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Ch 11 & 12 : Star Structure

This text delves into the interior structure of stars, focusing on hydrostatic equilibrium, energy generation processes, and how energy travels from the core to the surface. Hydrostatic equilibrium describes a star's stability, where inward gravitational forces balance outward pressure. Energy generation occurs primarily through hydrogen fusion in the core, varying by star mass. Different energy transport mechanisms, including radiation and convection, play critical roles. The stability of stars is maintained through negative feedback processes, allowing them to self-correct against changes in energy production.

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Ch 11 & 12 : Star Structure

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

  2. (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

  3. (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

  4. (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)

  5. (3b) Variation with star mass • details depend on internal properties • Higher mass stars : convective cores & radiative envelopes • Lower mass stars : radiative cores & convective envelopes

  6. (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.

  7. (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

  8. 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

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