A Major League PuzzleA Major League Puzzle
Foreword: Spring Training
Chapter 2: The Gamma-Ray Burst
Baseball Card Chapter 3: Watching The Game
Chapter 4: Pre-Game Analysis
Chapter 5: The First Pitch
Chapter 6: What Game Are We
Playing? Chapter 7: Extra Innings Glossary
Every game has its playing field. Whether it
is the baseball diamond, the hockey rink, or the football grid-iron,
the field of play is a stage on which events of the game are played
out. In order to understand the game being played, one needs to
have an understanding of the layout of the playing field. Why
are there bases on the infield? Why is there a small hill in the
middle of the infield? What role does the large wall in the outfield
play? What are all the white lines for? As spectators familiar
with the game of baseball, these questions are simple for us to
answer, almost second nature. Part of our understanding of the
game, however, depends on knowing the correct answers to these
questions relating to the field of play. Without this knowledge,
the game appears almost unintelligable.
Like the baseball fan, the astronomer is also a spectator, peering in on the events unfolding in the universe, the largest playing field imaginable. Just as the fans in the ballpark watch the game from their seats, we astronomers watch the celestial game from our seat here on Earth. Our seat, unfortunately, is not the best in the ballpark. Many parts of the field are very difficult to see from our location. As ballpark seating goes, the Earth is somewhere between general admission and the infamous "Bob Uecker" seats in the upper-deck. We have not been given a privileged vantage point to observe the events unfolding on the sky. Most of the action is quite far from our seat. We also do not have the luxury of getting up and moving to a better seat so that we have a better view of the field. We are forced to watch the game from our rather unfortunate vantage point. Before we can begin to understand gamma-ray bursts, as well as other events occurring in the sky, we need to know a little about the playing field and how we observe it.
We begin with our nearby environs. Our seat
is on one of the nine known planets
orbiting the Sun. This collection of planets, their various moons,
the asteroids, comets, and the Sun is known as the solar system.
There are two planets closer to the Sun than the Earth; Mercury
and Venus. Six are farther away; Mars, Jupiter, Saturn, Uranus,
Neptune, and Pluto. Despite their large distances from Earth,
we know quite a bit about our fellow planets. With the exception
of Pluto, each of the planets has been visited by at least once
by scientific probes from Earth. The Earth is located nearly 93,000,000
miles from the Sun, which is located at the center of the solar
system. To put this distance in perspective, at a typical freeway
speed of 65 miles per hour, it would take us about 163 years (not
counting stops at the rest-area) to drive to the Sun.
Assuming we made the drive, we would arrive at a destination that is also fairly common, universally speaking. As stars go, the Sun is extraordinarily average. It is average in size, average in composition, and average in temperature. The picture above is an X-ray image of the Sun taken in August 1992 by the Yohkoh satellite. Like most of the stars we observe, the Sun spends its time taking atoms of hydrogen in its interior and combining them into atoms of helium, releasing some energy in the process. We observe some of this released energy as sunlight. The Sun has been doing this for about 5 billion years, and should go on doing it for about another 5 billion years. The Sun, the ultimate source of life-sustaining warmth and energy, is even middle-aged.
Like a member of a rural community, the Sun's
nearest neighbor lives quite far away. The closest star to the
Sun is called Alpha Centauri, or "Alpha-Cen"
for short. This particular star is similar to the Sun in size,
temperature, and age. It, too, is a very average star. Alpha Centauri
is easily visible in the night sky from the southern hemisphere,
and is one of the 100 brightest stars in the sky. It is nearly
25 trillion miles away. Because of the tremendously large distances
involved, astronomers use more convenient distance units such
as light-years. One light-year is simply the distance the can
be traversed if one moves at the speed of light (roughly 186,000
miles per second) for a time period of one-year; approximately
5.8 trillion miles. Alpha Centauri is therefore about 4.3 light-years
away. This is an incredibly large distance. If we were to board
a jet aircraft bound for the nearest star, at a typical speed
of 600 miles per hour, we would arrive at Alpha-Cen in a mere
4.8 million years. This incredibly long flight could show every
movie ever made, and would provide the traveler with the world's
largest case of jet-lag.
