Foundations

For a spherical quasistatic Newtonian star, enclosed mass increases with shell volume and density, while the pressure gradient balances gravity due to enclosed mass.

In an optically thick stellar region close to local thermodynamic equilibrium, radiative diffusion relates luminosity to the temperature gradient through density and an appropriate mean opacity.

A stellar shell's luminosity divergence accounts for local energy production, change in specific internal energy and compression or expansion work.

A displaced parcel that adjusts pressure rapidly but exchanges little heat can continue rising when it becomes less dense than its environment.

The proton–proton chains and CNO cycles convert hydrogen into helium through different reaction sequences; CNO nuclei participate in a catalytic cycle.

An HR diagram compares luminosity with effective temperature or a related spectral classification.

A resolved relative orbit and period can constrain a binary's total mass through Newtonian two-body dynamics.

Cold dense regions of molecular clouds can contract gravitationally when support is insufficient.

Radial stellar pulsation has a characteristic gravitational/acoustic period scale proportional to √[R³/(GM)].

Stellar opacity includes electron scattering, bound–bound transitions, photoionization/recombination and free–free processes.

In a nondegenerate ideal ionized mixture in local thermal equilibrium, ions and electrons contribute their number densities to gas pressure; isotropic thermal radiation adds a radiation-pressure term.

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.

Dynamical readjustment has scale t_dyn∼(Gρ̄)⁻¹ᐟ², while radiating a gravitational energy reservoir gives Kelvin–Helmholtz scale t_KH∼GM²/(RL).

For a Newtonian hydrostatic spherical star with negligible surface pressure and classical monatomic ideal-gas support, integrating pressure balance gives 2U_th+W=0, where W is gravitational binding energy.

A spherical Newtonian hydrostatic polytrope assumes P=Kρ¹⁺¹⁄ⁿ.

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).

Neutron-star pulsars have rotating magnetized stellar remnants whose emission can sweep past the observer.

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.

Matter moving inward in a gravitational field can release binding energy if energy is dissipated.

For isotropic luminosity L and a constant flux-weighted opacity per mass κ, outward radiative acceleration is κL/(4πr²c).

In a circular two-point-mass binary's corotating frame, the effective potential per mass is Φ_eff=−GM₁/r₁−GM₂/r₂−Ω²(x²+y²)/2, with origin at the barycentre and Ω²=G(M₁+M₂)/a³.

The ppI branch builds deuterium and helium-3 before combining two helium-3 nuclei.

A classical black-hole event horizon is a causal boundary: signals from its interior cannot reach distant future observers in the exterior.

A collisionless distribution follows Hamiltonian trajectories in a mean gravitational potential.

The stationary spherical nonrotating Jeans moment equation connects tracer density and radial velocity dispersion to enclosed mass through velocity anisotropy.

A projected dispersion averages line-of-sight moments through the tracer system.

Discretize stellar structure, transport and composition into a residual vector F(y).

A stellar or planetary EOS can blend differently valid microscopic models.

Angle-dependent radiative transfer yields moments J,H,K; flux is 4πH.

NonLTE level populations solve coupled radiative and collisional rate equations with particle/charge constraints and the transfer solution.