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ASTRO 101

Principles of Astronomy

Instructor: Jerome A. Orosz

(rhymes with

“ boris ” )

Contact:

• Telephone: 594-7118

• E-mail: orosz@sciences.sdsu.edu

• WWW: http://mintaka.sdsu.edu/faculty/orosz/web/

• Office: Physics 241, hours T TH 3:30-5:00

Exam 2:

• N=53 (3 missing)

• Average = 68.8

• low = 33.5, high = 96.5

• A 90%--100%

• A85%--89%

• B+ 80%--84%

• B 75%--79%

• B70%--74%

• C+ 65%--69%

• C 60%--64%

• C50%--59%

• D 40%--49%

• F 0%--39%

Homework/Announcements

• Homework due Tuesday, April 16: Question 4,

Chapter 8 (Describe the three main layers of the Sun’s interior.)

• Chapter 9 homework due April 23: Question 13

(Draw an H-R Diagram …)

Next:

How Does the Sun Work?


• Some useful numbers:

 The mass of the Sun is 2x10 30 kg.

 The luminosity of the Sun is 4x10 26 Watts.

 The first question to ask is: What is the energy source inside the Sun?

Rate Equations

• You get 30 miles per gallon, how far can you drive using 3 gallons? 90 miles

• You get 30 miles per gallon, how many gallons does it take to travel 120 miles? 4 gallons


• Some useful numbers:

 The mass of the Sun is 2x10 30 kg.

 The luminosity of the Sun is 4x10 26 Watts.

 The first question to ask is: What is the energy source inside the Sun?

Energy Sources

• A definition:

Efficiency = energy released/(fuel mass x [speed of light] 2 )

• Chemical energy (e.g. burning wood, combining hydrogen and oxygen to make water, etc.).

 Efficiency = 1.5 x 10 -10

 Solar lifetime = 30 to 30,000 years, depending on the reaction.

Energy Sources

• A definition:


• Chemical energy (e.g. burning wood, combining hydrogen and oxygen to make water, etc.).

 Efficiency = 1.5 x 10 -10

 Solar lifetime = 30 to 30,000 years, depending on the reaction. Too short!

Energy Sources

• A definition:


• Gravitational settling (falling material compresses stuff below, releasing heat).

 Efficiency = 1 x 10 -6

 Solar lifetime = 30 million years.

Energy Sources

• A definition:


• Gravitational settling (falling material compresses stuff below, releasing heat).

 Efficiency = 1 x 10 -6

 Solar lifetime = 30 million years. Too short, although this point was not obvious in the late

1800s.

Energy Sources

• A definition:


• Nuclear reactions: fission of heavy elements (as in an atomic bomb), or fusion of light elements

(as in a hydrogen bomb). Fission is not important in the Sun since the heavy elements

(e.g. uranium) are extremely rare.

Energy Sources

• A definition:


• Nuclear reactions: fusion of light elements (as in a hydrogen bomb).

 Efficiency = 0.007

 Solar lifetime = billions of years.

Ways to Transport Energy

Ways to Transport Energy

• Conduction: direct contact

• Radiation: via photons

• Convection: via mass motions

The Phases of Matter

Phases of Matter

• Matter has three “ phases ”

1. Solid. Constant volume and constant shape .

2. Liquid. Constant volume but variable shape.

3. Gas. Variable volume and variable shape.

The Gas Phase

• In a gas, the atoms and/or molecules are widely separated and are moving at high velocities:

– Relatively heavy molecules such as CO

2 relatively slowly.

move

– Relatively light molecules like H

2 quickly.

move relatively

– The average velocities of the gas particles depend on the temperature of the gas.

Heating a Gas

• The velocity of a gas particle depends on the mass of the particle and its temperature.

Image from Nick Strobel ( http://www.astronomynotes.com

)

Heating a Gas

• For a given gas (e.g. hydrogen gas, CO

2

, etc.):

– A higher temperature means a higher velocity for the particles.

– A lower temperature means a smaller velocity for the particles.

Heating a Gas

• For a given temperature:

 A heavier gas (e.g. CO

2 lighter gas (e.g. H

2

).

) moves slower than a

Ideal Gas

• For a fixed volume, a hotter gas exerts a higher pressure:

Image from Nick Strobel ’ s Astronomy Notes ( http://www.astronomynotes.com

)

The 4 “ Forces ” in Nature

The 4 “ Forces ” of Nature

• There are 4 “ fundamental forces ” in nature:

1. Gravity: relative strength = 1, range = infinite.

2. Electromagnetic: rel. str. = 10 36 , range = infinite.

3.