The Sun, Alpha-Cen, and their
200 billion or so companion stars, along with all of their associated
comets, asteroids, and planets are all part of a larger structure
called the Milky Way Galaxy. The Galaxy is shaped something
like a pizza or a frisbee with a slight bulge in the middle. When
viewed from the top, the Galaxy looks round, while viewed from
the side, it is thin and flat. The picture above is not of our
own Galaxy, but instead a different spiral galaxy called M100
as seen by the Hubble
Space Telescope (HST). This is pretty much what our own Galaxy
might look like as viewed from the top. Our solar system is located
in a remote part of the Milky Way, about 2/3 of the way out from
the center of the disk, on the inner-edge of a spiral arm.
Roughly every 250 million years or so, the entire Galaxy rotates once about its center, carrying along the solar system and everything else in the spiral arms. On the last trip around the Galactic center, dinosaurs roamed the Earth. The distance between our position here in the Galactic suburbs and the center of the Galaxy, the "downtown" area, is a whopping 162,000,000,000,000,000 miles, about 27,000 light-years. Driving or flying there is obviously out of the question. If we were to travel at a speed of 17,000 miles per hour, roughly the speed of the space-shuttle in Earth orbit, we still would need nearly 1 billion years to reach the center of our own Galaxy.
Our Galaxy is rather modest
when compared to others. We don't have a particularly active nucleus
(or, if you prefer, a lot of activity "downtown") or
enormous jets of material spewing out from the center like some
other galaxies. The Milky Way sits in a neighborhood of galaxies
called the Local Group. The Milky Way has several satellite
galaxies, among them the Large and Small Magellanic Clouds. These
objects are visible to the naked eye in the night sky from the
southern hemisphere. The Magellanic Clouds are located nearly
7 times farther away from the center of our Galaxy than we are.
These are our closest galactic neighbors.
Despite being many times larger than the Magellanic Cloud galaxies, the Milky Way is not the largest galaxy in the Local Group. That honor belongs to another galaxy called Andromeda, a picture of which is located just above. Andromeda (or M31 for short) is the nearest spiral galaxy, similar in shape to the Milky Way. However, it is nearly twice as massive as the Milky Way and is roughly 13 times more distant from the Milky Way than the Magellanic Clouds. M31 is so far away from us that the light we observe from it has traveled for over 2.2 million years at a speed of 186,000 miles per second just to get here. Yet at a distance of 2.2 million light-years, Andromeda is one of our nearest neighbors.
Our neighborhood Local Group of galaxies is
a member of a larger collection of galaxies called the Virgo Cluster,
a collection of nearly 2500 galaxies. Not to diminish our importance
any further, but the center of the Virgo Cluster is roughly 62
million light-years away, 30 times farther than M31. At these
tremendous distances, universally speaking, we are just beginning
to leave our neighborhood. A picture of a cluster of galaxies
known as Abell 2218 is shown above, taken by the Hubble Space
Telescope. Each white knot of light in the photo is not a star,
but a galaxy.
The Virgo Cluster is just one cluster of galaxies in an enormous universe. Many objects are observed hundreds or thousands of times more distant than our own cluster. As we shall see later, it is possible that gamma-ray bursts originate at these or larger distances. It is also possible, however, that the burst sources are just outside our own solar system. The field that the astronomer watches to observe bursts and the other events occurring in the universe is unimaginably large. Our view of the universe truly is from the cheap seats.
