Astrophysics Internet Course

Unit 1 : Light Phenomenon and its ModelsWhat is the subject of astrophysics? Astrophysics is interested

in internal composition and evolution of stars and galaxies. But how can we learn about their structure if they are so far away? What kind of information can we obtain to devise models (Link - Eugenia) of these objects? This information must be produced by these objects and reach us. Some celestial objects radiate visible light (http://csep10.phys.utk.edu/astr162/lect/light/spectrum.html ) Some are invisible for our eyes but visible for radio telescopes (http://csep10.phys.utk.edu/astr162/lect/light/radio.html )or X-ray telescopes (http://xray.rutgers.edu/dev/trw.html ). Some radiate cosmic particles (http://www2.slac.stanford.edu/vvc/applications/morecosmic.html ; http://zebu.uoregon.edu/~js/glossary/cosmic_rays.html ; http://www-personal.umich.edu/~ande/cr/cr.html ;http://www.infoplease.com/ce5/CE012888.html )The only way to learn about celestial objects is to study what they send us.

Let us start with light. We call it a phenomenon because we can observe it. We study its properties in experiments. But how do we explain them? In physics, explanations that we give to the phenomena are called models. The word model is based on the idea that whatever explanation we devise, it will not comprise all the complexity of the phenomenon. It will explain some features of it under some circumstances, and for other circumstances a different model will be called for. The validity of models is tested in experiments. There are 2 major models that explain observable light phenomena, such as reflection, refraction, interference, diffraction, and the radiation and absorption of light. They are a wave model and a photon model of light.

Mechanical WavesTo understand the wave model of light, you need to refresh your

memory about mechanical waves. Use the following Web page to help you review this material :

http://www.glenbrook.k12.il.us/gbssci/phys/Class/waves/wavestoc.html

Question Set 1: Mechanical Wave Review 1) What do you need to have if you want to create wave motion?2) What is called a sinusoidal wave?

3) What are physical quantities that characterize a model of a sinusoidal wave?4) How can we measure each of them? 5) What do they depend on?6) What does it mean if the amplitude of a wave in a slinky is 20 cm?7) What does it mean if the frequency of a wave in a slinky is 2 Hz?8) What does it mean if the speed of a wave in a slinky is 2 m/s?9) For the previous conditions, determine the wavelength of the wave and explain what the number you calculated means.10) Describe the phenomena of interference and diffraction.11) Explain the phenomena of interference and diffraction. What modeling conditions did you use for your explanation?12) Give examples of wave interference and diffraction that you observed in everyday life.

Wave Model of LightNow we can start discussing why a wave model can be used to

explain the behavior of light. Think about light phenomena that resemble different phenomena that occur with waves. Does light reflect? Refract? Interfere? Diffract? The following Web pages will help you to answer these questions and move to the second set of questions in this lesson:

http://www.glenbrook.k12.il.us/gbssci/phys/class/light/lighttoc.html http://theory.uwinnipeg.ca/physics/light/index.html

Question Set 2 : Wave Model of Light1) How is light reflected by different surfaces? Are different colors reflected at the same angle?2) How is light refracted by different media? Are different colors refracted the same way?3) Why do you see a rainbow if white light goes through a prism?4) How do we know that different colors correspond to different wavelengths of light?5) If red light goes from air to water, what changes: its frequency, wavelength or speed? Why?6) What will happen if white light goes through two very narrow slits? Why?7) What will happen if a monochromatic light goes through a system of two very narrow slits? Why?8) What will happen if white light goes through a system of many narrow slits? Why? What do you need to know in order to calculate the separation of slits using this experiment?9) Why a diffraction grating should be called an interference grating?10) What phenomenon is called a spectrum of light?

The Electromagnetic Wave Model of LightPhenomena of interference and diffraction prove that the wave

model can be applied to study the propagation of light. But what kind of wave is the light wave? Is it a mechanical wave like a sound wave or a different kind? (http://www.glenbrook.k12.il.us/gbssci/phys/Class/sound/11l1a.html ) We know that light propagates in a vacuum and sound does not. This means that light wave is not transmitted by vibrating particles. If this is true, then what is oscillating in a light wave? Theoretical studies done by J. K. Maxwell (http://www.bc.cc.ca.us/programs/sea/astronomy/light/lighta.htm ; http://zebu.uoregon.edu/~js/glossary/maxwell.html ) and experiments carried out by H. Hertz (http://www.optonline.com/comptons/ceo/02190_A.html ) proved that light is a wave in which electric and magnetic fields oscillate perpendicular to each other (http://zebu.uoregon.edu/~js/ast122/lectures/lec04.html ) In order to produce an electromagnetic wave, an electric charge is accelerated (http://newton.hanyang.ac.kr/~jhkim/jhdocu5.html ).

Polarization experiments prove that light behaves like a transverse wave in which electric and magnetic fields (that is why it is called an electromagnetic wave) are perpendicular to each other and produce each other. It is extremely important to understand that in the polarization process you will be looking at, it is the electric field component that is being polarized (http://www.glenbrook.k12.il.us/gbssci/phys/Class/light/u12l1e.html ).The transverse wave nature of light can also be proved by the effects that magnetic field creates on the polarization of light (Link - Eugenia).

We also know that the geometry of experiments done with diffraction gratings shows that the color of light that we perceive is representative of its wavelength (and therefore its frequency) (Link - Mike). Frequencies of visible light range from 4.3 x 10 14 Hz to 7.5 x 1014 Hz. Electromagnetic waves with frequencies smaller than visible light (known as infrared, microwaves and radiowaves) as well as those with higher frequencies (ultraviolet, X-rays, gamma rays) possess the same properties.

