The Stars and the Sun II.Basic Properties of the Sun

Chu Ming-chung 朱明中

Department of Physics

The Chinese University of Hong Kong

mcchu@phy.cuhk.edu.hk

http://www.phy.cuhk.edu.hk/gee/mctalks/mcpdp.html

SummaryNuclear reactions: pp chain, CNO cycle,

quantum tunneling, solar neutrino problempressure-gravity balance: main-sequence star Pressure-temperature thermostatThe sun: features and activitiesThe sun and Earth’s climate

Basic Properties of the Sun

2.1* Stellar Energy2.2* Solar Neutrino Problem2.3* Stability of Stars2.4 The sun

2.1* Stellar energy

A star is a super nuclear plant

M41

The stars and the sun

-The sun is a typical main sequence star.

- If we understand the sun, we understand most stars.

Sun on 03/04/2006

The sun30

8

7

5 -3

3 -3

9

26

2 10 kg

7 10 m

5800K

1.6 10 K

1.5 10 kgm

1.4 10 kgm

4.6 10 years

4 10 W

o

o

E

c

c

o

o

M

R

T

T

t

L

mass

radius

effective surface Temperature

central T

central density

age

average density

Composition: 71% H, 27 % He, 2% heavy elements 0.61amum

luminositySun on 23/10/2003

How is energy generated from the sun?

Stellar EnergySolar output: 4x1026 W, stable for 109 yearsGravitational energy? Shrinking →sun hotter

→radiates energy. How much would the sun need to shrink per year to sustain the output?

http://www.aoc.nrao.edu/~smyers/courses/astro12/L15.html

2 41

2 2

26 41

7

Ans.: Gravitational PE / 4 10 J

/ / / /

need / 4 10 / 4 10 per second

7 10 m per second 22 m/year

V GM R

V GM R R V R R R R V V

R R

R

This does not contradict with the observation. So what’s wrong?

Ans.: Can only sustain this contraction for ~ 107 years! (Ro ~ 7x108 m)

Stellar EnergyChemical energy? H ions →H atoms release binding

energy. How much can be released? How long can this sustain the sun?

30 27 57

57 -19

Ans.: No. of protons / 2 10 /1.67 10 1.2 10

Binding energy per H 13.6 eV

Total atomic binding energy in the sun 1.2 10 13.6 1.6 10 J

o pM m

40

40 26 14 6

2.6 10 J

Can sustain for 2.6 10 /4 10 s 0.7 10 s 2.2 10 years.

Need a long term and stable source of energy! What is it?

Fundamental forces: Gravitation, EM, Weak, Strong

Nuclear reactions

p-p chain: 4 protons 1 helium nucleus + positrons (反電子 ) + neutrinos (中微子 ) + energy

Energy source: thermonuclear fusion

2 H ep p e 2H

e+ e

p

p

2H

p3He

photon2H + p →3He + photon

3He + 3He → 4He + 2p + photon

3He

4He

photon

3He

The p-p chainbottleneck: ep p d e

ep n e weak interaction, slow tunneling: mp < mn, very slow

d binding energy = 2.2 MeV

mass difference = 1.8 MeV

p-p fusion rate in the sun ~ 5x1013 s-1m-3

For each p, one fusion in 9x109 years, ~ lifetime of Sun.3fast step: Hed p d lives for 1s on average in Sun

Slow, but large energy release per reaction → sustain solar output for a long time!

Most d in the universe are primordial!

Some mass is converted to energy per reaction E = mc2.

Estimate the maximum thermal energy produced per reaction

4p→4He + 2 e+ + 2 neutrinos (assumed massless). Given:

mass of p = 938.27 MeV, mass of 4He nucleus = 3727.36

MeV, 1 MeV = 1.6x10-13 J.

. Ans.: 4x 938.27 - 3727.36 ~ 26 MeV ~ 4x10-12 J. Note that the

positrons also are annihilated soon to give out energy. KE of

particles are similar and small.

How long can the sun be sustained this way?

Ans.: Each reactions consume 4 protons. There are 1.2 x 1057 protons in the sun. Total energy output can be 4x10-12x3x1056 = 1.2x1045 J. Can sustain the sun for 1.2x1045/4x1026 s ~ 9.5x1010 years!