Just as every game has a playing field, every
game also has a medium. The football, the hockey puck, and the
baseball are all examples of such a medium. Though rather simple
in its own right, the medium is the entity which interacts with
the players and the field of play during the game. By observing
these interactions, we are informed of the progress of the game
and the outcome of events on the field. For example, if we see
the baseball flying over the left-field wall, we recognize that
a home-run has been hit. If we observe the ball being caught by
a fielder without first contacting the ground, we recognize that
the batter is out. The ball itself accomplished none of these,
however it was the medium through which the outcome of the play
was determined.
The medium of astronomy is electromagnetic radiation, the most common form of which is visible light. Astronomers collect it, count it, analyze it, and split it into its components all in an attempt to learn about the events occurring in the sky. Everything that astronomers have ever learned about the universe has been learned through the study of collected electromagnetic radiation. Like the baseball, radiation can be emitted (thrown), absorbed (caught), or scattered (bounce). This radiation itself does not cause a star to explode, sustain the rotation of a galaxy, or cause the gamma-ray burst, any more than the baseball makes a player safe or out. By watching the interaction of the players and the field with the baseball we learn about the outcome of the game; and by studying the radiation coming from space, we learn about the events occurring in the universe.
A piece of electromagnetic radiation is called a photon. The photon consists of two rapidly oscillating fields, one electric and one magnetic. These fields are oriented perpendicular to each other, and perpendicular to the direction that the photon is traveling. The speed of the photon is the speed of light: 186,000 miles per second.
Electromagnetic radiation comes in a wide-variety of forms. Radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma-rays are all different forms of electromagnetic radiation. What distinguishes each of these types of radiation from each other is their photon energy. The energy of a photon is determined by the frequency at which the electric and magnetic fields oscillate. The higher the frequency, the more energetic the photon. In visible light, our eyes distinguish these frequency or energy differences as color. Red light, which has a more slowly oscillating electric and magnetic field than blue light, is the lowest energy form of visible radiation. Microwaves and radio waves are lower in energy still, however our eyes are not sensitive to this region of the spectrum. Ultraviolet, X-rays, and gamma-rays are all more energetic than blue light. Their fields oscillate at a higher frequency.
Until the advent of space flight, astronomers were primarily forced to observe the universe in only the visible range of the electromagnetic spectrum. Visible light, unlike most of the electromagnetic energy reaching the Earth from space, is able to penetrate the Earth's atmosphere and reach observers on the ground. Most other radiation, with the exception of certain radio wave frequencies and a small amount of sunburn-causing ultraviolet radiation, are filtered out by the Earth's thick atmosphere. Therefore, to observe the sky by collecting other forms of electromagnetic radiation, one must place the detector above the Earth's atmosphere on a spacecraft or high-altitude balloon.
Although much has been learned about our universe through observations in the optical region of the spectrum, the ability to study the heavens in regions other than optical has given us tremendous new insight into the nature of the universe. Consider what might happen if you were forced to listen to an accomplished pianist play a very complex piece, but only using the center eight keys on the piano. The sound would be very different, possibly nothing like the sound one hears when the entire keyboard is used. Space-borne observations in different regions of the electromagnetic spectrum have opened new and exciting windows on the universe, allowing us to listen to the universal song played on all 88 keys. These observations have led to the discovery of phenomena which were not imaginable previously. Whole new research fields have been established and are flourishing because of these new observational capabilities.
The sky appears to be a very different place depending on the form of radiation one chooses to observe. We are very familiar with the sky in visible light. The stars are fixed points of light, reappearing each night in regular patterns or constellations. The great bear, the twins, the southern cross; these constellations appear the same to us over our entire lifetime. The sun, the moon, and planets execute predictable wanderings across the sky. If we are fortunate enough to be in a very dark place, we may observe the gentle, faint arc of the Milky Way, the collection of millions of stars from our own Galaxy splashed across the sky. In visible light, the sky is an extremely ordered place. Only on the rarest of occasions do we observe a new object or a change in the recognizable pattern of stars. Supernova 1987A, the first supernova visible with the naked eye in nearly 500 years, was one example of these extremely rare interlopers in the visible region of the spectrum.
