a white dwarf.

Step 3: Final Answer: A Sun-like star follows this life cycle: stellar nebula → protostar → main sequence → red giant → planetary nebula → white dwarf.

Example: Calculating the Schwarzschild Radius of a Black Hole

Question: What is the Schwarzschild radius for a black hole with 10 times the mass of the Sun?

Answer:

Step 1: Given Data:

Mass of the black hole $M = 10 \times M_{s u n}$ .
Gravitational constant $G = 6.674 \times 10^{- 11}$ m $^{3}$ kg $^{- 1}$ s $^{- 2}$ .
Speed of light $c = 3.0 \times 10^{8}$ m/s.
Solar mass $M_{s u n} = 1.989 \times 10^{30}$ kg.

Step 2: Formula: The Schwarzschild radius $R_{s}$ is given by:

$R_{s} = \frac{2 G M}{c^{2}}$

Step 3: Solution:

$R_{s} = \frac{2 \times 6.674 \times 10^{- 11} \times 10 \times 1.989 \times 10^{30}}{(3.0 \times 10^{8})^{2}}$

$R_{s} = \frac{2.648 \times 10^{21}}{9 \times 10^{16}}$

$R_{s} = 2.94 \times 10^{4}$ m

Step 4: Final Answer: The Schwarzschild radius for a black hole with 10 times the mass of the Sun is approximately 29.4 km.

Conclusion

The life cycle of stars varies significantly based on their initial mass. Smaller stars like the Sun end their lives as white dwarfs, while massive stars explode as supernovas and leave behind neutron stars or black holes. Stellar evolution plays a key role in the formation of different celestial objects in the universe, contributing to the recycling of matter and the ongoing creation of new stars.

Frequently Asked Questions (FAQs)

What happens to a star when it runs out of fuel? When a star runs out of fuel, it either becomes a red giant or supergiant, depending on its mass. It can end its life as a white dwarf, neutron star, or black hole.
What is a supernova? A supernova is a powerful explosion that occurs when a massive star exhausts its fuel and its core collapses.
What is the difference between a white dwarf and a neutron star? A white dwarf is the remnant of a low to medium mass star, while a neutron star is the remnant of a high-mass star after a supernova explosion.
How is a black hole formed? A black hole is formed when a very massive star’s core collapses under the force of gravity after a supernova explosion, leaving behind a singularity from which not even light can escape.

Stars and Stellar Evolution (Life Cycle of Stars)