Sun
by visible light
Sun
by X-raysLast modified 04 March, 2005 10:07 AM
Chapter 7 of the book, but we will omit much detail.
Sun
by visible light
Sun
by X-rays
Why study the Sun?
Big questions about the Sun.
The distance is 1 Astronomical Unit (by definition).
1.5 x 108 km, or 92 million miles. (we can ignore the ellipticity of the earth's orbit for now)
We got the distance originally by viewing the Sun from two places on Earth, or by making careful measurements while Mercury or Venus is "transiting" the Sun. Nowadays we get the distances to the planets by radar and then deduce where the Sun is from the orbits of the planets (The Sun itself does not reflect radio waves, so we can't use radar directly).
We get the actual diameter by first measuring the angular diameter of the
Sun, and then calculating the actual diameter from the 
distance
and the angular diameter
The angular diameter is about 0.5 degrees
The actual diameter is 1.4 x 106 km, which is about 1 million miles, or over 100 times the Earth's diameter.
We get the mass of the Sun by applying Newton's law of gravity to the orbits of the planets.
The mass is about 2 x 1030 kilograms, which is 2 x 1027 tons, or about 106 times the mass of the Earth
(Note that a metric tonne (~2200 lbs) is approximately the same as a US ton (2000 lbs) or a UK ton (2240 lbs)
The mass of the Sun is much more than all the planets put together.
Since we know the mass of the Sun, and we can calculate its volume from its diameter we can get its average density.
The average density is about 1.4 times the density of water.
This is denser than water but lighter than rock or metal. This is an important clue to what the Sun might be made of.
We will see later that different parts of the Sun have different densities.
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Most of the power we get from the Sun is in the form of light, so we need to digress a bit about the nature of light. We will also learn how we can use light to learn about distant objects such as the stars.
It has been known since the 1890s that light is an electrical disturbance in space, a bit like ripples in a pond, or sound waves. However, unlike sound, light can travel through a vacuum.
The velocity (speed) of light in a vacuum is 300,000 km/s: 3 x 108 meters/sec. This is one of the most fundamental constants of nature. You need to remember this number.
Light always travels at this speed in a vacuum, though it can be slowed up a bit traveling through matter such as air or glass.
Takes 8 minutes for light to get here from the Sun
Because the speed of light is so fundamental we use the idea of a light-second or a light-year as a measure of distance.
The velocity of light is often given the symbol c (for "constant")
The
wavelength is the distance between crests of the wave
Waves
of different wavelength have different color
White light is a mixture of waves of different wavelength.. A prism splits the different wavelength waves into a spectrum.
Visible light ranges from 400 nanometers ( 400 x 10-9 or 4 x 10-7 meters) for violet light to 700 nm for red light. A nanometer is one billionth of a meter, or one millionth of a millimeter, It is sometimes written "nm".
There are around 50 wavelengths of light across a single sheet of saran wrap
We often write wavelength with the Greek letter lambda (
)
Physics I demo: optics: basic prism
Light
is just part of a much wider range of radiation including
(but not sound waves). We call them electromagnetic waves, and the range of radiation is the electromagnetic spectrum. Radio waves are the longest (wavelengths up to kilometers long) Gamma are the shortest.
Tuning a radio is actually selecting radio waves of different wavelengths.
All travel through a vacuum. Nowadays astronomers observe the sky at almost all accessible wavelengths of the electromagnetic spectrum. As the figure shows, some kinds of wave penetrate the Earth's atmosphere (visible and radio) while others don't (X-rays and some infrared and ultraviolet).
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Waves come in bundles ("sets") of waves. These are called photons.
We don't notice these bundles with our eyes because they are so small and we see so many of them at once. Astronomers have sensitive instruments that can collect them one at a time.
Photons are particularly important when it comes to understanding processes which produce radiation.
The energy of a photon depends on its wavelength:
where E is the energy of the photon, c is the velocity of
light, lambda ()is the wavelength and h is
Planck's constant. Planck's constant is one of the constants of nature. You do
not have to remember this equation, but the important thing to remember is
that:
Even when you look at something fairly dim, your eye receives millions of photons per second, so you do not see the world "flickering". Astronomical cameras are so sensitive, however, that they can detect individual photons.
