Cosmic Dawn
Page 13
What If Dark Matter Is a Myth?
The astrophysicist Martin Rees has pointed out that “we should leave our minds open, or at least ajar, to concepts that now seem on the wilder shores of speculative”. I have presented the conventional arguments in favor of dark matter, most of which I find reasonably convincing. It does no harm, however, to look at unconventional arguments against dark matter and see if they stand up to scrutiny.
The dark matter issue has been with astronomers for over 50 years in the context of galaxies. One of the first discussions concerned the dark matter in the disk of our galaxy close to the Sun. For a very long time that evidence suggested that about half the matter in the disk in the solar neighborhood is dark. It is only quite recently that researchers have argued that there is no dark matter in the solar neighborhood. It is thus possible for age-old evidence to be reevaluated and new conclusions to be reached.
We began this chapter by discussing the motion of the planets, in particular, Uranus and Mercury. The anomalous motions of these two planets were used to predict the existence of two new planets. From Uranus’ motion, the existence of the planet Neptune was predicted. From the anomalous motion of Mercury, the existence of the planet Vulcan was predicted. You have probably heard of Neptune. It is a planet that is about 30 times farther from the Sun than the Earth is. It is about 17 times as massive as the Earth and 4 times bigger. I do not imagine that you know many facts about the planet Vulcan since it doesn’t exist. The anomaly in Mercury’s motion we now know is not due to the influence of another planet. The motion of Mercury cannot, in fact, be entirely explained by Newton’s theory of gravity. Einstein’s theory of General Relativity can account for all the known properties of Mercury’s orbit.
What do these planetary considerations have to do with dark matter and cosmology? The point is that we infer the existence of dark matter by applying Newton’s theory of gravitation. As we have seen in the case of the rotation of galaxies, the fact that galaxies have flat rotation curves enables us to infer the existence of dark matter. We believe Newton’s laws are a valid approximation of general relativity on these scales and densities. We should keep in mind that this hypothesis has not been tested. It is in fact possible that we are misguided in applying Newton’s laws on these scales. Some scientists have given thought to the manner in which Newton’s laws would have to be modified to reconcile the rotation speeds of galaxies with the presence of only the luminous matter. These scientists refer to their theory as modified Newtonian gravity. In Newton’s theory, the force of gravity falls off as an inverse square law, with distance. If we modify the inverse square law such that, on very large scales. the falloff is slightly slower than an inverse square law we can do away with dark matter in galaxies. The inverse square law has been tested to very high accuracy in the solar system, so we must modify it only on the scales of tens of thousands of light years.
As a temporary advocate of the case against dark matter, I discuss the rotation of galaxies because these provide the most direct evidence in favor of dark matter. The observations of the speed of motion of clouds of neutral hydrogen using radio telescopes are accepted by all astronomers. The observational evidence is very reliable. The issue comes with interpretation. Anyone arguing against dark matter has to provide a viablet alternative gravitational theory. It boils down, in a sense, to a matter of taste. Do you prefer to believe in the existence of an undetected component of matter, whose origin and nature is unknown and possibly unknowable, or do you prefer to make a slight modification to a well-tested theory of gravitation? Almost all astronomers choose the former option.
As we turn to larger scales, we reach the scales of galaxy clusters. As we have seen, the same problem arises. Individual galaxies that are members of clusters move too quickly. That is to say, the cluster mass that is inferred from the speeds of the galaxies is larger than the sum of the masses of the galaxies making up the clusters. Is there any way we can challenge this line of argument? The argument is based on applying the virial theorem. This theorem is derived on the assumption that the objects being considered are in equilibrium, that is, the objects are in a stable configuration and are unchanging with time. What should an object in equilibrium look like? An elliptical galaxy provides a good description. One has an elongated mass distribution that is denser at its center than on the outskirts, the density falls off smoothly from the center to the edge of the galaxy. Clusters of galaxies are similar in some ways. They are denser at their centers, and the density falls off as one moves away from the cluster center. Many clusters, however, do show features that are not consistent with the idea that clusters are in equilibrium. Many clusters have a clumpy galaxy distribution. The density distribution shows several peaks, not just one peak at the central location. One can thus make a case that clusters are in fact not in equilibrium, but are young structures that are still forming and one cannot therefore naively apply the virial theorem to these objects. The X-ray maps of clusters support this claim. They also show a clumpy mass distribution with evidence of recent collisions and infall of material. A compromise would be to say that there are a few clusters that do look in equilibrium, and one can reliably estimate the masses of these few clusters. In addition, it seems that estimates of cluster masses based on X-ray, galaxy and lensing observations agree. This may or may not be evidence that the mass estimates are reliable.
To conclude there is a small possibility that there is no dark matter. The strongest evidence in favor of dark matter comes from the rotation of spiral galaxies, and no theory has convincingly shown that this interpretation is false. Let us now review the evidence in favor of dark matter one last time, using a new and important concept the ratio of mass to light.