Question Set 3 : The Electromagnetic Wave Model of Light1) What experiments proved that light is an electromagnetic wave?2) State whether the following forms of electromagnetic radiation radio, TV, infrared, visible, ultraviolet, X, gamma are listed in order of increasing or decreasing wavelength, b) increasing or decreasing frequency, c) increasing or decreasing energy of their photons.

3) For each of the following forms of electromagnetic radiation, state one way that it is produced in nature, and one way that you might detect the presence of this form of radiation.4) What is known about the speed of different forms of radiation in a vacuum?5) What are the approximate wavelengths of red light, yellow light, blue light, radio waves, television waves, X-rays?6) What are two characteristics of sound waves that prove that they are not forms of electromagnetic radiation?7) An experiment in which white light is projected through a diffraction grating onto a screen shows that the red part of the visible spectrum is farther from the center of the screen than the blue part of the spectrum. Explain how this proves that red light has a larger wavelength than blue light.

8) How can the polarization of light provide evidence that the wave model of light works?9) A student believes that two polarizing filters, aligned perpendicular to each other, will eliminate any unpolarized light that is passed through both the filters because one filter removes the electric field and the other filter removes the magnetic field. Explain how you would correct this student’s ideas about polarized light.

The Photon Model of LightAt the same time, many experiments cannot be explained if we

apply a wave model to light. Some of these experiments have to do with the photo-electric effect, that is, the absorption of light by metals (http://theory.uwinnipeg.ca/physics/quant/node3.html ). Still other experiments are related to radiation of light by hot objects (solids or gases). Experimental data obtained by studying radiation of light by hot solid objects can be represented by a curve. One can obtain a similar curve recording the energy of light at different wavelengths. This information can be obtained if light from a hot object (such as a filament of an incandescent light bulb or back body) passes through a diffraction grating and is focused on a screen. With your eyes you can see a rainbow (spectrum) in which all colors are present. If your eyes were sensitive to shorter (UV) or longer (infrared) wavelengths, you would see that the light of these wavelengths is present too, but its intensity is different. The wavelength at which the maximum intensity that is radiated can be determined using Wien’s Law, which was obtained experimentally, and the total energy is given by Stephan-Boltzmann’s Law, which is also the result of experiments. None of these laws can explain the experimental curve of intensity versus wavelength, in which light of all frequencies are present but has different intensity at different wavelengths. This curve is called a continuous spectrum. The model for the radiation mechanism for the continuous black body spectrum was provided by Max Planck. The Web pages below should help you to learn more about the material discussed above as it relates to the photon model of light : http://zebu.uoregon.edu/~js/glossary/planck_curve.html ; http://zebu.uoregon.edu/~js/ast122/lectures/lec05.html ; http://csep10.phys.utk.edu/astr162/lect/light/radiation.html ; http://theory.uwinnipeg.ca/physics/quant/node2.html

Question Set 4 : The Photon Model of Light1) What experiments cannot be explained with the wave model of light?2) What are the main features of the photon model of light?3) What phenomena can be explained with the help of both models?What are the explanations (provide at least two examples).4) What is the difference between red and blue photons?5) Observations of the light of the stars indicate that they produce a continuous emission spectrum that is very similar to the black body spectrum. Using these data, determine the surface temperature of the Sun, assuming that is has yellow color.6) Using the datum for the surface temperature from item 5, determine the total energy radiated by the Sun every second. This rate of energy production is called the luminosity.

7) Compare this value for the luminosity of the Sun with the value that you obtain from the amount of energy that 1/2 of the Earth’s surface receives from the Sun. (Note : the Solar constant, which is the rate at which each square meter of the earth receives energy from the sun, is 1.37 x 103 Watts/m2)

The Doppler Effect Another phenomenon that can be explained with the wave

model of light is the Doppler Effect. Although many people are familiar with the Doppler Effect as it relates to sound, it is also a fundamental tool in the analysis of stellar phenomena. To begin learning about it, visit these Web pages:

http://www.glenbrook.k12.il.us/gbssci/phys/class/waves/u11l3b.html http://csep10.phys.utk.edu/astr162/lect/light/doppler.html http://zebu.uoregon.edu/~js/ast122/lectures/lec04.html

The mathematical expression for the Doppler Effect for light is different from the expression that you may be familiar with for sound. The derivation of the expression for the Doppler Effect for light can be found here (Link - Mike).

After reviewing all of the links above, you will be prepared to answer the next question set.

Question Set 5 : The Doppler Effect for Light1) Suppose a source is monochromatic yellow light. How does the appearance of the source change as the source (a) approaches the observer, or (b) recedes from the observer.2) Suppose the observed wavelength of the sodium line in a star is 5891 A, whereas in the laboratory the wavelength is 5890 A.(a) At what speed is the star moving relative to us?(b) Is the star approaching or receding?3) Describe in words how the sun’s rotation can be determined from an analysis of the spectra of light coming from various parts of the disk.4) Explain how the earth’s orbital speed can be determined from observations of the spectrum of a star.5) Light from a galaxy in the Constellation Virgo is observed to be 0.4% longer than corresponding light that has a wavelength of 656 nm when measured in the laboratory. What is the radial speed of this galaxy with respect to the earth? Is it approaching or receding?6) The period of rotation of the sun at its equator is about 24.7 days; its radius is 7 x 105 km. What Doppler wavelength shift is expected for light with wavelength 550 nm emitted fom the edge of the sun’s disk?

