ASTR 330: The Solar System Announcements 9/7/06 Dr Conor Nixon Fall 2006 Yellow forms - any more?...

ASTR 330: The Solar System

Announcements 9/7/06

Dr Conor Nixon Fall 2006

• Yellow forms - any more?

• Wait list.

• New materials on website: syllabus, Lecture 2, HW #1.

• Homework #1 due by Tuesday, September 12.

• Ignore the last part of Q4! “Which of these mechanisms…”

But instead you may want to think about: “What heat transport processes occur in the Sun?”


Lecture 3:

The Sun

Dr Conor Nixon Fall 2006Image: SOHO EIT


Discussion


• Which form of life on Earth rely on the Sun for food?

• Green plants• Other plants, fungii.• Herbivores• Carnivores• Humans

• Which forms or energy come from the Sun?

• Solar power• Fossil fuels• Wind power• Wave power• Nuclear power


Are all the stars suns?


• To begin to answer this question, we should be able to say how luminous the star really is.

• The apparent luminosity or brightness of the body is a reflection both of its actual or absolute brightness, and also its distance.

• If we can only find the distance to the stars, then we know the absolute brightness, and whether they are similar to the Sun or not!

• But how to find the distance?


Stellar Parallax


• The notion of parallax was used to measure stellar distances.

• Parallax measures the change in position of a ‘nearby’ object against the more distant background objects, when viewed from two different positions.

• This is the same principle as binocular vision! Try it!

• Astronomers used the Earth’s position on either side of the Sun, six months apart as the two viewpoints.

Figure credit: James Schombert, Univ. Oregon


Distances and masses


• Bessel in 1838 made the first successful measurement of stellar parallax, for the star 61 Cygni. He determined its parallax as around 1/12000 of a degree giving a distance of over 600,000 AU.

• The parallax of other stars was soon determined and all were found to be over 250,000 AU distant, implying luminosities similar to the Sun.

• Stellar masses were also first measured in the 19th century, by applying Newton’s laws to binary stars, once the period and separation was measured.

Picture: St. Andrews University


So, stars are like the Sun..


… a huge ball of hot, incandescent gas.

Image: SOHO EIT


The Sun By The Numbers:


MASS: 2.0 x 1030 kg = 333,000 Earth massesmore than 100x rest of solar system!

DIAMETER: 1.4 x 109 m = 109 Earth diameters = 10 Jupiter diameters

LUMINOSITY: 4 x 1026 watts = 4 million million million million, 100-watt light bulbs!

TEMPERATURE: 15 million Kelvin (core) 5800 K (surface)

DISTANCE: 1.5 x 1011 m = 1 AU


The Kelvin Temperature Scale


• Throughout this course we shall refer to temperatures in degrees Kelvin, named after Lord Kelvin, its originator (a Belfast-man like myself!)

•The Kelvin scale has the same size of degrees as the Celsius scale.

• BUT, whereas the zero of the Celsius scale is the freezing point of water, the zero point of the Kelvin scale is absolute zero, the point where atoms have no motion at all.

• Absolute zero is -273° C = 0 K (Kelvin), therefore 0° C = 273 K. There are no negative temperatures in the Kelvin scale!

• What is the boiling temperature of water in the Kelvin scale?



What is the Sun?


• OK, so the Sun is a star, and the stars are suns. But what is the Sun? We want to know:

• What is the Sun made of?

• How does the Sun shine?

• How old is it, and how did it form?

• How long will its energy last?

• But first, we need to review our knowledge of matter…


Atomic Ideas


• Democritus of Abdera (460-370 BC) was an early proponent of the atomic theory of matter.

• This theory held that matter was not infinitely divisible, but was ultimately composed of basic, granular, indivisible units called atoms.

• The theory was confirmed in the 19th century, when John Dalton, Dmitri Mendeleev and others clarified the nature of the different chemical elements.



Atoms


• An atom is composed of a positively charged nucleus, surrounded by a ‘cloud’ of one or more negatively charged electrons. The overall atom has a zero net charge.

Figure credit: Philip Grandinetti, Ohio State

• The nucleus contains almost all the mass of the atom, but is very small compared to the size of the electron ‘cloud’ (think of a pea in a football field). Hence, most of the atom is empty space!


The Atomic Nucleus


• The nucleus of the atom is composed of very small but ‘heavy’ particles:

• protons, which are positively charged• neutrons, which have no charge.

• The simplest stable atom has one proton and zero neutrons in the nucleus (and one orbiting electron). This atom is hydrogen.

