PART I - SOLAR SYSTEM

Introduction to Astronomy 110G

Goals for Astr 110G

1. Learn Astronomy
2. Learn basics of the scientific method: how to study the unknown
3. Help you to develop logical thinking skills.
4. Develop a broad appreciation for science & its impact on society.
   • Better comprehension & enjoyment of science articles in the newspaper.
   • Improve ability to vote intelligently on science-related issues.

5. Introduce you to a variety of sciences since Astronomy involves geology, physics, chemistry, & mathematics.

6. Have fun observing & looking at the sky with a new found appreciation of the Universe's attributes.

It's a Big Universe!

• Astronomers use powers-of-ten notation to express large numbers in compact form - example: 93,000,000 = $9.3 \times 10^7$.

• Basic units of distance are the meter (m) and the centimeter (cm):

  1 m = 100 cm,  1 m = 1.094 yards,

  1 kilometer (=1000 m) = 0.62 miles.

• An Astronomical Unit (AU) = $1.496 \times 10^8$ km is the average distance between the Earth & the Sun. The distance to Pluto is about 38 AU at its closest.

• A light year (ly) = $9.46\times 10^{12}$ km is the distance that light travels in one year. The distance between the Earth and the Sun is about 8 light minutes.

• A parsec (pc) = $3.09\times 10^{13}$ km = 3.26 ly. The distance to the nearest star is 1.3 pc. The distance to the center of the Galaxy is about 8.5 kpc (1 kpc = 1000 pc). The distance to the Virgo cluster of galaxies is 20 Mpc (1 Mpc = $10^6$ pc).

• Basic units of mass are the kilogram (kg) and the gram (g).

  1 kg is equivalent to 2.2 pounds (on Earth).

  1 kg = 1,000 g

• A solar mass ($M_{\odot}$) = $2\times 10^{30}$ kg is the total mass of the Sun. The Milky Way galaxy has a mass of about $10^{12} M_\odot$.

Scientific Method and Scientific Models

• New observation or discovery is made
• Make a HYPOTHESIS (a conjecture, a guess, an assumption).

  It does not even pretend to explain everything; just one feature, one side of what was found.

• Make new observations
• Build a MODEL: (partial) description of the thing

  (e.g., comet, asteroid, galaxy, quasar)

  Model tries to explain many details.

• Make new observations
• Build a THEORY: a system of rules, which explain the whole phenomenon. It can be applied for all events of the same kind.

  e.g. a theory, which explains motion of a comet, should be used for ANY comet.

• Science uses models to understand the Universe around us. It holds the essence of the scientific method.
• A functional model must:
  • explain our observations of the real world.
  • predict future observations.
• For example, a model of gravity & the solar system must explain the positions of the planets in the past and predict where they will be in the future.

The Solar System

The Planets

1. The Solar System consists of 2 kinds of planets:
   • The Terrestrial planets include Mercury, Venus, Earth, & Mars. These are Earth-like planets that are small, dense, rocky worlds with less atmosphere than Giant planets.
   • The Jovian planets include Jupiter, Saturn, Uranus, & Neptune. They do not have a solid surface & consist mainly of hydrogen and helium gas.
   • Pluto does not really fit either category.

2. Density is a key measure of the material which comprises a planet. It is a measure of how much matter is packed into a volume of space.
   
   $${Density} = {Mass \over Volume}$$
   
   
   Water has a density of 1 gm/cm$^3$, iron has a density of 7.8 gm/cm$^3$, and rocks have a density of 2-4 gm/cm$^3$. So, by knowing the density of a planet, one can roughly determine the internal composition. The Earth has a density of 5.5 gm/cm$^3$ whereas Jupiter has a density of 1.3 gm/cm$^3$. What does that tell you about the difference in compositions of these two planets?

3. Planets also rotate and revolve.
   • Planets spin on their axis or rotate. The period of rotation determines the length of a day. The inclination of a planet's rotation axis will determine its seasons.
   • Planets also revolve about the Sun. The period of revolution determines the length of a year for that planet. Planets further from the Sun revolve more slowly than those closest to the Sun.

Terrestrial Planets:

• Impact craters
• Volcanoes
• Rivers and Canyons
• Plate tectonics

• Moon (not a planet)
  • The Moon is 25% of the Earth's diameter.
  • Its density is 3.4 gm/cm$^3$ implying a mostly rocky core (vs. metallic core for the Earth).
  • It does not have any atmosphere.
  • Impact craters: The Moon's surface is heavily cratered.
  • Mares

• Mercury
  • Mercury is a heavily cratered planet closest to the Sun. In some ways, it most resembles the Moon.
  • The density of Mercury is 5.4 gm/cm$^3$.
  • Impact craters
  • Scarps
  • Hot/Cold, no atmosphere

• Venus
  • In mass & density, Venus is nearly the Earth's twin.
  • Venus' atmosphere is very thick and opaque.
  • The atmosphere is about 95% carbon dioxide (CO$_2$). Other components are also present: N, water vapor, sulfuric acid
  • Heat is trapped near the planet's surface by a runaway Greenhouse Effect that produces a surface temperature of nearly 470$^\circ$ C.
  • The planet has been imaged from orbit using the Magellan radar mapping system. The surface was photographed by the Russian Venera spacecraft.
  • Volcanoes
  • Coronae, archnoids, ``pancakes''
  • Impact craters: more than on the Earth, but less than on the Moon.

• Earth
  • The Atmosphere is 79% nitrogen, 20% oxygen, & 1% other trace gases.
  • The Earth's surface is active, constantly destroyed & renewed in large sections. This is called plate tectonics.
  • Plate tectonics: slow motion of large pieces of crust
  • Water and oceans. LIFE !!!

• Mars
  • Mars has a mass of about 10% that of Earth. Its density is 3.9gm/cm$^3$.
  • The peak surface temperature is nearly 20$^\circ$ C (but minimum is -140$^\circ$ C). Mars also has polar ice caps (water ice!) like that of Earth.
  • The atmosphere is again 95% CO$_2$, but much thinner than that for Venus or Earth.
  • Volcanoes: Olympus Mons
  • Canyons: Valles Marineris
  • Traces of erosion: dry river beds
  • Winds and dust storms
  • Polar caps: frozen CO$_2$
  • Underground water ??

Jovian Planets:

• Jupiter
  • Jupiter is the largest planet in the Solar System. Its mass is 318 times that of Earth. Its radius is 11 times that of Earth.
  • Jupiter's density is 1.3 gm/cm$^3$. So, it is composed mainly of gases with a rocky & (liquid) metallic core. This core generates a strong magnetic field (10 times that of Earth).
  • The atmosphere is 79% hydrogen (H), 20% helium (He)
  • Alternating zones & belts in atmosphere are produced by rising & sinking of hot gas (convection).
  • Jupiter has many moons ($>20$), including 4 satellites first discovered by Galileo (Galilean satellites).
  • One moon, Io, has active volcanoes!
  • Another moon, Europa, has oceans (icebergs!)

• Saturn
  • Saturn is the 2nd largest planet with a mass of 95 times that of Earth and a radius of 9 times that of Earth.
  • Saturn's density is the lowest in the solar system at 0.68 gm/cm$^3$.
  • The atmosphere is similar to that of Jupiter.
  • Saturn is best known for its spectacular ring system (although all the Jovian planets have rings).
  • Saturn also has many moons. Titan is the most interesting because it has an atmosphere made of 99% nitrogen that may be similar to that of the primitive Earth.

• Uranus & Neptune
  • These Jovian planets are also large and have low densities of about 1.5 gm/cm$^3$.
  • The main difference between these planets and Jupiter is that Uranus & Neptune are composed mainly of icy materials.
  • Composition is 15% H & He, 60% ices, & 25% Earthy (iron, rocky, etc.).

• Pluto
  • Pluto was discovered by NMSU Professor Clyde Tombaugh.
  • It is a peculiar tiny planet (18% that of Earth's radius). Its density is about 2 gm/cm$^3$ & so is composed mostly of rocky materials.
  • A large moon, Charon, was discovered in 1978.

Solar System Debris

• Asteroids are large chunks of rock that lie primarily between the orbits of Mars & Jupiter. The largest asteroid is named Ceres. Its diameter is 940 km. Only three asteroids have diameters between greater than 300km: Ceres, Pallas, and Vesta. About thirty other asteroids have diameters between 200 and 300 km. Most of asteroids are very small.
• Comets are like dirty icebergs which heat up near the Sun, partially vaporize, and leave a tail of gas & dust behind them. There are two reservoirs of comets. Beyond Pluto's orbit extending to 500 AU there is the Kuper belt, where comet's nuclei move around the Sun close to the plane of ecliptic. Another place for comets is the Oort cloud, which extends out at least 50,000 AU, one third the distance to the nearest star. Most of the comets never (or very rarely) come close to the Sun. Structure of a comet:
  • Tails form when a comet comes close to the Sun. The solar wind and sunlight blow comet's gases outward into one or more tails. Tails can be as long as 100 million kilometers. Tails always point away from the Sun.
  • Coma is a large envelope of gases around the nucleus of comet. Typical size of coma is 1 million kilometers
  • Nucleus is the solid body of a comet. It's typical size is only few kilometers across.
• Meteors are pieces of rock & ice, coming from asteroids & comets, which fall into the Earth's atmosphere (so-called ``shooting stars''). A few large ones strike planetary surfaces & produce impact craters.

The Closest Star: The Sun

• The Sun is the closest example of a star.
• The Sun generates its energy (heat & light) by thermonuclear reactions at its core.
• Convection: rising bubbles of hot gas
• Convection: granules
• Sunspots and Magnetic fields
• Active Sun: Prominences and Flares
• Every 11 yrs, the Sun undergoes a higher level of activity including the formation of many sunspots & solar flares.

Measures of Motion

• Gravity causes objects with mass to move. Examples include an apple falling toward the ground and the Earth going around the Sun. So, we need to understand a bit about motion.
• Velocity or speed is the rate of change of position of an object with time. The units of velocity are:
  
  $${Velocity} = {Distance \over Time},$$
  
  
  or meters per second (m/sec). When you are cruising down I-25 at the speed limit, your velocity is 65 miles/hr or 29.1 m/sec. This means that in 1 hr, you travel 65 miles or in 1 second, you travel 29.1 meters.
• Acceleration is the rate of change of velocity with time. The units of acceleration are:
  
  $${Acceleration} = {Velocity \over Time},$$
  
  
  or meters per second per second (m/sec$^2$). If you go from zero to 65 miles/hr (29.1 m/sec) in 10 seconds, your acceleration is 2.91 m/sec$^2$. Gravity causes objects to accelerate toward the center of mass of planets or the Sun or other stars.