If we stand on the Earth on a clear day with the Sun overhead we receive about 1300 W per square meter of surface. Less when the Sun is low in the sky, and zero at night. This is a lot of power, if we could harness it effectively. Most of this is light, but some is infrared and some is ultraviolet.
If we move closer to the Sun we will receive more power, (ie the Sun will appear to be brighter). We can express the change mathematically by watching how energy gets spread out into space:
As energy is radiated out into space, the same power gets spread out over a
larger and larger area, so the energy hitting an object of fixed area must
decrease. This leads to the inverse square law of
illumination:
Power received is proportional to inverse square of the distance.
This also means that the apparent brightness of an object falls off with the inverse square of the distance.
We can use the inverse square law to determine the power emitted by the Sun
Total power is about 4 x 1026 Watts
Types of solar energy we use
Types of non-Solar energy we use
Temperature is a measure of the random motions of atoms. As the temperature of something rises the atoms move faster. There is actually a mathematical connection between the temperature of a body and the random velocities of its atoms.
If the substance is a gas the atoms move through space until they hit another atom or a wall. It is the impacts of the atoms on a wall that gives us gas pressure.
Physics 2, heat, temp, speed, ke
In USA we use Fahrenheit scale, where ice melts at 32 degrees and water boils as 212 degrees
Rest of world uses Celsius or centigrade scale where ice melts at 0 degrees and water boils at 100 degrees.
The idea of absolute zero is important. It is the temperature when things stop moving. It is -273 degrees Celsius.
In
astronomy we use the Kelvin, or absolute temperature scale, which is obtained by
adding 273 degrees onto the Celsius scale. Absolute zero is written as 0 K, ice
melts at 273 K, water boils at 373 K.
The advantage of the Kelvin scale is that the energy of an atom due to its random motions is now proportional to its temperature. If you double the Kelvin temperature of a gas, its atoms have twice the energy (and four times the speed)..
Temperature scales are defined in Appendix2 of your book
Now we need to examine some of the effects caused by changes in temperature:
Increasing the temperature causes solids to turn into liquids and liquids into gases (Note that some solids go straight to a gas, without going through a liquid stage.)
If the substance is a solid the atoms are locked into place in the crystal and vibrate back and forth. The higher the temperature the more violent the vibration.
Physics demo 2, heat, 3 phases
As the temperature rises the vibrating atoms shake themselves apart from the crystal and become first a liquid and then a gas. (Note that liquids are rare in astronomy, so we really only need to consider the differences between a solid and a gas.
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One of the important results of heating something is that it gives off electromagnetic radiation. As we will describe below, by analyzing this radiation we can determine the temperature of an object.
When
a solid, or a liquid, or a dense gas is heated it gives off continuum
radiation. The meaning of the word continuum is that radiation is seen
over a broad (continuous) range of wavelengths, not just specific ones. An
example is the glow that is given off as something becomes red hot, then
white hot.
We
sometimes refer the spectrum of a hot dense object as a "Continuous
spectrum"
Continuous
radiation from a hot body is given off over a range of wavelengths that depends
on the object's temperature. Something that is perfectly efficient at radiating
is called a black body. Continuous radiation is sometimes referred to as Black-body
radiation The spectrum of radiation from a black body is described by
Planck's law, named after the German physicist Max Planck who first formulated
the law in about 1900. The equation tells us how much radiation to expect at
each wavelength from an object at some temperature. We shall not write down the
equation, but notice that the shape of the curve
has a maximum at some wavelength, and fades away towards both long and short
wavelengths. A continuous spectrum looks the same whatever kind of atoms the hot
dense object is made out of.
The wavelength of the maximum emission changes with temperature.
This is called Wien's Law
If you measure the wavelength in micrometers, and the temperature in Kelvin, the constant is close to 3000
As you increase in temperature you first get red-hot then white hot, then blue hot (though not really very blue)
We can use Wien's Law to measure the temperature of objects we cannot touch, including stars and pottery kilns.
Wien's law applies not only to light, but to other electromagnetic radiation as well. For example you can use Wien's law to show that an object at 300K radiates most strongly at around 10 micrometers, in the infrared.
For Wien's Law to be correct you must use Kelvin Temperature scales, rather than Celsius or Farenheit.
