Question

Main sequence stars of \(5 \mathrm{M}_{\odot}\) are thought to evolve into \(1 \mathrm{M}_{\odot}\) white dwarfs. What happens to the \(4 \mathrm{M}_{\odot}\) that do not become part of the white dwarf?

Short answer

The \(4 \mathrm{M}_{\odot}\) is lost as stellar wind and ejected outer layers during the star's evolution.

Step-by-step solution

Understand Stellar Mass Loss

Main sequence stars like the sun undergo nuclear fusion, converting hydrogen into helium, which gradually affects their mass. Larger stars, especially, lose significant mass during their life cycle through stellar winds and other processes.

Know the Star Evolution Phases

During their evolution, stars expand into red giants or supergiants. This phase involves the outer layers being expanded and lost into space, greatly contributing to the overall mass loss of the star.

Analyze the Mass Difference

In this specific case, a main sequence star initially has a mass of \(5 \mathrm{M}_{\odot}\). By the time the star becomes a white dwarf of \(1 \mathrm{M}_{\odot}\), it indicates a loss of \(4 \mathrm{M}_{\odot}\).

Identify the Fate of Lost Mass

The \(4 \mathrm{M}_{\odot}\) is lost during the transformation from a main sequence star to a white dwarf. This mass primarily becomes part of the star's stellar wind, getting ejected into space as the outer layers are blown off during the red giant phase and other stages.

Key concepts

Main Sequence Stars

Main sequence stars are the most stable phase in the life of a star and where they spend most of their existence. These stars maintain hydrostatic equilibrium, balancing gravitational forces with outward pressure from nuclear fusion in their cores. Fusion converts hydrogen into helium, releasing energy that makes the star shine. The mass of a main sequence star determines its lifespan and evolutionary path. For a star with a mass of 5 solar masses (\(5 \mathrm{M}_{\odot}\)), it will burn hydrogen faster than a star like our sun, leading to a shorter but more luminous existence. As fusion continues, helium accumulates in the core, eventually leading the star into the next phase of its life cycle.

Red Giant Phase

As a star exhausts the hydrogen in its core, it transitions into the red giant phase. This happens when the core contracts under the force of gravity, and hydrogen burning shifts to a shell around the core, causing the outer layers to expand significantly. This expansion makes the star much larger and cooler on the surface, giving it a reddish appearance. In this stage, the outer layers can extend to hundreds of times the star's original size. The red giant phase is marked by significant changes in the star's structure and leads to the ejection of its outer layers, contributing to mass loss. This process helps shape the subsequent phases of the star's evolution.

Stellar Mass Loss

Stellar mass loss is a critical aspect of a star's lifecycle, particularly for massive stars like those with an initial mass of 5 solar masses (\(5 \mathrm{M}_{\odot}\)). During the red giant phase and beyond, mass is lost through stellar winds — streams of gas blown away from the star's outer layers. This happens as the outer parts of the star become less gravitationally bound and more susceptible to being expelled. The strong stellar winds can remove significant portions of the star’s outer layers, contributing to a marked reduction in mass. For a star initially at 5 solar masses, losing up to 4 solar masses during its lifetime is common. This mass loss is a prerequisite for the transition to the next state of its evolution.

White Dwarf Formation

After losing its outer layers, the core of the star remains, transitioning into a white dwarf. White dwarfs are dense, compact remnants of stars and mark one of the final evolutionary stages of stellar life. The remaining core, primarily composed of electron-degenerate matter, ceases nuclear fusion, and the star gradually cools over billions of years. A typical white dwarf has a mass around 1 solar mass (\(1 \mathrm{M}_{\odot}\)), much less than its progenitor main sequence star, due to the preceding mass loss. White dwarfs are incredibly dense, with much of their mass packed into a volume similar to Earth's size. These "cosmic corpses" can persist as faintly glowing objects, cooling and fading into black dwarfs over astronomical time scales.