Ancient Astronomy

• The Greeks, led by Aristotle & Ptolomy, envisioned an idealized universe with the Earth at the center and all planets, the Sun, & the Moon revolving around us in grand circles.
• The Greek astronomers preferred an Earth-centered or geocentric universe because of the lack of observed parallax of the stars. Parallax is produced when a nearby object appears to move relative to a distant background due to the motion of the observer.
• Interestingly, the planets were observed to undergo retrograde motion on occasion. Planets basically move west to east relative to the stars, but occasionally will reverse direction and travel east to west for weeks or even months. To explain this, the Greeks resorted to the use of epicycles and deferents. This made for complex motions and did not do a good job of predicting future positions of planets.

About early history of science:

• Plato: 427 - 350 B.C.
  • Socrates's pupil and close friend. Socrates was executed by Athens (was forced to drink a fatal cup of hemlock. Reacting to shifting moral values of his time, Plato searched for UNCHANGING standards. He turned to the world of ideas (``Platonism''). The cause of the world coming into being is the idea. The world is generated to fulfill the idea.
  • Do not trust your feelings. Allegory of the Cave.
  • Saving the phenomena

• Aristotle: 384-322 B.C
  • Poetics: poetry - comedy and tragedy. Tragedy: six factors - scenic presentation, lyrical song, diction, plot, character, thought.
  • Look for the cause of things. ``Why'' is the main question.
  • Final cause - purpose of an action.
  • Motion: not just changing places, but more general as fulfillment of Potential. (Growth of a plant, growth of a society ...).
  • Every motion has its INTERNAL cause and purpose.
  • Logic: reductio ad absurdum.
  • Earth is a sphere in the center of the Universe.
  • The universe does not change: everything is on circular motion.
• Ptolemy: Second century A.D., Alexandria. Author of Almagest
• Pythagoras: 585 - 495 B.C. The theorem. NUMBER. Beginning of Math.
• Ionian Cosmology (now Turkey and Greek Islands): search for fundamental elements. Beginning of chemistry.
  • What was difficult? ``To know thyself''.
  • True philosopher pursues scientific inquiry for its own sake; others demand that science pay in practical results.
  • Ended in 494 B.C. : Persian invasion.

Copernicus: Beginning of a Revolution

• The problems & complexities of the geocentric model caused Nicholas Copernicus (1473-1543) to examine an alternative sun-centered or heliocentric model of the solar system.
• His model proposed that:
  • The Sun is at the center of the Universe.
  • The distance between the Earth and the stars is much greater than the Earth-Sun distance. This would explain the lack of observed stellar parallax.
  • The east to west daily motions of stars, planets, the Moon, and the Sun are caused by the rotation of the Earth on its axis.
  • The Earth and all the planets revolve around the Sun on circular orbits. This produces the change in constellations observed from one time of year to the next.
  • Retrograde motion is an illusion caused by the fact that we are observing other planets on the planet Earth which itself is moving around the Sun.
• Although Copernicus' idea of a heliocentric solar system is correct, his assumption of circular orbits made his model no more accurate than that of Ptolemy. But, it had the beauty of simplicity.

Implications of Heliocentric Model

• The Heliocentric Model offers additional explanations for some of the basic observations of the sky and the Earth environment made for thousands of years.
• Seasons:
  • Seasons are produced by the fact that the Earth's rotation axis is inclined by 23.5$^\circ$ with respect to the line drawn perpendicular to the Earth's orbital plane. Seasons are NOT produced by the varying distance to the Sun as the Earth makes its elliptical orbit about the Sun.
  • The sunlight intensity (or amount of heating) depends on the angle that the Sun's light rays make with respect to the ground. When the Sun is highest in the sky at noon during the summer in Las Cruces, the Sun's rays are nearly perpendicular to the ground - this produces the greatest heating of the year. This is caused by the fact that the northern hemisphere is pointing most directly at the Sun. The opposite occurs during the winter.
  • What other terrestrial planet has seasons?
• Eclipses
  • Eclipses occur when one astronomical body moves into the shadow cast by a second astronomical body.
  • A Lunar Eclipse occurs at Full Moon when the Moon moves through the shadow of the Earth.
  • A Solar Eclipse occurs at New Moon when the Moon's shadow falls upon the Earth.
  • Question: Why isn't there a total solar eclipse at each New Moon?

The Newtonian Universe

Tycho Brahe and Johannes Kepler

• Tycho Brahe's (1546-1601) precise observations of Mars set the stage for Johannes Kepler (1571-1630) to make major modifications and improvements on the heliocentric model.
• Kepler devised the following Laws of Planetary Motion:
  • Law of Ellipses - The orbit of a planet is an ellipse with the Sun at one focus. (Eccentricity of an ellipse is the ratio of the distance between the focii divided by the length of the major axis.)
  • Law of Equal Areas - A hypothetical line drawn between a planet and the Sun sweeps out equal areas in equal intervals of time. In simpler terms, this means that a planet travels faster when it is closer to the Sun.
  • Harmonic Law - If $P$ is a planet's orbital period around the Sun (measured in Earth years) and $A$ is the average distance between the planet and the Sun (measured in AU), then
    
    $$P^2 = A^3.$$
    
    
    For example, if a planet had an orbital period of 8 yrs, then $P^2 = 64 = A^3$; so A = 4 AU. So, by measuring the orbital period of a planet through careful observations of the planet with respect to the stars, one can determine its distance from the Sun.
• Kepler's laws are a correct description of planetary motion. However, they lack any explanation as to why planets move in this fashion.

Galileo: A Crisis in Conscience

• Galileo Galilei's (1564-1642) contribution to astronomy & physics was immense as a result of his careful observations & experiments. However, his beliefs in Copernican theory & his great ego caused him much mental anguish at the hands of the Inquisition.
• Among Galileo's best known accomplishments:
  • He determined that the acceleration of falling objects was independent of their mass.
  • With his simple telescope, he was the first to observe that Venus has phases. This proved that Venus must revolve around the Sun & thus supports the heliocentric solar system.
  • Galileo discovered the 4 brightest moons of Jupiter which move around the planet like a mini solar system.
  • Galileo discovered sunspots which violated Aristotle's view that the Universe was perfect & unchanging.

Newton: A Revolution Completed

• Isaac Newton (1642-1727) was the first great theorist in astronomy & physics. He invented calculus to provide the framework in which to understand motions. He explained Galileo's observations and Kepler's Laws using his theory of gravity.
• Newton's Laws of Motion:
  • Law of Inertia - The natural state of an object is either rest or motion in a straight line at constant velocity.
  • Force Law - The change in an object's velocity must be caused by a force. That force ($F$) is given by
    
    $$F = ma$$
    
    
    where $m$ = mass and $a$ = acceleration. Whenever acceleration is observed for an object, that object is subject to a force. For example, an apple accelerates when it drops to the ground implying that it is feeling a force - gravity.
  • Action/Reaction Law - For every applied force, a force of equal magnitude but opposite direction arises.
• Newton's 3rd Law has several additional consequences:
  • It is the basis behind the principle of Conservation of Momentum. Momentum ($p$) is defined as
    
    $$p = mv$$
    
    
    where $v$ = velocity. When there are no other forces present, the total momentum is a constant (or conserved). That is, if an object, like a bullet, is shot from a gun (the action), the gun will recoil (reaction) in the opposite direction. The gun recoil is with slower speed than the bullet because its mass is greater.
  • The 3rd Law is the basis behind rocketry. The rocket releases gas molecules (which each have low mass) at high speeds; the rocket reacts by moving the opposite direction. This is true for a launch off the Earth or for maneuvering in space.

The Law of Gravity

• Gravity is a central force. That is, the force of gravity between two objects (for example, Earth & Moon) acts along a line between the centers of the two objects. When a mass is released in a gravitational field (like an apple near the Earth's surface), it drops in a direction toward the center of a planet.
• Newton made the great leap of insight in realizing that the same force (gravity) is responsible for making an apple fall to the Earth and making the Moon orbit about the Earth.
• Gravity causes every body to attract every other body with a gravitational force. Newton described the force of gravity ($F_g$) acting between two masses ($M_1$ & $M_2$) as follows:
  
  $${F_g} = {{G M_1 M_2} \over R^2}$$
  
  
  where $R$ is the distance separating the two masses and $G$ is the gravitational constant (just a constant number). For example, the force of gravity on an apple would be the above where $M_1$ is the mass of the apple, $M_2$ is the mass of the Earth, and $R$ is the radius of the Earth.
  • Note that $F_g$ is directly dependent on the masses of the objects. Doubling the mass of one object will double the force of gravity. Mass is the primary factor which determines the force of gravity.
  • Note also that $F_g$ is inversely proportional to the square of the distance between the objects. Doubling the distance between the objects will decrease the force of gravity by a factor of 4. This inverse square law is universal - it also applies to the decrease in light intensity with distance.
• One can show from the force of gravity equation above and Newton's second law that the acceleration of gravity is independent of the mass of the falling object.
• Weight and mass are very different quantities. Mass is a fundamental quantity that is the same everywhere in the Universe. However, weight is the same as the force of gravity and so it depends on the mass of the planet that you are standing on - for example, the smaller mass of the Moon means that you would have only 1/6th of your Earthly weight on the lunar surface.