Unit 2 : The Ideal Gas ModelMany phenomena occurring to celestial objects can be

explained with the help of another model... the model of ideal gas. This model is connected to the Kinetic Molecular Theory. The following Websites will help you to review the major parts of this theory/model :http://www.bcpl.lib.md.us/~kdrews/kmt.html http://www.chem.ualberta.ca/~plambeck/che/p101/p01051.htm http://www.chem.ualberta.ca/~plambeck/che/p101/p01061.htm http://www.chem.ualberta.ca/~plambeck/che/p101/p01062.htm http://www.chem.ualberta.ca/~plambeck/che/p101/p01063.htm http://www.chem.ualberta.ca/~plambeck/che/p101/p01065.htm

Question Set 6 : The Ideal Gas Model1) What is gas? What do we know about its properties? How do we know what we know (What experimental observations give us the evidence for these statements? What theoretical assumptions we use and why?)2) What is ideal gas? What is the difference between real gas and ideal gas? 3) When can we say that real gas behaves like ideal? When can’t we say this?4) What are physical quantities that describe the behavior of ideal gas? What are their units? What is the relationship between them? How do we know that these laws are true?5) Can we use the model of ideal gas for the gas in a typical classroom? Approximately how much energy does it possess?6) What is the difference between words temperature, heat energy and heat?7)Calculate the speed of air molecules in this room.8) How often do molecules collide? (calculate the number of collisions per second).9) The best vacuum that can be produced in the laboratory is about 10-15 atm. How many molecules still exist in one cubic centimeter of space at this pressure and temperature 0°C?10) Why does the Moon have no atmosphere?

Unit 3: The Structure of AtomsAs we understand now, our knowledge of stars come from the

studies of electromagnetic waves that they radiate. But how do they radiate light? How do stars radiate UV radiation, or X-rays? This section will help you to understand how stars produce visible and UV radiation.

By the middle of the 19th century scientists learned how to analyze light radiated by hot gases. For example, the studies of hydrogen by Johann Balmer that atomic hydrogen does not radiate white light, but light of only certain wavelength. For example, he observed light of the following wavelengths: 656 nm, 486 nm, and 434 nm. The same phenomenon was observed for all gases at low density. Scientists were curious about the mechanisms that could lead to this kind of radiation. To explain the mechanism they needed to devise a model of the inner structure of atoms that would account for their stability, lack of total electric charge and their radiation spectra.The first step in this work was the discovery of the electron in the studies of cathode rays . After this J.J.Thomson proposed his “plum-pudding model”, and E. Rutherford came up with the planetary model (http://wine1.sb.fsu.edu/chm1045/notes/Atoms/AtomStr1/Atoms02.htm ; http://www.phys.virginia.edu/classes/252/rays_and_particles.html ). Unfortunately none of them accounted for all of the observed properties. This prompted N. Bohr to devise a new model which was later called the “Bohr hydrogen atom”. The following set of questions will help you to understand the features of this model and the limitations of the previous ones.

Question Set 7 : Models of Atoms1) What are cathode rays and what properties they have?2) Describe the main features of Thomson model of atoms and the experimental facts that it accounts for.3) What experimental facts cannot be explained with Thomson’s model?4) Describe the main features of Rutherford’s planetary model of atoms and the experimental facts that it accounts for.5) What experimental facts cannot be explained with Rutherford’s planetary model?6) In his model, Bohr modified planetary model for hydrogen to account for all experimental observations. The electron was still orbiting the nucleus but Bohr postulated that:• there are certain stationary states (radii) in which the electron

even moving in a circular orbit does not radiate electromagnetic waves. In these states the angular momentum of the electron is quantized: the magnitude of the orbital angular momentum (mvr)

equals a positive integer multiple of Planck’s constant (h) divided by 2

mvr = nh/(2) (n=1,2,3,...).• Radiation is emitted by the atom when the electron undergoes a

transition from one stationary state to another.• This energy is emitted in a form of a photon, which frequency is

determined by the difference in energies of the states:E = hf

Using these postulates, your knowledge about the energy of the electron in each state (taking into account that it has kinetic energy and electric potential energy due to Coulomb’s force of its interaction with the nucleus) and applying Newton’s laws to the motion of the electron, find out from what level to what level transitions were made to produce light of the wavelengths observed by Balmer (656 nm, 486 nm, and 434 nm) in the spectrum of hydrogen. All necessary constants are in the table (link to the table of constants here).7) Calculate the energy of a photon that can ionize the atom of hydrogen.8) Calculate the temperature of hydrogen at which all atoms are ionized.9) Imagine that you have white light produced by the hot filament (remember, it produces a continuous spectrum), what will happen if this light goes through a cloud of cold hydrogen? Hot hydrogen? Ionized hydrogen?10) If you look at the Sun through a spectroscope (http://infoplease.lycos.com/ce5/CE049035.html ), you will see a continuous spectrum with the brightest part around yellow light and dark stripes. The wavelengths at which there is no radiation coming can be easily recorded. Some of them are the same as the wavelengths of spectral lines radiated by different elements in the laboratory conditions (for example ionized Fe, Mg, Ca, Na, or atomic H). How can you explain this phenomenon?

Unit 4 : Stellar ParametersStellar parameters are physical characteristics of the stars that

astronomers use to classify stars and study their evolution. It is important to not only know what these characteristics are but also how to determine them.These parameters are:1) Stellar luminosities. The luminosity of the star is the total amount of energy it radiates every second. It is measured in J/s and depends on the surface temperature and the size of the star. (http://www.bc.cc.ca.us/programs/sea/astronomy/starprop/strpropb.htm ) Surface temperatures can be determined from the analysis of the spectrum of the star but the sizes of stars are very hard to measure.

One method that is used for it is lunar occultations. The moon occults a star when it passes in front of the star as viewed from the Earth. The observer makes very rapid measurements of the star’s light as the Moon occults it. The diameter of the star can be determined from the time of the occultation because the angular speed of the Moon is well known. Unfortunately this is not a very precise method. Another way of determining sizes of the stars comes from knowing the next parameter. 2) Stellar magnitudes (absolute and apparent) (http://csep10.phys.utk.edu/astr162/lect/stars/magnitudes.html http://zebu.uoregon.edu/~js/ast122/lectures/lec09.html ). As you understand, apparent magnitude can be determined from observations but absolute cannot. To determine the absolute magnitude, one must know the distance to the stars. One of the methods to measure distances is called “parallax” (http://csep10.phys.utk.edu/astr162/lect/distances/parallax.html http://zebu.uoregon.edu/~js/ast122/lectures/lec09.html ).The relationship between apparent and absolute magnitude allows astronomers to determine the luminosities of stars even when they do not know their radii.

