Question

Suppose two white dwarf stars have the same surface temperature. Why is the more massive of the two white dwarfs the less luminous?

Short answer

More massive white dwarfs have less surface area, making them less luminous for the same temperature.

Step-by-step solution

Understanding Luminosity

Luminosity is a measure of the total amount of energy emitted by a star per unit time. It depends on both the star's temperature and its surface area. For stars with the same temperature, like our white dwarfs, the one with the larger surface area will be more luminous.

Reviewing the Effects of Mass on White Dwarfs

In white dwarfs, an increase in mass causes the star to contract. This contraction increases the density and pressure, leading to a smaller radius. Due to this contraction, the more massive white dwarf will have a smaller surface area.

Connecting Mass, Surface Area, and Luminosity

Since luminosity, for stars of the same temperature, depends on the surface area, the white dwarf with the smaller surface area (hence, the more massive one) will be less luminous. This is because despite their surface temperatures being the same, the larger surface area of the less massive white dwarf means it emits more energy per unit time.

Key concepts

Luminosity in Stars

The luminosity of a star is essentially the total energy it emits in a certain period of time. It tells us how bright the star actually is.
This brightness is not just about how hot the star is; it also heavily depends on the size, or surface area, of the star.
To calculate a star's luminosity, we need two key ingredients:

• The surface temperature of the star, which is how hot its surface is.
• The surface area of the star, which is determined by the size of the star.

Another essential factor to consider is: For stars with the same temperature, the one with the larger surface area will naturally be more luminous.
This means it will shine more brightly because it can spread its heat across more space, much like how a bigger bonfire looks brighter than a smaller one.

Mass Effects on White Dwarfs

White dwarfs are fascinating stars because of how they behave under mass changes. Unlike regular stars, the dynamics of a white dwarf change notably with variations in their mass.
When a white dwarf gains mass, it doesn't get larger. In fact, because of an effect called electron degeneracy pressure, it contracts.
This contraction leads to a higher density and pressure inside the star, causing its radius to shrink.
The greater the mass of the white dwarf, the smaller it becomes.
Thus, a more massive white dwarf has a smaller surface area. This shrinkage has profound effects on how these compact stars behave, particularly their brightness.

Stellar Surface Area and Luminosity

The connection between a star's surface area and its luminosity is crucial for understanding why not all stars of the same temperature shine equally. In the case of white dwarfs, this relationship becomes quite apparent.
Let's think about two white dwarfs with identical temperatures:

• The less massive white dwarf, with a larger surface area, will have higher luminosity.
• The more massive one contracts, has a smaller surface area, and thus, lower luminosity.

This occurs because the energy emitted is spread over the star's surface.
So, the smaller the surface area, the less room there is to emit energy, resulting in lower brightness.
In the end, it is this balance of temperature and surface area that dictates the luminosity of these intriguing stars.