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Major League PuzzleA
Major League Puzzle
Foreword: Spring Training
Chapter 1: The Playing Field
Chapter 2: The Gamma-Ray Burst Baseball Card
Chapter 3: Watching The Game
Chapter 4: Pre-Game Analysis
Chapter 5: The First Pitch
Chapter 7: Extra Innings Glossary
Imagine your reaction
to the following situation. You've watched avidly all season. Spring training
came and lifted your winter blahs away. Your favorite team, the Cardinals,
got off to a great start in April. By the All-Star break in July they were
4 1/2 games ahead of second place Chicago.
By September, that lead was 12 games. They win the pennant going away. You
wait outside, sometimes in the rain, for three days to buy World Series
tickets. The Cardinals against the Yankees,
a re-match of the 1964 World Series, and you're going to be there. Game
one: a cool crisp night in St. Louis. You're excitement level is barely
containable as you sit down into your seat along the first base side with
a hot dog and a pretzel. The players are announced and the national anthem
is played. Its time for the game to begin. The players take the field. However,
something is terribly wrong. Instead of baseball gloves, the players are
wearing skates, pads, helmets, and brandishing hockey sticks. Hockey is
a great game, but this is the World Series...isn't it?
The initial results of BATSE that were discussed in the previous chapter were just as unexpected. A new type of science, gamma-ray burst astrophysics, had been spurred on by the discovery of this phenomenon in the early 1970's. Scientists labored through the infancy, the spring training, of the science. They had spent much of the past fifteen years collecting evidence, building a case for a Galactic neutron star origin of the bursts. BATSE was to be their "World Series", confirming the widely held theories on the origins of these enigmatic events. However, we have come away from the initial BATSE results not reveling in the confirmation of our ideas, but instead asking "What game are we playing?". The preferred theory for the origin of these strange and colossally energetic objects has been unequivocally invalidated.
Gamma-ray bursts cannot be members of the Galactic disk. After the shock of these results wore off, scientists again began asking questions. Where, then, can these events be if not in the disk of the Galaxy? To answer that question, we need to envision a distribution of objects that appears to be centered on the Earth, but is of finite extent, possessing an edge which is visible to the BATSE detectors.
According to scientists, there are three scenarios which, at least geometrically, can correctly account for both the observation of angular anisotropy and the concurrent spatial inhomogeneity.
Comets are a rather
familiar part of our solar system. The most famous, Halley's Comet, orbits
the Sun once every 76 years, spending most of its time in the far outer
reaches of the solar system. Cometary bodies are thought to populate a region
of the solar system known as the Oort Cloud, named after the astronomer
Jan Oort who first proposed the existence of such a cloud of comets. Several
astronomers have theorized that the Oort Cloud may be the source of gamma-ray
bursts.
The Oort Cloud is centered on the Sun, not the Earth. At first glance, this scenario would seem to immediately violate the angular isotropy observed in the burst distribution, because the Earth is offset from the center of the Oort Cloud by nearly 93,000,000 miles. However, the extent of the Oort Cloud is extremely large compared to the distance between the Earth and the Sun. The cloud of cometary bodies is believed to extend to distances 100,000 times the distance from the Earth to the Sun. The Earth is offset from the center of the cloud, but only by a small amount relative to the extent of the cloud itself. Consequently, it still appears as if the Earth is at the center of this distribution of objects. Consider again standing at the exact center of a large open building like the Astrodome. The building completely surrounds you, and the distance to any exit is roughly the same. Now, if you move your position just a few inches or perhaps a foot, you still have the perception that you are standing in the center of the building, although you actually are slightly offset. The amount of offset from the center, however, is very small compared to the dimensions of the building, so it still appears to you that you are standing in the middle.
The typical distance to a gamma-ray burst in this scenario is 1,000 times larger than the distance from the Earth to the Sun. Among the three scenarios, this is the one with the closest distance scale, and therefore requires the least amount of energy at the source of the gamma-ray burst production. Remember, a gamma-ray burst, like a light bulb, can appear bright either because it is nearby yet relatively weak (low energy output), or because it is farther away but much stronger (high energy output).