It is important to know that the luminosity as we defined it before is related to electromagnetic energy in all wavelengths. As you already know, according Wien’s Law, the amount of energy that hot objects radiate at different wavelengths depends on their surface temperatures. That is why astronomers distinguish luminosities in different parts of the spectrum and bolometric luminosities.3) Stellar spectra. The studies of stellar spectra in the 19th century demonstrated that though stars’ spectra look different (http://instruct1.cit.cornell.edu/courses/astro101/lec13.htm http://csep10.phys.utk.edu/astr162/lect/stars/spectra.html ; http://csep10.phys.utk.edu/astr162/lect/sun/spectrum.html http://zebu.uoregon.edu/~js/ast122/lectures/lec10.html ), they can be classified. We will use Harvard spectral classification (http://csep10.phys.utk.edu/astr162/lect/stars/harvard.html ). The studies of stellar spectra allow astronomers to determine chemical composition of stars, their surface temperatures, density of the atmospheres, their motion, whether they belong to binary systems, and their age.4) Chemical composition. Stellar spectra exhibit absorption lines that can be used to identify chemical elements whose atoms could absorb recorded frequencies. At the same time this information can be deceiving because the conditions for absorption vary with temperature. Most of the stars are made of the same chemical elements : 70% H and about 25% He (http://csep10.phys.utk.edu/astr162/lect/sun/composition.html ). Chemical composition changes slightly as the star evolves.

5) Stellar masses. This parameter can be determined rather accurately for binary stars (http://csep10.phys.utk.edu/astr162/lect/binaries/binaries.html ; http://csep10.phys.utk.edu/astr162/lect/binaries/visual.html ) through observations of their orbital periods and speeds. One needs to know Kepler’s laws to understand this method (http://csep10.phys.utk.edu/astr162/lect/binaries/astrometric.html ). For single stars that are on the Main Sequence, the experimental relationship between mass and luminosity (called the Mass-Luminosity Relation ) is used to determine their masses (http://csep10.phys.utk.edu/astr162/lect/binaries/masslum.html ).

Question Set 8 : Stellar Parameters1) Determine the Solar luminosity using two methods: a) data about its surface temperature and radius; b) data about the energy that every square meter of the Earth receives every second (Solar constant). How will the luminosity of the sun change if the observer moves away from it twice the distance between the Earth and the Sun? How will the Solar constant change it this happens? Explain.2) Use the table shown below to derive the relationship between two apparent magnitudes and stars’ brightness.

Difference in apparent magnitude Ratio of Brightness

0.0 1 : 10.5 1.6 : 10.75 2 : 11.0 2.5 : 11.5 4 : 12.0 6.3 : 12.5 10 : 13.0 16 : 14.0 40 : 15.0 100 : 16.0 251 : 110.0 10,000 : 115.0 1,000,000 : 120.0 100,000,000 : 125.0 10,000,000,000 : 1

3) Can two stars have the same apparent magnitudes but different absolute magnitudes? Give an example. Explain.4) Can two stars have the same absolute magnitudes but different apparent magnitudes? Give an example. Explain.5) At what distance one half of the Earth’s orbit would have a parallax of

1 arcsec?6) If a star’s parallax is 0.04 arcsec, what is its distance in parsecs, in light years, in astronomical units, in kilometers? (25 pc, 81.5 LY, 5.16 x 106 au, 7.7 x 1014 km)7) The smallest parallaxes that can be measured are about 0.01 arcsec what is the maximum distance that can be measured by the method of stellar parallax? (d= 1/0.01=100 parsecs)8) What would be the advantages of measuring stellar parallaxes from Mars rather than from Earth? (Mars’ orbit is 50% larger than the Earth’s, so all parallaxes will be 50% larger, we will be able to measure the distances to the stars that we can do from Earth)9) Derive the relationship between the apparent, absolute magnitude and the distance to between the star and the observer.10) Derive the relationship between the absolute magnitude of the star and its luminosity.11) Why is the star’s apparent magnitude not a good indication of the star’s energy output?12) Why is the star’s absolute visual magnitude not an accurate measure of a starís total energy output?13) Which kinds of stars are expected to emit large amounts of ultraviolet radiation?14) Which kinds of stars would be expected to emit large amounts of infrared radiation?15) Which characteristics of a star can be determined by one night’s observing with a naked eye? 16) Which characteristics of a star can be determined by one night of telescopic observations, including auxiliary instruments? 17) What characteristic determines the color of the star?18) Two stars of equal luminosity. Star B is blue, star Y is yellow-orange. Which star appears brighter to the eye? Which star appears brighter on the photo? 19) The spectral class of the star depends on which two properties of the star?20) List the following stars in order of increasing surface temperature: A0, B3, F2, M3, G2, O8.21) Determine the color and approximate surface temperature of the following stars:SiriusA1 Centauri G2 Arcturus K2 Rigel B8 Betelgeuse M2 Crucis B0 22) Three stars are observed to put out their maximum light at the following wavelength. Estimate the spectral class of each.

2.6 x 10-7m 5.0 x 10-7m 9.7 x 10-7m

23) In which stellar spectral class is each of the following most likely to be found in the spectrum?(a) Strong hydrogen lines(b) Lines of neutral metals(c) lines of neutral helium.24) How do astronomers estimate the chemical compositions of stars?25) How do astronomers estimate stellar rotation rates?26)What different kinds of information can be obtained from the analysis of stellar spectra?

