The Missing Mass in the Universe – Dark Matter

Introduction

One of the greatest unsolved mysteries facing astronomers today is the unseen matter in the universe or dark matter. With their advanced instruments and space-borne observatories astronomers admit that they can only see a small percentage of the universe’s content. Over the last century numerous examples of dark matter have been inferred and through recent advances we seem poised to finally grasp the true composition of the universe around us.

History and Background

In 1933 Fritz Zwicky concluded that the speed of galaxies within large galaxy clusters could not be explained by the amount of visible matter²⁵. The galaxies he studied were moving so fast that they should be flung out of their clusters if the visible matter was the only source of gravitational attraction. These clusters were obviously not falling apart before his eyes and therefore they must contain a huge amount of dark matter. He concluded that these clusters contained 10 to 100 times more mass than what could be seen emitting radiation²³.

The case for large amounts of dark matter associated with galaxies was further developed in the 1970’s with the analysis of rotation in spiral galaxies (Figure 1). Many studies found that galaxies rotated much faster than they should if only the visible matter was responsible for holding a galaxy together²³. This lead to the conclusion that up to 90% of their mass was dark matter and this significantly changed how astronomers view of the universe.

 An example of a galaxy’s rotation at different distances from the centre is shown in Figure 2. These rotation curves show huge discrepancies with what is expected due to the visible matter within the galaxy. This is evident in the difference between the black and blue curves. Studies of galaxy rotation have shown that in addition to the dominant abundance of dark matter it is also distributed very differently to the visible matter within galaxies⁴.

The rotation curves of typical spiral galaxies are flat over most of their radius and this can be seen in the black curve in Figure 2. This flatness indicates that the dark matter is not concentrated in the disk of the galaxy like the visible matter¹⁸. There are several other pieces of evidence that point towards this unique distribution of dark matter. These include: a wide vertical distribution of stars, the distribution of their velocities and the observation of very thick hydrogen gas in the disks of galaxies, especially at large distances from the centre (hydrogen flaring). These facts and the results of computer modelling indicate that galaxies are encased in a spherical halo of dark matter many times larger than the visible component of the galaxy¹⁸.

Another way we have been able to detect dark matter is via the phenomenon of gravitational lensing (Figure 3). The total mass and its distribution within a galaxy cluster can be determined if we can observe the distorted light from distant background galaxies behind the cluster. These distant galaxies are observed as arcs of light and studies confirm the large amounts of dark matter in clusters determined by the motions of their galaxies. In some cases the mass of these clusters is measured at more than 10 times the visible mass and the haloes of dark matter around its galaxies are found to be 10 to 20 times larger than their visible components¹⁵.

 
The observation of dark matter’s influence on the velocities, rotation and images of galaxies has firmly established the existence of dark matter. This matter is known to clump with ‘ordinary’ matter in haloes around galaxies and is contained within a spherical halo many times larger than their visible component. Within galaxy clusters the dark matter is similarly concentrated around the visible matter in the cluster and can constitute as much as 90% of the cluster’s mass¹⁸.

It is clear that we have learned much of the distribution of dark matter on many scales. The central mystery that now remains is the nature of all this elusive matter that dominates the universe. The search for dark matter has developed into a major field in astrophysics and involves studies ranging from the smallest to the largest scales. The combined efforts of specialists from particle physics to cosmology have developed many theories about the nature of dark matter. We are now in an era where theorists are developing predictions for these theories that can then be tested through observation. 

Dark Matter Candidates

The differences in both visibility and distribution of visible and dark matter naturally lead us to speculate that they are different types of matter. Currently the most popular theory is that dark matter consists of invisible, slow-moving and collisionless particles that exert and feel the force of gravity¹¹. This view is favoured because this cold dark matter (CDM) has been the most successful at predicting current observations. This is strengthened by theories of particle physics which predict such particles should exist. Many other dark matter candidates exist and all have their inherent strengths and weaknesses in explaining observations.