Gravity as a Mass Probe

• The mass of a planet can be determined by measuring how it perturbs the motion of a smaller object such as an asteroid or a spacecraft. Mercury's mass was determined by watching how the Mariner 10 spacecraft was accelerated as it approached Mercury. Similarly, the orbit of Pluto's moon Charon was used to determine the mass of Pluto for the first time during the last decade.
• Newton was able to derive Kepler's Laws of Planetary Motion from his own Laws of Motion and the Law of Gravity. In particular, he generalized Kepler's 3rd Law and showed that it depended upon the mass of 2 orbiting bodies as follows:
  
  $${P^2} = {{A^3} \over {M_1 + M_2}}$$
  
  
  where $P$ is the orbital period (in yrs), $A$ is the average distance between the bodies (in AU), and $M_1$ and $M_2$ are the masses of the bodies (in $M_{\odot}$). For our solar system, $M_1$ is the mass of the Sun (1 $M_{\odot}$) and $M_2$ is the mass of a planet which is always much less than that of the Sun.
• This version of Kepler's 3rd Law can now be used for any situation in which two objects are orbiting about each other (for example, a binary star system) and can be used to determine the total mass of the system ($M_1 + M_2$). For example, the Galilean satellites orbit about Jupiter. We can measure the orbital period by observing the motion of a Jovian moon over time and we can measure the orbital radius ($A$) from a photograph. Then, plugging into Newton's version of Kepler's third law above, we can determine the mass of Jupiter (which is much larger than that of any of the moons, $M_{Jupiter} + M_{moon} \approx M_{Jupiter}$).

Gravity in Action

Orbits & Spaceflight

• The orbiting of an artificial satellite or the Moon around the Earth implies that there is a force present. Otherwise, these objects would go flying off into space in a straight line according to the Law of Inertia. The central force of gravity is the key to holding these objects in their orbits.
• To place an object into orbit, the spacecraft must have enough velocity along the orbit. Too little velocity and the spacecraft will fall back to Earth. Too much velocity and the object will escape into space. The exact orbital velocity needed depends on the mass of the planet & the orbital altitude (Law of Gravity equation).
• The above gives us guidance on how to go from one planet to the next. To go to Mercury, a spacecraft must reduce its velocity relative to that of the Earth going around the Sun so that it can ``fall'' toward the center of the solar system. On the other hand, the Galileo spacecraft heading toward Jupiter had to increase its velocity to move outward away from the Sun.
• Why do astronauts appear to be ``weightless'' on the Space Shuttle if gravity is present? This is an illusion. The Space Shuttle is really free falling toward the Earth constantly but because of its orbital speed, it misses the edge of the Earth. Any free-falling objects appear to be weightless (person dropped from an airplane in an enclosed box) because both the object and the container are falling at the same rate.
• Artificial gravity can be created in space using a large spinning object like a wheel. Because of the Law of Inertia, such objects will press up against the edge of the wheel and feel an effective force like gravity.

The Rings of Saturn

• The rings of Saturn are a good example of gravity in action. The rings are believed to be the remnants of the material from which Saturn formed. The rings are relatively thin - less than 5 km in width; this flattening was caused by the rapid circular motion of the rings. The rings are actually made of rocky material covered with ice that range in size from small stones to a small car.
• Each rock in the ring follows an orbit around Saturn obeying Kepler's Laws of Planetary Motion. So, you can predict the orbits of the rings.

The Discoveries of Neptune and Pluto

• Neptune was discovered in 1846 as a direct consequence of Newton's Law of Gravity.
• Following the visual discovery of Uranus in 1781 by William Herschel, further observations of Uranus showed that it did not exactly follow the predicted path. How could this be?
• The only way the orbit of Uranus could be perturbed would be by another massive object (a planet) which was outside the orbit of Uranus. If massive enough, it would exert a gravitational pull on Uranus & cause its orbit to be slightly distorted.
• Using Newton's laws of gravity & motion, one can work backward from the orbital perturbations to predict approximately the mass and orbit of the mystery planet. Observers used these predicted positions to discover Neptune in the middle of the last century.
• A similar prediction about the perturbation of the orbit of Neptune led Clyde Tombaugh to search for & eventually discover the planet Pluto. Pluto, however, turned out to be much less massive than predicted. Also, we know today that the supposed perturbations in Neptune's orbit do not exist. So, Pluto's discovery was pure serendipity.

Comets: From Fear to Triumph

• Comets were much feared by peoples of ancient times & the Middle Ages. They were thought to forecast ominous events. For example, one of the earliest recordings of Halley's comet in 1066 coincided with the conquest of England by the Normans - not good for the Saxons!
• However, Halley's comet became a great triumph for Newton's theories. Edmond Halley used Newton's newly developed theories to predict the orbit of what came to be known as Halley's Comet. He predicted that it would reappear every 75 years which was confirmed on its passage near the Earth in 1758.
• Comets are on highly elliptical orbits with the Sun at one focus. They spend most of their time far beyond the orbit of Pluto. An entire collection of proto-comets are believed to exist in a halo surrounding the solar system at about 50,000 AU from the Sun - the Oort Cloud.
• Comets are best described as dirty icebergs. The tail is the most spectacular part of the comet - it can be millions of kilometers in length. It is composed of gas molecules which are left behind marking a trail of the comet nucleus.

• Some individuals have speculated that a giant comet or comets struck the Earth 65 million yrs ago & was responsible for the death of the dinosaurs in the Tertiary/Cretaceous period.

PART II - MATTER.

The Milky Way Galaxy

The Structure of the Milky Way

1. The Milky Way galaxy consists of 3 parts:
   • The Bulge is the center of our Galaxy. It is densely packed with stars.
   • The Disk is a flattened plane of stars, gas, and dust which rotates about the center of the Galaxy.
   • The Halo is a spherical cloud of thinly scattered stars and Globular (star) Clusters.
2. The Earth lies about 2/3rds of the way out from the galactic center (8.5 kpc or 28,000 ly).

Stars & Star Clusters

• The Milky Way contains several hundred billion stars. Some are bigger & brighter, and many are smaller & less luminous than the Sun.
• More than half of the stars in our Galaxy are double or binary stars. The closest star system, Alpha Centauri, is a triple system.
• Possibly all stars in the galactic Disk are born in galactic star clusters.
• The distance between stars is very large in our stellar neighborhood. Alpha Centauri is 4.2 ly away. The density of stars like the Sun is quite low. The Milky Way galaxy is mainly empty space!
• Stars, like people, go through a life cycle: they are born, live steadily through most of their lives, and then die.

The Interstellar Medium

• The space between stars is not totally empty. It contains gas and dust but with a very low density - about 1 atom/cm$^3$ (compared to $6 \times 10^{20}$ atoms/cm$^3$ for the Earth's atmosphere). This is the interstellar medium (ISM).
• Occasionally, gas gathers into larger & somewhat denser clumps called nebulae. These gas clouds are often red in color. These nebulae house stellar nurseries.
• The ISM contains mainly hydrogen gas.
• The ISM also contains significant dust which dims the light of the stars that lie behind the dust clouds.

The Universe of Galaxies

Individual Galaxies

1. There are a variety of galaxy types in the Universe:
   • Spiral galaxies rotate, have a relatively cool ISM, and are like our own Milky Way.
   • Elliptical galaxies are somewhat shaped like a football, do not have spiral arms, do not rotate, and have a hot ($10^7$ K) ISM.
   • Irregular galaxies have no organized shape, no symmetry, contain young stars and much gas.

Groups and Clusters of Galaxies

• Most, if not all, galaxies are in groups or clusters.
• Our galaxy and about 22 others are part of the Local Group of Galaxies. It is about 10 million ly in diameter.
• There are some truly gigantic rich clusters which contain about 1000 galaxies and are more than 20 million ly in diameter.

The Expanding Universe

• In 1929, Edwin Hubble discovered that the Universe is expanding. All galaxies are rushing away from all other galaxies.
• On very large scales the Universe is homogeneous

Gravity in Action II:

Binary Stars

1. Binary stars revolve around each other and around a central point called the center of mass. This is a kind of balance point between the stars. The center of mass is closer to the more massive star. (For our solar system, the center of mass is actually inside the Sun since the Sun has 99% of the mass of the solar system.)
2. Binary stars are fundamentally important to astronomy because they are the only way that we can directly measure the mass of stars. This is done using Newton's version of Kepler's 3rd Law - we measure the orbital period, $P$, and the average separation between the stars, $A$, and this gives us the sum of the masses of the stars in the binary system.
3. From these masses, astronomers find a tight relationship between the mass and the luminosity of a star where luminosity is the total energy radiating from a star per second (Watts). This means that more massive stars radiate more energy than less massive stars.

Galactic Rotation & Dark Matter

• The Sun revolves around the center of the Milky Way galaxy with a speed of 200-300 km/sec. It takes the Sun 200,000,000 yrs to make one orbit around the Galaxy. The Sun revolves around the Galactic Center in response to the gravitational pull of the hundreds of billions of stars that lie interior to the Sun's orbit.
• In the outer parts of the Galaxy, astronomers expected the orbital speed to drop off with distance since the mass interior to the orbit was not expected to increase. Much to our surprise, it was discovered about 18 yrs ago that the rotation velocity remains constant out at large distances and does not decrease as expected. What is happening here?
• The best explanation for these higher than expected velocities is that the mass is not decreasing as expected. But, since not many stars are seen in the outer part of the Milky Way, this implies that the matter must be dark or non-luminous.
• What is the nature of this dark matter? We really don't yet know. It might be burned out stars, brown dwarf stars, Jupiter-like planets, black holes or possibly exotic high energy particles which only weakly interact with normal (like us) matter. Something to ponder - the rotation velocities imply that there may be 10 times more dark matter than luminous, so we may be the abnormal matter!

Clusters of Galaxies

• Clusters of galaxies can contain a few galaxies (like the Local Group) or thousands of galaxies bound together by gravity. They are the galaxy analog of the star clusters discussed above. Gravity keeps the galaxies within the clusters and stops them from flying off into space.
• In the 1930's, Fritz Zwicky discovered that there does not appear to be enough luminous matter (stars) within the cluster galaxies to keep the clusters together. To prevent such clusters from flying apart, there must be substantial amounts of dark matter present within the clusters as well.
• More recently, substantial amounts of X-ray emission have been detected & imaged in clusters. This is very hot gas ($10^8$ K) that lies between the galaxies. To keep this hot gas bound to the clusters, again there must be about a factor of 10 more dark matter than luminous matter in clusters of galaxies.

Summary

• All objects with mass attract all other objects with mass. Mass is the driver behind gravity.
• Because gravity is a force, it causes smaller mass objects like moons and satellites to accelerate when they encounter larger mass objects. By observing the motion of such objects, we can calculate the mass of the planet or star which is responsible for the gravitational attraction using Newton's Law of Gravity or Kepler's 3rd Law of Planetary Motion.
• Gravitational force also rapidly diminishes with distance. The force of gravity decreases as $1 \over R^2$ where $R$ is the distance. The closer you are to a planet or star, the stronger the force and the more energy is required to escape.