• Isotopes of hydrogen have the same number of protons, but varying numbers of neutrons:



Elements


• Adding further protons and neutrons builds up different atoms.

• Atoms which have different numbers of protons are chemically distinct, and known as elements.

• For example, carbon-12 has 6 protons and 6 neutrons.



Quick quiz


1.Are there likely to be more: (a) elements, or (b) isotopes in nature?

2.How many neutrons are in: (a)16O (b) 18O(c) 13CO2 (d) D2O?


Periodic Table


• There are 92 naturally occurring elements in nature:

•The heaviest is Uranium, with 92 protons and typically 143 or 146 neutrons.

• Heavier elements have been created artificially and are unstable.

• Unstable heavy atoms undergo ‘fission’ (splitting) to become smaller and hence stable.

Figure credit: L. Gardiner, UCAR


Molecules and Compounds


• Atoms may join together to form molecules, such as water.

• Water forms when two hydrogen atoms bond with one oxygen atom, hence the symbol H2O (below, left).

Figure credit: M. Pidwirny, Okanagan U Coll

• In turn, water molecules may also join together by a weaker bond to form solid water ice (right).

• These inter-molecular bonds are easily broken when the ice warms to 273 Kelvin (0° C) and melts.


Light, photons and radiation


• The colors of the rainbow are the visible types of electromagnetic (EM) radiation.

• EM radiation can be imagined in two ways, which are both valid:

• as a wave of electric and magnetic fields• as a stream of particles, called photons.

• Photons have:

1. No mass2. Travel at the speed of light3. Have a corresponding wavelength: the shorter the wavelength

the more energetic the photon.


The Electromagnetic Spectrum


• Visible light is just one type of EM radiation: there are also radio waves, microwaves, infrared, ultraviolet, X-rays and gamma rays.

Figure credit: GSU


EM Spectrum Continued


• The wavelength and frequency of the radiation are inversely proportional to one another; the frequency and energy are directly proportional.

Figure credit: LBL Laurence Berkeley


Spectroscopy


• When light is passed through a glass prism it becomes dispersed into the separate component colors (wavelengths).

• This is the same process as in a raindrop, forming a rainbow.

• Scientists use a prism, or a diffraction grating, to disperse the light from stars and planets, a technique called spectroscopy.

• This analysis provides information on the composition and physical state of the object. Picture: Andrew Davidhazy, RIT


Solar Spectrum


• When light from the sun was passed through a prism, as well as the different colors, a pattern of dark, sharp line features was seen:

• Top left is an early sketch drawing (1817) of the solar spectral lines and intensity.

• Bottom left is a modern photograph of the same spectrum.

Figure credit: Jose Wudka, UC Riverside


Emission and Absorption Lines


• Both emission (bright) and absorption (dark) lines are seen in astronomy, and were explained in the 20th century by quantum theory.

• Lines form when an atom or molecule emits or absorbs a photon of a particular wavelength, corresponding to the difference between two energy levels.

• Emission lines form when a bright (hot) object is seen directly: absorption lines occur when a dark (cold) object comes between the bright object and the viewer, ‘subtracting’ certain wavelengths.

Figure credit: Jose Wudka, UC Riverside


Composition of the Sun


• Many of the dark lines on the solar spectrum were identified with spectrum of atoms seen in the laboratory, e.g. the bright ‘D’ lines at 589 and 590 nm due to atomic sodium.

• In 1868, Norman Lockyer observed a bright yellow line in the spectrum of solar prominences, and proposed that it was due to a new element, unseen on Earth. He named it helium, after the Greek word for Sun.

• In 1895 the gas was separated from minerals on the Earth and the existence of helium, the second lightest element, and second most abundant in the universe, was confirmed.


Cosmic Abundances of the Major Elements


Element Symbol Atomic No. of atomsNumber per million H atoms

Hydrogen H 1 1,000,000Helium He 2 97,000Carbon C 6 360Nitrogen N 7 110Oxygen O 8 850Neon Ne 10 120Sodium Na 11 2Magnesium Mg 12 40Aluminum Al 13 3Silicon Si 14 40Sulfur S 16 20Argon Ar 18 4Calcium Ca 20 2Iron Fe 26 32Nickel Ni 28 2


How does the Sun shine?


• The Sun currently radiates 4x1026 joules of energy per second (or watts) to space: it must generate the same amount of energy internally.

