Some substantial fraction of the x-ray background is believed to be from un- resolved sources e. Likewise, a substantial fraction of the faint radio sources are radio-bright galaxies at high red shift.
Both the Shane-Wirtanen Lick catalogue of about a million galax- ies with effective depth of about It-1 Mpc see Fig.
Direct evidence for the homogeneity of the distribution of galaxies is more tenuous. Galaxy counts in deep surveys provide supporting evi- dence, but their interpretation is not so straightforward. Moreover, since light does not necessarily trace mass, such surveys only determine the dis- tribution of light i. In particular, if the mass-to-light ratio varies depending on the local environ- ment e. Moreover, it is somewhat disturbing—although perhaps not totally unexpected—that in the largest red shift surveys corn- the frame defined by these distant sources is at rest with respect to the CMBR.
About 2 million galaxies are represented in this image from [16]. As larger red shift surveys are completed the largest survey completed contains only about 9, galaxies , the distribution of light, if not mass, should be better understood. Finally, we mention the evidence for homogeneity from determina- tion of the "peculiar velocity field of the Universe.
In practical terms, it corresponds to a galaxy's velocity after its "expansion velocity" has been subtracted. Note too, that in principle, peculiar velocity measurements have the attractive feature that galaxies serve only as test particles tracing out the gravitational potential and thus provide direct information about the mass distribution rather than just that of the light.
We will discuss the peculiar velocity field in more detail in Chapter 9. At present, all techniques yield results consistent with the range 10 to 20 Gyr. However, the uncertainties, especially the unknown systematics, pre- clude a definitive determination by any of the above techniques.
In princi- ple the present age of the Universe provides a very important test of cos- mological models. We remind the reader of the discrepancy that existed until the 's between the expansion age, 2 Gyr for the then Hubble constant of km sec-1Mpc-1, and the age of the solar system, about 4. That discrepancy led to the birth of the "ageless" steady state cosmology.
For the range of plausible values of Ho h 0. Much work has been carried out to determine the ages of the oldest globular clusters, those which contain very metal-poor, pop II stars. Roughly speaking, the age of the globular cluster is determined by the position of the turn-off point on the main sequence for the red giant phase.
The point where this occurs determines the mass of the stars that are just now en- tering the red giant phase. With recourse to stellar models for such stars one can calculate their ages.
The hypothetical generation of even older stars possibly pre-galactic in origin are referred to as pop III. Sys- tematics inherent to this ingenious and powerful technique stellar mass loss, convection, metallicity effects, uncertainties in the distance scale, in- terstellar reddening, etc. Since the oldest globular clusters likely formed much less than 1 Gyr after the Galaxy formed, and the Galaxy itself formed less than a few Gyr after the bang, these age determinations also serve to date the Universe.
Since Rutherford, cosmologists have used radioactive clocks to date the Universe and many other objects within it. In order to use these clocks one must know the relative abundances of these isotopes or pairs of isotopes today and at the epoch of their production.
All of these isotopes are so-called r-process elements, elements thought to be produced by rapid neutron capture in an early generation of stars. To illustrate this technique, consider the pair U and U. If we knew that all the r-process elements were produced shortly after the Galaxy formed, At would provide an accurate age for the Galaxy—but we don't!
If r-process elements have been formed continuously since the formation of the Galaxy then the age of the Galaxy must be considerably greater. Our simple example illustrates some of the inherent difficulties involved with this technique. Many, much more sophisticated, analyses have been carried out, with derived ages for the Galaxy spanning the range 10 to 20 Gyr. Recently, Winget, et al. The oldest white dwarf stars are of course the coolest and least luminous.
The observed number of white dwarfs drops precipitously below a luminosity of 3 x —presumably due to the finite age of the Galaxy. Based upon this observation and models of white dwarf cooling, these authors conclude that the age of the Universe is This in itself is very reassuring, cf. Moreover, even this somewhat inprecise dating of the Universe provides an important test of cosmological models.