The Properties of Matter

Structure of the Atom

1. Atoms are the fundamental building blocks of matter. Their structure and arrangement will determine the chemical composition & basic properties of an object (a human being vs. a house). Atoms are also responsible for producing light & can strongly interact with light. So by studying the spectra of light emitted by a star, we can determine the atomic structure of the star & its basic properties.
2. The Nucleus lies at the center of an atom. The diameter of a hydrogen nucleus is about $1.6 \times 10^{-15}$ meters. The nucleus is further composed of
   • Protons which are positively charged particles; and
   • Neutrons which are uncharged particles.
3. Electrons are tiny, small mass (0.05% of the proton mass), negatively charged particles that orbit about the nucleus of the atom. The electron charge is equal in magnitude but opposite in sign to that of the proton.
4. The electron is bound to the nucleus by an electric force which acts somewhat like the gravitational force but is much stronger on small scales. The strength of the electric force is proportional to $1 \over R^2$ where R is the distance between the nucleus & the electron. (Electrons at larger distances from the nucleus are said to be less tightly ``bound'' to the atom since the electric force is weaker than for a nearby electron.) However, for the electric force, opposite charges attract and like charges repel.
5. When an electron is removed from a atom (as a result of a collision with another atom, for example), the atom becomes ionized.
6. The main difference between various chemical elements is the number of protons, neutrons, and electrons that each atom of the element possesses. Hydrogen has 1 proton, no neutrons, & 1 electron. Helium has 2 protons, 2 neutrons, and 2 electrons. Uranium has 92 protons, 146 neutrons, & 92 electrons. Also, the distances from the nucleus and the energies of electrons in each atom are different from all other atoms.

Temperature & Pressure

• Temperature is a measure of the speed of motions of atoms or molecules in a gas. The faster the motion of the atoms/molecules, the higher the gas temperature. Two temperature scales are commonly used in science as follows:
  • The Celsius scale is based on the freezing and boiling points of water. That is, $0^{o}$ C corresponds to the freezing point and $100^{o}$ C corresponds to the boiling point of water.
  • The Kelvin scale is based upon the absolute zero point where the velocity of gas atoms or molecules would be zero. That is, 0 K corresponds to $-273^{o}$ C. The relationship between the Celsius and Kelvin scales is then
    
    $$K = {^{o}}C + 273.$$
    
    

• Pressure is defined as force per area. For a gas enclosed in a container, the gas pressure is a measure of how many atoms hit the walls of the container and at what speed. It is related to density and temperature as follows:
  
  $$P = nkT$$
  
  
  where $P$ is the pressure, $n$ is the density, $k$ is a constant, and $T$ is the temperature. The higher the temperature, the faster the atoms will be moving and so these atoms will hit the container walls more often thus increasing the pressure. Similarly, the larger the number of atoms in the volume of the container (density), the more often the container will feel the ``push'' from an atom striking a wall and thus increases the pressure.

Molecules

• A molecule is a bonding together of 2 or more atoms. Common examples are molecular hydrogen ($H_2$), which is found in the atmosphere of Jupiter & cooler stars; carbon dioxide ($CO_2$), which dominates the atmospheres of Venus & Mars; and ammonia ($NH_3$) which is an important constituent in the atmospheres of Jupiter & Saturn.
• The abundance of a particular molecule is dependent upon the temperature and pressure. High temperatures lead to more collisions between molecules which can cause them to dissociate or break-up into individual atoms. So, molecules tend to be found in cooler environments like planetary atmospheres and interstellar clouds, and not at the cores of stars or on the surface of the Sun.

Macroscopic States of Matter

• Matter in the Universe is found in three states:
  • A solid usually has the highest density. Examples include the surfaces of planets, asteroids, and neutron stars.
  • A liquid usually has an intermediate density. Examples include the Earth's ocean, a possible methane ocean on Titan (a moon of Saturn), and the liquid metallic cores of the Earth & Jupiter which are responsible for generating the planetary magnetic fields.
  • A gas is usually the lowest density state. Examples include the atmospheres of the planets, stars, the interstellar medium, and the intergalactic medium. It is the most common state of matter in the Universe.
• The particular state of matter of a given chemical composition depends critically upon its temperature and pressure. For example, water takes less time to boil at higher elevations; this is because the boiling point of water is lower when the atmospheric pressure is lower. Similarly, some states of matter cannot even exist if the pressure is too low; this is true for the Moon and Mars where water can only exist in either the frozen (ice) state or the gaseous state.
• The electrical properties of matter can also depend upon the temperature & pressure. Even though the temperature is high near the center of Jupiter, hydrogen has a liquid state which has electrical properties like that of a metal.

Applications

Planetary Atmospheres

1. The density and composition of the atmosphere of a planet depends critically upon the temperature and mass (gravity) of the planet. These effects produce atmospheres which range from a high vacuum on Mercury to the thick atmosphere of Jupiter.
2. The concept of escape velocity is important in understanding planetary atmospheres. Remember that the force of gravity holding us to a planet depends directly upon the mass of the planet. The larger the mass, the higher the velocity or kinetic (motion) energy necessary to escape from the planet. For small planets like Mercury or satellites like the Moon, the gravitational force is low and so is the escape velocity. Atoms & molecules do not have to move very fast to escape from these bodies; such small planets as Mercury do not retain their atmospheres whereas massive planets like Jupiter are able to keep virtually all their original atmosphere. Similarly, this is why Earth's atmosphere is denser and has a higher pressure than Mars' atmosphere (because Mars' mass is only 11% that of Earth).
3. A second effect on planetary atmospheres is the temperature of the planet. The higher the temperature, the faster the atoms & molecules in the atmosphere move. Fast moving atoms mean that many of them will achieve escape velocity and will leave the planet. This effect is important on Mercury where the high temperature further helped the atmosphere to escape whereas the cold temperatures near Jupiter mean that the atoms & molecules rarely achieve escape velocity.
4. A third effect on atmospheric composition is the mass of the atom or molecule. In a gas of a given temperature, lower mass atoms will move more rapidly than higher mass atoms. So, lighter atoms will be closer to the escape velocity than heavier atoms. Therefore, more lower mass atoms will be lost from a planet's atmosphere than higher mass atoms. This is why the Earth's atmosphere contains little hydrogen but more heavy molecules & atoms (like nitrogen & oxygen), whereas the massive Jupiter (& the Sun) is composed mainly of hydrogen since the escape velocity is high.
5. Our technology has advanced to the state where humans can significantly affect and alter the atmosphere of Earth. Two developments are of concern:
   • The increased levels of $CO_2$ in the atmosphere produced by industry, aircraft, etc. has led to a warming of the atmosphere, termed the Greenhouse Effect, according to some scientists. The $CO_2$ traps heat (infrared radiation) near the Earth's surface & can cause the average temperature of the planet to rise. Potentially, this can have catastrophic effects (melting of polar ice caps producing coastal erosion; crop failures). Venus is an example of a planet with a Runaway Greenhouse Effect that developed naturally as a result of early outgasing of carbon & oxygen into the atmosphere; the surface temperature is 700 K! There is a lesson to be learned here.
   • Another potential human-made problem is the ozone hole. Ozone is a molecule consisting of 3 atoms of oxygen. Ozone absorbs ultraviolet radiation in our atmosphere. However, chlorofluorocarbons from spray cans, jet engine exhaust, etc. are slowly breaking down the ozone layer, especially over the Antarctic. Further erosion of the ozone layer would permit more ultraviolet light onto the Earth's surface which would lead to an increase in skin cancer and to crop failures.
6. On the positive side, human technology may allow us to someday ``terraform'' other planets like Mars - that is, to increase the atmospheric density & pressure, thus allowing humans to breathe the Martian atmosphere & allowing liquid water to again run on Mars' surface.

Powering a Star

• Astronomers were puzzled for many years by how stars like the Sun produce their energy. Do they burn coal at their core? (No, this is not efficient enough.) Is the Sun continually contracting, heating up, & then radiating this heat into space? (No, the Sun's lifetime of 5 billion yrs is too long.) What is the macroscopic state of this matter? The answer came with an understanding of nuclear reactions in the middle of this century.
• The energy generation process in the core of the Sun is called the p-p or proton-proton chain. Protons are converted into helium, and in the process light energy is given off. In particular,
  
  $$p + p + p + p \rightarrow He + energy + \nu$$
  
  
  where $He$ is a helium nucleus and $\nu$ is a very low mass, neutral particle called a neutrino. The protons must come together at very high speeds (& so high temperature like that at the Sun's core, $1.6 \times 10^7$ K) in a high density region so the protons will fuse together. This kind of nuclear reaction is called fusion.
• The key to energy production in fusion is to recognize that the mass of the helium nucleus is less than that of the 4 protons. Where does the extra mass go? Einstein told us in 1916 that energy & mass are equivalent such that mass can be converted into energy, and energy can be turned into mass via
  
  $$E = m c^2$$
  
  
  where $E$ is the energy (light), $m$ is the difference in mass between the helium nucleus & the 4 protons, and $c$ is the speed of light.

