EXAM IIMonday Oct 19th

(this coming Monday!)

HW5 due Friday midnight

Our Sun

Msun = 333,000 x Mearth

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 1H (1+)

n Neutron

Recall: the nuclei of elements are made of

Neutral, aids in nucleon binding

(strong force)

Mostly 1H+ at high temps and pressure. Fuse to make 4He with a release of energy

“Fusion”

The sun creates energy (in its youth) by fusing H into He

Hydrogen plasmaBackground of free electrons

Light elements can release energy when fused

2H

+ release of energy

Nuclear force binds them when they’re close enough together

1Hcommon in sun!

rare

Binding decreases the net mass energy

Light elements can release energy when fused

2H

Neutron unstable when alone

Stable when bound

eepn

Energy

decays in about 15 mins.

rare

Neutron decay is reversible:

+ ‘energy’If

+ ‘energy’Then

What if we try fusing two hydrogen nuclei?

1H

common in sun!

1H

?

What if we try fusing two hydrogen nuclei?

1H

common in sun!

1H

+ release of energy

Borrows some binding

energy …

2H

Converting to a neutron

The sun creates energy (in its youth) by fusing H into He

1H

1Hrare

rare4He

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

energy

energy

energy

energy

energy

energy

energy

energy

energy

H2

H2

He3

He3

He4

energy

The proton-proton chain

ee HHH 211

HeHH 321

pp HeHeHe 433

Energy release

Annihilates with plasma electron to make a g -ray photon

Escapes the sun (2% total energy

energyH2HeH6 141

energyHeH4 41

The net result:

back into circulation

Why must it be hot to start fusion?

+ +V V

Coming in from far away with this velocity (temperature)

Two protons colliding…

Long-range electrostatic repulsion 2

1

d

Strong force is short range – no nuclear attraction yet

+ +

+ +

d

STOP

Distance of closest approach

+ +

+ +V V

+ +

Td

1

KE

1

d

Distance of closest approach

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

Temperature T

Dist

ance

of c

lose

st a

ppro

ach

Temperature T

Range of strong force (attractive)

Dist

ance

of c

lose

st a

ppro

ach

Minimum temperature forp-p fusion

~13.6 ×106 K !

How it got started ….

Gravitational Compression:

Cool

hot

Kelvin-Helmholtz heating

Gravitational Compression:

Cool

really hot!

fusion!

Kelvin-Helmholtz heating

T > 13.6 ×106 K

Core regulation !(negative feedback system)

The sun in equilibrium

(a big gas ball)

• Gravitational equilibrium

• Thermal equilibrium

Ball ofgaseous hydrogen

some small volume

r

P - pressureT - temperaturen - density

Ball ofgaseous hydrogen

nkTP

Hydrostatic or Gravitational equilibrium:

r

Three forces must balance at each point ….

inM

inM

1: Weight of mass shell itself

inM

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 source

heat sink

Convection

hot

expand

less dense

cool

contract

more dense

float

sink

heat source

heat sinkcools and contracts

heat and expands

ready to go again

Convection

the steady-state situation:

heat sink

heat source

convection cells

T, P and r at everypoint is constant intime.

Fusion, compression

Matter and energy into space

Heat/Light source(fusion)

Relatively‘transparent’

Relatively‘opaque’

Mostly ions

Mostly 1H atoms

p+ and e-

Radiative diffusion

Radiative diffusion

photon Relatively‘transparent’

Relatively‘opaque’

Atomic absorption and re-emission:Build up of heat

e- scattering

pressuretemperaturedensity

For any radius

Hydrostatic equilibrium

Thermal equilibrium

Complicated model of equilibrium solar

structure

Solution

Fusion energy source

Fusion core

13.6 ×106 K

5,800 K

Summaries of Solar Interior:

Fusion Core:R

4

1

Mass:

R2

1

94% of all mass inside

Density: center 14 × lead

0.3R lead

0.5R water

0.9R 2 × air

0.7 RT ~ 2 MK

Opacity:

transparent

opaque

ions

atoms

0.7 RT ~ 2 MK

Heat Transfer:

transparent

opaque

photons

Radiative zone

Convective zone5,800 KThermal radiation

“hundreds of thousands of years”