Ch 11 & 12 : Star Structure

Ch 11 & 12 : Star Structure • What is the interior structure of stars?

(1) Hydrostatic Equilibrium • When a star is stable • (neither expanding or contracting) • Everywhere within the star : • inwards force = outwards force • gravity = pressure • This condition is called : • Hydrostatic equilibrium • Hence : P↑ as R↓ • Since P = ρ x T (density x Temp) • We have : • ρ ↑ as R↓ hot, dense, high • T ↑ asR↓ pressure cores • e.g. Sun : P = 1011 atm; ρ = 150 gm/cm3 • T = 14 x 106 K

(2) Energy generation in the core • Hydrogen fusion occurs in the core : 4H  4He + Energy • Detailed reactions depend on star mass • Low mass low T  p-p chain (e.g. the sun) • High mass  high T  CNO cycle (12C acts as catalyst) • [ C,N,O have high Coulomb barrier  needs high T ] p-p chain CNO cycle

(3) Energy Transport : core  surface • Energy generated in the core gets to the surface • How does it travel ? • Three possible transport mechanisms : • Radiation (yes), convection (yes), conduction (no) • e.g. for the Sun : inner 80% radiation; outer 20% convection • Radiative transport is slow (~107 yr); convection is rapid (days)

(3b) Variation with star mass • details depend on internal properties • Higher mass stars : convective cores & radiative envelopes • Lower mass stars : radiative cores & convective envelopes

(4) Stability : stellar thermostat • Why isn’t a star like a giant H-bomb? • e.g. nuclear reactions increase with T  runaway explosion ? • Imagine if there is a change in the core : • e.g. an increase in energy production (i.e. L ↑) • L↑  P↑  core expands  ρ↓ (& T↓)  L↓ • Conversely, what about a decrease in L • L↓ P↓  core contracts  ρ↑ (& T↑)  L↑ • In both cases, the core is self-correcting! • There is negative feedback and the core is stable.

(5) Stellar Computer Models • interior conditions can be expressed mathematically • Hydrostatic equilibrium; Energy transport ; Energy generation • 4 coupled differential equations  solve on computer • result must match star radius; luminosity; surface temp; mass Solution is a stellar model ρ( r,t) T(r,t) L(r,t) Note: models evolve over time

mass mass temperature luminosity density density temperature luminosity (5b) Model Results : The Sun • Graphing the computer results for the present day Sun: •  dense energy producing core + large thin envelope

Ch 11 & 12 : Star Structure