White dwarfs, neutron stars and stellar black holes
Earth & cosmos
Different evolutionary outcomes leave different compact remnants.
Key knowledge
After loss of outer layers, many lower-mass stellar progenitors leave white dwarfs. Core collapse of sufficiently massive progenitors can leave neutron stars or stellar black holes. These outcomes depend on remnant properties and evolutionary history, rather than one universal initial-mass threshold.
Conditions and scope
This describes common stellar evolutionary channels, not the origin of every black hole or every transient.
Binary interaction, mass loss and explosion dynamics can change outcomes; not every core collapse produces an identical visible supernova.
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References
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After loss of outer layers, many lower-mass stellar progenitors leave white dwarfs. Core collapse of sufficiently massive progenitors can leave neutron stars or stellar black holes. These outcomes depend on remnant properties and evolutionary history, rather than one universal initial-mass threshold.
Compact remnant outcomes depend on the progenitor's evolution.
For an ideal spin-½ electron gas with k_BT much smaller than its kinetic Fermi energy, occupied momentum states extend to p_F=ℏ(3π²nₑ)¹ᐟ³. The nonrelativistic limit has P=ℏ²(3π²)²ᐟ³nₑ⁵ᐟ³/(5mₑ); the ultrarelativistic limit has P=ℏc(3π²)¹ᐟ³nₑ⁴ᐟ³/4. These leading pressures are temperature-independent.
Electron support is relevant to white dwarfs; other remnants need further matter physics.
Cold noninteracting electron support and spherical Newtonian hydrostatic balance give a nonrelativistic n=3/2 polytrope with R proportional to μₑ^(−5/3)M^(−1/3). As electron momenta become relativistic, the pressure approaches K_URρ^(4/3), an n=3 polytrope whose mass is independent of central density. Its ideal limiting mass is M_Ch=4π ω₃[K_UR/(πG)]^(3/2), proportional to μₑ^(−2). This is a limiting electron-support model, not a universal initial stellar-mass threshold.
White dwarfs differ physically from neutron-star and black-hole remnants.
Neutron-star pulsars have rotating magnetized stellar remnants whose emission can sweep past the observer. For a rotation-powered model with constant moment of inertia I, E_rot=IΩ²/2=2π²I/P² and rotational energy loss is −dE_rot/dt=4π²IṖ/P³. This inferred power is distinct from luminosity measured in one observing band. Under constant PṖ and negligible initial period, the characteristic age is τ_c=P/(2Ṗ).
The neutron-star remnant interpretation differs from white-dwarf electron support.
Core-collapse supernovae involve loss of support in an evolved stellar core, rapid contraction and an explosion whose energy transfer involves dense matter and neutrinos. Electron capture can reduce electron support; photodisintegration can absorb energy. Type Ia supernovae instead arise from thermonuclear burning in a white-dwarf system. Spectral classification and physical mechanism are distinct: core-collapse events need not retain a hydrogen envelope, and no single binary progenitor channel accounts by definition for every Type Ia event.
Collapse and explosion affect the resulting compact object.
A classical black-hole event horizon is a causal boundary: signals from its interior cannot reach distant future observers in the exterior. In the stationary nonrotating uncharged asymptotically flat Schwarzschild black-hole model, the horizon's areal radius is r_s=2GM/c². It is not a material surface.
A black-hole remnant requires a causal model distinct from electron/neutron support.