Chandrasekhar limiteffect
A white dwarf is a star the size of Earth, but with the mass of the Sun. It resists gravity with the help of quantum pressure from electrons. The Chandrasekhar limit is the mass at which electrons 'give up', and the star collapses into a neutron star or black hole. Roughly speaking, 1.4 solar masses.
How it works
In a white dwarf, electrons fill all the lowest energy levels (Pauli principle). When compressed, they acquire enormous kinetic energy, creating pressure. If the mass exceeds the limit, even relativistic electrons cannot hold off collapse, and the core becomes a neutron star.
💡 It is because of this limit that exploding white dwarfs have become cosmic 'beacons' by which the expansion of the Universe is measured.
M_{\text{Ch}} = \frac{\omega_3^0 \sqrt{3\pi}}{2} \left(\frac{\hbar c}{G}\right)^{3/2} \frac{1}{(\mu_e m_H)^2}
ω_3^0 is the Lane-Emden constant for a polytrope with index n=3 (approximately 2.018), ℏ is the reduced Planck constant (ℏ ≈ 1.0546×10⁻³⁴ J·s), c is the speed of light (c ≈ 3×10⁸ m/s), G is the gravitational constant (G ≈ 6.674×10⁻¹¹ N·m²/kg²), μ_e is the mean molecular mass per electron (for fully ionized carbon μ_e = 2), m_H is the mass of the hydrogen atom (m_H ≈ 1.673×10⁻²⁷ kg).
M_{\text{Ch}} \approx 1.4 \, M_{\odot}
M_☉ is the solar mass (M_☉ ≈ 1.989×10³⁰ kg), numerical value about 1.4 solar masses.