The
wavelength of the maximum intensity from the Sun is about 0.5 micrometers, or
500 nanometers. From Wien's law we can deduce that the "surface" temperature
is about 6000 K. More accurate measurements put it at 5800 K.
This temperature makes the Sun truly white hot. In fact the true color of the Sun is sometimes taken as the definition of white. The apparent yellow or red color of the Sun at certain times is due to distortions caused by sunlight traveling through the Earth's atmosphere.
The temperature inside the Sun is going to be hotter than this, since heat is flowing out of the Sun.
This temperature is so hot that no solids or liquids can survive. We therefore deduce that the Sun must be a hot gas. This helps us understand why the density of the Sun is lower than that of the Earth.
If the Sun is a gas, then one has to ask exactly what one means by "surface". We will come back to this later.
To answer this question, and to understand how we answer it we need to understand the basics about atoms.
Typical size of an atom is a little less than 1 nanometer. (10-9
meters) Get several million across a period.
Just remember it is very small.
An
individual atom resembles a miniature solar system in some ways.
has a nucleus (analogous to the Sun) with one or more electrons in orbit around it. The electrons are a bit like planets except that they are not "hard" like planets. Think of it more like a cloud of electrons orbiting the nucleus.
The nucleus has a positive electric charge, and the electrons have a negative electric charge. Electricity is the force that binds them together.
The nucleus has most of the mass of the atom, but it is tiny. Most of the volume of an atom is empty space that the electrons move about in.
If you examine a nucleus of you find it contains several protons. (It may also contain some neutrons but we will postpone them until later.
The proton is a particle that carries one unit of positive electric charge.
The number of protons in a nucleus determines is called the atomic number and determines which kind of element (sometimes called chemical element) the atom is. Examples
| Number of protons (Atomic number) |
Element |
| 1 | hydrogen |
| 2 | helium |
| 6 | carbon |
| 8 | oxygen |
| 92 | uranium |
Every atom has to be made of one or other chemical elements. There are 92 naturally occurring elements plus a few that have been made in physics labs. They are organized in a Periodic Table.
The negative electrical charge on an electron is equal to the positive electric charge on a proton, so a neutral atom has the same number of electrons as protons in it. However it is possible for an atom to temporarily lose on or more electrons by some means and become an ion. The nucleus is unaffected when an atom is ionized, so it remains the same element.
When at atom is unionized it is referred to as neutral. An ion can revert to being a neutral atom by recombining with enough electrons to equal the number of protons in the nucleus.
There are several ways of making ions. One way is inside fluorescent light bulbs, using electricity. Another is to heat gas so hot that the collisions between atoms literally knock an electrons off of one of the atoms.
An ionized gas is sometimes referred to as a plasma.
On
Earth we sometimes find material in the form of single atoms, but usually atoms
combine together to form molecules such as water, which is a combination
of oxygen and hydrogen. When atoms form molecules it is the electrons that get
together. The nuclei stay distinct.
The science of how elements interact with each other is called chemistry. The earth's environment is particularly good for encouraging atoms to combine to form molecules. In astronomy, on the other hand, it is common to find atoms acting individually, and not in molecules. This makes astronomy simple.
Most
nuclei also contain one or more neutrons. A neutron has almost the same
mass as the proton, but no charge. The usual kind of helium contains two protons
and two neutrons in its nucleus.
A major difference between the Solar System and an atom is that in an atom an electron can only travel in certain "orbits". Intermediate orbits are not allowed. The reasons for this depend on quantum theory, which is one of the major theories of physics.
Different
electron orbits require different energies On this figure the distance of
each orbit from the center represents the energy of the electron in the
orbit. To move an electron from a small
orbit near the nucleus to a larger orbit farther away from the nucleus requires
you to give the atom energy. If an electron jumps from a large orbit to a
smaller one the atom gives out energy. The energy comes out in the form of a
photon of electromagnetic radiation. Since the wavelength of a photon depends on
its energy, only certain wavelengths of light can be produced as a result of
electrons changing from one orbit to another.
Similarly, only photons with certain wavelengths can be absorbed by an atom.
Because
of the importance of the energies of different orbits, we usually don't use the
term orbit at all. Instead we think of the atom in terms of its energy
levels. These are the energies of the allowed orbits in an atom. Photons are
produced and absorbed when atoms jump from one energy level to another.