Despite the fact that the scenario may satisfy the geometric constraints imposed by the observation of angular isotropy and spatial inhomogeneity, an Oort Cloud explanation for the gamma-ray bursts still has substantial problems.
Comets are cold, rocky, icy bodies inhabiting a region of space where the Sun is merely a bright star in the sky. Gamma-rays, on the other hand, are produced in the hottest, most energetic environments imaginable. It is unclear how exactly one gets gamma-rays in a thermonuclear-like explosion from these cold, icy, and rocky bodies in this remote region of the solar system.
Although it is likely that the comets are spatially inhomogeneous, (i.e. their number density is not constant throughout the solar system) the exact form of spatial inhomogeneity may be incorrect. We have observed that the strong bursts obey the special mathematical relationship in the brightness distribution, indicating that they are distributed with roughly a constant density. As one moves to weaker bursts, there are fewer than expected if this constant density had continued out to these large distances. For the strong nearby bursts to appear homogeneous, the nearby comets would also have to be distributed with a constant density. This is not believed to be the case for comets in the inner regions of the Oort Cloud.
The Oort Cloud scenario does not enjoy widespread acceptance among burst scientists as an explanation for the origin of the gamma-ray bursts. Recently, several scientific papers have been written, showing that the Oort Cloud scenario has such severe problems that it is unlikely to be the true explanation for the bursts. However, the possibility remains that bursts are in the Oort Cloud, although this possibility is generally thought to be small.
The second geometrically viable scenario is one where the gamma-ray bursts occur on or near neutron stars that are distributed not in the Galactic disk, but instead in a huge spherical halo surrounding the entire Milky Way Galaxy. This scenario is particularly pleasing to many astronomers because it helps to partially preserve the nearly fifteen years of work done in exploration of associations between gamma-ray bursts and neutron stars. It simply moves the neutron stars that generate gamma-ray bursts to a different location.
If this scenario is the correct one, the halo around the Galaxy must be enormous. Remember, out solar system sits nearly 2/3 of the way from the center of the Galaxy to the edge. We are definitely not at the center of this Galactic halo. In order, therefore, to preserve the apparent angular isotropy, the size of the halo must be made extremely large so that the offset of the solar system from the Galactic center is very small compared to the size of the halo itself. The argument is identical to that presented in the Oort Cloud case, however it is now deployed on a much larger distance-scale involving the Galaxy instead of the solar system.
The typical burst distance in this scenario is approximately 15-20 times the distance to the Galactic center. Because we are moving the bursts farther away, we need to have a larger energy reservoir to maintain their apparent brightness.
Like the Oort Cloud scenario, this particular explanation for the distribution of the gamma-ray bursts is not without problems. For example, the size of the halo that is required to meet observational data is larger than any previously observed component of the Galaxy. There is no prior or corroborating evidence that a halo this large even exists. Furthermore, if such a large corona does exist, the gravitational forces of the Galaxy should squash it in such a manner that it is no longer spherical. A non-spherical corona would most likely provide an angular distribution of burst sources that was not isotropic, contradictingthe observational evidence of BATSE.
If our Galaxy does have a large, spherical corona of gamma-ray burst sources, other galaxies should also. The current size of the Galactic corona required to meet the observations of BATSE is so large that there should be substantial overlap with the burst coronae of the Magellanic Clouds (our satellite galaxies) and with the corona of M31 (our nearest spiral galaxy neighbor). In the event of overlap between the coronae of our Galaxy and that of other galaxies, we should be detecting bursts from these other galactic coronae. This detection would show up as a concentration of burst positions around the direction to these other galaxies. We have already noted, however, that there is no observed clustering in the positions of the gamma-ray bursts. If BATSE is allowed to operate for several more years, enough bursts might be collected to rule out many models utilizing this scenario. With a few thousand bursts in hand, and if the bursts are distributed in a suitable large galactic corona, some predictions indicate that the corona from M31 must be observed. If M31's corona is not observed in such a large sample of events, many of these coronal models can be ruled out.