The Ratio of Mass to Light
We can discuss the amount of dark matter to visible matter in, say, a galaxy by comparing the densities of the dark and visible matter component. A common way of restating the problem is to use mass-to-light ratios. This number is commonly listed in terms of the mass and luminosity of the Sun. In these units, which we shall use from now on, the mass to light ratio of the Sun is 1 (in more conventional units it is actually one half. The mass of the Sun is about 2 ×1033 grams and the Sun’s luminosity is 4 ×1033 ergs per second. ). We can calculate the mass-to-light ratios of stars as a function of their mass. A low mass star having a mass ten times smaller than the Sun has a mass to light ratio of 4,000. In other words, a star that has one tenth of the mass of the Sun is 40,000 times less luminous than the Sun! A star ten times as luminous as the Sun has a mass to light ratio 100th that of the Sun. Such a star is 1,000 times more luminous than the Sun. For the mix of stars close to the Sun in our galaxy, we get a mean mass-to-light ratio of about 2. That is to say if we sum the masses of all the stars close to the sun and divide that number by their total luminosities we get in solar units a number roughly equal to 2. Interestingly, the mix of nearby stars is such that most of the mass comes from stars having less than half the mass of the Sun, while most of the light comes from stars having 1.5 times the mass of the Sun.
What are the mass-to-light ratios of galaxies? If we look at the cores of elliptical galaxies, we get a mass-to-light ratio of about 10. For spiral galaxies, the issue is difficult. The spiral galaxies have flat rotation curves as far out from the center as we can measure. We do not know where the edges of the dark matter halos surrounding spiral galaxies lie. Mass-to-light ratios calculated for spiral galaxies range from about 10 to 200. In terms of their contributions to the density of the universe, the visible parts of galaxies contribute . If we include the dark matter components of galaxies, we get at most , it follows that most of the dark matter is distributed between galaxies.
One way to study the matter between galaxies is to study groups and clusters of galaxies, as we have discussed above. By studying the motion of the galaxies in our local group of galaxies, which includes the Andromeda nebula, a large spiral galaxy, we arrive at a mass-to-light ratio of 100 for the local group. For rich
clusters, as we have seen, mass-to-light ratios can also be computed. In the cases of rich clusters containing hundreds of galaxies within a few million light years, the mass-to-light ratio is about 300. As we go to increasingly large objects, we obtain larger and larger mass-to-light ratios. There is more and more dark matter compared to visible matter as we go to larger scales.
We have seen that low-mass stars have mass-to-light ratios that are very high. Why not account for the mass-to-light ratios of 2–300 by choosing a population of stars with suitably low mass? There are two problems here. First, we have to account for the colors of stellar populations. When we look at a galaxy and study its colors, only a certain range of masses is allowed for its stellar population. We cannot arbitrarily decree what masses the stars in a galaxy should have simply to satisfy a mass to light ratio requirement. Second, as we have seen for spiral galaxies, there is a large amount of matter in the outer parts and no visible matter. The halos of spiral galaxies thus cannot be made of stars.
We have presented in this chapter a view of the current situation with regard to dark matter. The key facts are that we live in a universe that will expand forever whose density is dominated by dark energy. The stars that shine in the universe only contribute 1 % of the density of the universe. About one quarter of the density of the universe is comprised of dark matter whose nature is at present unknown. We can speculate about the precise properties of the dark matter that are required for galaxies to form and be distributed in space in the manner that we observe. We have yet to detect such a particle using detectors on Earth but there are hints that we may have done so.
Since the formulation of the dark matter problem in the 1930s we have made enormous strides in this field. We have conclusive evidence for the existence of dark energy. We can calculate the composition and density of the universe to an accuracy of about 1 %. Our models of galaxy formation based on dark matter are providing good fits to the data. All this suggests that we are on the right path to unveiling the formation of the first objects in the universe using the Big Bang theory and structure formation driven by dark matter. Some of these points are summarized in Table 4.1. Table 4.1The composition of the universe
Type
Composition
Main evidence
Amount %
Visible matter
Atoms in stars
Telescopes
1
Baryonic matter
All atoms
WMAPb
4.6
Non-baryonic matter
WIMPSa
WMAP
23
Dark energy
Cosmological constant
SN & WMAPc
72
aWeakly interacting massive particles
bThe NASA satellite Wilkinson Microwave Anisotropy Probe
cSupernova observations used in conjunction with WMAP data
Further Reading
In Search of Dark Matter. K. Freeman and G. McNamara. Springer-Praxis, 2006.
The Extravagant Universe: Exploding Stars, Dark Energy, and the Accelerating Cosmos. R Kirshner, Princeton University Press, 2002.
Rotation Curves of Spiral Galaxies. Y. Sofue and V. Rubin in Annual Review of Astronomy and Astrophysics, Volume 39, Page 137–174, Sep 2001.
