test 2 results

Slide 1

test 2 distribution

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score bins

nu

mb

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ents

Test 2 results

Test 2 average: 77 (test 1: 82)Test 2 median: 79 (test 1: 87)

Slide 2

SOHO: The Solar and Heliospheric Observatory

1.5 million km from the Earth at the L1 point

Slide 3

The Lagrange Points

L4,5: Trojans (stable points)L1: SOHOL2: WMAPL3: empty

(unstable points)

Slide 4

Gravitational potential in the corotating frame

Slide 5

What we want to know:

• Internal structure and composition

• Source of energy

• Lifetime

Slide 6

Slide 7

Life of stars:Gravity is everything

• Stars are born due to gravitational collapse of gas clouds

• Star’s life is a battle between thermal pressure generated by nuclear reactions and gravity

• Eventually, a star loses this battle, and gravity overwhelms

Slide 8

Gravity is balanced by thermal gas pressure

Stars are held together by gravity. Gravity tries to compress everything to the center. What holds an ordinary star up and prevents total collapse is thermal and radiation pressure. The thermal and radiation pressure tries to expand the star layers outward to infinity.

Slide 9

Stars are gravitating spheres: they are held together by their own gravity. The gravity force acting on each volume element of a star is exactly balanced by gas pressure (Hydrostatic equilibrium)

This balance is steady

gravity

gas pressure

No gravity: the Sun will disperse in 1 day

No gas pressure: the Sun willcollapse in 20 minutes

km/s103

m

Tkv Bthermal

22

2

m/s274;2

~ R

GMg

gtR Central pressure ~ 1010 atmospheres

Slide 10

Hydrostatic equilibrium

Temperature in the center of a star

A =1 m2

RRAM column

R

GM

R

GMMP

~

2gravitycolumn

TkP thermal=

K10~ 7

kR

GMTc

Slide 11

Internal structure

Central temperature Tc 1.5107 K

Surface temperature Tc 5800 K

Heat transfer from the center to the surface!

Heat transfer determines both the internal compositionand the luminosity of the Sun

Slide 12

Internal source of energy

• Gravitational energy?

• Chemical energy?

• Nuclear reactions?

The Sun’s luminosity is L = 4x1026 Watt. Where does this energy come from?

Slide 13

Chemical energy?

This is the energy associated with breaking chemical bonds in molecules

1. Typical energy released per proton is ~ 1-10 eV

2. There are M/mp ~ 1057 protons in the Sun

Total available energy is Echem ~ 10x1057 = 1058 eV ~ 2x1039 J

Chemical energy will be radiated away during the time

years105chem L

Et

But the Sun’s age is at least 4.6 billion years!Also, there is too hot for molecules in the sun

Slide 14

Note:

If E is total energy stored in the sun (in J);

L is luminosity, or the rate with which this energy is spent(in J/sec);

Then the time it takes to spend all energy is T = E/L sec

Slide 15

Gravitational energy?

J104 41R

GMMU g

As the Sun radiates its thermal energy to outer space, it shrinks, and the central temperature is increased (!)

The energy source is the gravitational energy of a star

If the energy is radiated away with luminosity L = 4x1026 J/s,The Sun would radiate all its energy during the time

years103 7L

Ut g

But the Sun’s age is at least 4.6 billion years!

Slide 16

Nuclear reactions?

Slide 17

Nuclear reactions?

• Fission: decay of heavy nuclei into lighter fragments

•Fusion: synthesis of light nuclei into a heavier nucleus

Energy released per proton is ~10-20 MeV!!

Slide 18

Energy is released in fusion reaction if the sum of masses of initial nuclei is larger that the mass of the final nucleus

mp + mp

MD + me < 2 mpDeuterium

Positron (antielectron)

neutrino

Deuterium has larger binding energy than protons (more tightly bound)

M = 2 mp- MD - me

Energy released E = M c2

Famous Einstein’s relation: E = mc2

hydrogen

hydrogen

Slide 19

What is binding energy?

It exists due to attractive forces between parts of a compound system: protons and neutrons in a nucleus, electrons and ion in an atom, Earth and moon, etc.