The Missing ‘Normal’ Matter

Logically the first question we ask ourselves is have we detected all of the ‘normal’ matter in the universe? This may not be the case since it was not until the advent of space-borne X-ray observatories that we discovered the presence of large amounts of hot intracluster gas (Figure 4). These clusters have been found to contain more mass in this hot gas than there is in all the stars within its galaxies¹⁸. We can therefore speculate that our cosmic census of ‘normal’ matter may still not be complete and recent studies are indicating that this is the case²⁰.

Modified Newtonian Dynamics (MOND)

A basic assumption in proving the existence of dark matter has been that gravity operates in the same way over large scales as we understand it to here in the solar system. One explanation for dark matter has challenged this assumption and involves modifications to Newton’s laws of motion. This has been successful in explaining many dark matter phenomenon related to the dynamics of galaxies and their clusters. Unfortunately no one has yet been successful in incorporating this with general relativity so it can be applied universally¹⁹.

MOND theories generally propose that gravitational forces become stronger at greater distances. The niche that these have filled is mainly where CDM predictions experience difficulty¹⁹. Despite this and the passionate support this theory enjoys from its proponents there is not enough observable evidence to suggest that MOND could be considered a favoured candidate.

Massive Astrophysical Compact Halo Objects (MACHOs)

A long standing candidate for dark matter is ‘normal’ or baryonic matter in the form of MACHOs. These include a wide variety of objects that can easily remain unobserved. One group of these are the dead remnants of stars including black holes, neutron stars and white dwarfs. Other related objects that are just as elusive include planets and low mass brown dwarf stars. All these objects can remain unobserved because they can give off relatively little radiation. Other factors like the huge distances across our galaxy make them difficult to find or they are obscured by other objects like interstellar dust.

Regardless of the difficulty in observing them in large numbers we are certain that these MACHOs exist. The key uncertainty is not their existence but their abundance and therefore how much of the universe consists of this baryonic matter? Baryonic matter is the matter we see around us and that contains protons and neutrons. These particles are distinguished from others as baryons because each is constructed from three fundamental particles called quarks. Since the majority of the mass of the atom is protons and neutrons this matter is commonly called baryonic matter.

Astronomers have identified the ‘fingerprints’ of baryonic matter in the light from objects throughout the entire observable universe. We have seen previously that this visible matter does not account for several observations. We therefore assume there must be large amounts of this mysterious dark matter. To be sure of this we must determine if the amount of baryonic matter we observe is all there is to be seen.

The formation of elements following the big bang (the birth of the universe) is described by the theories of big bang nucleosynthesis. These theories relate to the formation of matter in the early universe and are able to predict what types of matter were formed and their relative abundances. This is one way that we can assess if there could be enough baryonic matter in the universe to explain the dark matter phenomenon. Our current understanding is that if we have the correct proportion of baryonic matter in the universe the predicted abundances of the elements are in good agreement with observations¹⁵. Although it appears certain that baryonic matter is a significant constituent of the universe current evidence indicates that it is far less abundant than non-baryonic dark matter.

Baryonic matter is a viable candidate if you disregard evidence such as the differing distribution of dark matter or the predictions from the theories of big bang nucleosynthesis. Until we have established the nature of dark matter it would be unwise to totally rule out any possibility. Through an increased understanding of the processes of star formation and stellar evolution astronomers continue to improve their estimates of MACHO numbers. As we also continue to perform large surveys of the heavens to ever increasing distances we will further uncover the truth about the populations that exist within typical galaxies like our own.

One of the most appealing MACHO candidates is black holes. Although it is impossible to directly image a black hole we are confident they exist across a broad range of masses ranging from the mass of a star to millions of times the mass of the Sun. Recent studies have indicated that although there may be as many as 1 billion stellar mass black holes in our galaxy alone they only constitute at most approximately 1% of its mass⁹. Another possibility is primordial black holes (PBHs) which may have formed in large numbers in the very early universe¹⁷. These PBHs would have masses less than a typical asteroid but may be extremely numerous. Searches have been conducted to detect the background radiation from the evaporation of PBHs (via Hawking radiation) but their existence remains theoretical³.