Dead Stars

• An interesting example of an extreme state of matter can be found in dead stars. These are stars that have burned all their hydrogen fuel at their cores and then gravitationally collapsed to a small size but very high density. The very high pressure within these stars produces very exotic states of matter.
• At the end of its lifetime in another 5 billion yrs, the Sun will become a white dwarf star.
  • White Dwarfs have a size less than that of the Earth but a density of 1,000,000 gm/cm$^3$ or a million times the density of water! When a star like the Sun stops burning its nuclear fuel, there is no longer any thermal pressure to resist gravity. So, the star collapses under its own weight.
  • Such stars are very hot on their surfaces (about 15,000 K vs. 6000 K for the current Sun) and emit most of their energy just by cooling down. The stars became hot when they collapsed much like the frictional heating when you rub your hands together.
  • The core of a white dwarf is made almost entirely of carbon - a kind of carbon crystal.
  • White dwarfs have been observed in a number of cases. The most famous is the companion of the luminous star Sirius, which is one of the brightest objects in the night sky.
• Neutron Stars possess an even more exotic type of matter - a star made up entirely of neutrons.
  • For stars more massive than the Sun, the gravitational forces can cause a star to collapse even beyond the white dwarf stage. They achieve densities of $10^{14}$ gm/cm$^3$. At this high density, protons and electrons are crushed together & form neutrons:
    
    $$p^+ + e^- \rightarrow n + \nu$$
    
    
    .
  • The astronomer S. Chandrasekhar first described this process theoretically in the early 1930's using a combination of the new theories of Relativity and Quantum Physics. He found that stars greater than 1.4 M$_\odot$ will become neutron stars at the end of their lifetimes.
  • Neutron Stars have diameters of only 15 km with masses greater than that of the Sun! The escape velocity is 80% of the speed of light. A 150 pound person on the Earth would weigh $2 \times 10^{11}$ pounds on a neutron star. Furthermore, a marshmallow dropped onto a neutron star from a mile above would impact with a kinetic energy greater than that of a nuclear bomb.
  • Have we actually seen a neutron star? In 1968, J. Bell and A. Hewish at Cambridge University discovered a peculiar, very regular, pulsing radio source now known as a pulsar. Because the period of pulsation is less than a second, it was concluded that only a spinning neutron star can produce this kind of very regular changes in radio emission. A spinning neutron star is believed to emit radio waves along its magnetic poles when the poles come into view of the Earth - this is the Light House model for pulsars. The Crab pulsar in the constellation Taurus is the best studied to date.

PART III - LIGHT

The Wave Nature of Light

1. Unlike other branches of science, astronomers cannot touch or do field work on their samples. The only information that we have is from the light that is imaged by our telescopes. Fortunately, light contains a wealth of physical information about the Universe.
2. Light can be viewed as a traveling wave (like an ocean wave). It is made up of electric & magnetic fields so light is referred to as electromagnetic radiation.
3. The wavelength is the distance between wave crests (units are length). For optical light, a shorthand notation of angstroms (Å ) is used such that 1 Å $=10^{-10}$ meters. So, visible wavelength light is about 5000 Å.
4. The frequency is the number of wave crests that pass by a detector per second of time. The units are Hertz (Hz), where 1 Hz is 1 cycle/sec. A typical radio frequency is 100 MHz (where MHz is a million Hz).
5. Light travels very fast at $c=3 \times 10^5$ km/sec. This speed is constant throughout space for all wavelengths.

The Electromagnetic Spectrum

• In the visible, the rainbow of colors make up the spectrum. Color is the same as wavelength. Blue light has the shortest wavelength and red light has the longest.
• The only difference between various parts of the electromagnetic spectrum (such as radio and x-rays) is the wavelength. In order of increasing wavelength: gamma-rays, x-rays, ultraviolet, visible, infrared, and radio. Gamma-rays have wavelengths $<1$ Å and radio waves have wavelengths of meters.
• The atmosphere is mostly opaque to the electromagnetic spectrum. Only visible and radio waves easily penetrate the atmosphere with a bit of ultraviolet & infrared as well. This means ground-based telescopes operate in the visible & the radio, whereas space-based telescopes (above the atmosphere) function at other wavelengths.

The Doppler Effect

• The Doppler Effect is the shift of the wavelength of light produced by motion of an object toward or away from us. We experience a similar effect with sound when a train approaches us & then moves away from us - the pitch or the wavelength of the sound changes.
• The change in the wavelength between that observed for a moving object and that measured when the light source is at rest is directly proportional to the wavelength. For stars moving away from us, the wavelength change is toward the red and is called a redshift. For stars moving toward us, it is a blueshift.
• The Doppler Effect provides astronomers with a powerful tool for measuring radial velocities of planets, stars, & galaxies. All we need to do is measure the difference between the observed wavelength and the wavelength measured in the laboratory.

The Inverse Square Law

1. When we look at the night sky, we see that all stars are not the same color or brightness. Brightness is the amount of energy per second per area that falls on a detector such as a photographic plate or on the retina of our eyes. Brightness depends upon two factors:
   • The total energy per second or luminosity emitted by a star or other object. For example, a 200 Watt light bulb appears brighter than a 100 Watt light bulb if they are side by side.
   • The distance of the light source from the observer. The further away the light source, the less bright it appears.
2. This dependence of brightness upon distance is called the Inverse Square Law. Once again, it is very much like the Gravity Force Law in that the brightness of a light source is proportional to $1 \over R^2$, where R is the distance between the light source and the observer.
3. So, when we look at a star, it may be faint because it is far away or it is low luminosity or a combination of the two.

Kirchhoff's Laws of Spectral Analysis

• To understand how stars and galaxies function, we must first understand how such objects produce the light that we observe with our telescopes - light is the only information that we can sample from most astronomical objects.
• In the last century, Gustav Kirchhoff (1824-1887) formulated 3 rules or laws which govern how light is produced by various states of matter. He stated that:
  • A dense, hot substance produces a continuous spectrum with all the rainbow colors. An example is a fireplace poker or the filament of a light bulb.
  • A low density, hot gas emits bright emission lines. An example is the gas around new stars like the Orion nebula.
  • If a continuous spectrum passes through a gas at a lower temperature, the cooler gas produces dark absorption lines.
• The Challenge: Explain these interesting rules for the production of light using our knowledge of matter.

Continuous Emission & Blackbody Radiation

• Notice that a fireplace poker starts off looking a dull red then a brighter red and finally is blue-white hot as we increase the temperature of the metal. An object like this whose light emission properties depend only upon temperature is called a blackbody. It is a perfect radiator of energy. As a blackbody heats up, it begins to radiate away its energy as light, first starting off with most of its emission in the infrared then in the visible and finally in the ultraviolet. Stars are good approximations of blackbodies.
• A blackbody emits continuous radiation and meets the conditions outlined by Kirchhoff. The properties of a blackbody include:
  • The electromagnetic radiation from a blackbody is strongly peaked at a particular wavelength that depends only on the temperature of the blackbody. A hot blackbody will appear to be blue and a cool blackbody will appear to be red. So, by just looking at the color of a star, you can get a pretty good idea of its temperature! A yellow star like the Sun has a temperature of 5500 K, whereas a red star like Betelgeuse has a temperature of only 3000 K.
  • A blackbody emits some radiation at all wavelengths.
  • The energy per area radiated by a blackbody will increase with temperature. In other words, for two stars at the same distance with the same radii, the star with the highest temperature will appear to be the brightest.

Spectral Lines & the Bohr Model

• The German physicist Max Planck proposed in the late 1800's that light can be viewed as both a wave and a massless particle. The light particle or quanta is called a photon. Each photon carries both momentum and energy. The photon energy directly increases with frequency so gamma-ray photons have more energy than infrared photons.
• Neils Bohr in the early part of this century first correctly described a working model for the hydrogen atom. He hypothesized that electrons can only occupy certain orbits at selected distances from the nucleus. They cannot lie between these particular orbits. Furthermore, each atom has a unique set of orbits which corresponds to different orbital energies. So, the electron orbits are said to be quantized.
  • The lowest orbit or energy level of an atom is called the ground state.
  • When an electron is in some orbit above the ground state, it is said to be excited.
• Next, Bohr recognized that when an electron jumps from a larger radius (or higher energy level) orbit to a lower radius orbit, it must give up energy. This energy is in the form of a photon which has exactly the energy that corresponds to the difference in energy between the two orbits. Such an electron transition produces an emission line.
• In practice, an emission line can be produced as follows. A gas, say around a young star, is heated by the energy radiated from the new star. This higher temperature means that the atoms are moving faster. When the atoms collide, some of their energy goes into causing the electron to rise to a higher orbit or energy level. But, electrons like to be in their ground state which is accomplished by emitting a photon and thus giving up the energy gained via the collision. Such gas around young stars produced what are called emission line nebulae.
• An absorption line is produced when an atom absorbs a photon and the electron jumps to a higher orbit or energy level. It is important to note that only photons with exactly the energy corresponding to the difference in energy between the two electron orbits will be absorbed. All other photons will be ignored. This is why only discrete wavelengths will be missing from an absorption line spectrum. The missing wavelengths correspond to the energy levels of particular atoms. Since each atom has a unique set of orbits & energy levels, the corresponding spectrum will be unique.
• With only the spectrum from a star, we can determine its temperature and its chemical composition.

Further Thoughts on Light

The Sun

1. The Sun's atmosphere has three layers:
   • The photosphere is the layer that we see. It has a temperature of about 5800 K.
   • The chromosphere lies above the photosphere. Surprisingly, it is hotter - up to a million degrees K.
   • The corona is the outermost layer that extends out to several solar radii. Its temperature is about 2 million degrees K.
2. More about the photosphere:
   • It has a characteristic temperature of 5800 K.
   • Since this temperature is lower than that of the interior (which is 16,000,000 K at the core), we have the classic situation described by Kirchhoff for absorption lines. The Sun has an elaborate absorption line system arising from most of the known elements. Interestingly, helium was first detected on the Sun (via its absorption lines) before it was discovered on Earth.
   • The surface of the photosphere has a mottled appearance with a pattern of light & dark structures known as granulation. This granulation is the result of the heat rising from the interior to the surface of the Sun much like a pot of boiling water. This type of heat transport is called convection and occurs in stars with masses similar to and less than that of the Sun.
3. The surface of the Sun is not always peaceful, but can undergo periods of activity which are related to the magnetic fields. Astronomers can measure magnetic fields on the Sun; in the presence of strong magnetic fields (8000 times that on Earth), the energy levels in atoms will further divide. This means that in the spectrum of a gas with a strong magnetic field, two lines rather than one will appear. The separation of the line pair is directly proportional to the strength of the magnetic field.
4. Activity on the Sun is manifested in several ways:
   • Sunspots are dark, cooler regions on the Sun's surface. These are regions with enhanced magnetic field. The magnetic field pressure holds back some of the hot gas rising from the interior to make the sunspots cooler. Sunspots usually come in pairs where one sunspot corresponds to the magnetic north pole & the other to the south pole where field lines stretch between them. The period between sunspot maxima (when there is the largest number of sunspots) is 11 yr and this appears to be related to the time needed for the Sun's overall magnetic field to become tangled and untangled.
   • Solar prominences are loops of hydrogen gas that rise above the solar surface. They usually appear near sunspot groups and appear to trace out magnetic field lines going from a north to a south magnetic pole.
   • Solar flares are very energetic streams of protons, electrons, and ions which leave the Sun in bursts. They produce the auroras on Earth and can also interfere with our communications. These particles are energized in regions on the Sun where magnetic field lines reconnect producing a burst of light, radio emission, X-rays, and gamma-rays in addition to these energetic particles.
   • Coronal holes appear in the outermost layer of the sun and were discovered by the Skylab mission in the mid-1970's using X-ray sensitive film. Because the corona has a temperature of about 1,000,000 K, it's blackbody spectrum peaks in the X-ray. Holes were detected in this coronal X-ray emission which appear to coincide with regions where magnetic field is streaming outward from the Sun (and not immediately looping back) and carrying gas away with it.