Hertzshprung-Russel Diagram

After we established the system of stellar parameters, it would be interesting to find out, if there is any relationship between different parameters of the stars. For example, do stars of the same spectral class have different luminosities, or the same spectrum leads to the same luminosity? To answer this question, one must examine observational data from different stars. We offer you data on 65 stars:

Star Proper name

Luminosity

Mass

Radius Temperature

Color Spectral Class

Arietis

Sheratan

20 2.5 1.8 8800 White A5 V

Bootis A

0.5 0.8 0.9 5300 Yellow G8 V

Bootis B

0.19 0.6 0.8 4400 Orange

K4 V

Cassiopeiae A

1.2 1.1 1.1 6000 Yellow GO V

Cassiopiae B

0.05 0.4 0.6 3700 Red MO V

Centauri

2900 11 6 19000 Blue B2 V

Centi 0.7 0.9 0.9 5600 Yellow G5 VEridany C

0.02 0.3 0.4 3300 Red M4 V

VZ Hydrae

3.5 1.5 1.2 7200 Green F5 V

Hydri 7 1.8 1.4 7400 White FO V

Lac 9352

0.04 0.4 0.6 3400 Red M2 V

Leonis

Denebola

27 2.7 1.8 9000 White A3 V

70 Ophiuchi A

0.4 0.8 0.9 5200 Orange

KO V

70 Ophiuchi B

0.12 0.66

0.7 4200 Orange

K6 V

Orionis

3.0 1.4 1.2 6300 Green F6 V

Persei

Algol 200 5.2 3 12000 Blue B8 V

Scorpii

Dschubba

12000 17 7.6 28000 Blue BO V

Ursae Majoris

Alkaid 1100 8 4 15000 Blue B5 V

Virginis

4 1.5 1.3 7100 Green F2 V

Ophuiuchi

16000 19 8 30000 Blue O9.5 V

Spica 1800 14 7 23000 Blue B1 V Archern

ar720 10 5 17500 Blue B3 V

Regulus 164 5.5 3.2 13000 Blue B7 V Vega 55 3.8 2.6 1000 White AO VUrsae Mejoris

Merak 70 3.6 2.43.6 9900 White A1 V

Austrini Formalhaut

20 3.0 2.0 9000 White A3 V

WW Aurigae A

1.81

1.9 8800 A5 V

Aquilae Altair 12 2.1 1.5 8100 White A7 VVZ Hydrae

3.0 1.12

1.05 6200 Green F7 V

UV Leonis

1.0 0.95

1.05 5800 Yellow G2 V

Ceti 0.44 0.8 0.9 5300 yellow G8 V Herculis

0.51 0.78

0.89 5100 Orange

KO V

YY Gemino

Castor C

0.04 0.58

0.6 3600 Red M1 V

riumKrueger 60 A

0.01 0.3 3300 Red M3 V

Crusis

Beta 6000 21 10 28000 Blue B0.5 V

Crusis Centauri

Hadar 10400 15 10 23000 Blue B1 III

Orionis Rigel 60000 43 22 11200 Blue B8 ICygni A Deneb 60000 42 44 9300 White A2 I Carenae Canopu

s1500 15 60 7400 white Fo I-II

Ursae Minoris

Polaris 6000 14 90 5300 Yellow G8 III

Aurigae

Capella 150 4 13 5300 Yellow G8 III

Geminorum

Pollux 34 4 15 4600 Orange

KO III

Cephei 9200 16 220 5000 Orange

K1 I

Bootis

Arcturus

115 4 18 4400 Orange

K2 III

Tauri Aldebaran

160 5 45 3900 Orange

K5 III

Ophiuchi

300 6 50 3300 Red M1 III

Scorpii Antares 9500 24 600 3200 Red M1.5 I Orionis Betelge

use15000 27 750 3200 Red M2 I

Pegasi Sheat 700 7 100 3000 Red M2 II-III

Herculis Ras-Algethi

1600 9 100 2700 Red M5 II

Sun 1 1 1 5800 Yellow G2 VCentauri A

Rigil Kent

1.0 1.0 1 5800 yellow G2 V

Centauri B

0.2 0.6 0.8 4400 Orange

K4 V

Centauri C

0.01 0.2 0.3 3000 Red M5 V

Baranards Star

0.004 0.2 0.3 2500 Red M5 V

Wolf 359

0.001 0.1 0.2 2400 Red M8 V

Lalande 21185

3400 Red M2 V

Canis Majoris A

Sirius 28 2.7 1.8 9900 White A1 V Canis Majoris B

0.0027 1.1 0.02 9300 White White Dwarf

UV Ceti 0.005 0.15

0.25 2800 Red M6 V

Eridani 0.3 0.7 0.85 4800 Orange

K2 V

61 Cygni A

0.18 0.6 0.7 4400 Orange

K5 V

61 Cygni B

0.08 0.5 0.7 4000 Orange

K7 V

Canis Minoris A

Procyon 7 1.8 2.2 6500 Green F5 IV-V

Canis Minoris B

0.0006 0.7 0.01 9100 White White Dwarf

To find the patterns in this data, you need to graph it. We suggest that you obtain log paper (desirable for 6 - 8 orders of magnitude) and graph the data from the table for luminosity and temperature. Because luminosity of stars varies so much, it is convenient to graph the log of the ratio of the star’s luminosity and the Sun’s luminosity (y axis) versus temperature (x axis). Notice, that traditionally astronomers graph temperatures backwards : the highest are closest to the beginning of the axis and the lowest are at the right end. After you are done with graphing, compare your graph with the graph conventionally known as Hertzshprung-Russel diagram (http://zebu.uoregon.edu/~js/ast122/lectures/lec12.html ; http://instruct1.cit.cornell.edu/courses/astro101/lec13.htm ;http://www.bc.cc.ca.us/programs/sea/astronomy/starprop/strpropd.htm )

Question Set 9 : The H-R Diagram1) For the stars in the table:Which star has the hottest surface?Which star has the coolest surface?Which star is the nearest?Which star is the farthest?