The third scenario that astronomers are currently investigating is the possibility that gamma-ray bursts are cosmological, originating from the far-reaches of the universe. The typical distance to a gamma-ray burst in this scenario would greatly exceed the distance to the center of our own Virgo Cluster of galaxies. This huge distance would require that gamma-ray bursts be one of the most energetic objects in the known universe. Just think how bright a light bulb or other emission must be so that you can see it from a distance of several hundred million light years. For this scenario, the energy output of the typical gamma-ray burst in just a few seconds would exceed the energy production of the Sun over its entire normal lifetime. We truly would be dealing with an exotic object.
The observed angular isotropy in this scenario is a consequence of the universe looking the same in all directions, rather than contriving a distribution which is large compared to the offset of the Earth from its center. The observed spatial inhomogeneity is caused not by a change in the density of objects, but instead by effects related to the expansion of the universe. Since the early part of this century, it has been known that nearly every galaxy outside of our own group appears to be moving away from us, with farther galaxies appearing to recede faster than nearby objects. This observed expansion is one of the factors which leads most astronomers to believe that the universe originated in a colossal explosion called the "Big-Bang". These cosmological effects related to the expansion of the universe are only noticeable, however, if one can observe to a sufficiently large distance. Thus previous gamma-ray burst instrumentation were not capable of detecting these cosmological effects in the burst brightness distribution because of their limited sensitivity.
This scenario, like the previous two, is also not without difficulty. Most of these difficulties involve the detailed physics of how to make such a large gamma-ray burst. How does one store up a solar-lifetime worth of energy in a volume of space that is roughly the size of New Jersey, and then release all of the energy (only in gamma-rays) in just a few seconds? In some cases, a cosmological gamma-ray burst should create other visible effects which are not seen in the data, while other production models require physical parameters and conditions which should suppress a burst instead of create one. Physicists and astronomers are working frantically to show just why and why not such an event can and cannot take place.
Which scenario (if any) is the guilty party? The jury is still out. A recent straw-poll taken at a scientific conference showed that support is roughly split equally between the Galactic Corona scenario and the Cosmological Scenario. Only a handful of the scientists gathered at the meeting believed that the Oort Cloud was responsible for the gamma-ray bursts. There are valid reasons why each of these scenarios cannot possibly be the explanation for the origin of gamma-ray bursts, yet each has features that make it more attractive than the other two.
When BATSE was first launched, we expected that in approximately 6 months we would confirm that gamma-ray bursts are distributed in the Galactic disk and that the bursts were associated with Galactic neutron stars. Four years after launch we found ourselves farther from the answer than ever before. We could not have hoped for a greater scientific challenge. Today, gamma-ray bursts are one of the premier questions to be answered in astrophysics. When all is said and done, the question of the origin of gamma-ray bursts will likely take its place as one of the greatest debates in the history of science. Regardless of the which scenario is the correct answer, BATSE and the Gamma Ray Observatory have again demonstrated the wonder, the excitement, and the challenge of scientific exploration. We have again been vividly reminded that when we push back the frontiers of knowledge, it is the unexpected discoveries that often make the endeavor most worthwhile. We will not know the answer to the origin of the gamma-ray bursts without more data from BATSE and more time to discover important clues leading to the origin of these events. The spacecraft is in excellent working order and should be operational for many years to come: our relief pitchers and our bench players are well rested. The game is going to extra-innings.
SUPPLEMENT VI.In the past 45 years or so, the Oort Cloud has been a subject of active study, although not in the context of an explanation for gamma-ray bursts. We only observe a few of the members of the Oort Cloud as they wander into the inner part of the solar system. It is clear, however, that there must be a reservoir or large supply of cometary bodies in the extreme outer reaches of the solar system that we cannot observe directly. The development (and subsequent demise) of the heliocentric paradigm as a viable candidate distribution for the gamma-ray bursts has been largely due to geometrical considerations, which require a large, roughly spherical distribution of objects that appears to be centered on or near the Earth. The relative proximity of the bursts in this scenario can also be an advantage, as the small distance to the burst sources minimizes the amount of energy required to make to burst. A few ideas concerning the actual production of gamma-ray bursts have been put forward by scientists, for example bursts produced in cometary collisions, but none of these ideas have gained widespread acceptance.
