Stellar Structure Hydrostatic Equilibrium: Radiation Mass Gas Energy Hydrostatic Equilibrium: Radiation Mass Gas Energy Generation Density Transport Temperature Radiative Composition Convective

Hydrostatic Equilibrium A Fp Dm DFg Dr F’p

The Pressure Integral A m = cosq q DA p v Dx

Overcoming the Coulomb Barrier Ucl = (3/2) kTcl → kTcl ~ 1010 K Ut = (3/2) kTt → kTcl ~ 107 K rt ~ ldeBrogle = h/p

The PP Chain

The CNO Cycle p 42He g 126C ne 137N p 157N e+ ne 136C p 158O g e+ 147N p 42He g 126C ne 137N p 157N e+ ne 136C p 158O g e+ 147N g p

Binding energy per nucleon Endothermic Energy can be liberated via nuclear fission Exothermic Energy can be liberated via nuclear fusion

Convection Adiabatic expansion: P = K*rg

Favorable Conditions for Convection Large Opacities → Large |dT/dr|rad Partial Ionization Zones → Brings g close to 1 → small |dT/dr|ad Low g → small |dT/dr|ad = g/Cp Strongly T-dependent energy generation (CNO cycle!) → large |dT/dr|

Stellar energy transport structure as a function of stellar mass R/R* 1 M/M0 90 0.08 0.25 1.2 1.3 Sun-like stars (0.25 M0 < M < 1.2 M0): Radiative core; convective envelope High-Mass stars (M > 1.3 M0): Convective core; radiative envelope Low-mass stars (M < 0.25 M0): Completely convective

=> Almost 1-dimensional Zero-Age Main Sequence (ZAMS) Vogt-Russell Theorem The mass and composition of a star uniquely determine its radius and luminosity, internal structure, and subsequent evolution. => Almost 1-dimensional Zero-Age Main Sequence (ZAMS)

Masses of Stars in the Hertzsprung-Russell Diagram Masses in units of solar masses 40 18 The higher a star’s mass, the more luminous (brighter) it is: High masses 6 3 L ~ M3.5 1.7 1.0 High-mass stars have much shorter lives than low-mass stars: Mass 0.8 0.5 tlife ~ M-2.5 Sun: ~ 10 billion yr. Low masses 10 Msun: ~ 30 million yr. 0.1 Msun: ~ 3 trillion yr.

Convective Core, radiative envelope; Summary: Stellar Structure Convective Core, radiative envelope; Energy generation through CNO Cycle Sun Mass Radiative Core, convective envelope; Energy generation through PP Cycle

Energy Transport Structure Inner convective, outer radiative zone Inner radiative, outer convective zone CNO cycle dominant PP chain dominant