Which are the largest stars?Which are the smallest stars?Which star is bluest?Which are the reddest?Which star is most like the Sun?Which stars do not follow the intuitive temperature-brightness relationship for stars?2) Why were you asked to find the relationship between luminosity and temperature, not between color and temperature, temperature and spectral class?3) Is there a relationship between stars’ luminosities, temperatures and radii? Chose several stars from the table to prove your answer qualitatively.4) What is the theoretical model that will allow you to determine the radius of a star when its temperature and luminosity are known? Test it quantitatively using the data from the table for several stars.5) H-R diagram is used to determine distances for the stars. Can you offer a method to do it?6) What is the difference between different groups of stars represented on H-R diagram? Why, do you think they are so different?7) What does it mean if most of the stars are located on the region called “The Main Sequence”?8) What does it mean if only very few stars are “white dwarfs”, i.e., hot and tiny stars.9) Why are some luminosities in the table rather estimates that measured quantities.

Unit 5 : Stellar Structure, Composition, and Evolution.

H-R diagram shows that stars spend most of their life on the Main Sequence. Our sun is on the Main Sequence too. It means that it is going through the longest phase of its evolution. What do we know about the Sun that might help us to learn about its interior? We know its color, its size, the energy that is sends in all directions every second and its approximate age : this can be deduced from the age of the Earth that is estimated to be at least 4.5 billion years. Let us try to figure out how the Sun maintains its tremendous luminosity for billions of years and what is the source of its energy.

Question Set 10 : Energy of the Sun1) How old is our Sun?2) Will it shine forever? Why not?3) What affects the length of time the Sun can shine? How would you express its life time in terms of the energy that it possesses and the energy it loses every second?

4) How long can it shine using its heat energy? To calculate the heat energy of the Sun, estimate that it is made of hydrogen, and the average temperature of the Sun is 50,000 K. In what state (gas or plasma) is hydrogen at this temperature? How do you know? (The mass of the Sun is listed in the data table).5) How long can it shine using its gravitational potential energy?(Link - Mike) Assume that half of the total GPE can be radiated as electromagnetic radiation if the Sun shrinks to a point.6) What other sources of energy might it have? Can it use chemical energy? Why not?7) What is fusion? How much energy is radiated when a nucleus of helium is produced in a fusion reaction? 8) How many protons (in terms of mass in kg) should fuse to maintain the present luminosity of the sun for 5 billion years? Is this number reasonable for the Sun?9) What conditions are necessary so that fusion might take place in the core of the Sun? 10) Calculate the temperature at which two protons can come close enough for nuclear attraction forces to start acting on them. Why can’t they come close at lower temperatures? References to nuclear forces can be found at (http://csep10.phys.utk.edu/astr162/lect/energy/reactions.html ; http://zebu.uoregon.edu/~js/ast122/lectures/lec06.html ; http://www.scri.fsu.edu/~jac/Nuclear/whatis/forces.html http://library.advanced.org/tq-admin/month.cgi )11) How does this relate to the possibility of fusion in the core of the Sun? The temperature in the core of the Sun is estimated to be 10 million degrees K. Does it mean that fusion is impossible?12) What is a p-p cycle? What is a CNO cycle? (http://csep10.phys.utk.edu/astr162/lect/energy/ppchain.html ; http://csep10.phys.utk.edu/astr162/lect/energy/cno.html ; http://csep10.phys.utk.edu/astr162/lect/energy/cno-pp.html )13) What might be an indicator of the presence of the fusion in the core of the Sun? Estimation show that it takes 100 million years for a photon radiated in the fusion reaction in the core of the Sun to reach the surface (because of absorption, reemission, and scattering). It means that the photons that we are seeing on the surface of the Sun now, were born very long time ago. What particle that is emitted in fusion reactions, does not get absorbed on its way out?14) What are the results of Solar Neutrino experiments? 15) What is your conclusion about the sources of stellar energy?

The next step in our understanding of stars will be learning about their evolution. This deals with the question such as: Where do stars come from? Do they change over the years? What will their life path

depend on? Do they ever die? What happens to stars after death? How do we know this?Essentially, the evolution of a star involves 6 stages : “birth”, “childhood”, “adulthood”, “old age”, “death”, and “life after death”. For a good overview of these stages, carefully read lectures 14, 15, 16, 17, 18, 20, 21, and 23 at the University of Oregon Astronomy website (http://zebu.uoregon.edu/~js/ast122 ). Another good overview is the entire “Lives and Deaths of Stars” section at the Bakersfield College Astronomy website (http://www.bc.cc.ca.us/programs/sea/astronomy/evolutn/evolutna.htm )Novae, supernovae, and supernovae remnants are part of the last two stages in the life of a star. In addition to the previously recommended sites, more can be learned about these phenomena, as well as open (galactic) and globular clusters by (1) clicking on the Novae and Supernovae chapters at “The Death of Stars” site at the University of Tennessee (http://csep10.phys.utk.edu/guidry/violence/death.html ). The UTenn site also has a good illustration of a Type 1A Supernova (http://csep10.phys.utk.edu/astr162/lect/supernovae/type1.html ) , as well as information about star clusters (http://csep10.phys.utk.edu/guidry/violence/starclusters.html (2) clicking on lectures 19, 22, and 23 at the Cornell University Astronomy 101/103 website (http://instruct1.cit.cornell.edu/courses/astro101/index.htm )(3) clicking on a site provided by NASA http://imagine.gsfc.nasa.gov/docs/introduction/supernovae.html Finally, there is a type of star called the Cepheid variable, which plays an important role in determining distances to stars. Read more about Cepheid variables at these sites: http://zebu.uoregon.edu/~soper/MilkyWay/cepheid.html http://annie.astro.nwu.edu/labs/m100/measdist.html http://www.ast.cam.ac.uk/~mjp/cepheids.html http://imagine.gsfc.nasa.gov/docs/science/mysteries_l1/cepheid.html

Question Set 11 : Stellar Evolution

1)What is a proto-star? How do they form? Why doesn’t every gas/dust interstellar cloud becomes a proto-star?2)Where in the Galaxy are likely places to search for proto-stars? What is the observational evidence for the model of a proto-star?3)What kind of radiation would a proto-star be expected to emit?How do the main sequence stars contribute to the content of heavy elements in the interstellar medium?