The heliocentric scenario places the bursts much nearer to the Earth than they would be in a Galactic corona or in a cosmological distribution. Consequently, the energy output of the bursts in this scenario is the smallest. A typical energy output for the bursts under the heliocentric paradigm is a modest 10^27 (a "1" with 20 "0"'s after it) ergs. By terrestrial standards, this is a very large amount of energy. Astrophysically speaking, however, the amount is rather small, only one-millionth of the energy output of the sun in one second.
Several investigations into the details of the geometry of a heliocentric distribution of burst sources have been performed by scientists. Their efforts have raised serious doubts as to whether a distribution of burst sources in the Oort Cloud can reproduce the observed angular and brightness distributions of the gamma-ray bursts.
Scientists investigating the Oort Cloud have analyzed the motion of comets in the solar system to determine the cometary number density, the number of comets per unit volume in the solar system. In a standard model of the Oort Cloud, the cometary number density n(r) is given to be
where R is the extent of the Oort Cloud, approximately 100,000 times the distance between the Earth and the Sun. We have noted that the brightness distribution of gamma-ray bursts tells the observer something about the number density of burst sources. It is therefore reasonable to determine if the number density of comets can reproduce a brightness distribution consistent with the BATSE data.
From our analysis of the BATSE brightness distribution, we have determined that the special -3/2 relationship is obeyed for bright bursts, indicating that they have a number density that is approximately constant in nearby space. By looking at Equation (6.1), we observe that the number density of the comets is believed not to be constant for small values of r. It is therefore unlikely that a cometary number density as shown in Equation (6.1) can reproduce the special -3/2 relationship that we observe in the BATSE data.
We also know by observation of the BATSE brightness distribution that the instrument is seeing the "edge" of the gamma-ray burst distribution. This is indicated by the roll-over or deviation from our special -3/2 relationship. If BATSE is seeing far beyond the edge of our own Oort Cloud distribution, it is possible that the instrument is capable of detecting the Oort Cloud distribution around other nearby stars as well, such as Alpha Centauri. Such a detection would manifest itself in the angular distribution as a slight concentration of weak burst sources in the direction of the nearest star. We have already noted that there is no observed concentration in the BATSE data.
The angular distribution generated by a collection of burst sources in a large heliocentric distribution may also be in conflict with the observed data for other reasons. We have noted earlier that the Sun, the planets, and their moons all lie in approximately the same plane, called the Ecliptic. A significant number of comets have orbits that lie in or very near to this preferred plane. If, as we have observed, the comets are distributed preferentially near the plane of the Ecliptic, and bursts are hypothesized to be produced in some way by cometary bodies, one would expect the angular distribution of the bursts to reflect this concentration of sources towards the Ecliptic plane. As we have seen, no such concentration is present in the BATSE data.
A more detailed look at this scenario has shown that there are quite a few inconsistencies between the predictions of a heliocentric distribution of burst sources and the observed BATSE data. Even if a satisfactory explanation for these geometrical features can be generated, one still has the difficulty of physically generating gamma-ray bursts from cold, rocky, and icy comets. For these reasons, scientists as a whole are not considering this possibility as seriously as the two remaining scenarios that we will subsequently discuss.
Galactic coronal models of gamma-ray burst distributions have been the subject of intensive research by scientists. In this scenario, gamma-ray bursts are created on or near the surface of neutron stars that inhabit the large corona surrounding the center of our Galaxy. The distance to the burst sources in this scenario implies that intrinsic burst energies are in the neighborhood of 10^41 (a "1" with 41 "0"'s following it) ergs. In this scenario, bursts release as much gamma-ray energy in just a few seconds as the Sun releases in a few years over all wavelengths.
Astronomers believe that the number density of sources in a Galactic cornona can be expressed as
where the number Rc is called the core-radius, and r is the distance from the Galactic center. This number Rc represents the distance out to which the density of sources is roughly constant. Remember, a constant number density is required for nearby sources to produce the observed -3/2 relationship in the brightness distribution of bursts.
Using the number density provided in Equation (6.2), astronomers have explored the ranges of Rc and various halo sizes that generate both brightness and angular distributions consistent with the BATSE data. It is clear that the core-radius must be at least as large as the offset from the solar system to the Galactic center. Imagine the case where Rc is very small; most of the sources are packed in tightly around the Galactic center. In this case, a strong concentration of bursts would be observed towards the direction of the center of the Galaxy, in conflict with the data collected by BATSE. Therefore, we expect that Rc must be at least 10 kPc or larger. In fact, even for values of 10-20 kPc, a substantial concentration of sources in the direction of the Galactic center, a dipole-moment, should be observed.