In Chapter 3 we will show that for a matter- dominated model a lower bound to the age of the Universe of 10 Gyr provides an upper bound to no of 6.
Flux measurements of the CMBR ranging from wavelengths of about 70 cm down to wavelengths of less than 0. Such a temperature corresponds to a present photon number density of cm The observed high degree of isotropy not only provides strong evidence for the present level of large-scale isotropy and homogeneity of our Hubble volume, but also provides an important probe of conditions in the Universe at red shifts of order As we will discuss in Chapter 9, the primeval density inhomogeneities necessary to initiate structure formation result in predictable temperature estimated the age of the disk.
If, as some suspect, the disk formed several Gyr after the galaxy, then several Gyr should be added to these estimates for the age of the galaxy. If their result stands it will have profound implications for cosmology.
In fact, the current lim- its to the anisotropy come within factors of 3 to 10 of the predictions of the most attractive scenarios of structure formation: inflation-produced adiabatic density perturbations with hot or cold dark matter, and cosmic string-induced density perturbations with hot or cold dark matter. Spec- tral distortions in the CMBR, if they exist, may provide fossil evidence for the early history of galaxy, and possibly even star, formation.
Nu- clear reactions that took place from t ''. Deuterium and Helium-4 are of par- ticular importance as there are apparently no contemporary astrophysical processes that can account for their observed abundances. While the observed Deuterium abundance is very small, even this small amount is difficult, if not impossible, to account for, as almost all astrophysical pro- cesses destroy the weakly-bound deuteron which burns at the relatively low temperature of about 0.
The comparison of the predicted abundances with "inferred" primor- dial abundances provides a very powerful test of the standard cosmology. The standard cosmology passes this very stringent test with flying colors, and further provides im- portant information about the density of baryons in the Universe. In fact, primordial nucleosynthesis provides the most precise determination of the baryon density. Most significantly, primordial nucleosynthesis implies the fraction of critical density in baryons, am must be less than one: For SZB ,--, 1, Deuterium would be severely underproduced, and both 4He and 7Li would be overproduced.
If 10 is equal to 1, then primordial nucleosyn- thesis provides the strong indication that most of the mass density of the Universe is in a form other than baryons.
We have already men- tioned that it provides an important constraint to the baryon density. Such species would contribute to the en- ergy density of the Universe, and thereby affect the predicted abundances. Chapter 4 is devoted to a detailed discussion of primordial nucleosynthesis.
Measuring the mass density of the Universe is a challenging task! Figuratively speaking, the average n Chapter 4 we will discuss two unconventional scenarios of primordial nucleosyn- thesis which, if correct, would allow 1g — 1. Measuring the mass of a galaxy by dynamical means involves detecting the gravitational effect of the mass in the galaxy in one way or another. Ap- plying this technique to spiral galaxies taking the measured rotational velocity to be v , and taking r to be the radius within which most of the light emitted by the galaxy is emitted, one finds that the fraction of critical density directly associated with light is 1LUM 0.
When astronomers extended this technique to distances beyond the point where the light from a galaxy effectively ceases by observing the rare star, or 21 cm emission from neutral Hydrogen, or HI, gas clouds they found that M r continued to increase. By definition, the additional mass is "dark," i. Further, there is no convincing evidence for a rotation curve that "turns over" i.
There is additional weak evidence that the dark matter is roughly spherically distributed, implying that PDARK cc r Vertical bars indicate the point where the optical light is less than 25 blue mag arc second Based upon this we can conclude: niikL0 Z. This is not a great surprise, as there are a variety of forms that baryons can take that are not "luminous," e. The average mass per galaxy in a cluster can also be determined by dy- namical means. The estimates of Ro based upon this technique yield values of the order 0.
Are projection effects important only projected velocities and positions are measured? Are some of the galaxies misidenti- fied interlopers—thereby raising v2 —rather than cluster members? The amount of matter in the Universe can be measured by a number of other dynamical methods. Virgo infall samples no on a scale of about 20 Mpc.