4)Why is it that we can know so much about the formation of stars, which are so far away, whereas we know so little about the formation of planets, one of which is just outside the door?5)What is the predominant energy source for each of the following kinds of stars:(a) pre-, (b) main sequence, (c) red giant, (d) white dwarf?6)Once the proton-proton reaction begins in the core of the star, why isnít all hydrogen converted to helium instantly?7)When hydrogen is converted to helium plus energy inside stars, where does the energy come from?8) A main sequence star of 20 solar masses is about 10,000 times more luminous than the Sun. assuming the star to be pure hydrogen, how long would it take for the star to convert all its hydrogen into helium?9) When a main sequence star exhausts its hydrogen fuel in its core,(a)what happens to the core of the star? (b) what happens to the starís outer layers?10) What two reactions are believed to occur in red giants, and where in the star do they occur?11) What property of a star determines where it is located on the main sequence?12) Describe the basic differences between: a) a main sequence A0 star and a white dwarf A0 star; b) a main sequence M2 star and a red giant M2 star.13) Why is it believed that stars spend the major portion of their lives on the main sequence?14) Why do upper main sequence stars (O & B) spend much less time on the main sequence than do lower main sequence stars?15) Describe and explain the differences between H-R diagrams for a typical globular cluster and a typical open cluster.16) What are possible end stages for stars?17) What property of a star determines how it will end?18) What will be the fate of the Sun?19) How is it known that dwarfs are dying stars, and not stars at some active stage of evolution? What is believed to be inside a whit dwarf? How do we know that this is true?20) What are neutron stars and how are they detected?21) Why is it difficult to detect black holes in space, if they exist?22) If black holes do exist but emit no electromagnetic radiation, then how might they be detected?23) Why doesn’t a proto-star just continue to collapse until it becomes a planet or a black hole?24) What will happen if fusion reactions start in the degenerate gas?25) Why does fusion occurs peacefully in the stars on the main sequence but leads to explosions in Novae stars? Supernovae Stars?

Or on Earth? (hint: the reasons are the same in principle but different in details).26) Describe the phenomenon of a Nova star. 27) Provide possible explanation for the phenomenon of A Nova star.28) Describe the phenomenon of different types of Supernovae stars.29) Provide possible explanations for the phenomenon of different types of Supernovae.30) Describe the phenomenon of Cepheid variables and explain how they are used to determine the distance to stars.

Missing links:

Models in PhysicsThe word “model” is used for many purposes. It usually stands for “simple version” of something. In physics one can say that this something can be:a) an object;b) a change;c) a phenomenon;d) a technical device.Also there is a completely different set of models, I would call them the conditions of geometry and symmetry. For example, on our world we are using the model of Euclidean space, and the ideas of symmetry (homogeneity of space and time, isotropy of space, barion symmetry, left-right symmetry, etc). For each type of symmetry there is a law of conservation (time - energy, space- momenta).For any model (from a, b, c list) one should separate the definition of it (what are the main features of the model) and the criteria of application of this model (when can we apply this model explaining the behavior of real systems).Models of objectsThe first group can be called models with localized properties1. A particle (dimensionless object) - an object that has no size or

volume but can be located in space, possesses mass, has velocity and acceleration and can be acted upon by forces. A real object can be described as a particle when its size is much smaller than the distances in the problem or all its points follow the same path with the same velocity.

2. Ideal gas - an object that is made up of particles that do not interact with each other than in elastic collisions and obey Newton’s laws. Real gas can be described as ideal when the distances between the particles are much greater than their dimensions and the temperatures are high.

3. Point-like charge - a charges particle. Can be a small charged object, or a spherical dielectric object, or a spherical metal object if we are very far away from it.

4. Electron gas - an object that is made up of the ideal gas of electrons in metals which collide with ions and move with constant velocity from a collision to a collision. Real electrons can be described as ideal at temperatures above superconductivity. This model explains Ohm’s and Joule’s law but does not explain linear dependence of metals’ resistivity on the temperature.

The second group can be called models with continuously distributed properties1. Model of a regular wave - all particles of the medium or space

participate in wave motion. Real wave can be described by this model when the size of the container is much larger that the wavelength.

2. Model of a field (gravitational, electric, magnetic, electromagnetic).

3. Model of a uniform field.

Models of change1. Linear change (motion with constant speed, Ohm’s law, thermal

expansion).2. Quadratic change (motion with constant acceleration).3. Sinusoidal change (circular motion with constant speed, simple

harmonic motion, sinusoidal wave).4. Exponential change (amplitude for damped motion, radioactive

decay). Models of phenomenaHere I include models of phenomena we study in the physics course and models of scientific phenomena (the first person to do this was Galileo, the same way he was the first to start thinking about the model of change for position of a falling object).1. Free fall (phenomenon in which we neglect all forces acting on an

object except the force f gravity). Can be used when the force of friction is much smaller that the force of gravity.

2. Existence of an inertial reference frame. Can be used when the acceleration of the reference frame is much smaller than the acceleration of gravity.