As one raises the value of the core-radius, making the distribution larger and larger, it is clear that there will be a correspondingly smaller concentration of sources towards the center of the Galaxy. By increasing the value of Rc, one is effectively reducing the amount of offset between the solar system and the center of the distribution compared to the distribution's overall extent. However, at some level, the concentration of sources towards the Galactic center should be apparent. Remember our example of standing slightly offset from the center of the Astrodome. Even if you are offset by an inch or two, a careful enough measurement could reveal your displacement from the center of the building.
It may be the case, however, that you have too few bursts in the data set to make such a careful measurement and thereby discern the small amount of anisotropy in the angular distribution. This problem is analogous to determining the fairness of a coin flip. If the coin only slightly favors "heads" over "tails", you may need quite a large number of flips before the bias becomes evident. Likewise with gamma-ray bursts, if there is only a slight amount of anisotropy or bias in the angular distribution, you may need to sample the distribution many times (collecting a large number of bursts) before that level of anisotropy can be detected.
Clearly, then, as one detects more and more bursts, the allowable amount of anisotropy that can be present in the distribution yet still go undetected is diminished. This provides an ever-increasing minimum value for the core-radius of the Galactic-halo. If Rc were smaller than the limiting value, the angular distribution would have enough anisotropy that BATSE could detect it given the number of bursts observed.
Currently, this limiting value for Rc is on the order of 100 kPc, or about 12 times the distance between the solar system and the Galactic center. We know of no other Galactic coronal distribution of sources that is this large. This core-radius (not to mention the large part of the corona that must exist outside the core radius) is larger than the distance to the nearest galaxies, the Large and Small Magellanic Clouds. The Milky Way Galactic corona of burst sources must therefore overlap any burst corona that exists around these smaller galaxies. We have noted many times that there is no concentration of burst sources in the direction of these galaxies. One therefore must invoke some reason why the Milky Way has a large Galactic corona, yet these galaxies do not, or why these galaxies do in fact make bursts, yet the distribution appears isotropic from Earth.
With each newly detected burst the angular distribution of gamma-ray bursts is measured with greater precision, the amount of allowable anisotropy in the direction of the Galactic center is diminished, and the minimum size of the corona is increased. By the time that BATSE has collected a few thousand bursts, the limiting size of our own Galactic corona may be large enough that there could be some overlap between it and the corona from M31, our nearby spiral-galaxy neighbor. At this point in time, if no concentration of sources from the direction of M31 is found, many models belonging to the Galactic corona family will have to be reexamined for validity.
Cosmology is one of the most intriguing realms of astrophysics. It attempts to address very fundamental questions involving the nature of the large-scale universe, its past, its present, and its future. Simple everyday concepts such as distance and time take on a whole new and complex meaning when addressed in the context of cosmology. Non-intuitive effects such as "time-dilation", "cosmological red-shift", and "space-time curvature" are simple, natural consequences of the structure of the universe. The prospect that gamma-ray bursts are located at cosmological distances is most intriguing to astronomers. These events would be among the most distant objects known. Bursts in a cosmological scenario are required to release about 10^51 ergs of gamma-ray energy. This is more energy than the Sun will release over its entire lifetime. The physics and energy production mechanisms of such a cataclysmic gamma-ray explosion must truly be quite exotic. Cosmological gamma-ray burst production ideas quite often involve the collisions of neutron stars or the accretion of a neutron star by a black hole. Only in these exotic scenarios can one release the massive amount of energy required to power a gamma-ray burst at such large distances.
These cataclysmic collisions should be taking place in the universe. Theories predict that such events should also release blasts of gravitational radiation, or episodes of gravitational energy. Detectors are currently being constructed to search for the gravitational radiation from these events. If a burst of gravitational radiation were detected at the same time as a gamma-ray burst and from the same direction in space, one might be convinced that gamma-ray bursts are associated with this phenomenon.