“ Weak ” nuclear: rel. str. = 10 25 , range = 10 -10 meter.

4.

“ Strong ” nuclear: rel. str. = 10 38 , range = 10 -15 meter.





3.


4.


• Gravity is an attractive force between all matter in the Universe. The more mass something has, the larger the net gravitational force is.





3.


4.


• The electromagnetic force can be repulsive (+,+ or -,-) or attractive (+,-). Normal chemical reactions are governed by this force.





3.


4.


• The weak force governs certain radioactive decay reactions.

• The strong force holds atomic nuclei together.

The Strong Force.

p = proton, positive charge n = neutron, no charge n p p n

• Here is a helium nucleus. The protons are held together by the strong force.





3.


4.


• Gravity is the most important force over large scales since positive and negative charges tend to cancel.

How to get energy from atoms

• Fission: break apart the nucleus of a heavy element like uranium.

• Fusion: combine the nuclei of a light element like hydrogen.

More Nuclear Fusion

• Each atomic nucleus has a

“ binding energy ” associated with it. The curve is increasing as you go up to iron from small nuclei, and decreasing as you go down from large nuclei.

• The tendency of Nature is to increase binding energy, much like the tendency of water to flow downhill.

Image from Vik Dhillon ( http://www.shef.ac.uk/physics/people/vdhillon/teaching/phy213/phy213_fusion1.html

)

More Nuclear Fusion

• Fusion of elements lighter than iron can release energy (leads to higher BE ’ s).

• Fission of elements heaver than iron can release energy (leads to higher BE ’ s).

Nuclear Fusion

• Summary: 4 hydrogen nuclei (which are protons ) combine to form 1 helium nucleus

(which has two protons and two neutrons ).

• Why does this produce energy?

 Before : the mass of 4 protons is 4 proton masses .

 After : the mass of 2 protons and 2 neutrons is 3.97 proton masses .

 Einstein: E = mc 2 . The missing mass went into energy! 4H ---> 1He + energy

Nuclear Fusion







Nuclear Fusion



• Extremely high temperatures and densities are needed!

Images from Nick Strobel ’ s Astronomy Notes ( http://www.astronomynotes.com

)

Nuclear Fusion



• Extremely high temperatures and densities are needed! The temperature is about 15,000,000K at the core of the Sun.

More Nuclear Fusion

• Fusion of elements lighter than iron can release energy (leads to higher BE ’ s).

• As you fuse heavier elements up to iron, higher and higher temperatures are needed since more and more electrical charge repulsion needs to be overcome.

– Hydrogen nuclei have 1 proton each

– Helium nuclei have 2 protons each

– Carbon nuclei have 6 protons each

– …..

• The Sun is presently only fusing hydrogen since it is not hot enough to fuse helium.

Nuclear Fusion







Nuclear Fusion



• The details are a bit complex:


)

Nuclear Fusion

• Summary: 4 hydrogen nuclei

(which are protons ) combine to form 1 helium nucleus (which has two protons and two neutrons ).


Nuclear Fusion




 In the Sun, 6 hydrogen nuclei are involved in a sequence that produces two hydrogen nuclei and one helium nucleus. This is the proton-proton chain.

Nuclear Fusion




 In the Sun, 6 hydrogen nuclei are involved in a sequence that produces two hydrogen nuclei and one helium nucleus. This is the proton-proton chain.

 In more massive stars, a carbon nucleus is involved as a catalyst. This is the CNO cycle.

Nuclear Fusion

• The CNO cycle (left) and pp chain (right) are outlined.

Nuclear Fusion



• Why doesn ’ t the Sun blow up like a bomb?

There is a natural “ thermostat ” in the core.

Controlled Fusion in the Sun


• First, note that the rate of the p-p chain or CNO cycle is very sensitive to the temperature .



 Rate ~ (temperature) 4 for p-p chain.




 Rate ~ (temperature) 15 for the CNO cycle.





 Small changes in the temperature lead to large changes in the fusion rate .






• Suppose the fusion rate inside the Sun increased:






• Suppose the fusion rate inside the Sun increased:

 The increased energy heats the core and expands the star. But the expansion cools the core, lowering the fusion rate. The lower rate allows the core to shrink back to where it was before.