By contrast,
the universe observed in other regions of the spectrum can appear
very different than the one we see in the visible range. As an
example, consider the photograph at left. This is actually two
pictures of a galaxy known as NGC4736. The upper portion of the
picture was taken by the Ultraviolet
Imaging Telescope (UIT) which was flown twice aboard the space-shuttle.
The lower picture is an image of the same galaxy taken in red
light. The difference in the appearence of the object depending
on which wavelength you use is readily apparent.
When observed at the high-energy end of the electromagnetic spectrum, in gamma-rays, the universe is a violent, ever-changing, and unpredictable place. Objects can suddenly appear in places where no object was ever seen before, erupting in a time-span of days to become the brightest source in the sky. Then, weeks or months later, the same source can fade without warning, never to be seen again. Other gamma-ray sources called pulsars can cycle on and off more than 30 times per second, with a regularity far better than most clocks. Some objects flicker in gamma-rays like a Fourth-of-July sparkler, possibly hinting at the presence of a black-hole near the source of emission. Many sources outshine the Sun in the gamma-ray region of the spectrum. Despite its close distance to the Earth, the Sun is a comparatively weak source of gamma-rays. Objects called Soft Gamma Repeaters have been observed to erupt like a popcorn machine, giving off short "pops" of gamma-ray energy, then turn quiet for ten years or more before being observed again. Gamma-ray bursts, violent explosions of gamma-ray energy, release incomprehensible amounts of energy in very short periods of time.
In baseball, power-hitters generate line drives and home runs. The power-hitters of the universe, the most energetic and high-temperature objects and processes, generate gamma-rays. The gamma-rays emitted from these objects carry clues and information regarding the physical nature of their exotic environments. In order to understand the message the high-energy photons are carrying regarding the most violent and energetic processes in the universe, we need to study the sky in gamma-rays and scrutinize the powerful flashes of energy contained in the gamma-ray bursts.
SUPPLEMENT I.More on the Playing FieldIn Chapter 1, we have rather matter-of-factly described the environs of the solar system, the Galaxy, and the local cluster. Although presented in a unified summary, our current picture of how the universe is put together is the result of literally centuries of slow and difficult work. Distance is an extremely difficult quantity to measure reliably in astronomy, and is one of the most important questions regarding gamma-ray bursts. Our current picture of the organizational structure of the solar system, the Galaxy, and the universe is a mosaic of boot-strapped measurements to farther and farther distances, each of which depend critically on the reliability of previous distance measurements to more nearby objects.
In the early 1600's, a major breakthrough in the discovery of the structure of the solar system was made when Johannes Kepler showed that the orbital paths of the planets were ellipses, with the Sun at one of the focal points of the ellipse. He also discovered that in the process of orbiting the Sun, a line connecting the planet and the Sun sweeps out an equal amount of area in an equal amount of time. This is equivalent to saying that planets travel faster during the portion of their orbit that is nearer to the Sun, and more slowly during the times when they execute the portion of their orbit that is more distant from the Sun. Kepler also showed that the square of the orbital period P is proportional to the cube of the semi-major axis a of the orbit,
These three statements are known as Kepler's laws of orbital motion. Later, Isaac Newton showed that these empirical laws obtained by Kepler can be derived from the assumption that the magnitude of the gravitational force F between two objects with masses M1 and M2 obeys an inverse-square relationship to distance r
where G is known as the gravitational constant.
Although P, the amount of time it takes for a body to complete one orbit, can be measured for any object in the sky, the constant of proportionality in Equation (1.1) cannot be determined unless a reliable distance can be measured for some object in the solar system. Thus with Kepler's laws of motion, a reasonably accurate scale model of the solar system can be developed by observing the sky very carefully; however, the scale of the model cannot be determined without a distance measurement.