Prof. Hans Bethe

Nobel Prize in Physics 1967, “for his contributions to the theory of nuclear reactions, especially his discoveries concerning the energy production in stars"

How many neutrinos are produced by the sun each second? How many come to Earth? Given: 1 MeV = 1.6x10-13 J

How can we test this theory of solar energy production?

Ans.: By measuring the neutrinos produced in the p-p fusion! Neutrinos penetrate through the sun and carry information of the conditions at the solar core.

Ans.: Each p-p chain reaction produces 4x10-12 J. So there should be 4x1026/4x10-12 = 1038 reactions per second. Two neutrinos are produced per reaction. So the sun should produce 2x1038 neutrinos/s. These are spread out uniformly. At Earth’s distance, the surface area is

2 11

2 6

2 2 10

4 , where is the Earth-Sun distance 1.5 10 m.

Cross sectional area of Earth ; 6.4 10 m.

Fraction of area taken up by Earth / 4 4.55 10 .

No. of neutrinos passing through Earth per s

o o

o

D D

R R

R D

38 10 282 10 4.55 10 9.1 10 .

Neutrino flux on Earth ~ 4x1010 cm-2s-1.

r

Z1+ Z2+

151 210 m (1 fm) barrier height MeVN hr E Z Z

r

V(r)

rN rc

E

-Vo

Eh

But: Is the temperature high enough to ignite p-p fusion?Given: nuclear force is short-range ~ 10-15 m

21 2

potential between two ions (atomic nuclei):

Coulomb + nuclear potential ( ) ( ) ( ) (2.1)4o N N

o

Z Z eV r V r r r r

r

attractive, dominates at short range, approximately flat

Ans.: Fusion happens: require KE of particles > Coulomb potential barrier (classically)

2192 29

15 230 0

9

1.6 103 2 2~ ~ 10

2 4 3 4 3 10 1.4 10

~ 10 K

e ekT T

r rk

T

Quantum mechanics: Nuclear reaction can occur even if KE is not high enoughTunneling effects (隧道效應 ):very small amount of protons may undergo reactions!

710 K keV .hT kT E E But the core temperature of the sun is

Classically, there’s a turning point when E = PE.

Quantum mechanics: particles are also waves →uncertainty principle: tunneling: if , the particle has some probability of having a large p

/ 2x p h x

( 0)p

Rate of reactions is very sensitive to temperaturehigher temperature much faster reaction rate.p-p chain starts at about 107 K. 4R T

r

V(r)

rN rc

E

-Vo

Eh

wavefunction

Carbon-Nitrogen-Oxygen cycle (CNO cycle)

Much more efficient than p-p chain, rate T 20, T1.5107 K

Dominant reaction in massive star (>1.1M) →

massive stars burn much faster → massive stars have much shorter lives

Alternative fusion process: only ~10% of solar energy

CNO Cycle12C

13N13N

13C

14N

15O

15O

15N

e

e

e+

e+

p

p

p

p4He

15N

12C

How is the nuclear energy transported to the surface?

Radiation (輻射 ): Energy carried by EM radiation

Convection ( 對流 ): Hot gas rises and cooler gas

sinks, carrying energy outward

2.2* Solar neutrino problem Neutrinos hardly interact with matter

they penetrate the interior layers of the sun and reach the earth directly

neutrinos = direct signals from the center of the sun

detection of which is an indirect evidence of nuclear reactions in the solar core

The sun should produce 2x1038 neutrinos/s

Earth should receive ~4x1010 neutrinos/cm2/s

Background: about 300/cm2/s are from Big Bang; each person emits about 3x108/day (radioactive materials) and receives about 1010/day from nuclear power plants

but we detect only ~1/3 as theoretically expected

something is wrong with our theory?

May have been solved by neutrino oscillationhttp://wwwlapp.in2p3.fr/neutrinos

Neutrino telescopesTelescopes: use a large area to collect signals

from far awayMake use of neutrino reactions with protons

or neutrons, eg.