• What about chemical reactions, i.e. oxidation (burning)?No: the energy released from a material such as coal is far too small per unit mass: the entire Sun would be ‘burned up’ in just a few thousand years.

• A likely explanation was gravitational contraction, proposed by Kelvin and Helmholtz. This mechanism proposed that energy due to gravity (potential energy) is converted to energy of motion (kinetic energy) and finally to heat (thermal energy) – imagine a meteor falling to the Earth and producing a huge fireball.

A small contraction of only 40 m per year would be enough to power the Sun, or 400 km over human history. The entire Sun could shine by this mechanism for a predicted 100 million years.


But …


• By the beginning of the 20th century, evidence was mounting that the Earth was 100s of millions of years, perhaps a billion years old.

• But, all theories of Solar System formation agreed that the Earth formed at the same time or later than the Sun.

How could the Earth then be older than the Sun?


A New Source of Energy


• The answer came from an completely new concept, mass-energy equivalence, from a completely unknown (in 1905) scientist…

Picture: St. Andrews Univ.

… Albert Einstein.• Einstein’s Theory of Special Relativity has a number of consequences, including the constancy of the speed of light in a vacuum, and the famous formula:

E = mc2

When converting mass to energy, we multiply by a very large number, the speed of light squared, so a small mass becomes a huge amount of energy.


Energy from mass


• A simple calculation shows that by converting 4 million tons of matter per second to energy, the 4x1026 watts needed to power the Sun is released. This is miniscule compared to the mass of the Sun!

• Working out the details took several more decades of work…

• The Sun is 99% composed of hydrogen and helium, so the source was probably in those materials.

• The crucial observation was that a helium atom has a mass just a bit less than four hydrogen atoms combined – if four hydrogen atoms were fused together, they would release a tiny bit of mass, converted into energy, every time!

• It takes enormous temperatures and pressures to overcome the mutual repulsion of the positive nucleii, but those conditions do occur in the interior of the Sun.


Proton-proton chain


This figure shows how the Sun shines!

Graphic: Univ Tenn. Knoxville


Energy from Thermonuclear Fusion


• The net effect of this chain is take 4 hydrogen nucleii (protons) and convert to:

• 1 helium nucleus (most of the original mass-energy)

• gamma rays – energy!

• 2 anti-electrons, or positrons (anti-matter), which annihilate with 2 electrons to make more gamma rays.

•2 neutrinos, neutral, nearly mass-less subatomic particles.

• Neutrinos travel close to the speed of light and hardly interact at all with normal matter, the Earth and Sun are almost transparent to them!


Announcements 9/12/06


• Homework #1 due TODAY, September 12.

• Yellow forms - any more? (Missing from students: Gilkey, Kim, Kneib, Moffitt, Snyder, Wallick, Wrieden).

• Test e-mail(s). Who didn’t get one?

• New materials on website: Lectures 3 (Sun) & 4 (Planets)

• Course evaluation.


Questions from last time


• Elements not found naturally on Earth (Technetium?)• Technetium was the first element to be artificially produced, in 1937.• All isotopes are radioactive, and have t1/2< 4.2 Myr.• However, Tc was later discovered to occur naturally in miniscule quantities, as a by-product of natural Uranium fission.

• Atomic mass and relative atomic mass?• The atomic mass is the mass of the atom relative to carbon-12.• On your periodic tables, the number in the top right is the relative atomic mass, or the abundance-weighted average of all the common isotopes on Earth.


Revision Quiz


1. What is meant by parallax, and why is it useful to astronomers?

2. What is the diameter of the Sun, in terms of Earth diameters, closer to: (a) 10x, (b) 100x, (c) 1000x ?

3. What is the temperature of solar photosphere closer to: (a) 6000 K, (b) 8000 K, (c) 10000 K?

4. Describe the main properties of an atom. Of what three types of sub-atomic particle is an atom composed?

5. Name 3 types of electromagnetic radiation.


Energy Transport Mechanisms


• OK, so we know how the energy is made deep in the core of the Sun, but somehow the energy has to escape to the surface.

• There are three mechanisms to transport heat:

1. CONDUCTION: a microscopic process which conveys heat in solids. Molecules vibrate and bang into one another, causing the next one to vibrate and so on.

2. CONVECTION: a macroscopic process, when whole parts of a liquid or gas heat up, expand and move under gravity. Hot, less dense parts move upwards, conveying heat to cooler regions.

3. RADIATION: is the primary mechanism for heat transport in a vacuum, and occurs when matter releases some heat energy as a photon (EM wave) which travels at the speed of light.


