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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”