13.6 Stellar Evolution

13.6 Stellar Evolution

The kinetic theory of gases, when extended to astrophysical systems like stars and galaxies, helps us understand the evolution of stars in a galaxy or gas atoms in a stellar atmosphere.

Stellar evolution deals with the star changes over time. Star can have range of lifetime from a few million years to trillions of years. The life of a star depends on the mass of the star. The most massive have longer life which is even longer than the current age of the universe. All stars are formed from the clouds of gas and dust which are often called nebulae or molecular clouds. This is also called a proto-star. As the cloud contracts, its density and temperature increase due to the rise in K.E. of particles ($\mathrm{K.E.} \propto T$). After a millions of years, these proto-stars can become a star having achieved a state of equilibrium. The rms velocity of gas molecules in the star increases with rise of density. This in turn increases the average kinetic energy and finally temperature increases with time. Figure 13.4 represents the competition between gravity and pressure.

(Figure 13.4: Gravity compression is balanced by pressure outward. Greater gravity compresses the gas, making it denser and hotter)

As the temperature increases, the internal pressure also rises. A stable star is formed when the inward gravitational force is exactly balanced by the outward pressure. This condition is described by the hydrostatic equation: $\dfrac{\Delta P}{\Delta r} = -\dfrac{GM_{r}\rho_{r}}{r^{2}}$

This equation ensures that the star neither collapses under gravity nor expands indefinitely.

$P$ is the pressure inside the star (force per unit area), $\Delta P/\Delta r$ is the rate of change of pressure with radius (how pressure changes from the centre outward), $r$ is distance from the centre of the star, $G$ is gravitational constant ($6.67 \times 10^{-11}\,\mathrm{N\,m^{2}\,kg^{-2}}$), $M_{r}$ is mass enclosed within radius $r$, $\rho_{r}$ is density at radius $r$, and negative sign indicates that pressure decreases outward, while gravity pulls inward. There are two possibilities if the balance between pressure force and gravitational force is not maintained.

(i) Gravitational force $>$ Internal pressure

(ii) Gravitational force $<$ Internal pressure

As the temperature within a star's core reaches about $10^{7}\,\mathrm{K}$, nuclear fusion is initiated, allowing hydrogen nuclei to combine and form helium. This process releases an immense amount of energy, which sustains the star and powers it for the majority of its lifetime. The continuous energy production not only maintains equilibrium against gravitational collapse but also leads to a gradual increase in internal temperature. As a consequence, the star begins to expand.

With further increases in temperature and changes in core composition, the star may expand significantly to become a red giant. At this stage, stars possessing at least about half the mass of the Sun are capable of initiating helium fusion in their cores, producing heavier elements such as carbon and oxygen. In more massive stars, the process continues with the fusion of even heavier elements in successive stages, forming increasingly complex nuclei up to iron.

The final fate of a star depends primarily on its mass. Once a star exhausts its nuclear fuel, it can no longer support itself against gravitational collapse. In low and intermediate mass stars, the core contracts into a dense white dwarf, while the outer layers are expelled into space, forming a planetary nebula. In contrast, stars with masses roughly ten times greater than that of the Sun undergo a dramatic supernova explosion. During this event, the inert iron core collapses under gravity, leading to the formation of dense remnants such as neutron stars or black holes.

Red dwarf stars, due to their low mass and highly efficient fuel consumption, follow a much slower evolutionary pure. The universe is not yet old enough for any red dwarf to have completed its life cycle. However, theoretical models indicate that these stars will gradually become hotter and more luminous over time before eventually exhausting their hydrogen fuel and evolving into low mass white dwarfs.

(Fig 13.5: Life cycle of a star)

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A parsec is a unit of distance that is used by astronomers as an alternative to the light-year, just as kilometres are being used as an alternative to miles. In fact, one parsec is approximately $3.26$ light years, or almost $19$ trillion miles ($31$ trillion km).