by Jaan Einasto
6.2.4 Cold dark matter
In the early 1980’s difficulties with baryonic dark matter were well known and non-baryonic dark matter was seriously considered. Also difficulties with neutrino based dark matter were known, thus dissipationless particles heavier than neutrinos were suggested by Blumenthal et al. (1982), Bond et al. (1982), and Peebles (1982). Here hypothetical particles like axions, gravitinos or photinos play the role of dark matter.
Primack & Blumenthal (1984) discussed arguments that dark matter is not baryonic, based on the deuterium abundance, and the absence of small-scale fluctuations in the microwave background radiation. The authors suggested the following classification of elementary particles as dark matter candidates: hot, if free streaming erases all but supercluster-scale fluctuations; warm, if free streaming erases fluctuations smaller than galaxies; and cold, if free streaming is unimportant. Hot particles are light (∼100 eV) and remain relativistic until just before recombination. Warm particles are 10-100 times heavier and thus become non-relativistic sooner. Cold dark matter candidates are either very heavy particles that become non-relativistic very early (gravitinos, photinos), or are particles that have almost zero peculiar velocity (axions) (Faber, 1984).
The nature of dark matter can be checked also by numerical simulations of the structure evolution based on various assumptions on the form of the power spectrum of density perturbations for different species of the non-baryonic dark matter, and by comparison of simulations with the observed large-scale distribution of galaxies.
With these simulations the dark matter problem was closely related to the problem of the structure of the Universe on large scales, i.e. the structure of the cosmic web.
Numerical simulations made by the Zeldovich team in the 1970’s were based on the assumption that small-scale density perturbations were damped, due to the interaction of matter and radiation during the radiation dominated era of cosmic history. Such a perturbation spectrum is essentially equivalent to the perturbation spectrum of neutrino-dominated dark matter due to the high speed of neutrinos which smear out small-scale perturbations. As shall be discussed in the next Chapter, the neutrino-dominated model has several difficulties: the absence of the fine structure of the cosmic web, and the late formation of superclusters (Frenk et al., 1983; Melott et al., 1983).
One of the first to simulate the formation of the cosmic web using both neutrino-dominated (Hot Dark Matter) and axion-dominated (Cold Dark Matter) dark matter was Adrian Melott. In summer 1983 Adrian visited Moscow to discuss his models with the Zeldovich team. We were also interested in analysing his models, so we invited him to Tallinn. He came together withAnatoly Klypin and Sergei Shandarin. Our first goal was to compare both models using our connectivity and multiplicity criteria. The first attempt failed, as our computers were too slow to analyse such large datasets as given by models with a resolution 323 particles. Then Enn asked us to pause for a few days, and he will try to elaborate a new program for the analysis which would admit the use of large datasets.
Enn invented a different algorithm to calculate the connectivity of a sample of particles, which was several hundred times faster than the previous one (among us we called the program for its exceptional efficiency WW — Wunderwaffe, to parody Nazi-Germany attempts to create wonder-weapons). So, a few days later we continued our analysis. Results of the analysis showed that the CDM model fits both the connectivity as well as the multiplicity criteria. Thus the CDM model is to be taken seriously. The main body of the paper by Melott et al. (1983) was already written, but not finished, because we did not yet have results of the connectivity and multiplicity tests. In a few days these tests were completed with the new program. The paper was finished and sent to the publisher rapidly. The paper appeared at the end of 1983, just in time. This paper is probably the first one where the advantages of the CDM model were discussed using several quantitative tests.
In the CDM scenario the structure formation starts at an early epoch, and superclusters consist of a network of small galaxy filaments, similar to the observed distribution of galaxies. Presently, the CDM model with some modifications (the cosmological constant or Λ term was added) is the generally accepted model of structure evolution. The properties of the Cold Dark Matter model were analysed in detail in the paper by Blumenthal et al. (1984).
In 1988 Joel Primack visited Tartu Observatory, and we discussed among other topics the formation of the CDM concept. He told me the story of the Blumen-thal et al. (1984) paper (another description of the formation of the CDM concept is given in the interview by Sandy Faber to the American Institute of Physics). Sandy and Joel met during the Vatican Study Week in 1981. Joel is a theoretical physicist while Sandy is an exceptionally talented observer with good theoretical background. So they started to think about how to explain the formation of galaxies and the structure of the Universe from tiny fluctuations of the primordial hot gas. Step-by-step they understood that in order to explain the smallness of CMB fluctuations it is needed to assume that dark matter particles must be not only non-baryonic, but heavier than neutrinos, which allows an earlier start to the growth of density fluctuations. The terms Hot, Warm and Cold Dark Matter were suggested by Joel. The Blumenthal et al. paper is written very clearly. With the acceptance of the CDM model the modern period of the study of dark matter begins.
6.2.5 Dark matter in dwarf galaxies
The importance of the possible presence of dark matter in dwarf galaxies was clear already in the late 1970’s. In those years Vera Rubin measured rotation curves of bright galaxies. I wrote a letter to Vera asking whether it would be possible to measure rotation curves also for dwarf galaxies. We met during the IAU General Assembly in 1997 and discussed the issue. She remembered my letter and answered that it was very difficult to measure rotation curves of dwarf galaxies using the equipment she had.