Examples


• Examples of these three mechanisms in action can be found in an everyday setting - boiling water on the kitchen stove:

CONDUCTION occurs when the bottom of the saucepan heats up and warms the water in contact with it.

CONVECTION occurs in the water when hot ‘blobs’ of water rise and cooler ones sink.

RADIATION occurs in the glowing hot metal element of an electric stove, or the incandescent gas of a gas range.

• Can you think of other examples?


Heat Transport in the Sun


• Different energy transport processes dominate at different distances from the center:

Graphic: Derek Homeier, Univ. Georgia

• A core where the thermonuclear reactions take place.

• A radiative zone where photons carry energy upwards.

• A convective zone in the outer third of the Sun, where columns of warm gas rise and hot gas sinks.


Solar Evolution


• One of the questions we set for ourselves was: how long will the Sun last?

• If the Sun was able to convert all its hydrogen completely to helium, it would take about 100 billion years to burn out.

• The Sun is about 5 billion years old, so it has 95 billion years left… right?

• Wrong! As the Sun fuses more and more hydrogen, its internal structure changes; it becomes hotter and hotter, eventually swelling up into a red giant star which will envelop the inner solar system. This is predicted to happen in about 5 billion years from now.


Helium burning in the Sun?


• After a long period of stable hydrogen burning (1010) temperatures in the center of the Sun (and similar stars M>0.8 MS) reach ~108 K - sufficient to begin helium burning in the core.

• At these temperatures, three helium nuclei can participate in a three-way collision, to form a 12C nucleus.

• The onset of helium burning results in a ‘helium flash’ - the star expands rapidly and becomes a cooler red giant.

• The star then enters a stable helium burning phase for about 108 years, before exhausting fuel and shrinking to Wolf-Rayet stars (small but very hot), and then into long-lived white dwarves which cool slowly over 1010 years.


Appearance of the Sun: The Photosphere


• The solar photosphere shows several interesting features:

1. Sunspots – the irregular dark patches which come and go.

2. Granulation – a speckled appearance which always covers the whole surface.

3. Limb darkening – the darkening seen towards the edges.

• The photosphere is the visible ‘surface’ of the Sun, about 5800 Kelvin.

Picture: Derek Homeier, Univ. Georgia


Granulation: Close-Up!


Image from the Swedish Solar Telescope (SST), 24 July 2002. Large ticks are 1000 km apart.


Explanation of photosphere


• Limb darkening is explained as follows. As we look towards the edges of the Sun we are looking higher up in the photosphere. This shows us that the higher photosphere is cooler (4400 K), and hence darker.

• Granulation (below left) is simply the visible appearance of the convection cells in the atmosphere.

Graphics: Derek Homeier, Univ. Georgia

• Below right is schematic cross-section through the top of the photosphere. At the top of an ascending convection cell, hotter gas is brighter.

• At the edges of a cell, cooler, descending gas is relatively darker.


Sunspots


• Sunspots have been observed since ancient times. The amount of sunspots is quite variable, but follows an 11-year cycle of minimum and maximum activity, first noted by Heinrich Schwabe (1843).

Solar maximum Solar Minimum

Images: Derek Homeier, Univ. Georgia


What is a sunspot?


• The sunspot mechanism is complex and still debated, but basically sunspots are caused by loops in the Sun’s internal magnetic field, which push hot, electrically charged gas (plasma) upwards.

• The plasma cools to around 4300 Kelvin in the center (umbra) of the spot, hence the dark appearance.

• This cooler material is still electrically charged and hence trapped in the magnetic field, which leads to the persistence of individual spots, up to 2 months or 2 solar rotations.

Image: T. Rimmele, M. Hanna/NOAO/AURA/NSF


The Sunspot Cycle: ‘Butterfly’ Diagram


• At the start of the 11-year activity cycle, spots appear around 35° north and south latitude. As the number of spots increase, they gradually ‘migrate’ towards the equator, eventually disappearing as new spots arrive at the mid-latitudes.


Solar Flares


• Energy is released right across the EM spectrum: from radio waves through to X-rays, as in the image (right).

• Charged particles: protons, electrons and heavy nucleii are accelerated outwards at great speeds.

• Temperatures can rise within minutes to 5 million K, releasing a total 1030 J of energy...

= equivalent to 100 million million 1-megaton H-bombs!

Image: Yohkoh Soft X-Ray Satellite

• Flares are massive eruptions from the Sun, when magnetic energy that has built up is suddenly released.