Models of the Solar Interior

• The interior of the Sun is relatively simple because it is an ideal gas , described by three quantities:

1. Temperature

2. Pressure

3. Mass density


• The interior of the Sun is relatively simple because it is an ideal gas , described by three quantities:

1. Temperature

2. Pressure

3. Mass density

• The relationship between these three quantities is called the equation of state .

Ideal Gas

• For a fixed volume, a hotter gas exerts a higher pressure:


)

Hydrostatic Equilibrium

• The Sun does not collapse on itself, nor does it expand rapidly.


• The Sun does not collapse on itself, nor does it expand rapidly. Gravity and internal pressure balance:


)


• The Sun does not collapse on itself, nor does it expand rapidly. Gravity and internal pressure balance. This is true at all layers of the Sun.


)


• The Sun (and other stars) does not collapse on itself, nor does it expand rapidly. Gravity and internal pressure balance. This is true at all layers of the Sun.

• The temperature increases as you go deeper and deeper into the Sun!


• The pieces so far:

 Energy generation (nuclear fusion).

 Ideal gas law (relation between temperature, pressure, and volume.

 Hydrostatic equilibrium (gravity balances pressure).






 Continuity of mass (smooth distribution throughout the star).







 Continuity of energy (amount entering the bottom of a layer is equal to the amount leaving the top).







 Continuity of energy (amount entering the bottom of a layer is equal to the amount leaving the top).

 Energy transport (how energy is moved from the core to the surface).


• Solve these equations on a computer:

 Compute the temperature and density at any layer, at any time.

 Compute the size and luminosity of the star as a function of the initial mass.

 Etc…….

Solar Structure Models


• Here is the model of the structure of the Sun.


• The Sun is mostly hydrogen and helium.


• Here is the model of the structure of the Sun.

• Next: Characterizing Stars

The Sun and the Stars

• The Sun is the nearest example of a star.

• Basic questions to ask:

– What do stars look like on their surfaces? Look at the Sun since it is so close.

– How do stars work on their insides? Look at both the Sun and the stars to get many examples.

– What will happen to the Sun? Look at other stars that are in other stages of development.

Stellar Properties

• The Sun and the stars are similar objects.

• In order to understand them, we want to try and measure as many properties about them as we can:

 Power output (luminosity)

 Temperature at the “ surface ”

 Radius

 Mass

 Chemical composition

Observing Other Stars

• Recall there is basically no hope of spatially resolving the disk of any star (apart from the Sun). The stars are very far away, so their angular size as seen from Earth is extremely small.

• The light we receive from a star comes from the entire hemisphere that is facing us.

That is, we see the “ disk-integrated ” light.

Observing Other Stars

• To get an understanding of how a star works, the most useful thing to do is to measure the spectral energy distribution, which is a plot of the intensity of the photons vs. their wavelengths (or frequencies or energies).

• There are two ways to do this:

 “ Broad band ” , by taking images with a camera and a colored filter.

 “ High resolution ” , by using special optics to disperse the light and record it.

Broad Band Photometry

• There are several standard filters in use in astronomy.

• The filter lets only light within a certain wavelength region through (that is why they have those particular colors).

Color Photography

• The separate images are digitally processed to obtain the final color image.

Color Photography

Color Photography

Broad Band Photometry

• Broad band photometry has the advantage in that it is easy (just need a camera and some filters on the back of your telescope), and it is efficient (relatively few photons are lost in the optics).

• The disadvantage is that the spectral resolution is poor, so subtle differences in photon energies are impossible to detect.

High Resolution Spectroscopy

• To obtain a high resolution spectrum, light from a star is passed through a prism (or reflected off a grating), and focused and detected using some complicated optics.

High Resolution Spectroscopy

• Using a good high resolution spectrum, you can get a much better measurement of the spectral energy distribution.

• The disadvantage is that the efficiency is lower

(more photons are lost in the complex optics).

Also, it is difficult to measure more than one star at a time (in contrast to the direct imaging where several stars can be on the same image).

Stellar Properties

• The Sun and the stars are similar objects.

• In order to understand them, we want to try and measure as many properties about them as we can:

 Power output (luminosity)

 Temperature at the “ surface ”

 Radius

 Mass

 Chemical composition

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How Does the Sun Work?

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