It is possible to use the infall method on a larger scale, by relating the velocity of the Local Group with respect to the CMBR to the velocity expected from the local cosmic gravitational field that arises due to the inhomogeneous distribution of galaxies.
The local gravitational acceleration can be determined from the distribution of matter out to some appropriate distance see Chapter 9. Using the matter distribution deduced from the IRAS survey, a value of no greater than 0.
Finally, on even larger scales one can use the cosmic virial and energy theorems to relate the kinetic energies of galaxies relative to the Hubble flow to the gravitational potential energies determined by the mass density. Based upon this technique, values for flo approaching unity have also been found [23]. With these dynamical determinations of fto, there is a very important caveat that should be kept in mind: All of the aforementioned determi- nations are only sensitive to material that clusters with bright galaxies.
Galaxies and clusters represent large local enhancements in the density of the Universe, 5p1p On the other hand, the kinematical techniques discussed ear- lier Hubble diagram, galaxy number count test, angle-red shift test, etc.
While the kinematical techniques have thus far proven inconclusive, the dynami- cal methods strongly indicate that the material which clusters with bright galaxies on scales less than about 10 to 30 Mpc contributes CI 1O 0.
The implications for proponents of a flat Universe including both the authors are both obvious and very significant. We will address this important issue, often referred to as "the ft problem," in more detail in Chapter 9. For purposes of illustration we mention here only three of the possibilities for a smooth component of the matter density: i high-velocity particles, such as light 90h2 eV , relic neutrinos, or a sea of undiscovered relativistic particles, which by virtue of their great speeds would not become bound to systems as small as 10 to 30 Mpc; ii a relic cosmological term or vacuum energy which by definition is spatially constant; iii a yet undiscovered or unidentified population of very dim galaxies that are significantly less clustered than bright galaxies.
Summarizing our knowledge of no based upon dynamical methods: i luminous matter contributes only a small fraction of the critical density less than 0.
Such a description for the early Universe, comprised of a soup of elementary particles with short mean free paths, or for the Universe today when viewed on large scales greater than Mpc , is both well-motivated and quite a good approximation. However, on smaller scales such a de- scription glosses over some of the most salient and conspicuous features of the Universe today—the existence of structures including planets, stars, galaxies, clusters of galaxies, superclusters, voids, etc.
The existence of such structures is an important feature of the Universe, and is likely to provide a key to understanding the evolution of the Universe. While an understanding of the origin and evolution of stars and planets is outside the realm of cosmology, the origin and evolution of galaxies and larger structures is definitely not. As emphasized previously, it is not a priori true that light faithfully traces the mass distribution. An ambitious, but more realistic, goal would be to survey a suitably large volume of the Universe, obtaining sky positions, velocities, and dis- tances for a few million galaxies.
The largest galaxy catalogue, the APM Galaxy Survey, consists of some 5 million galaxies and has an effective depth of h-1 Mpc [16]. Only a total of 28, galaxy red shifts are known, and the largest systematic survey, the CfA slices of the Universe survey [25], contains about 9, red shifts.
The hang-up is obtaining red shifts: Using traditional techniques, a single red shift de- termination requires about a half hour of telescope time, and a typical telescope has only about 3, useful hours of observing time per year and more than 10, hours of requests for that time! The present sit- uation then is far from ideal; however it promises to improve dramatically as larger red shift surveys employing automated and multiple object spec- trograph techniques are completed in the next decade.
In fact, a group of astronomers at Chicago and Princeton have begun a decade-long project to obtain red shifts for a million galaxies—a survey of the northern sky out to a red shift of about 0. We began with the above lengthy preface to place the present obser- vational situation into proper perspective. Stated bluntly, we are just beginning to develop a picture of the distribution of galaxies in the Uni- verse.
What then do we know about the distribution of bright galaxies in the Universe and the nature of the large-scale structure?