Original distance measurements for objects in the solar system were extremely crude. Only in the latter portion of this century are we finally able to accurately measure distances to objects in our solar system. For example, the Apollo astronauts left several highly reflective mirrors on the surface of the moon. By bouncing a signal from the Earth off of these reflectors and measuring the time interval between transmission and receipt of the reflected signal, the distance to the moon can be determined to within a few inches.
Once we have determined the scale of the solar system, we are then ready to move on to measure more distant objects. A variety of methods can be used to determine the distance to the nearby stars such as Alpha Centauri. One of the most common methods for measuring the distance to relatively nearby objects is known as parallax.
Parallax is a concept that is familiar to all of us. If you hold out your thumb at arms length and then alternate looking at your thumb with only one eye at a time, you will see your thumb appear to move against the background. When you look at it with only your right eye, your thumb will appear a little to the left of some object in the background. When you use your left eye, your thumb will move a little to the right. This apparent shift in the position of your thumb is known as parallax, and occurs because your left and right eyes view your thumb from slightly different angles.
A similar method is used to measure the distance to nearby stars, as illustrated in the picture above. We know from our model of the solar system that the Earth orbits the Sun with a period P equal to one year. At six-month intervals, therefore, the Earth (the blue dot) is on opposite sides of the Sun. If we observe a given nearby star (the red dot), say in January, and then observe it again in June or July, the star (like your thumb in the previous example) will appear to shift slightly against the background of more distant stars (the three yellow dots). By knowing the diameter of the orbit of the Earth, as determined from measurements of solar system distances (roughly 186 million miles), and measuring the amount of apparent shift in the position of the star in question, a distance to the star can be determined. The above illustration of parallax produced by the Earth's motion around the sun is extremely exaggerated. The amount of parallax shift that stars typically exhibit is so small that only the nearby stars in the Galaxy can be measured, and even these measurements are very difficult to execute.
For more distant stars and for distant galaxies where individual stars cannot be resolved, the measurement of distance requires more indirect methods. With each increase in distance one usually must employ a different (and usually less precise) measurement technique that is based, at least in part, on all of the previous measurements to more nearby objects.
At the farthest reaches of the universe, astronomers have observed that all objects appear to be moving away from us with very high velocities. This observation is one of the factors that supports the notion that the universe originated in a colossal explosion called the "Big-Bang". The apparent recessional velocity v that is observed for a given galaxy, for example, depends on how far away the galaxy is through the relationship
where Ho is a number known as the Hubble Constant. Therefore, if we measure an apparent recessional velocity for a given galaxy, we can, in principle, use Equation (1.3) to determine its distance. However, astronomers do not know the value of the Hubble Constant to an accuracy better than about 50%. Therefore, this technique for determining distance is only accurate to within a factor of about two.
Although Chapter 1 offers a rather tidy view of the layout of the solar system, the Galaxy, and the universe, it is obvious that we are only presenting a rough sketch. The precise determination of the distance to an object is a process that is loaded with uncertainty and depends heavily on the quality of many inherent assumptions. In astronomy, the measurement of distance truly is a challenging and uncertain proposition. We shall see later on that determination of the distance to any one of the ~1500 observed gamma-ray bursts is still not possible, even after more than 25 years of study and observation.
Electromagnetic
RadiationThe motion of a photon is governed by the wave equation
where c is the speed of light (approximately 186,000 miles per second), and nu is the frequency at which the electric and magnetic fields of the photon are oscillating. Frequency is usually measured in units called Hertz (Hz). One Hz represents one complete oscillation in one second. Ten Hz represents ten complete oscillations per second, and so on.
The remaining quantity in the previous equation, lambda, is called the wavelength. It is the distance between successive peaks or valleys in the amplitude of the oscillating electric and magnetic fields, and can be measured in many different units of length such as meters, feet, or even miles. Any form of radiation, whether it is radio waves, visible light, or X-rays, obeys this fundamental equation.