The observed angular isotropy of the gamma-ray bursts is an inherent part of this scenario. Unlike the previous two paradigms, where the angular isotropy was generated by a minimal offset between the Earth and the true center of the burst distribution, in a cosmological paradigm, the universe looks the same in all directions. Consequently there are equal numbers of burst sources in every direction.
Early in this century, astronomers Vesto Slipher and Edwin Hubble noted the property that objects at large distances appeared to be moving away from us at high rates of speed. The farther away an object is from us, the faster it appears to be moving away. This rather startling conclusion was derived by examining the spectra of these objects and analyzing their apparent Doppler-shift. Most of us are familiar with standing beside a railroad track as a train passes blowing its whistle. When the train is moving towards us, the whistle has a characteristic pitch or tone. As the train goes by us, eventually moving away from us, the pitch drops to a lower frequency sound. This is an example of a Doppler-shift. Similarly, objects in the universe that emit radiation and move toward us will have their radiation shifted slightly towards higher energies (blue-shifted), and objects that appear to be moving away from us will have their radiation red-shifted to lower energies. The magnitude of the shift depends on the velocity with which the object is moving relative to the observer.
Why does it appear that objects in the universe are rapidly moving away from the Earth? We don't really believe that the Earth inhabits a special place in space from which all other objects are receding. The true situation can be visualized by placing three dots on a balloon and then inflating the balloon. Place yourself on any one of the three dots and observe the motion of the other two relative to your dot. As the balloon is inflated, the other two dots appear to be moving away from your own location. The farther the dots are from you, the faster they appear to be moving away. In fact, this observation is the same regardless of the dot you choose. This simple example illustrates that the fabric of the balloon is itself expanding, not that the dots on its surface are moving away from a given point. Likewise, astronomers believe that the "fabric" of space itself is expanding. Just as the view from one of the dots on the balloon seemed to indicate that all other dots were moving away, our view from our own Galaxy gives the impression that all the other galaxies are receding from us.
This expansion creates many interesting effects on our observations of the universe. The most relevant for our study of gamma-ray bursts is the effect on the observed brightness distribution. We have already discussed in detail the behavior of the brightness distribution in the case where the bursts are uniformly distributed throughout all of observed space. In this special instance, the brightness distribution obeys our special -3/2 law. If, however, bursts are distributed uniformly in a cosmological distribution, the amount by which the entire burst spectrum appears to be red-shifted also affects the brightness of a burst. This additional factor creates a deviation from the special -3/2 law discussed for non-expanding, or Euclidean space, and can help to explain the BATSE observations of a roll-over in the distribution of burst brightnesses.
Burst spectra were discussed previously in the text. We have seen that bursts produce fewer gamma-rays at high energies than at lower energies. Consequently when a spectrum appears red-shifted to lower gamma-ray energies, an observer (such as the BATSE experiment) sees a lower-intensity burst (fewer gamma-rays in a fixed energy range) the more that the burst is red-shifted. More distant bursts therefore appear dim not only because they are far away, but additionally because the lower-intensity portion of the burst's spectrum is red-shifted into the detector's energy range.
Although this effect may seem rather complicated, with only minimal assumptions about the structure of the universe (how the red-shifting is taking place) and an estimate on the maximum distance to an observable gamma-ray burst, one can generate a model distribution of cosmological burst sources that reproduces the observed BATSE brightness distribution with exceptional fidelity.
The turn-over in the gamma-ray burst brightness distribution from the -3/2 law at large brightnesses is simply a consequence of the expanding universe, not related to any actual depletion of sources at large distances. Simultaneously, the observed angular isotropy is a simple consequence of the universe's similar appearance in all directions. The cosmological scenario for gamma-ray bursts is perhaps the easiest to accept on geometric grounds, however much work still needs to be done regarding the physics of gamma-ray burst production in such a scenario.
Foreword: Spring Training
Chapter 1: The Playing Field
Chapter 2: The Gamma-Ray Burst Baseball Card
Chapter 3: Watching The Game
Chapter 4: Pre-Game Analysis
Chapter 5: The First Pitch
Chapter 7: Extra Innings Glossary
return to:
Author: Dr. John M. Horack
Curator: Linda Porter
Responsible Official: Gregory
S. Wilson