Searches have also been conducted for MACHOs by observing large numbers of stars in clusters and nearby galaxies for long periods of time³. These observations are used to search for gravitational microlensing events. Gravitational microlensing is the periodic brightening of a star due to the concentration of its light in our direction by the gravity of an intervening object. Many of these events have been detected and results indicate there is a large amount of dark matter in the form of MACHOs.

There is large uncertainty in MACHO abundances from microlensing due to the small number of detections. Theoretical abundances of baryonic matter show that MACHOs are not likely to be present in unexpectedly large quantities. These two factors indicate that MACHOs are not likely to be abundant enough to be a dominant component of dark matter¹¹. This conclusion is far from certain and we should therefore not dismiss MACHOs as a viable candidate for dark matter. MACHOs have gone in and out of favour as dark matter candidates and currently popular opinion identifies WIMPs as the preferred candidates.

Weakly Interacting Massive Particles (WIMPs) and axions as CDM

The currently favoured dark matter candidates belong to a subset of the WIMPs classified as CDM. An entire branch of particle physics has emerged with the goal of detecting these particles and one such candidate is the neutralino⁶. This particle is predicted by theories of particle physics involving super symmetry. These theories predict a new massive partner to every known particle¹⁴. New particle accelerators like the Large Hadron Collider (currently under construction) will probe super symmetry and refine the case for the neutralino⁶.

A similarly favoured candidate that is not a WIMP is called an axion. This is a much lighter particle that is thought would behave like CDM. There are efforts currently underway to detect these particles directly through their weak electromagnetic interactions.

If axions and / or neutralinos form the majority of dark matter, galaxies should be full of these almost collisionless particles and they should be passing through everything constantly. Researchers are currently searching for the minute heat, electrical or light signatures from interactions with these particles (Figure 5). Typically the weak interactions with these particles are expected at a rate of less than one event per kilogram per day¹⁸ and detectors are placed underground to interference form cosmic rays. Neutrino detectors also offer a detection method for very rare but postulated annihilations of these WIMPs. These annihilations would produce very high energy neutrinos which may be detectable in current instruments.

From the scale of efforts to detect particulate CDM it is clear it is a favoured candidate. Another line of evidence for this comes from big bang nucleosynthesis models. In addition to dark matter not being baryonic matter this theory also predicts that 20-30% of the universe should be CDM¹⁸. This is in agreement with recent calculations from Cosmic Microwave Background (CMB) observations which indicate that the universe should contain 23% CDM (Figure 6). It is now thought that no single particle will be responsible for most of this dark matter and theories now being developed are investigating mixtures of these particles.

There have been tantalising results in the past that point towards a mixed nature of particulate dark matter. The study of Ikebe et.al. (1996) assumed that X-ray emitting hot gas in the Fornax galaxy cluster traced the distribution of dark matter. Their observations uncovered two distinct densities of hot gas. One was concentrated on the galaxies and another distributed throughout the cluster. One explanation for their results is that two kinds of dark matter are present. These are thought to be cold dark matter (CDM) on the scale of galaxies and hot dark mater (HDM) on the scale of the whole cluster¹².

The hot and cold nature of dark matter refers to the speed at which these particles are typically moving. The currently preferred theory is that dark matter consists mainly of CDM. This consists of invisible, slow-moving and collisionless particles that exert and feel the force of gravity. The significance of the speed of the motion of these particles is that slow moving particles are more able to ‘clump’ in regions on a scale much smaller than galaxies⁶. This property has lead CDM to become a favoured model among most astronomers.

The main evidence that has propelled CDM to its current popularity is that models based on the theories of CDM have been extremely successful in predicting the formation of the large scale structures in the universe. Galaxy formation and evolution are no exception and CDM models have given us our best tool so far to model galaxies from their earliest seeds to their present day forms²².