The left-hand side of the equation, c, is a constant. Its value is the same for all forms of electromagnetic radiation, and nothing can travel faster than this value according to Einstein. The energy of a photon, unlike the baseball, is not dependent on how fast it is traveling (since all forms of radiation travel at the same speed), but instead on the frequency (or wavelength) of the photon. This energy can be computed using the equation
where h is a number called Planck's constant. This small number h shows up in quite a few surprising places in physics, and is one of the important fundamental constants of nature. Photon energies, like wavelengths, can be measured in many units. The most common energy units used by astronomers in the gamma-ray region of the spectrum are electron-Volts (eV). It takes 9 electron-Volts to move one electron from the "+" terminal of a 9-Volt battery to the "-" terminal. The electron-Volt is an extremely tiny quantity of energy when contrasted with our everyday experience. For example, a 100 Watt light bulb consumes about 620 billion billion eV of energy every second.
Although the energy associated with an individual photon is small by everyday standards, the typical frequencies of photons are comparatively large. The electric and magnetic fields associated with a photon oscillate extremely rapidly. It is quite illustrative to compare some of the frequencies, wavelengths, and energies of different forms of electromagnetic radiation to see just how large of a dynamic range one can observe.
On your radio dial, a station at 1120am has a transmitter that emits radio waves with a frequency of 1.12 million Hz. Although this number might seem quite large, remember that radio waves are among the lowest-frequency forms of electromagnetic radiation. Given this frequency value, we can use the wave equation to determine the corresponding wavelength of this radiation. With a value of c equal to 186,000 miles per second, we find that the wavelength of this particular radio station is approximately 877 feet.
By contrast, yellow-green visible light oscillates with a frequency of nearly 600 trillion Hz. Because of this large frequency, we observe from the wave equation that its corresponding wavelength is small, nearly 0.0005 millimeters. In this range of the electromagnetic spectrum, astronomers usually characterize the various photons by their wavelength instead of their frequency, using units called Angstroms. One Angstrom is equivalent to one ten-billionth of a meter. In these units, our example here has a wavelength of approximately 5000 Angstroms.
Still higher in frequency (and energy) are the gamma-rays. The electric and magnetic field frequencies of gamma-ray photons oscillate so rapidly that scientists rarely talk about these photons in terms of their frequency. The size of the numbers are simply too large to be easily manipulated in calculations. As an example of how ludicrous it can become, a gamma-ray of moderately low frequency still has field oscillations of 24,000,000,000,000,000,000 Hz. (Who wants to carry around that many zeros?) Instead of using frequency as the quantity characterizing the photon, astronomers use the energy of these photons as descriptors. The particular gamma-ray photon used here as an example has an energy of 100,000 electron-Volts, or 100 keV. Although a small amount of energy by everyday standards, as photons go, this one is quite energetic.
Through these few examples, we get a feeling for just how wide of a range the electromagnetic spectrum offers us. The tremendous difference in energy between the various forms of radiation is the property that makes exploration of the universe in many different regimes so attractive and informative.
With a total of only 88 keys, the piano is capable of producing music written by Chuck Berry as well as Tchaikovsky. Even though "Johnny B. Goode" sounds nothing like "The Nutcracker", the piano music for both of these compositions consists of different combinations of the same 88 keys. If a limited set of 88 different sound frequencies can produce such different pieces of music, imagine the incredible variety, beauty, and information that the can be communicated regarding the universe by using the unbelievably large dynamic range of the entire electromagnetic spectrum. This is the reason for astronomers' attempts to observe the sky in many different regimes such as high-energy gamma-rays, not just in the narrow region of the visible spectrum.
Foreword: Spring Training
Chapter 2: The Gamma-Ray Burst
Baseball Card Chapter 3: Watching The Game
Chapter 4: Pre-Game Analysis
Chapter 5: The First Pitch
Chapter 6: What Game Are We
Playing? Chapter 7: Extra Innings Glossary
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