Stellar astrophysics

Stellar astrophysics studies the structure, formation, energy production, observable properties, and evolution of stars.

Stellar structure follows from mass conservation, hydrostatic equilibrium, energy generation, and energy transport together with an equation of state and opacity law.

A stellar polytrope obeys $P=K{\rho }^{1+1/n}$ for constant $K$ and polytropic index $n$. Its dimensionless density profile satisfies the Lane-Emden equation.

Homologous stellar models have the same dimensionless radial profiles after mass, radius, density, pressure, and temperature are scaled by characteristic values.

In a radiative stellar region, photons carry luminosity down the temperature gradient. Dimensional scaling of the radiative-diffusion equation gives $L\sim R{T}_c^4/({\kappa }_c{\rho }_c)$.

The mass-luminosity relation connects a star's mass to its luminosity. Its slope depends on opacity, nuclear burning, pressure support, composition, and evolutionary state.

Balancing outward radiative acceleration against gravity givesIt is an approximate upper luminosity for a hydrostatic star of opacity $\kappa$.

Stellar nuclear fusion converts light nuclei into more tightly bound nuclei and supplies most main-sequence stellar luminosity.

The proton–proton chain converts hydrogen to helium and dominates hydrogen burning in stars near and below the Sun's mass. Near $2\times 10^7\mathrm{K}$, its specific energy generation is roughly proportional to $\rho T^4$.

The CNO cycle catalyses hydrogen fusion through carbon, nitrogen, and oxygen nuclei. Near $2\times 10^7\mathrm{K}$, its specific energy generation is approximately proportional to $\rho T^{17}$ and is therefore strongly concentrated near a star's centre.

A main-sequence star is in a long-lived phase of core hydrogen burning.

The zero-age main sequence is the locus where stars begin stable core hydrogen burning with nearly their initial composition.

Stellar evolution is the change of a star's structure and composition as nuclear reactions, energy transport, mass loss, and interactions proceed.

A binary star is a gravitationally bound pair orbiting their common centre of mass.

A Roche lobe is the region around one component of a circular binary inside the critical effective-potential surface through the inner Lagrange point.

Conservative binary mass transfer moves matter between the components while preserving total binary mass and orbital angular momentum.

Binary mass transfer is dynamically stable when the donor's radius decreases relative to its Roche-lobe radius after a small mass loss, reducing overflow instead of amplifying it.

A common-envelope phase occurs when unstable binary interaction engulfs both stellar cores in one envelope. Orbital energy and angular momentum may eject the envelope, leaving a compact binary, or the cores may merge.