Before the CDM models most cosmologists believed that at least some galaxies formed through classical or monolithic collapse²². The subsequent predictions of CDM models and their agreement with recent observations are numerous. This is why the hybrid hierarchical model has gained credibility²². This model is indicated as the most successful so far and predicts hierarchical formation and clustering on many scales within the universe.

Our current understanding of galaxy formation and evolution has been shaped by many observations over the last decade. In combination the results of these observations favour a hybrid hierarchical model. This model provides a good explanation of the observed galaxies although the numerical evidence is less certain²². This model is a combination of the classical collapse and merger models and a simplistic outline is shown in Figure 7.

In this hybrid model²², galaxy formation is thought to be seeded by CDM concentrations (or haloes) from the very earliest times in the universe¹. The CMB radiation is the remnant radiation we can observe that was emitted around 300000 years after the birth of the universe (the big bang). The small variations we detect in this radiation across the sky are thought to show that the distribution of matter in the early universe was slightly ‘lumpy’ or clumped. These clumps of matter are thought to have formed the cores of the first protogalaxies (or gas clouds) that would eventually mature into the galaxies we see in the universe today⁷.

The first protogalaxies are thought to have merged to form larger structures⁷. Stars formed in these larger structures and the first population of galaxies as we know them followed. If these newly formed galaxies merged with others over a time when they were still condensing or collapsing they would have produced spheroidal shaped galaxies^8,22. As they condensed further a disk would form leading to spiral galaxies. We see these spirals today with spheroidal bulges at their centres as remnants of their past form (Figure 1). If major mergers only occurred after the time period of collapse then elliptical galaxies form. These spheroidal structures in galaxies contain approximately half the stars in the observable universe and provide a valuable window into galactic evolution¹⁰.

One of the strengths of this model is that it explains the large variation in different types of galaxies that we observe throughout the history of the universe. This is because there is no one time when certain types of galaxies had to form and galaxies can evolve through many forms throughout their history. The success of these models indicates that dark matter cannot be neutrinos (HDM) because these could not have seeded the first galaxies. Some of the most successful simulations however, have involved a mixture of HDM and CDM¹⁵. This is another example indicating the nature of dark matter is not simply a single particle but a mixture.

On scales smaller than that of galaxies the CDM models have encountered significant difficulties¹⁵. On these scales the situation is no longer totally dominated by gravity and is therefore much more complex. These complexities arise through the self-interactions between matter and the interactions between matter and radiation. It is clear that there is much work to be done and unfortunately the uncertainty of dark matters nature is the biggest cause of uncertainty.

These deficiencies of CDM models on small scales are seen as a major drawback. Problems start to arise when considering interactions of galaxies and smaller dwarf galaxies. The distribution of dark matter inferred from observation is also more homogeneous than predicted. In particular, the distribution of dark matter in the centre of galaxies is expected to rise significantly but this does not agree with observations¹⁵. These problems can be lessened if we postulate that there is an unknown interaction in these central regions or our predictions are not as certain as we think.

Overall there is a general discrepancy between predicted central densities and those observed across dark matter haloes of all scales. Proposed properties of particulate dark matter that could account for problems limit the central concentration problem¹⁵. These proposals include: dark matter that strongly self interacts therefore altering its behaviour in dense regions, warm dark matter (WDM) that has moderate energies and therefore would not cluster like CDM because of its internal energy and repulsive CDM that repels over small distances and therefore significantly reducing high density regions. Another mechanism that has been proposed is that there are many more black holes in central regions of galaxies than we think and these would deplete those regions of dark matter.

The picture continues to form that we are far from a concrete answer. The significant number of alternatives indicates that we can look forward to advances in the near future. These advances will be brought about by the systematic elimination of alternatives as we are able to confirm or refute predictions through observation.