Part 2
The Emergence of Galaxies
George RheeAstronomers' UniverseCosmic Dawn2013The Search for the First Stars and Galaxies10.1007/978-1-4614-7813-3_5© Springer Science+Business Media, LLC 2013
5. A Map of the Universe
George Rhee1
(1)Department of Physics & Astronomy, University of Nevada, Las Vegas, Nevada, USA
Abstract
The smallest object detected with a telescope is an asteroid about the size of a beach ball. The largest asteroids, debris left over from the formation of the planets range are a few hundred miles in diameter. Our sun is almost 1 million miles in diameter. Some red giant stars are large enough that one could fit all the planets up to the orbit of Mars inside them. The largest star we know of is so big that if it were located in the center of the solar system its outer envelope would extend past Jupiter. The Milky Way galaxy disk which we inhabit has a diameter of about 100,000 light years. The largest galaxy we know of lies at the center of a cluster of galaxies and has a huge diameter of 5 million light years.
Like the fifteenth century navigators, astronomers today are embarked on voyages of exploration, charting unknown regions. The aim of this adventure is to bring back not gold or spices or silks but something far more valuable: a map of the universe that will tell of its origin, its texture, and its fate.
Robert Kirshner
The smallest object detected with a telescope is an asteroid about the size of a beach ball. The largest asteroids, debris left over from the formation of the planets range are a few hundred miles in diameter. Our sun is almost 1 million miles in diameter. Some red giant stars are large enough that one could fit all the planets up to the orbit of Mars inside them. The largest star we know of is so big that if it were located in the center of the solar system its outer envelope would extend past Jupiter. The Milky Way galaxy disk which we inhabit has a diameter of about 100,000 light years. The largest galaxy we know of lies at the center of a cluster of galaxies and has a huge diameter of 5 million light years.
We can study the universe on such large scales that galaxies themselves appear as dots, just like large cities appear as dots on a globe of the Earth. In the past two decades a large effort has gone into mapping out the structures that are traced by galaxies. The largest known structure in the universe is called the Sloan Great Wall. It was discovered in 2003. The Sloan Great Wall is about 1.4 billion light years in length and is located about 1 billion light years from earth. The structure spans about one quarter of the sky.
How do we discover such gigantic structures? How did they come into existence?
The Large Scale Structure of the Universe
The largest structures in the universe are found by making galaxy maps. We measure the distances to lots of galaxies and plot them on a map. A map of the town you live in will be two dimensional. That is the map can be drawn on a sheet of paper. Our maps of the universe are three dimensional, we use three numbers to specify a galaxy’s location in space. The first two are angular coordinates which specify where in the sky a galaxy is located. We could just say a few degrees to the north of the two bright stars in the big dipper. We achieve greater precision by using two numbers to specify where in the sky a galaxy is located. A third number we use is the redshift. The redshift gives us an estimate of the distance to a galaxy.
The first step in planning a survey is to select the galaxies whose redshifts we are going to measure. To understand the biases in our survey we must select galaxies using quantitative criteria. We cannot measure distances to all the galaxies within a fixed volume of space because some galaxies are too faint. We thus have to select some fraction of the galaxies in the volume of interest. The telescope we use can measure redshifts of galaxies to a brightness limit in a reasonable amount of time. So if we specify the condition that a redshift must be measurable in less than 1 h (for example) that in turn specifies the faintest galaxies that we can survey.
To implement this approach we must first image the sky to construct a catalog of galaxies. From this catalog we select a sample galaxies whose redshifts are to be determined. When a survey is completed astronomers will analyze the results very carefully looking for correlations between say a galaxy’s color and the color of its neighbor. One must be sure that any effect that is found is not a consequence of the method of observing but rather a reflection of a genuine trend found in nature.
Pollsters face similar problems. Let us say that the pollsters take a poll in a city to find out who will be elected mayor in a forthcoming election. The results show that the republican candidate will win by a large majority. When election time comes the democrat wins by a landslide. What went wrong? It turns out the p
ollsters only went to the most expensive neighborhoods to take their poll and thus came away with a biased sample. In the jargon of astronomy there was a strong selection effect in the polling. By polling people in affluent neighborhoods the pollsters biased the outcome of the poll. They did not have a fair sample of the population of the town. This is what astronomers must always ask themselves when analyzing data, what man-made error or measurement error could have produced this result. Pollsters face an even greater problem, the polling results when made public can influence the outcome of the election.
Once a galaxy survey has been carried out, the results are used for statistical studies by astronomers. The simplest measurements we can make are of the clustering properties of galaxies. Are the galaxies distributed randomly in space? Wet already know the answer to that! Does a large structure dominate the survey?
Edwin Hubble’s original studies of galaxies included a few dozen galaxies. The analyses have become more sophisticated as the numbers of galaxies surveyed have increased. By 1976 the redshifts of about 2,700 galaxies were known. Surveys by a team from the Harvard-Smithsonian Center for Astrophysics provided strong evidence for the filamentary nature of the distribution of galaxies (Fig. 5.4). The extended survey included about 15,000 galaxy redshifts. The next step involved two large projects. The 2-degree field Galaxy Redshift Survey was carried out between 1997 and 2002 on the 4 m Anglo-Australian telescope in Australia. The survey obtained redshifts for over 200,000 galaxies located within 1,500 million light years of our galaxy. Located at Apache Point Observatory in New Mexico, the Sloan Digital Sky Survey imaged a quarter of the sky and obtained spectra for about one million objects. These projects and the results they delivered will be discussed in more detail below.