3. Phenomenon of an isolated system. 4. The motion of a particle attached to a massless spring which obeys

Hooke’s law (mass on a spring). Can be used when the size of the mass is much smaller that the spring and the spring stretches much less that its own size.

5. Motion of a simple pendulum (particle on a string). Can be used when the length of the string is much greater than the size of the bob.

6. Carnot cycle.7. Phenomenon of wiring with no resistance.8. Phenomenon of resistivity (scattering of phonons).9. Phenomenon of superconductivity (interaction of electron pairs -

Cuper pairs).10. Phenomenon of a white dwarf.11. Phenomenon of a neutron star.12. Phenomenon of a black hole.13. Phenomenon of a Solar corona.

…………………………………………………..

Models of technical devices1. Internal combustion engine.2. Model of a bridge.…………………………………………………..

The Doppler Effect for LightDoppler Effect situations for light involve the relative motion of the source, S, and the detector, D. In other words, “source moving toward detector” and “detector moving toward source” are physically identical situations. This is based on the relativistic fact that the speed of light is constant for any observer. (With sound waves, these are 2 different physical situations, which lead to different equations for the Doppler Effect for sound.)

Suppose that there is a source of light, S, that moves at a speed u relative to the detector, D. The source, for our purposes, may be a galaxy, a quasar, a star, or even (for one of the questions that follow) our sun. The detector is an observatory here on earth that receives the light.

Case A) Source Recedes from Detector at Relative Speed u

Suppose that the source S is moving away from the detector (earth observatory) at a relative speed u. What effect does this have on the wavelength(s) of light received here on earth?

If S emits a light wave, it will travel a distance in a time T. This is based on the fact that the speed of light, c, is found by

c = /T (1)

Now suppose that at the instant S emits wave 1, it begins receding from D at a relative speed u:

By the time T that S emits wave 2, there is a separation uT between wave 1 and wave 2. This separation represents the Doppler-shifted wavelength ’ of the waves reaching the detector D :

’ = + uT (2)

Clearly, ’ > , resulting in the detected wavelengths being “shifted” toward the red end of the spectrum, where the longer wavelengths of visible light are found.

By solving equation (2) for the relative velocity u we get

u = (’ - )/T (3)

The term 1/T represents the frequency of the source, fs. And, the frequency of the source can be represented by the fundamental wave equation

fs = c/ (4)

As a result, the expression for the recessional velocity (which we’ll be using in our lab exercise) is given by

u = (’ - (c/)

or u/c (5)

The value for ’ - is referred to as the Doppler shift of the wavelength received by the detector.

Case B) Source Approaches Detector at Relative Speed u

The mathematical reasoning here is similar to Case A), with the exception that the waves reaching the detector have a Doppler-shifted wavelength ’ found by

’ = - uT

Here, the wavelength reaching the detector is less than the wavelength emitted from the source, resulting in a “blue shift”, or a shifting of wavelengths to the shorter end of the spectrum.

This leads tou = (’)/T

u = (’)(c/)

- / = u/c

General Result : If is (+), then a red shift has occurred and the source moves at a relative speed u away from the detector.

If is (-), then a blue shift has occurred and the source moves at a relative speed u towards the detector.

Gravitational Potential Energy

The formal expression for gravitational potential energy is :

Ug = -GMm/R.

Where does this expression come from? It does not look like the more familiar mgh. The truth is, you need to be able to perform a calculus operation known as integration to fully understand how this expression is determined. Any calculus-based college level physics text will include a derivation of this expression.

In the absence of calculus, we are going to offer some arguments for the validity of this expression (sometimes this is called hand-waving).

Hopefully these arguments will persuade you to accept the expression. Here goes:

(1) When you lift something, you are doing work because you are applying a force (which we measure in Newtons) through a distance (which we measure in meters). This work results in that something gaining gravitational potential energy. The unit for work is the Joule.

1 Joule = 1(Newton) x (1 meter)

If you check the unit associated with (-GMm/R), you will see that it is(Newtons) x (meters). So this expression does represent energy.

(2) The force one applies in lifting something (at a nice steady rate) must equal the force of gravity, which we know is GMm/R2. And, we are going to separate m and M until they are some distance R apart. So, we can see that the product of this force and this distance “sort of” yields our gravitational energy expression. (Beware! It is not as simple as just multiplying the two terms. Why not? Because as the R value changes, so does the force of gravity! This is why calculus is needed.)

(3) On a universal level, physicists have agreed to set gravitational potential energy equal to 0 when M and m are infinitely far apart. The further apart two masses are, the greater the gravitational potential energy (remember, the higher you lift something, the further it is from the center of the earth, and the more gravitational energy it acquires). So, the most gravitational energy a mass m can have is 0 Joules, which happens when it is infinitely far away from M. Therefore, any lesser separation means that the gravitational potential energy must be negative, which it is in our expression!!!

(4) You are probably familiar with the expression of gravitational potential energy as mgh, where h is the height above the surface of the earth that a mass m has been lifted. This expression does represent force (mg) times distance (h). It also represents the change in the gravitational potential energy, because m has been moved from one position to another. So,

Ug = mgh (1)

According to our expression,

Ug = Ufinal - Uinitial = [-GMm/(R+h)] - [-GMm/R](2)

As an exercise, you can show that if h << R, then the right side of equation (2), when simplified, will equal the right side of equation (1).

Note 1 : g = GM/R2Note 2 : The denominator in the expression for Ug represents the distance between the centers of m and M. At the surface of the earth, this distance equals the radius of the earth.Note 3 : If you substitute k for G, and q1 and q2 for M and m, the same hand-waving argument as above (particularly steps 1, 2, and 3) should help you to accept, by way of mathematical similarity, that electric potential energy is given by (-kq1q2/R).