Despite the problems on smaller scales CDM models have performed extremely well on larger scales²¹. Measurements of the CMB indicate that the ‘lumpiness’ of the early universe cannot be explained by baryonic matter and radiation alone. Explanations point toward weakly interacting CDM particles as a major constituent of the early universe to help explain the formation of the structure we now observe. This seems to have explained one of the problems that has faced cosmologists for more than a decade. This problem is that the structures in the universe seem to be too mature at times very close to the big bang.

Theorists have indicated that baryonic matter could not produce the fluctuations in density in the early universe required to form significant structures. If baryonic matter was responsible it would have produced much larger variations than those observed in the CMB¹⁵. Baryonic matter and radiation would have remained tightly coupled until they ceased interacting at the time of decoupling. This was the epoch where atomic nuclei bound with electrons for the first time to form atoms. Radiation was then able to move freely for the first time and this radiation is what we observe as the CMB today⁴.

The coupling of matter and radiation before decoupling would have prevented matter from clustering until a long time after the big bang and therefore the structures we see today would not have formed so early in the universe. The advantage of CDM is that it would not have coupled with radiation and this would have permitted fluctuations to grow for a long time before matter decoupled from radiation¹⁸. If this was the case, matter would therefore have been able to cluster rapidly after decoupling within the dark matter haloes that were already well formed. This would have allowed the maturity of structure we observe in the early universe to exist.

Predictions from these ideas say that the initial density fluctuations in the CMB should be of a certain size. The Cosmic Microwave Background Explorer (COBE) and Wilkinson Microwave Anisotropy Probe (WMAP) spacecrafts detected fluctuations that were on the scale expected for this to be true^15,16. This gives great confidence to theorists that they are on the right track and has generated an independent argument for the existence of dark matter.

If dark matter has relatively high energy (i.e. if it is HDM) then it is thought that the fine detail from the CMB would have been blurred over time¹⁸. The outcome of this prediction is that CDM is favoured to produce the observed CMB. This therefore further weakens the case for baryons and low-mass particles like neutrinos as dark matter. There have however been some theoretical successes with dark matter having intermediate energy or warm dark matter (WDM)¹⁵. This variant has a low non-zero temperature and solves some problems with predictions from simulations.

In recent years the significant similarities between CDM structure simulations and the observed structure of universe has become clearer²¹. This is due to a number of surveys of the locations and motions of galaxies over a large volume of the universe and advances in computing power. Surveys such as the 2 Degree Field Galaxy Redshift Survey (2DFGRS) and the Sloan Digital Sky Survey (SDSS) will continue to strengthen the link between CDM and the structure of the universe.

The particular success of CDM simulations in agreeing with observations has been in matching the motions and spatial distributions of galaxies and their clusters¹⁵. The evolutionary history that has been constructed using CDM models is summarised in Figure 8. The basic idea is that CDM formed the first dark matter haloes which were smaller than our Milky Way galaxy and much less massive³. These then merged forming a range of sizes for the early structures in the universe and these evolved into the network of galaxy clusters we see today.

There is an obvious qualitative agreement between simulations and observed structures and one study has indicated a quantitative link from the 2DFGRS data. This study compared the variations in the CMB radiation with those in the 2DFGRS galaxy distributions⁵. These have found remarkable agreement on large scales and an independent measure of the correlation between dark matter and the structure of the universe today¹³.

Quantitative agreement between currently observed structures and those present in the CMB has also been simulated. These studies concluded that measurable correlations between the structure of today and at the time of decoupling should exist²¹. This means that theory indicates that the structure of the universe observed in the CMB should be seen reflected in the universe today. If the conclusions of the 2DFGRS team are correct then this quantitative correlation has been observed⁵. This further strengthens our confidence in the role of CDM in the formation and evolution of structure in the universe.