The Interstellar Medium

• Recall that the distance between stars is very large. But, this space is not empty. It is filled with a gas that has an average density of 1 atom/cm$^3$ called the interstellar medium (ISM). The temperature of the ISM varies from very cold (10 K) at the centers of molecular clouds to $>10,000$ K near young stars.
• Emission lines originate from the hot gas around young stars. As new $O$ and $B$ stars ``turn on'', the ultraviolet light from these stars heats the gas and ionizes the hydrogen atoms in the surrounding nebula. When these free electrons collide with the ionized hydrogen atoms, they recombine and the electrons cascade back down through the energy levels emitting light at discrete wavelengths. Such Emission Line Nebulae appear red in color because of the abundance of red wavelength emission lines on visible wavelength images. Emission Nebulae are seen in both the Milky Way (example: the Orion Nebula) and in the spiral arms of other galaxies - anywhere that young, hot stars are being born.
• Even the neutral hydrogen gas that is away from young stars can produce emission line radiation, but in the radio part of the spectrum. This spectral line has a wavelength of 21 cm. It was discovered first in the early 1950's by groups in the U.S. & the Netherlands. The 21 cm line is produced by a spin-flip transition even though the atom is in its ground state. That is, both the electron & the proton in the atom are spinning. The very lowest energy state is when they are spinning in opposite directions. A transition from parallel spins to anti-parallel spins produces a 21 cm spectral line.
• In dense ($10^4$ atoms/cm$^3$), cold (10 K) clouds (where stars have not yet ignited), molecules are abundant. They, too, can emit spectral lines particularly in the IR and radio. Molecules such as $H_2$, OH, CO, and even $H_2O$ are observed.
• Dust is the final important ingredient in the ISM. It does three things to observations of distant stars in the visible:
  • Dust dims light. This is called interstellar extinction. This will tend to make stars look further away than they actually are, so we need to be careful to correct for this effect.
  • Dust reddens light as a result of preferentially scattering blue light; that is, more red light makes it through a dust cloud while blue light is scattered in many directions. This is the same effect that produces red sunsets on Earth.
• Reflection Nebulae are the result of dust scattering; these nebulae appear to be blue in color because the blue light has been scattered into our line of sight. Such reflection nebulae ``shine'' by reflected starlight.

PART IV - ORIGINS Star Formation & Evolution

Stellar Classification

1. The spectra of stars and their colors can be used to classify their physical properties. This was recognized in the early 20th century as both Kirchhoff's Laws and the Bohr model began to be applied to stars.
2. From our knowledge of blackbody radiation, we know that the color of a star is directly related to temperature where cooler stars are red and hotter stars are blue. The stellar classification system today in astronomy uses letters to signify temperatures as follows:
   
   $$O B A F G K M$$
   
   
   where $O$ stars are hot (30,000 K), $G$ stars are intermediate temperature like the Sun (5500 K), and $M$ stars are cool (3500 K).
3. The distribution of spectral lines in a star are even more sensitive probes of temperature. This has to do with ionization and collisional excitation. For example, $O$ stars have weak Balmer lines because most of the hydrogen gas is ionized in these hot stars. $A$ stars, which have temperatures of 10,000 K, have the strongest Balmer lines. On the other hand, $K$ and $M$ stars have weak Balmer lines because most of the hydrogen is in the ground state and/or part of molecules in these cool stars.

The Hertzsprung-Russell (H-R) Diagram

• An extremely useful tool for understanding the evolution of a star is the H-R diagram first devised in the early part of the century. It is a plot of stellar temperature (or spectral class) on the horizontal axis versus stellar luminosity on the vertical axis. It was found that particular types of stars lie on certain regions in this diagram according to their evolutionary state and their mass.
• Regions on the Diagram:
  • The Main Sequence runs from the top left to the bottom right in the H-R diagram. These are all ``ordinary'' stars, which like the Sun, are burning nuclear fuel at their centers. Stars in the upper left are luminous & have very high temperature; from the mass-luminosity relationship, we also know that these are the most massive main sequence stars. Stars in the lower right are low of luminosity, cool, and have masses smaller than the Sun. Notice the position of the Sun about mid-way on the Main Sequence.
  • Giant & Supergiant stars lie in the upper right hand portion of the H-R diagram. These stars are luminous but have cool outer envelopes. According to our knowledge of blackbodies, a star which is cool can only be luminous if it has a large surface area (and, therefore, large radius) from which energy is emitted; thus, their position on this diagram requires such stars to be giants.
  • Finally, the lower left portion of the H-R diagram contains white dwarfs. These stars are hot but relatively low luminosity. Again, using the same reasoning for blackbodies, such a hot star will have limited total energy emitted if it is small in radius.

Protostar Formation

• Gravity and energy are the keys to understanding star formation & evolution.
  • Gravity is constantly trying to pull matter toward the center of mass of a gas cloud or a star.
  • Since stars do not have an infinite supply of energy, they must readjust their structure in response to the energy supply. Initially, gravitational collapse is the only source of heat. Later, nuclear reactions power a star; the thermal pressure from the heat at the core balances gravity. When the nuclear energy is exhausted, the star's structure must again change in response to the changing energy balance.
• Stars begin as roughly spherical, cold (10 K) molecular clouds. They probably are rotating very slowly. A shock wave (possibly from a supernova) may be the stimulus which causes the gas cloud to begin to collapse. The shock compresses the gas & makes it denser. Then, the self-gravity of the cloud causes the gas to contract toward the center, further increasing the density.
• Conservation of Angular Momentum plays an important role in the evolution of a star-forming nebula. Angular Momentum (L) is defined as:
  
  $$L = MVR$$
  
  
  where $M$ = mass of the cloud, $V$ = rotational velocity of the cloud, and $R$ = cloud radius. For an isolated cloud, angular momentum must be conserved (that is, remain constant) as the cloud gravitationally collapses. But, for $L$ to be constant while $R$ is decreasing (and $M$ does not change), $V$ must increase; thus, the star must rotate faster as it collapses.
• Now, as the cloud continues to collapse, the center becomes denser and hotter much like heat being generated when you rub your hands together. At this point in time, the dense object at the core of the gas cloud is called a protostar - an object not yet a star, but it is one in the making.

``Turning On'' a Star

• The evolution of a protostar can be followed on the H-R diagram. The early protostar is relatively cool and low luminosity (much of the energy is radiated in the infrared). So, the star first appears on the extreme lower right portion of the H-R diagram.
• The protostar's original free-fall contraction is slowed by the increasing density and internal pressure at its center. The star still is not hot enough to begin nuclear reactions so it must contract further as it radiates energy from its surface.
• During its contraction phase, the protostar converts gravitational energy into heat energy. Half the energy is radiated into space and the other half goes to further raise the temperature of the protostar's core.
• Finally, when the core is hot enough (about $10^7$ K for a 1 $M_{\odot}$ star), thermonuclear reactions begin. At this point, the star enters onto the Main Sequence of the H-R diagram for the first time. For a star like the Sun, it will remain on the Main Sequence for about 10 billion yrs.
• While on the Main Sequence, stars are in pressure equilibrium. That is, there is a balance between the force of gravity (directed toward the star's center) and thermal (or heat) pressure caused by energy released from the nuclear reactions in the core (directed outward). During its life on the Main Sequence, the star neither expands nor contracts.

How Do Different Mass Stars Evolve?

• The mass of a star has an important role in determining its evolution. The larger the mass, the more quickly the star will evolve onto and off of the Main Sequence. A 1 $M_{\odot}$ star takes about 30 million yrs to evolve onto the Main Sequence, but a 15 $M_{\odot}$ takes only about 160,000 yrs and a 0.2 $M_{\odot}$ star takes about 1 billion yrs.

Evolution Off of the Main Sequence

• Massive stars consume their fuel quickly & live relatively short lives on the Main Sequence whereas low mass stars conserve their fuel & shine for billions of years. For example, a 25 $M_{\odot}$ will live only 7 million yrs on the Main Sequence, whereas a $K$ star can continue to burn its nuclear fuel for 17 billion yrs.
• Main Sequence stars ``shine'' by fusing hydrogen into helium. When about 90% of that hydrogen has been exhausted, great changes occur in the structure, luminosity, & size of the star. The star begins to evolve off of the Main Sequence.
• Once the hydrogen in the core is depleted, $p-p$ nuclear reactions cease and the helium core begins to contract (thermal pressure no longer can offset gravity). The core temperature begins to rise. The larger core temperature results in the ignition of a shell of hydrogen which surrounds the core.
• The star moves toward the upper right portion of the H-R diagram - the Giant Branch. The hydrogen shell burning has caused the star's envelope or atmosphere to rapidly expand with the outermost layers cooling due to the expansion. After another 5 billion yrs, our Sun will become a Red Giant. A star can remain a Red Giant only for about 10% of its total lifetime.
• Meanwhile, the helium core continues to contract & heat. Once the core temperature reaches 100 million K, nuclear reactions begin again. This time, three helium nuclei fuse to produce a carbon nucleus in what's called the Triple Alpha process.
• For stars with masses of $>9 M_{\odot}$, subsequent contraction and core heating can result in the production of even heavier nuclei all the way up to iron in the core.