Weak interaction: 1 ton → few events/dayUse large amount of materials

enp epnmeasurable

Kamiokande 神岡宇宙素粒子研究中心

50,000 tons of pure water

41.1m

39.3m

1 km below ground Masatoshi KoshibaNobel Prize in Physics, 2002

Drawing from Superkamiokande http://dumand.phys.washington.edu/~superk/

Photoelectric tubesSuperKamiokande

Photo from Superkamiokande http://dumand.phys.washington.edu/~superk

enpe

SuperKamiokande

Detected by 11,000 PMT’s

Emits light

Photos from Superkamiokande http://dumand.phys.washington.edu/~superk

Photo from Superkamiokande http://dumand.phys.washington.edu/~superk

Pure water

Photo from Superkamiokande http://dumand.phys.washington.edu/~superk

Inside the Kamiokande neutrino telescope

Photo from Superkamiokande http://dumand.phys.washington.edu/~superk

2.3* Stability of stars: Pressure-temperature thermostat

Balance of: gravity vs. pressure

gradient, radiation vs. fusion

energy

Why is it stable against perturbations?

If nuclear reactions slow down

temperature decreases,

lower thermal pressure

gravity contracts the star

compression heats the core,

increases

increases nuclear energy

generation

,T

4T

If nuclear reactions are too fast

temperature increases;

higher thermal pressure

stellar core expands

expansion cools the core,

decreases the density

slows down the nuclear

reaction rate

A star is very stable in the main sequence (a star of

1 solar mass lasts for 10 billion years)

Sun on 2003/07/31

Taken in CUHK

Sunset on 26/12/01

2.4 The sun

Solar activities Flares (耀斑 ) - energetic

outbursts Prominences (日珥 ) -

ejected hot gas Coronal (日冕 ) mass

ejection Sunspots (黑子 ) -

unexplained connection to Earth’s climate

Solar cycle: min-max-min ~11 years

Solar storms

Aurora, magnetic storms, ...

http://solar.sec.noaa.gov/today.htmlSpace weather:

All are associated with magnetic fields!

Coronal Mass Ejection: speeds as high as 1000 km/s (average 400 km/s)

Solar Cycles (太陽週期 )

Aurora 極光

Solar constant (太陽常數 ) Solar constant = total solar energy reaching the surface of

the earth ~1360 J/m2s 1% change in the constant may cause 1-2C change in Earths

temperature. Variations cause long term changes in the earth’s climate, e.g.

the ice ages.

There are exceptional periods of time when the sun is almost clear of sunspots, e.g., the Maunder Minimum (1645-1715) [蒙德極小期 ], which coincide with cold weather on Earth: connection between solar activities and Earth’s climate?

The solar constant varies by only ~ 0.2%, unaffected by solar cycles → stability of Earth’s climate

Observing the sun

Don’t need a large telescope: very brightNeed proper filters!Hydrogen-alpha filters: select light emitted

by Hydrogen only – see prominences and other surface features clearly

White-light filters: reduce light uniformly

Sun on 28/04/03 in H-alpha

sunspot

prominences

flares

granules

limb darkening

23/10/2003 24/10/2003 25/10/2003 26/10/2003 27/10/2003 28/10/2003 29/10/2003 30/10/2003 31/10/2003 01/11/2003 02/11/2003 03/11/2003 04/11/2003

05/11/2003 06/11/2003

Solar storms

Mercury Transit 水星凌日 on 2003/05/07 Taken in CUHK

Venus Transit 8/6/2004 Taken in CUHK

Measuring Earth-Sun distance

SummaryNuclear reactions: pp chain, CNO cycle,

quantum tunneling, solar neutrino problempressure-gravity balance: main-sequence star Pressure-temperature thermostatThe sun: features and activitiesThe sun and Earth’s climate

Basic Properties of the Sun

2.1* Stellar Energy2.2* Solar Neutrino Problem2.3* Stability of Stars2.4 The sun

The Stars and the Sun II.Basic Properties of the Sun

Chu Ming-chung 朱明中

Department of Physics

The Chinese University of Hong Kong

mcchu@phy.cuhk.edu.hk

http://www.phy.cuhk.edu.hk/gee/mctalks/mcpdp.html