We
separate the photons into their different colors or wavelengths by using either
a prism or a diffraction grating. This is the basis of the science of spectroscopy,
which allows us to identify different elements in the light of distant stars.
Demonstration of gas tubes.
Do not worry how diffraction gratings work.
Do not worry about what makes electrons jump up into the higher levels.
Each different chemical element has an entirely different set of energy
levels, so that each element has its own set of wavelengths that it an absorb
and emit. We can identify a gas by wavelengths it gives out. When at atom is
ionized, its ion has different energy levels from the neutral atom.
Link to Barnes spectra webpage
The kind of spectrum that we see here, where there are bright lines on a dark background, is called an "Emission Line spectrum" or just "Emission spectrum". Generally you get this kind of spectrum when you look at a hot, low density gas, such as a nebula.
If the gas density is high enough, or if the emitting object is a solid, we get a continuous spectrum instead, which we dealt with already.. (The question of what happens to gas of intermediate density is beyond the scope of this course).
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The
spectrum of light from the Sun consists of continuous emission (corresponding
to a black-body temperature of 5800 K) with dark lines crossing it corresponding
to wavelengths of transitions of various different kinds of atoms in the
Sun.
The dark lines are called "Absorption lines"
while this kind of spectrum is called an "absorption
spectrum". It occurs when light from a hot dense
region passes through a region of cooler, lower gas density.
The
same region of gas can produce emission lines or absorption lines depending on
the path of the light traveling to you.
The
absorption line spectrum is the third of the three main types of spectra, and
the one that is most common in astronomy.
We can identify spectral lines from about 3/4 of all the known elements in the Sun. The more of a particular kind of atom, the stronger will be the absorption lines, though the relationship between strength of lines and concentration is not a simple one.
When we do the measurements and the follow-up calculations we find that the
Sun is about 73% hydrogen, 25% helium, 2% the rest (by mass). What we
measure is actually the composition of the Sun's outer layers, but the Sun is
much the same inside as well. the composition of the Sun is very different from
that of the Earth, where oxygen, silicon and iron are the most common.
Later we will see that the Sun's composition is the normal composition of stars in the Galaxy. Our Earth is the exception
To answer this we first need to understand the forces that hold a ball of gas together
Sections 7.7- 7.8
We
cannot see into the interior of the Sun, so we must investigate its interior by
making calculations based on the laws of physics.
Inside the sun there is a balance between gravity and pressure, with the pressure increasing towards the center.
We calculate that the temperature at the center of the Sun is about 15 million K.
The density is 158 times density of water
Compare this with rocks (~3), gold (~20), air (~0.001)
At
this temperature the interior of the Sun is completely ionized all the way to
the center
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Why does the Sun get hotter as go deeper? Several reasons. One is that when something falls it gathers speed. Matter nearer the center of the Sun has fallen farther and so the atoms have acquired extra speed. This extra speed manifests itself as a higher temperature. We see this on Earth: the atmosphere at the top of a mountain is colder than that at the bottom (even going over the Pali). Also, you can measure the temperature difference between the top and bottom of a waterfall; the bottom is warmer than the top.
The sun is radiating about 4 x 1020 Megawatts of power into space, mainly as light and infrared energy (heat). It would quickly cool down unless the energy is replaced from some source.
The source of this power was one of the great mysteries of astronomy until the 1930s when it was realized that the key to understanding the Sun lies in the science of nuclear physics
Nuclear physics is the science of how nuclei (including protons and neutrons) interact with each other directly. It is quite different from chemistry which involves the reactions of the electrons in the atoms with each other. In chemistry the nuclei stay apart and distinct. In nuclear reactions the nuclei themselves are rearranged. In nuclear physics you change the elements. In chemistry you don't.
Nuclear reactions are uncommon on earth, except for natural radioactivity, which we will meet later.. You have to go to great lengths (physics lab, nuclear reactor, nuclear bomb) to get nuclear reactions to work.
The type of nuclear reactions taking place on the Sun are called thermonuclear fusion. (Fusion = joining)
Thermonuclear fusion occurs when light elements of low atomic number combine to make an element of higher atomic number
Effectively,
the process going on in the Sun is 4 hydrogen nuclei fuse together with 2
electrons to form a helium nucleus.