Star Death

• For a medium-mass star like the Sun, the triple-alpha process is the last nuclear reaction in the core. Once the core has been converted into carbon, the star begins to collapse again and becomes a white dwarf, where degenerate gas pressure halts the collapse. It moves to the lower left portion of the H-R diagram. As the white dwarf radiates its energy into space, the star cools off and the luminosity declines. Eventually the star becomes a cold & dark carbon cinder called a black dwarf.
• For stars with mass $>10 M_{\odot}$, the end can be quite spectacular. Such a star is layered like an onion with an iron core, surrounded by a layer of silicon, then oxygen, then carbon, then helium, and finally an outer ``skin'' of hydrogen. The evolution then proceeds as follows:
  • As the star develops an iron core, the energy production declines (iron has a very tightly bound nucleus) and the core contracts. As the core reaches 5 billion K, the photons have reached gamma-ray energies which break up iron nuclei and cause the core to collapse VERY rapidly.
  • This rapid collapse triggers a star-destroying explosion called a supernova. The contraction of the innermost degenerate core allows the rest of the core to fall inward producing a huge shock (or compression) which propagates outward and blows off the outer part of the star. This explosion results in a rapid rise in luminosity, $10^{10} L_{\odot}$, for a brief period of time.
  • The core collapse transforms iron to heavier nuclei, all the way to the end of the periodic table. A supernova is the ONLY way that elements heavier than iron can be produced in nature.
  • The remaining core of the star may be either a neutron star (which can produce a pulsar) or a black hole.
  • Observations of supernovae have been recorded in historical records in 1054 A.D. (now the Crab nebula), Kepler, etc. The most recent, closest supernova was seen in 1987 in the Large Magellanic Cloud. Spectra of supernova remnants have very wide line widths indicating gas is moving outward at up to 10,000 km/sec!

Formation of the Solar System

Review of Solar System Properties

1. Let's review the major properties of the solar system which must be explained by a model of its formation.
2. Dynamical Properties
   • All planets revolve in a counterclockwise direction as seen above the north pole of the solar system.
   • Planetary orbits are nearly all in the same plane.
   • Most moons revolve counterclockwise & near the planet's equatorial plane.
   • Orbits are nearly circular.
   • Most planets rotate in a counterclockwise direction.
   • Most of the angular momentum in the solar system is in the orbital motion of the planets rather than the rotation of the Sun.
   • Planetary rings are found around all the gas giant Jovian planets.
3. Chemical Properties
   • Terrestrial Class - Silicon, iron, aluminum, and other rocky materials which melt around 2000 K.
   • Icy Class - carbon, nitrogen, oxygen, water, methane, ammonia, etc. which melt at around 273 K ($0^{\circ} C$).
   • Solar Class - hydrogen, helium, neon, argon, etc. which remains a gas down to around 10 K.

Table of Compositions of Objects by %

Object	Terrestrial	Icy	Solar
Terrestrial Planets	70%	30%	0%
Asteroids	70%	30%	0%
Jupiter/Saturn	1%	10%	89%
Uranus/Neptune	10%	80%	10%
Comets	15%	85%	0%

The Nebular Model

• The Nebular Model for the formation of the solar system is an extension of that proposed for star formation in general. The model originated in the 1700's by Kant and LaPlace.
• Our solar system began from a roughly spherical gas cloud. The cloud was enriched with heavy elements from a previous generation star which exploded as a supernova - a crucial aspect for life as we know it. The gravitational collapse was again stimulated by a shock wave.
• As the nebula contracted, it rotated faster according to the Conservation of Momentum. This faster rotation also resulted in a flattening of the gas cloud as expected by Newton's Law of Inertia. Eventually, the cloud flattened into a relatively thin plane which eventually formed the planets and the protosun was at the center.
• One major problem for this model is the distribution of angular momentum in the solar system. With such a collapse, we would have expected the Sun to be rotating more quickly and the planets revolving more slowly than is observed. How was the angular momentum transferred to the planets? The current model suggests that this was done via magnetic fields while the solar system was still in a gaseous state. Magnetic fields, which stretched from the protosun to the outer nebula, acted to break the rotation of the Sun and to ``stir'' the outer nebula.
• Tiny dust grains formed when molecules collected together, much like the growth of a snow flake.
• Next, the dust grains began to stick together. These objects grew to the size of large boulders (up to a 100 km in diameter) called planetesimals which probably resembled today's asteroids.
• These planetesimals collided to form protoplanets which were the massive objects that eventually became planets. The most massive protoplanets grew fastest since they had more gravity and would attract even more mass.
• Finally, the planets cooled and atmospheres formed. In the case of the terrestrial planets, surface evolution continued via meteoritic cratering and erosion.
• Now, return to the list of solar system characteristics to see how successful the Nebular Model is in explaining them.

Origin & Evolution of the Moon

Formation of the Moon

1. Four major theories have been proposed for the formation of the Moon:
   • The Fission hypothesis proposed that the Moon broke away from a rapidly spinning Earth. The problem is Moon rocks (from Apollo) fundamentally differ from those on Earth.
   • The Condensation hypothesis suggests that the Earth and Moon condensed out of the same cloud of material in the solar nebula. The problem is that the densities of the Earth & the Moon are quite different.
   • The Capture hypothesis suggests that the Moon was formed elsewhere in the solar system & later gravitationally captured by the Earth. This scenario has a very low probability.
   • The Large-Impact hypothesis proposes that the Moon was formed from the debris of an impact between a proto-Earth and a large Mars-sized object.
2. The Large-Impact hypothesis is currently favored because it explains a number of observations. For example, a glancing collision would have ``spun up'' the resulting material & would thus explain the present angular momentum in the Earth-Moon system. A glancing collision would also have ejected mainly lower density mantle material which coalesced to form the Moon.

History of the Moon

• The first of four stages of evolution of the Moon involved differentiation. Although the Moon is relatively poor in iron, what was there sunk to the center and the low density material floated to the top. The surface solidified 4.1-4.6 billion yrs ago.
• Intense cratering characterized the second stage. This formed the large impact basins on the Moon.
• The third stage involved volcanic activity and lava flow. Radioactive decay may have heated the subsurface layers to produce volcanoes. The lava filled the impact basins and produced the Maria or darker regions which we can see on the Moon today.
• The final stage of on-going evolution is lower level impact cratering which is caused by some remaining rocky debris falling onto the lunar surface.

Galaxies & Galaxy Formation

Two Populations

1. In the 1940's, W. Baade was the first to recognize two different populations of stars in spiral galaxies which are today believed to be understood within the spiral-density wave theory. They are:
2. Population I stars are like the Sun. They are second generation stars, rich in heavy elements, often blue in color, and are found within spiral arms.
3. Population II stars are older, previous generation stars. They contain relatively little heavy elements, are red in color, and are found in the galaxy halos (globular clusters), galactic nuclei, and in the general disk. Few Pop II stars are found near the spiral arms where active star formation is taking place. Also, Pop II stars dominate elliptical galaxies.
4. POPULATION I:
   • Metal-rich young stars in disk
   • H$_{II}$ regions (hot gas around young stars
   • Open clusters and stellar associations
   • Cepheids (bright variable stars: period is 3-30 days

5. POPULATION II:
   • Old stars: metal-poor
   • Globular clusters: 10 pc, 1 million stars
   • RR-Lyrae stars

Galaxy Diversity

• An unresolved question in astronomy is how are the different kinds of galaxies produced? Recall that the 3 basic galaxy types are ellipticals, spirals, and irregulars. They have very different characteristics:
  • Spirals have prominent spiral arms in their disks; the disks rotate about the galaxy centers; there are young stars in the disk; there is an abundance of cool ($<10^4 K$) gas in the ISM.
  • Ellipticals are not flattened into disks like spirals; there is little or no organized rotation; there is no new star formation taking place within ellipticals; the ISM is hot ($10^7 K$) & emits X-rays.
  • Irregulars are chaotic in appearance; there are young stars within them; there is cool gas inside the ISM.

Interacting Galaxies

• The probability of galaxies interacting, especially in clusters, is relatively high. In fact, it is more likely that 2 galaxies will collide than 2 stars in the Milky Way. This is because the ratio of the galaxy size to the average distance between galaxies is much larger than a similar ratio for stars.
• When galaxies come near each other, the mutual gravitational forces can tear stars & gas out of each galaxy. This can produce very interesting ``tails" of stars & gas that stretch into intergalactic space.
• Sometimes, galaxies can actually merge together. It has been suggested that elliptical galaxies form as a result of mergers of spiral galaxies. This has been demonstrated using computer modeling called N-body simulations.
• Also, large galaxies at the cores of rich clusters may be formed by ``galactic cannibalism" in which these large galaxies grow as a result of digesting smaller galaxies that occasionally come close to the cluster center.
• It is also likely that such galaxy interaction can trigger activity within the nucleus of a galaxy resulting in the production of extended radio sources. Such interaction causes gas to fall toward the nucleus of galaxies which in turn may provide fuel to fire the radio source ``engine".

Large Scale Structures in the Universe

• Groups of Galaxies: 2-20 galaxies, size=0.5 Mpc, 1/2 of all galaxies belong to a group. Galaxies in groups are mostly spiral galaxies and irregulars.
• Filaments: a dozen or more galaxies in a chain, mostly spirals or irregulars, few Mpc long.
• Clusters: a thousand of galaxies, mostly ellipticals and spirals with a very small amount of gas. There is hot gas between galaxies (100 million degrees). Galaxies move with very large velocities: 1000 km/s. Size of clusters: 1- 3 Mpc. Often there is a large central elliptical galaxy.
• Superclusters: Long (30-100 Mpc) very anisotropic structures. Each supercluster includes many groups, filaments, and few clusters.
• Voids: Large, almost empty areas. The same linear size as for superclusters.
• The driving force behind the formation of galaxies and large scale structures, such as superclusters, is gravity. Gravity attracts matter into increasingly larger scales of structure.
• Supercomputer models are successful in reproducing the observed distribution of structures on scales of hundreds of millions of light years ONLY if the Universe is composed of at least 90% dark matter. The exact form of this dark matter is not known at present
• Galaxies and larger structures begin as gaseous density fluctuations in the early Universe. These regions are slightly denser than the surrounding gas. Gravity causes them to collapse much like the star-forming nebulae discussed earlier.
• In the early 1970's, the Russian astrophysicist Y. A. Zeldovich proposed that large (a billion ly) clouds collapsed to form pancake-like structures which became the filamentary superclusters that we observe today. The empty regions left behind would produce the cosmic voids.