Such is the current confidence of CDM models that galaxies are now commonly thought to lie along regions in the universe concentrated with dark matter. This correlation has been demonstrated in many CDM computer simiulations^2,13. By simulating the distribution of both CDM and galaxies astronomers have then been able to conclude that they evolve together. This strengthens their relationship and leads astronomers to infer this situation also occurs in the universe. The predicted distributions of galaxies in these studies have also been compared to observations and the clustering matched very well².

Figure 9 shows a computer simulation of both CDM (grey) and galaxies (coloured circles). These two structures were found to develop in parallel and reflect currently observed structures^2,13. The regions indicated in the two coloured boxes are very reminiscent of typical galaxy clustering patterns observed today. It is through these models that we are able to glimpse the probable distribution of dark matter that remains so elusive to astronomers.

Apart from the successes of CDM models to reproduce structure they have also been able to explain large scale flows of galaxies¹⁵. Most galaxies have what are called ‘peculiar velocities’. These are typically shared by groups of galaxies in the direction of larger galaxy clusters. The visible matter in the direction of these motions cannot explain these induced motions. CDM matter models however have predicted that these massive ‘flows’ should occur due to large concentrations of dark matter.

Conclusion

It is clear that CDM models have left no stone unturned when it comes to predicting large scale features. In the coming years it will certainly require some quite remarkable evidence to refute our current confidence in the existence and distribution of CDM. There are however many alternatives and their value is that they can provide alternate testable predictions. Testing these predictions through observation will provide further constraints on nature of dark matter. This is evident in the work on simulating structure with CDM which is mainly responsible for CDM’s current popularity.

The advancement of computing power and observational instrumentation has played a large role in developing our current understanding. As these improve further we can look forward to a refinement of this understanding. Of particular interest will be the progress of large scale surveys of the sky. These will enable large samples of data to be studied and test predictions of alternate models. We can only hope that investment in this research continues for the sake of our understanding.

The evidence is clear that dark matter exists. The numerous observations that betray its presence cannot be explained by any other means. Perhaps most compelling is that it is distributed differently to visible matter and therefore is of a different nature. This diminishes the possibility that we are just missing much of the ‘normal’ matter in the universe and several lines of evidence refute this. The task at hand is therefore to determine the true nature of dark matter.

Some of the most profound results in this field have been the verification of predictions by CDM models. The clustering of galaxies observed in the 2DFGRS survey has been shown to agree with the expected clustering of CDM and galaxies from computer modelling. This supports the relationship between CDM and galaxies in the universe and gives us an indication of the distribution of dark matter on the largest scales.

Although no absolute conclusion can be reached at this time it seems that CDM is the most likely candidate. It is surely only a mater of time before we deduce the true nature of dark matter. What we have learned so far is that the universe is laced with a web of unseen matter that binds the galaxies together and guides their evolution. The shift of cosmology from the theoretical and philosophical to the observational and experimental has been profound and it has been this shift that has allowed us to search for answers to mankind’s biggest questions.

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Image Credits

Figure 1. Accessed at and adapted from http://www.aao.gov.au/images/captions/int004.html on 8/4/05.

Figure 2: Accessed at and adapted from http://burro.astr.cwru.edu/JavaLab/RotcurveWeb/back_DM.html on 9/6/05.

Figure 4. Chandra X-ray Observatory: NASA / CXC / UCI / A.Lewis et al. Optical: Pal.Obs. DSS.

Figure 3. Accessed at and adapted from http://www.yale.edu/opa/newsr/05-01-06-01.all.html on 9/6/05.

Figure 5. Accessed at http://www.europhysicsnews.com/full/22/article2/article2.html on 9/6/05.

Figure 6. Accessed at http://rst.gsfc.nasa.gov/Sect20/A9.html on 9/6/05.

Figure 7. Original.

Figure 8. Accessed at map.gsfc.nasa.gov/ m_mm/mr_firststars.html on 8/4/05.

Figure 9. Benson. A.J., Baugh. C.M., Cole. S., Frenk. C.S. & Lacey. C.G. (Monthly Notices of the Royal Astronomical Society, 311, 793, 2000).

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