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Chapter 17: Problem 29

How do white dwarfs differ from brown dwarfs? Which are more massive? Which are larger in radius? Which are denser?

Short Answer

Expert verified
White dwarfs are more massive, smaller in radius but denser compared to brown dwarfs. Brown dwarfs are less massive, larger in radius and less dense when compared to white dwarfs.

Step by step solution

01

Identify Characteristics of White Dwarfs

A white dwarf is a compact star that is no longer generating nuclear energy through fusion. It has high density and low volume. It is composed mostly of electron-degenerate matter. After stars like our Sun have finished burning their nuclear fuel, they shed their outer layers and become white dwarfs.
02

Identify Characteristics of Brown Dwarfs

A brown dwarf is a type of substellar object that has a mass between those of the heaviest gas giant planets and the least massive stars, approximately 13 to 80–100 times that of Jupiter. Unlike a star, a brown dwarf does not have sufficient mass to sustain nuclear fusion of ordinary hydrogen to helium in its core. However, it is usually significantly more massive than the planets.
03

Comparing Mass

White dwarfs are more massive than brown dwarfs. The mass of a white dwarf is high due to its composition of degenerate matter. It is typically between 0.2 and 1.4 times the mass of the Sun. On the other hand, brown dwarfs have relatively low mass, usually 13 to 80–100 times that of Jupiter.
04

Comparing Radius

Despite having lower mass, brown dwarfs have larger radius than white dwarfs. A brown dwarf has a radius about 1.2 times that of Jupiter, whereas a typical white dwarf has a radius similar to that of Earth, which is about 10 times smaller than Jupiter.
05

Comparing Density

White dwarfs are denser than brown dwarfs due to their high mass and small volume. The average density of a white dwarf is 1.0 x 10^9 kg/m^3, whereas the average density of a brown dwarf is much lower because of its larger volume.

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