EXAM II Monday Oct 19 th (this coming Monday!) HW5 due Friday midnight

Our Sun

M sun = 333,000 x M earth 98 % H and He 2 % others

What makes it glow so? Can’t be burning chemically, it’d burn out in 10,000 years! Can’t be due to Kelvin Helmholtz heating, it’d be only 25 My old! It’s HOT  Nuclear fusion

Nuclear physics 101

p + Proton 1 H (1+) n Neutron Recall: the nuclei of elements are made of Neutral, aids in nucleon binding (strong force)

Mostly 1 H + at high temps and pressure. Fuse to make 4 He with a release of energy “Fusion” The sun creates energy (in its youth) by fusing H into He Hydrogen plasma Background of free electrons

Light elements can release energy when fused 2H2H + release of energy Nuclear force binds them when they’re close enough together 1H1H common in sun! rare Binding decreases the net mass  energy

Light elements can release energy when fused 2H2H Neutron unstable when alone Stable when bound Energy decays in about 15 mins. rare

Neutron decay is reversible: + ‘energy’If + ‘energy’Then

What if we try fusing two hydrogen nuclei? 1H1H common in sun! 1H1H ?

What if we try fusing two hydrogen nuclei? 1H1H common in sun! 1H1H + release of energy Borrows some binding energy … 2H2H Converting to a neutron

The sun creates energy (in its youth) by fusing H into He 1H1H 1H1H rare 4 He A four particle collision, two of which are rare when isolated! A very unlikely scheme

The proton-Proton chain How our sun makes He !

energy

The proton-proton chain Energy release Annihilates with plasma electron to make a  -ray photon Escapes the sun (2% total energy

The net result: back into circulation

Why must it be hot to start fusion?

+ + Coming in from far away with this velocity (temperature) Two protons colliding… Long-range electrostatic repulsion Strong force is short range – no nuclear attraction yet

+ +

+ + STOP Distance of closest approach

+ +

+ +

+ + Remember: temperature of a gas is just related to the average kinetic energy of the gas particles

Temperature T Distance of closest approach

Temperature T Range of strong force (attractive) Distance of closest approach Minimum temperature for p-p fusion ~13.6 ×10 6 K !

How it got started ….

Gravitational Compression: Cool hot Kelvin-Helmholtz heating

Gravitational Compression: Cool really hot! fusion! Kelvin-Helmholtz heating T > 13.6 ×10 6 K

Core regulation ! (negative feedback system)

The sun in equilibrium (a big gas ball) Gravitational equilibrium Thermal equilibrium

Ball of gaseous hydrogen some small volume

P - pressure T - temperature n - density Ball of gaseous hydrogen

Hydrostatic or Gravitational equilibrium:

Three forces must balance at each point ….

1: Weight of mass shell itself

2: Combined Weight of all gas above

3: Pressure exerted by the gas below

Thermal equilibrium:

Thermal energy generated (fusion) For T to remain constant here … Heat in = Heat out Heat flow

Thermal energy generated (fusion) = energy radiated from surface

Two major mechanisms of heat flow (in stars): 1) convection 2) radiative diffusion

Convection heat sink heat source

hot cool Convection heat sink heat source

Convection hot expand less dense cool contract more dense heat sink heat source

Convection hot expand less dense cool contract more dense gravity heat sink heat source

heat sink Convection hot expand less dense cool contract more dense float sink

heat source heat sink cools and contracts heat and expands ready to go again Convection

the steady-state situation: heat sink heat source convection cells T, P and  at every point is constant in time. Fusion, compression Matter and energy into space

Heat/Light source (fusion) Relatively ‘transparent’ Relatively ‘opaque’ Mostly ions Mostly 1 H atoms p + and e - Radiative diffusion

photon Relatively ‘transparent’ Relatively ‘opaque’ Atomic absorption and re-emission: Build up of heat e - scattering

pressure temperature density For any radius Hydrostatic equilibrium Thermal equilibrium Complicated model of equilibrium solar structure Solution Fusion energy source

Fusion core

13.6 ×10 6 K 5,800 K

Summaries of Solar Interior:

Fusion Core:

Mass: 94% of all mass inside

Density: center 14 × lead 0.3 R lead 0.5 R water 0.9 R 2 × air

0.7 R T ~ 2 MK Opacity: transparent opaque ions atoms

0.7 R T ~ 2 MK Heat Transfer: transparent opaque photons Radiative zone Convective zone 5,800 K Thermal radiation “hundreds of thousands of years”