ASTR 230 · Lecture 07

The Death of Sun-Like Stars: White Dwarfs and the Chandrasekhar Limit

What is left when fusion stops

Learning Goals

Describe the evolutionary sequence from red giant to planetary nebula to white dwarf for a Sun-like star.
Explain electron degeneracy pressure as the force that supports a white dwarf against gravity.
Compute a white dwarf’s density from its measured mass and radius, and state why the Chandrasekhar limit exists.

Reading anchor: OpenStax Astronomy 2e, Chapter 23.1 (the death of low-mass stars).

Why This Matters

Sirius B, the first white dwarf discovered (from its gravitational effect on Sirius A’s motion, long before it could be directly imaged), forced nineteenth- and twentieth-century astronomers to accept that stellar matter can exist in a state with no terrestrial analog: matter compressed to planetary size while retaining roughly a solar mass, supported not by thermal pressure but by a purely quantum-mechanical effect.

Opening Phenomenon

Sirius B has a measured mass of 1.018 M☉ (from its orbit around Sirius A) yet a measured radius of only 0.008098 R☉ — about the size of Earth. Packing a solar mass into an Earth-sized volume implies an extraordinary density.

First question: what here is directly observed, and what is inferred from a physical model?

Terms for This Lecture

white dwarf

Definition: A white dwarf is supported against further gravitational collapse not by thermal pressure but by electron degeneracy pressure, a quantum-mechanical consequence of the Pauli exclusion principle: electrons packed to extremely high density resist further compression regardless of temperature.

Why it matters here: A white dwarf is a stellar remnant supported by electron degeneracy pressure rather than fusion, and this quantum-mechanical support has a hard mass limit (Chandrasekhar, about 1.4 M☉) above which no white dwarf can exist.

Relationship: Because degeneracy pressure has a maximum it can supply for a given mass, there is a maximum possible white dwarf mass, the Chandrasekhar limit (about 1.4 M☉); above this mass, degeneracy pressure cannot halt collapse.

Boundary or common confusion: Thinking a white dwarf is still generating energy by fusion. A white dwarf has no nuclear fuel left; its faint residual glow (and its slow cooling over billions of years) is purely leftover thermal energy radiating away, not ongoing energy production.

Evidence We Need to Explain

Sirius B: mass = 1.018 ± 0.011 M☉, radius = 0.008098 R☉ = 5,634 km, effective temperature = 25,000 K, luminosity = 0.0245 L☉ (Bond et al. 2017, Hipparcos parallax of 2.637 pc).
No known main-sequence star has anywhere near Sirius B’s combination of solar-scale mass and Earth-scale radius; ordinary thermal (ideal-gas) pressure cannot support such an object.
No white dwarf has ever been observed with a mass above about 1.4 M☉, and theoretical calculations independently predict exactly this mass as the maximum electron degeneracy pressure can support.

Model

When a Sun-like star exhausts its core hydrogen and later helium, it sheds its outer layers as a planetary nebula, exposing a hot, compact carbon-oxygen core: the white dwarf.
A white dwarf is supported against further gravitational collapse not by thermal pressure but by electron degeneracy pressure, a quantum-mechanical consequence of the Pauli exclusion principle: electrons packed to extremely high density resist further compression regardless of temperature.
Because degeneracy pressure has a maximum it can supply for a given mass, there is a maximum possible white dwarf mass, the Chandrasekhar limit (about 1.4 M☉); above this mass, degeneracy pressure cannot halt collapse.

Quantitative Tool

\[ \rho = \dfrac{M}{\tfrac{4}{3}\pi R^{3}}, \qquad M_{\rm Chandrasekhar} \approx 1.4\ M_\odot \]

Worked Example

Sirius B: M = 2.025e+30 kg, R = 5.634e+06 m.
Volume = (4/3)πR³ = 7.490e+20 m³.
Density = M / V = 2.703e+09 kg/m³ ≈ 2.70e+06 g/cm³.
For comparison, water has a density of 1,000 kg/m³ and Earth’s average density is about 5,510 kg/m³: Sirius B is roughly 2703302 times denser than water and about 490617 times denser than the entire Earth.
Sirius B’s mass (1.018 M☉) sits safely below the Chandrasekhar limit (1.4 M☉), consistent with its stable, observed existence as a white dwarf rather than undergoing further collapse.

Visual Reasoning

Study this lecture’s figure, built from the same numbers used in the worked example above.

What quantity is plotted, measured, or compared, and over what range?
What trend, shape, or contrast in the figure carries the physical argument?
What would change in the figure if the underlying assumption or data point were different?

Lecture 07 figure: The Death of Sun-Like Stars: White Dwarfs and the Chandrasekhar Limit.

Common Misconception

Thinking a white dwarf is still generating energy by fusion. A white dwarf has no nuclear fuel left; its faint residual glow (and its slow cooling over billions of years) is purely leftover thermal energy radiating away, not ongoing energy production.

Active Learning Segment

Using the Chandrasekhar limit, predict what happens to a white dwarf in a binary system that slowly accretes mass from a companion star and approaches 1.4 M☉ (this scenario returns in Lecture 08 as one supernova pathway).

Lab Connection

Lab 04 uses Sirius B’s measured mass and radius to compute its density and compare it to the Chandrasekhar limit and to nuclear density, quantifying just how extreme a white dwarf is.

Synthesis

A white dwarf is a stellar remnant supported by electron degeneracy pressure rather than fusion, and this quantum-mechanical support has a hard mass limit (Chandrasekhar, about 1.4 M☉) above which no white dwarf can exist.

References

OpenStax Astronomy 2e, Chapter 23.1 (the death of low-mass stars).
Local reference copy: references/openstax-astronomy-2e-extracted.txt.
Course dataset used in this lecture’s worked example: materials/ASTR230/data/.