By suitable integration techniques galaxies with surface brightnesses of only a few percent of the night sky can be detected. If bright galaxies were a factor of 3 larger in linear size they would fade into the night sky. This fact suggests that there could be substantial numbers of low surface brightness galaxies which have escaped detection. This survey is not really a catalogue in that sky positions are not given for individual galaxies, rather just the number of galaxies per 10 arc minute bin on the sky.
The Zwicky catalogue of galaxies and clusters contains some 31, galaxies. Many galaxies are found in binary systems or small groups of galaxies. The Virgo cluster and Coma clusters are familar nearby clusters. The best- known catalogue of rich clusters is the Abell catalogue, where clusters are categorized by their Abell richness class classes that roughly correspond to the number of galaxies within the cluster.
Abell's combined northern and southern catalogues contain some 4, clusters. The fact that clusters seem to cluster more strongly is a surprising result—if light faithfully traced mass this would not be true. This suggests that light may be a "biased" tracer of mass; we will return to this issue in Chapter 9. When considering the quantitative difference between the two correlation functions, one should keep in mind 17Abell compiled his catalogue in the 's using the Palomar all-sky survey plates.
He identified clusters and cluster membership by subjective criteria: Clusters were defined visually by an enhancement in the local density of galaxies. Since the exposure time of the plates varied significantly across the sky, and the density of field stars also varied, selection effects depth of the survey, and the ability to pick out enhancements in the galaxy density are significant.
The Zwicky catalogue of clusters which contains some clusters suffers from similar shortcomings. A recent analysis has attempted to quantify and correct for selection effects inherent in the Abell catalogue [27]. The white band is caused by obscuration due to the disk of the Milky Way. The Antlia, Centaurus, Hydra, and Virgo clusters are indicated. The linear feature across the diagonal is referred to as the supergalactic plane from [26]. Even larger structures seem to exist—superclusters, loosely-bound, non- virialized objects with densities about twice the average density of the Universe, containing several to many rich clusters.
Of order 20 or so such structures have been identified, and attempts have even been made to quantify their clustering properties. Several surveys have found evidence for the existence of voids in the distribution of bright galaxies.
For example, the KOSS survey [29] showed the existence of a void in BoOtes of diameter about 50h-1 Mpc, and the CfA slices of the Universe seem to indicate that voids of size about 20h-1 Mpc in diameter are quite common.
The spectra of many high-red shift QSO's exhibit series of absorption lines with red shifts less than that of the quasar itself. These absorption line systems are classified by the nature of the absorption lines: Lyman-a systems, damped Lyman-a systems, Lyman-limit systems, and metal systems.
The study of QALS's internal densities, number densities, masses, clustering properties, etc. It is clear that an understanding of the present distribution of matter in the Universe is crucial to understanding the origin of structure in the Uni- verse and to testing the detailed scenarios of structure formation that have been developed in recent years.
In turn, this will also test the theories of the very early Universe that give rise to these scenarios of structure forma- tion. Hope- fully, larger red shift surveys will answer pressing questions like: What is the topology of the galaxy distribution and is it "bubbly?
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This is a preview of subscription content. Change institution. Buy article Get time limited or full article access on ReadCube. References 1 Weinberg, S. Google Scholar 2 Misner, C. Google Scholar 3 Landau, L. Article Google Scholar 5 Goldman, T. Google Scholar 8 Schramm, D. Nature , 35 Google Scholar 15 Harvey, J. Article Google Scholar 18 Waldrop, M. Article Google Scholar 24 Buffington, A. Google Scholar 27 Turner, M. Article Google Scholar 31 Bond, J.
Google Scholar 45 Guth, A. Google Scholar 49 Dicke, R. Google Scholar 50 Hu, B. B in the press. Article Google Scholar 54 Zee, A. Turner Authors Edward W. Kolb View author publications. View author publications. Rights and permissions Reprints and Permissions. About this article Cite this article Kolb, E.
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