The Chromosphere


• Above the photosphere lies the chromosphere (‘sphere of color’).

• The chromosphere is normally visible only during an eclipse, as a pinkish fringe around the moon, due to hydrogen emission of red light.

Image: Derek Homeier, Univ. Georgia

• Temperatures rise through the chromosphere, which is only a few thousand km thick, reaching 25,000 K at the top.

• The chromosphere has an irregular appearance, with many small gas jets called spicules, and larger features called prominences and filaments.


Chromosphere: prominences


• Solar prominences can get very large…

… such as this “Grand Daddy of June 4th, 1946”!


The Corona


• The corona (‘crown’) is the outermost part of the Sun, reaching out several million km to the start of the solar wind. It is composed of very thin but hot gas: up to 4 million K! The gas is ionized (positively charged).

• Due to its thinness, the corona is several million times fainter than the photosphere, and usually visible only during a solar eclipse.

• The corona has a very irregular appearance.

• Much of the energy is emitted as X-rays.


The Solar Cycle


• 12 X-ray images of the Sun from the Yohkoh spacecraft SXT instrument.

• The images, 120 days apart from 1991 to 1995, show the change in the corona during the waning part of the solar activity cycle.

Images: Derek Homeier, Univ. Georgia


The Solar Wind


• The solar corona does not have a sharp boundary: the hot gases in the corona are barely affected by the Sun’s gravitational pull, and flow outwards in a stream known as the solar wind.

• Although the solar wind is always present, it varies greatly in strength, as massive CME events periodically erupt.

• The solar wind is responsible for the glorious aurora borealis (northern) and aurora australis (southern), as charged particles from the solar wind follow the Earth’s magnetic field lines around to the poles, where they crash into the upper atmosphere (more in a later lecture).

Image: NASA GSFC “Living With A Star”


Coronal Mass Ejections (CMEs)


• CMEs are sudden violent events when 1012 kg of matter is thrown into space at speeds of 200-2000 kilometers per second (km/s).

• This movie clip from the LASCO instrument onboard the SOHO spacecraft shows a CME event.

• CMEs are related to solar flares, which occur later. The mechanism seems to involve the breaking of initially closed magnetic field lines.

• These particles can cause havoc when they reach the Earth, disrupting communications, and crippling satellites!


Numerical Examples


• Given that the solar luminosity is 4x1026 watts, 1 AU = 1.5x1011 meters, and the area of a sphere is 4πr2 (r=radius), calculate the amount of solar luminosity reaching a solar panel on the Earth which is 1 m2 in area, when the Sun is directly overhead (assume no clouds).

The solar luminosity Lsun spreads out into a spherical area around the Sun. The area of a sphere is 4πr2, and so, the amount of sunlight per square meter is Lsun/4πr2.

At the distance of the Earth, r=1 AU. So, the amount of solar luminosity per square meter = 4x1026/(4π x (1.5 x 1011)2) = 1415 watts.

• What is the corresponding value for a solar panel carried by a spacecraft at the orbit of (i) Mars (1.5 AU), (ii) Saturn (9.5 AU), (iii) Pluto (39.5 AU)?

• Answers: (i) 629 W (ii) 16 W (iii) 0.9 W.


Numerical Examples (continued)


• If a spacecraft requires 500 watts of power and uses solar panels with 10% efficiency of converting sunlight into electrical power, what size of solar array is needed (i) in Earth orbit, (ii) at Mars, (iii) Saturn, (iv) Pluto.

The solar intensity at the Earth is 1415 watts per m2. Therefore 500/1415 = 0.35 m2 would be needed if all the solar energy could be converted to electrical power.

BUT, the solar array is only 10% efficient, so we need 10x as much area, or 3.5 m2.

Mars: (500/629) x10 = 7.9 m2

Saturn: (500/16) x10 = 313 m2

Pluto: (500/0.9) x10 = 5555 m2

• Comment on the practicality of such arrays. What other sources of power might be used?


Final Quiz


1. What is the name given to the study of the composition of EM radiation, in terms of its different constituent colors or wavelengths?

2. Name one astronomical use for the technique in Q1.

3. How old is the Sun, and what is the name of the mechanism which powers it?

4. What is the fuel for the Sun?

5. Name the three visible layers of the Sun’s atmosphere, and give an approximate temperature for each.

6. Name three transient features of the Sun, with a brief explanation of each.

ASTR 330: The Solar System Announcements 9/7/06 Dr Conor Nixon Fall 2006 Yellow forms - any more?...

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