Binding energy is negative!: Ub = -|Ub|

Total energy of a system is the sum of energies of its parts plus binding energy:

E = E1 + E2 + Ub = E1 + E2 - |Ub|

Slide 20

Energy is released in fission reaction if the mass of an initial nucleus is larger that the sum of masses of all final fragments

MU > MRb + MCs + 3 mn

Rubidium and Cesium are more tightly bound, or have larger binding energy than Uranium.

It is energetically favorable for Uranium to split.

When is the energy released in fission reactions?

M = MU – (MRb + MCs + 3 mn)

Energy released E = M c2

Famous Einstein’s relation: E = mc2

Slide 21

There are no heavy elements on the stars

|Ub|

Slide 22

Energy ProductionEnergy generation in the sun

(and all other stars):

Nuclear Fusion

= fusing together 2 or more lighter nuclei to produce heavier ones.

Nuclear fusion can produce energy up to the production of iron;

For elements heavier than iron, energy is gained by nuclear fission.

Binding energy due to strong force = on short range, strongest of the 4 known forces: electromagnetic, weak, strong, gravitational

Slide 23

Slide 24

Proton-proton cycle: four hydrogen nuclei fuse to form one helium nucleus

Hydrogen Fusion

Slide 25

Einstein’s relation: E = mc2

!04 mmm Hep

J103.4MeV8.26 122 cmE

Energy released in one reaction:

(Binding energy)

kg10048.0 27m

Hans Bethe 1939

0.007, or 0.7% of the rest energy of protons (4mpc2) is released

This is 107 times more efficient than chemical reactions!

Slide 26

There is more than enough nuclear fuel for 1010 years!

years10310104 10

5612

Lt

Does nuclear fusion provide enough energy to power the Sun?

Assume 1056 protons in the core:

Slide 27

600 million tons of hydrogen are fused every second on the Sun!

How much hydrogen should be fused per second to provide the Sun’s luminosity?

W104sec1

007.0 262 cm

L

Nuclear fusion efficiency:0.7% of the hydrogen mass is converted into radiation in the p-p cycle

Matter-antimatter annihilation has even higher efficiency: 100% !!

kg106007.0

104 112

26

c

m

Slide 28

Proton-proton cycle

Slide 29

Proton-proton cycle

Step 1

Step 2

Step 3

All positrons annihilate with electrons creating gamma-quanta

Slide 30

Step 11H + 1H --> 2H + positron + neutrino

To fuse, two protons need to be as close as 10-15 m to each other

They need to overcome the Coulomb barrier

r

keU c

2

Coulomb repulsion energy:

Slide 31

Protons should be hot!

Slide 32

But we need T > 109 K to overcome the Coulomb barrier!

• Quantum tunneling helps

Still, a proton has 1 chance in 10 billion years to fuse!

Such reaction is nearly impossible

Slide 33

Step 2

Takes 6 seconds to occur

Slide 34

Step 3

Takes 1 million years to occur

Slide 35

The solar neutrino problem

Slide 36

•Matter is effected by forces or interactions (the terms are interchangeable) •there are four fundamental forces in the Universe:

•gravitation (between particles with mass) •electromagnetic (between particles with charge/magnetism) •strong nuclear force (between quarks) •weak nuclear force (that changes quark types)

Matter is effected by forces or interactions (the terms are interchangeable)

There are four fundamental forces in the Universe: gravitation (between particles with mass) electromagnetic (between particles with charge) strong nuclear force (between quarks) weak nuclear force (that changes quark types)

Slide 37

10,000 years

Neutrino have zero or very small mass and almost do not interact with matter

Slide 38

Neutrino image of the Sun

Slide 39

The Davis experiment

400,000 liters of perchlorethyleneburied 1 mile deep in a gold mine

About 1 Chlorine atom per day is converted into Argon as a result ofinteraction with solar neutrino

Much more difficult than finding a needle in a haystack!!

There are 1032 Cl atoms in a tank!

Slide 40

Sudbury neutrino observatory: 1000 tons of heavy water D2O

Slide 41

32,000 ton of ultra-pure water13,000 detectors

Slide 42

Slide 43

Slide 44

Observed neutrino flux is 2 times lower than the theoretical prediction!

Slide 45

Slide 46

The problem has been finally solved just recently:

Neutrinos “oscillate”! They are converted into other flavors: mu and tau neutrinos

Neutrinos should have massParticle physics models should be modified

Slide 47