The Formation of the Milky Way

• In many ways, spiral galaxies like the Milky Way are the most complex and have the greatest diversity of properties. It is believed that spiral galaxies begin as slowly rotating, giant, gas clouds. Gravity causes the cloud to collapse. As in the case of the solar system, the proto-galaxy cloud spins faster and flattens into a disk as it collapses. This gives the Galaxy its organized rotation and the thin galactic disk.
• As the Galaxy collapses, some of the gas fragments into smaller clouds which become the sites for the first epoch of star formation. These first generation stars are very massive ( $(10-100) M_{\odot}$), go through their lifetime quickly, and explode as supernovae.
• Galaxies form hierarchically: A small cloud forms. Then it collides and merges with another small cloud. Then it collides and merges with even bigger cloud, and so on.
• Spiral galaxies form in a process of multiple mergers with small proto galaxies.
• Quick and violent merging produces an Elliptical galaxy.

How do the spiral arms form in galaxies like the Milky Way?

• The most popular idea since the 1950's is the spiral density wave theory. It proposes that spiral shock waves rotate about the galaxy.
• When gas clouds encounter the spiral density wave pattern, the shock waves compress the gas and trigger star formation. This explains why young $O$ & $B$ stars, emission nebulae, and neutral hydrogen clouds (radiating via 21-cm radio emission) serve to define spiral arms in the Milky Way and other galaxies.
• An important aspect of the Spiral-Density Wave theory is that star-formation is an on-going activity within spiral galaxies. This leads to multiple epochs of star formation - second or even third generation stars like our Sun which are enriched with heavier elements.

Black Holes & The Theory of Relativity

Overview of Relativity

1. By the beginning of the 20th century, it became clear that Newton's Laws of Motion & Gravity were not completely general. In particular, Newton's Laws do not correctly describe motions of objects that are traveling near the speed of light or that are in a very strong gravitational field.
2. Einstein developed several important postulates about motion:
   • There is no absolute rest frame in the Universe. The best that one can do is measure relative motions.
   • The speed of light, $c$, is constant with respect to all observers, independent of velocity. This makes light a very different phenomenon from objects with mass that have different apparent velocities depending on the motion of the observer. This result gives rise to different relative measures of time and length as determined by two observers in motion.
3. The above postulates gave rise to Einstein's famous $E=mc^2$ law relating the equivalence of mass of energy.
4. Although Einstein's Theory of Relativity produced different results from Newton for velocities near light and for strong gravity, it completely agrees with Newton for lower velocities and gravity fields like that on Earth.

The Curvature of Space-time

• Einstein's recognition that time was measured differently for different relative observers led him to treat time as a fourth coordinate in describing an event - one needs to have 4 dimensions to specify an event including $x, y, z,$ & $t$ where $t$ is time. For example, we see the Sun as it was 8 minutes ago. Einstein unified the concepts of space & time together as space-time.
• Einstein did not use the concept of force to understand motions in a gravitational field. Instead, his theory of gravity is a theory that involves the geometry of space-time.
• When no masses are present, the geometry of space-time is flat. A 2-dimensional analog is a flat, frictionless table top. Start a ball moving at a given velocity across the table. It will continue to move in a straight line at that velocity following the simple flat geometry of the table. The same is true for 4 dimensional space-time.
• Now, when a mass is present, this mass produces a curvature of space-time. The 2-dimensional analog would be a stretched piece of thin rubber with an indentation at the center where the mass is located. Let a ball go near the edge of the indentation & it will accelerate toward the bottom. If you give the ball a little velocity in a tangential direction, it will ``orbit'' the indentation. Thus, the basic observed features of motion in a gravitational field can be understood through this theory of curved space-time.
• Keep in mind that time, also, will flow differently depending upon the location of the observer on this curved, 4-dimensional space-time.

Black Holes

• Einstein's Relativity Theory predicts that the larger the mass, the greater the curvature (or indentation) of space-time. A black hole is the extreme example in which the indentation is infinitely deep.
• Consequences include:
  • At the ``event horizon'' or Schwarzschild radius of a black hole, the escape velocity is equal to the speed of light. For an object with the mass of the Sun, this radius is only 1.5 km; for an object with $10 M_{\odot}$, this radius is 15 km.
  • Once an object falls inside the event horizon, it can never come back out. It is lost forever to us. This includes light which is the reason we call this object a ``black hole''.
  • Although time would appear to run normally for an astronaut approaching a black hole, an outside observer would judge that the astronaut's clock is running slowly. In fact, that outside observer would see that it would appear to take an infinitely long time for the astronaut to fall into the black hole at the event horizon. This is due to the extreme curvature of space-time near the black hole.
• It is important to note that although the gravity within a few Schwarzschild radii of a black hole is very large, beyond this distance the strength of gravity drops to that predicted by Newton for an object of mass $M$. That is, the gravity force (in Newton's terms) drops as $1 \over R^2$, where $R$ is the distance from the black hole.
• How does a black hole form? For stars at the end of their lives (after Red Giant & supernova stages) which are $>$5 $M_{\odot}$, there is no barrier to total gravitational collapse. The gravity is strong enough to overcome the degenerate gas pressure which halts the collapse of lower mass white dwarfs & neutron stars. The volume becomes very small and the density is infinitely large. The resulting curvature of space-time is infinitely deep & the object becomes a black hole.
• Have we ever seen a black hole? Since the black hole Schwarzschild radius is small & the hole is black, we cannot hope to directly observe the hole. However, we can possibly see it through the strong gravitational effects it has on nearby objects. A black hole in a binary star system with a Red Giant companion will accrete gas from the companion; the resulting accretion disk will heat & produce X-rays. The Cygnus X-1 star system is a good candidate for a black hole; it has a visible Red Giant star and an invisible companion with an inferred mass of $>8 M_{\odot}$ using Kepler's 3rd Law.

Other Observational Consequences of Relativity

• Light must follow the curvature of space-time like any object with mass. So, the path of light in the vicinity of a massive object will curve toward the object. This is not expected from Newton's Law of Gravity.
  • The deflection of starlight near the Sun was observed for the first time during the solar eclipse of 1919.
  • Subsequently, the VLA has been used to measure the deflection of radio waves from distant radio sources near the Sun.
• Another consequence of Relativity is that galaxies can act as gravitational lenses on images of more distant galaxies or quasars. Light from a more distant galaxy bends toward a nearby galaxy on its way to us. The result is a distortion of the image of the more distant galaxy much like a lens. This can produce multiple images of the distant galaxy or even a ``ring'' of light.

Cosmology

What Is Cosmology?

1. Cosmology is the study of the physical Universe's nature & evolution. It involves the origin and evolution of the Universe and the structure within the Universe.
2. General facts and assumptions used in cosmology include:
   • The Universality of Physical Laws - Newton's Laws, Kepler's Laws, Einstein's Relativity, etc. are assumed to hold on Earth and everywhere else in the Universe.
   • Cosmological Principle - The Universe is homogeneous (matter is uniformly spread throughout space) and isotropic (the Universe is the same in all directions) on very large scales. This is not an assumption

The Hubble Law

• Edwin Hubble in 1929 discovered a direct relationship between the velocity of a galaxy (redshift) and distance. It is expressed as
  
  $$v=Hd$$
  
  
  where $v$ is the galaxy velocity (measured from the Doppler shift of galaxy spectral lines), $d$ is the galaxy distance, and $H$ is today called the Hubble constant. This Law implies that the Universe is not static but is expanding and probably evolving in time.
• Hubble's conception of the Universe is that all galaxies are rushing away from us and each other (this is why we see only redshifts for galaxies).
• In Einstein's view, the Hubble Law is the result of the expansion of space-time. It is an expansion of the geometry of the Universe and not simple recession of galaxies. The Universe is like a raisin bread that is rising in the oven, where the raisins are galaxies.

The Steady State Model

• Throughout the 1950's and early 1960's, the most popular model of the Universe was the Steady State model.
• The Steady State model assumes the Perfect Cosmological Principle in which the Universe is the same at all times and in all locations. Thus, the Universe had no beginning and will have no end.
• For this to be true in light of the Hubble expansion, there must be continuous creation of matter to keep the average density of the Universe constant. This requires about 1 hydrogen atom per liter every billion years to ``pop'' into existence.

The Big Bang Model

• An alternative model first proposed in the late 1940's is today called the Big Bang. It requires the Universe to have a definite beginning about 15 billion yrs ago. At that time, all matter, photons, and space was compressed into an infinitesimally small region.
• This small volume suddenly erupted, creating an expanding space-time that we see today. In this model, there is no center or edge of the Universe. The Universe began everywhere at the same time.
• In the earliest epochs, the Universe was very hot. It resembled an extremely hot blackbody. The model predicts that as the Universe expands, the temperature of this cosmic or primordial background radiation will decrease.
• In 1964, A. Penzias and R. Wilson from Bell Laboratories accidentally discovered this radiation while making very sensitive observations of the sky with a new radio receiver and telescope. More recent measurements by NASA's COBE (Cosmic Background Explorer) satellite has confirmed that the broad spectral shape of this background radiation perfectly matches a blackbody and has a temperature of 2.74 K.
• The background radiation matches well the predictions of the Big Bang. However, it conflicts with the Steady State model because this radiation shows that the Universe has cooled and evolved with time; therefore, it violates the perfect cosmological principle.
• The energy of the Universe was dominated by radiation for the first 100,000 yrs. After this time, the Universe cooled enough to become transparent to radiation. Matter formed into protons and atoms. These eventually combined to produce the larger scale structures previously discussed.

The Inflation Model

• At a very early moment, the Universe had a phase of VERY fast expansion (``inflation''). Energy of the vacuum was the source of the expansion. Once upon a time the vacuum ruled. At the beginning was vacuum.
• Inflation ended with heating the Universe to a very high temperature. That was the beginning of the Big Bang

How Will It All End?

• The future of the Universe depends upon the geometry of space-time which in turn depends upon the total mass and average density within the Universe. Since dark matter appears to be the dominant form of mass in the Universe, its density will determine the future history of the Universe.
• If the density is above a critical value ( $2 \times 10^{-6}$ atoms/cm$^3$), the Universe will curve back upon itself (like a giant sphere in two dimensions). The gravity will be large enough to halt the expansion of the Universe, causing it to eventually re-collapse into a Big Crunch. This is called a Closed Universe.
• If the density is below this critical value, the Universe will continue to expand forever. This is called an Open Universe.
• If the density of the Universe is exactly at the critical value, this is called a Flat Universe because the geometry of space-time is flat. The Universe is effectively infinite.
• Thus, the answer to ``How will the Universe end?'' will be known only after we understand the nature and density of the dark, unseen matter which gravitationally rules the Universe.