White-dwarf M–R track for n = 3/2 cold degenerate electrons; UR n = 3 marks the ~1.44 M☉ scale (μ_e dependent).
About this model
This page uses the textbook Newtonian Lane–Emden model for a spherically symmetric star supported by a cold, completely degenerate electron gas. In the non-relativistic limit the pressure scales as P ∝ ρ^(5/3), corresponding to a polytrope of index n = 3/2. Homologous scaling along that sequence gives M ∝ ρ_c^(1/2) and R ∝ ρ_c^(−1/6) in Newtonian gravity. In the ultra-relativistic limit P ∝ ρ^(4/3) (n = 3), the Lane–Emden mass becomes independent of central density in Newtonian theory and sets the Chandrasekhar mass scale M_Ch ∝ (ħc/G)^(3/2)/(μ_e m_u)^2. General relativity, finite temperature, Coulomb corrections, and composition gradients change the numerical maximum to about 1.4 M☉ for carbon/oxygen white dwarfs; the plotted UR line is the Newtonian schematic (~1.45 M☉ at μ_e = 2).
Who it's for: Upper-level undergraduate astrophysics after degenerate matter and polytropes; pairs with neutron-star TOV and HR diagram pages.
Key terms
Chandrasekhar mass
white dwarf
Lane–Emden equation
polytrope
degenerate electrons
mean molecular weight per electron
How it works
A cold, spherically symmetric white dwarf is modeled as a Newtonian self-gravitating polytrope with P ∝ ρ^(5/3) from a non-relativisticT = 0degenerate electron gas (Lane–Emden index n = 3/2). Along this sequence M ∝ ρ_c^(1/2) and R ∝ ρ_c^(−1/6), so more compact cores carry more mass in this toy EOS. The ultra-relativisticP ∝ ρ^(4/3) limit (n = 3) yields a mass plateau in Newtonian theory — the ChandrasekharscaleM_Ch ∝ μ_e^(−2) (here ~1.45 M☉ for μ_e = 2). General relativity and finite-temperature / composition effects move the physical maximum to ≈ 1.4 M☉; this page is schematic only.
Frequently asked questions
Why can the n = 3/2 track exceed the gold Chandrasekhar line?
The cyan curve is the Newtonian non-relativistic EOS only; it has no upper mass bound. Real stars need the relativistic crossover and GR, which cap the stable mass near ~1.4 M☉.
What is μ_e?
Electrons per baryon in the ionized bulk: μ_e = 2 for equal carbon and oxygen (one electron per two nucleons on average), lower for hydrogen-rich compositions in the same counting convention.