White Dwarf
A white dwarf is the dense, compact stellar remnant left behind after a low-to-intermediate mass star (0.5–8 M☉) has shed its outer layers as a planetary nebula, leaving an Earth-sized sphere of electron-degenerate matter composed primarily of carbon and oxygen at densities of ~10⁶ g/cm³. Unlike main sequence stars, white dwarfs are not powered by nuclear fusion; they simply radiate their residual thermal energy, cooling over billions to trillions of years from initially blue-white temperatures through yellow and orange to the theoretical endpoint of a cold, dark "black dwarf". The maximum mass a white dwarf can have before collapsing is the Chandrasekhar limit of ~1.4 M☉.
Key Formula
Chandrasekhar limit M_Ch = 5.83 / μe² × M☉ ≈ 1.4 M☉
LaTeX: M_{\text{Ch}} = \frac{5.83}{\mu_e^{2}}\,M_\odot \approx 1.4\,M_\odot
| Symbol | Meaning | Unit |
|---|---|---|
| M_Ch | Chandrasekhar limiting mass | M☉ |
| μe | Mean molecular weight per electron (≈2 for C/O) | dimensionless |
| M☉ | Solar mass (1.989×10³⁰ kg) | kg |
Worked Example
Problem
Sirius B is a white dwarf with mass 1.02 M☉ and radius 0.0084 R☉ (R☉ = 6.957×10⁸ m). Calculate its average density in g/cm³.
Solution
Step 1 – Find mass: M = 1.02 × 1.989×10³⁰ = 2.029×10³⁰ kg. Step 2 – Find radius: R = 0.0084 × 6.957×10⁸ = 5.844×10⁶ m. Step 3 – Find volume: V = (4/3)πR³ = 4.189 × (5.844×10⁶)³ = 4.189 × 1.996×10²⁰ = 8.36×10²⁰ m³. Step 4 – Calculate density: ρ = M/V = 2.029×10³⁰ / 8.36×10²⁰ = 2.43×10⁹ kg/m³. Step 5 – Convert: 2.43×10⁹ kg/m³ × 10⁻³ g/kg × 10⁻⁶ m³/cm³ = 2.43×10⁶ g/cm³.
Answer
The average density of Sirius B is approximately 2.43×10⁶ g/cm³, about 2.43 million times the density of water.
Properties of Well-Known White Dwarfs
| White Dwarf | Mass (M☉) | Radius (R☉) | Temperature (K) | Companion Star |
|---|---|---|---|---|
| Sirius B | 1.02 | 0.0084 | 25,200 | Sirius A (A-type) |
| Procyon B | 0.60 | 0.0123 | 7,740 | Procyon A (F-type) |
| 40 Eridani B | 0.50 | 0.0136 | 16,500 | 40 Eridani A (K-type) |
| Van Maanen's Star | 0.68 | 0.0113 | 6,200 | None (isolated) |
| LP 145-141 | 0.61 | 0.0130 | ~8,500 | None (isolated) |
Interactive Tools
Wikimedia Commons, CC BY-SA
Related Terms
Red Giant
A red giant is a luminous, greatly expanded star in a late stage of stellar evolution that has exhausted the hydrogen fuel in its core; the core contracts and heats up while the outer layers expand dramatically, cooling and reddening to surface temperatures of 3,500–5,000 K. For Sun-like stars (0.5–8 M☉), the red giant phase follows departure from the main sequence when hydrogen shell burning drives the envelope to expand up to 200 times the star's original radius. Red giants eventually shed their outer layers to form planetary nebulae, leaving behind a white dwarf, while more massive stars may become red supergiants and ultimately explode as supernovae.
Neutron Star
A neutron star is an extraordinarily dense stellar remnant formed when the core of a massive star (8–20 M☉) collapses during a Type II supernova, compressing a mass of 1.2–2.1 M☉ into a sphere only ~10–13 km in radius, resulting in densities comparable to atomic nuclei (~10¹⁴ g/cm³). The star is supported against further gravitational collapse by neutron degeneracy pressure—a quantum mechanical effect arising from the Pauli exclusion principle—rather than thermal or radiation pressure. Neutron stars often manifest as rapidly rotating pulsars, emitting beams of electromagnetic radiation from their magnetic poles at highly regular intervals, and they are key sources of gravitational waves when in binary systems.
Supernova
A supernova is an extraordinarily energetic stellar explosion that marks the catastrophic death of certain types of stars, releasing in seconds as much energy (roughly 10⁴⁴ J) as the Sun will radiate over its entire 10-billion-year lifetime, and briefly outshining an entire galaxy. Type Ia supernovae occur when a white dwarf in a binary system accretes enough mass to exceed the Chandrasekhar limit (~1.4 M☉), triggering runaway nuclear fusion; Type II supernovae occur when the iron core of a massive star (>8 M☉) collapses under gravity, producing a shockwave that ejects the outer layers. Supernovae are the primary source of elements heavier than iron in the universe and are used as "standard candles" in cosmology to measure vast intergalactic distances.
The term "white dwarf" was coined by the Dutch-American astronomer Willem Luyten in 1922, describing the faint, hot (white-coloured) but compact (dwarf) nature of these objects, in contrast to the cool red dwarfs. "Dwarf" derives from Old English "dweorh" via Proto-Germanic. Subrahmanyan Chandrasekhar derived the theoretical mass limit in 1930–1931.