The major reason why nuclear reactions do not widely occur naturally is that nuclei are positively charged, so repel each other; nuclei have to be forced together. In the Sun the pressure and temperature are so high that the protons can blast their way through the force of the electric repulsion. On Earth the only way to do this is inside a hydrogen bomb
A lot of energy is given off when this happens. The energy comes from the destruction of some of the mass of the hydrogen.
About 0.7% of the mass just disappears. It is converted according to Einstein's formula
Each second 4 million tons of the sun is turned into energy, But there's enough fuel in the Sun (hydrogen) to last about 10 billion years, twice the current estimated age of the Solar System.
All the nuclear reactions take place in the center of the Sun, which is the
only place where the temperature and density are high enough. The photons that
are generated carry the energy outward to the surface, but they are absorbed and
re-produced billions of times in the journey. The energy actually takes millions
of years to seep out of the sun Towards the surface heat is carried by
convection, with hot fluid rising and cooler fluid falling.
What we see is the surface of the Sun, so we will now examine the surface and see what variations we can see.
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We
often talk loosely about the "surface" of the Sun, but there is no
hard surface, of course. The photosphere is the layer from which light
reaches us directly. Below the photosphere the Sun is opaque.
The density of gas in the photosphere is only 0.01% of that of the air we breathe, and is about 400 km thick.
The
photosphere is constantly changing due to granulation produced by convection.
The temperature of the gas in the photosphere falls as you move away from the Sun. This is why you see stellar absorption lines.
Sun is constantly changing. It is monitored every day by a number of ground-based and space-based telescopes.
NASA page with daily images allow us to monitor what the Sun looks like each day.
DO NOT STARE AT THE SUN WITHOUT EYE PROTECTION!
Sunspots
are small dark regions (about the diameter of the Earth) that last for a few
weeks on the surface of the Sun.
They are the easiest way to study the rotation of the Sun, which is approximately 1 month. (Though the Sun does not rotate as a solid body: The Equator rotates faster than the poles)
Sunspots are dark because they are relatively cool (typically 4200 instead of 5800 K). They are caused by variations in the magnetic field of the Sun.
Sunspots
come and go in an approximately 11-year
cycle (strictly speaking a 22-year). We are moving from a maximum towards a
minimum.
The theory of sunspots involves magnetic fields and is beyond this course, although it is discussed in the book. The presence of sunspots also goes along with other changes on the Sun's surface. Regions near Sunspots are often called active regions.
For
example the X-ray emission of the Sun changes drastically as the sunspot
number increases. These are X-ray photos taken over a period of about 4
years. Although the changes at X-ray wavelengths is quite drastic, only a
very small amount of the Sun's power comes out in the form of X-rays.
Sunspots
sometimes go away completely (the "Maunder Minimum" at the end of the
17th century)
There is some evidence to link Earth's weather to Sunspot cycle, but the evidence is controversia
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Prominences
are eruptions on the surface of the Sun. Vast amounts of gas are thrown into
space. Their shapes are controlled by the Sun's magnetism.
Movie of X-ray emission from Yohkoh satellite
The
most violent events are flares which erupt
for a few minutes and eject vast numbers of particles to Space. They can be a
danger to astronauts. Since the particles are charged they can create electrical
disturbances on Earth such as radio blackout and power cuts.
The
outer layer of the Sun's atmosphere is the Solar Corona
It is very thin and spreads out farther than the diameter of the Sun. It is very hot, about 1 million degrees but we do not properly know why. Note the application of Wien's law; Because the Corona is so hot, the wavelength of its radiation is very small (X-rays)
We
can see inner corona during an eclipse, and using special telescopes, and with
X-ray telescopes such as the Japanese Yohkoh satellite.
Particles (mainly protons) from the solar corona travel all the way to Earth and beyond. They traveling at several thousand kilometers per second.
When
they reach the Earth's upper atmosphere they can cause Aurorae
near the Earth's magnetic poles.
See also Aurora movie
There is a steady solar wind, but also there are major increases associated with Coronal Mass ejections,
Solar Flares, and Coronal Mass Ejections can have a serious effect on the Earth, including interrupting radio communications.
Quicktime movie from Starry night 4 number 8
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