Dwarf spiral and irregular galaxies contain hydrogen gas, and using radio observations of the 21-cm line it is possible to derive rotation curves for faint galaxies. Actually the Bosma (1978) thesis contains rotation data for a number of dwarf galaxies with flat rotation curves at the level between 50 and 150 km/s. Thus his data strongly suggest the presence of dark matter in dwarf galaxies.
Faber & Lin (1983) calculated masses and mass-to-luminosity ratios for dwarf spheroidal satellites of our Galaxy using the tidal limit theory. The mean mass-to-luminosity ratios are about one order of magnitude larger than those of globular clusters. Thus dwarf spheroidal galaxies contain large amounts of non-luminous matter and resemble in this regard bigger galaxies. In contrast, globular clusters of similar luminosity have low M/L-ratios and contain no dark matter.
Lin & Faber (1983) discussed the implications of non-luminous matter in dwarf spheroidal galaxies. They showed that phase-space constraints in dwarf galaxies sets a lower limit of several hundred eV on particle mass, if the dark matter consists of noninteracting fermions. This limit rules out neutrinos as dark matter particles.
6.2.6 Missing satellite problem and warm dark matter
As the power of computers improved larger and more detailed simulations were performed. This allowed the study of the evolution of fine structure in dark matter halos and their substructure represented by subhalos. The best possibility to compare results of these calculations with observations are satellites of nearby galaxies, especially satellites of our own Galaxy. A detailed comparison of the inner structure of halos with the structure and abundance of satellites of our Galaxy was made by Klypin et al. (1999). The authors find that the ΛCDM model predicts that there should be a remarkably large number of DM satellites with circular velocities Vcirc ≈ 10 − 20 km s−1 orbiting our galaxy, approximately a factor of 5 more than the number of satellites actually observed in the vicinity of the Milky Way or Andromeda galaxy. Thus these calculations raised the question: Where are the missing satellites?
This result may be explained by dissipative processes such as gas cooling, supernovae explosions, star formation and other processes
that decouple the dynamical evolution of the baryons from that of dark matter (Parry et al., 2012).
Springel et al. (2008a) and Navarro et al. (2010) performed a detailed numerical study of the distribution of mass and velocity dispersion of DM halos in the framework of the Aquarius Project. The Aquarius Project addresses the internal structure of halos by studying the highly non-linear structure of Galaxy-sized CDM halos in detail. The authors were particularly interested in the inner regions of these halos and of their substructures, where the density contrast exceeds 106, and the astro-physical consequences of the nature of dark matter may be most clearly apparent. In the highest resolution simulation the number of particles within a radius of 50 kpc was about 1.5 billion. The authors find that the mass profiles of halos are best represented by the Einasto profile (3.1). The shape parameter N varies slightly from halo to halo.
One possible way to solve the missing satellite problem is to assume that dark matter is not cold but warm. Warm dark matter particle mass is ∼1 keV, whereas the particle mass of cold dark matter is ∼1 GeV. In this case the power spectrum of density fluctuations is truncated. Warm dark matter (WDM) particles decouple from the other particles in the early Universe with relativistic velocities and become nonrelativistic when about a Galactic mass is within the horizon. This possibility was investigated by Polisensky & Ricotti (2011), Lovell et al. (2012) and a number of other authors.
Lovell et al. (2012) resimulated Aquarius N-body halos with the power spectrum suppressed at small scales, as expected in the WDM case, using a resolution much higher than in previous studies. The authors find that WDM halos form later and are less concentrated than CDM halos. They conclude that WDM is one possible explanation for the observed kinematics of the satellites, and the relatively small number of dwarf satellites.
6.2.7 Searches for dark matter particles
As discussed above, in the early 1980’s it was clear that dark matter must be non-baryonic. The first natural candidate for DM particles was the massive neutrino. However, massive neutrinos (Hot Dark Matter) cannot form the dominating population of DM particles, since the large-scale-structure of the cosmic web would be in this case completely different from the observed structure. For this reason hypothetical weakly interacting massive particles were suggested, which form Cold Dark Matter. The CDM model satisfies most known astronomical restrictions for the dark matter.
Until recently it was thought that DM particles form a fully collisionless medium. However, it is natural to assume that in the most realistic cases, where the DM comprises some sort of elementary particle, those particles may have other, non-gravitational couplings to the rest of the matter. If this is the case, the phenomenology of DM could in principle be much richer. Indeed, there has been a lot of recent activity trying to detect DM particles in high precision nuclear recoil experiments.
Results from neutrino oscillation experiments require at least one of the neutrinos to have a mass not less than ∼0.05 eV (e.g. Dolgov (2002)). This immediately implies that the corresponding density parameter Ωv 0.001, i.e. approaching the density parameter of the baryons visible in the form of stars! Although neutrinos cannot form the dominant component of DM, due to reasons discussed above, it shows that the general idea of the existence of dark matter in Nature is surely not fiction.
Springel et al. (2008b) studied the implications for the detectability of dark matter annihilation within the Milky Way’s dark matter halo. Such detections could be indirect hints for the existence of the DM particles. Particularly interesting is the cosmic ray positron anomaly as revealed by the measurements of the PAMELA and HESS experiments. This anomaly could be an indirect indication for the existence of an annihilating or decaying DM particle with a mass at the TeV scale.
Our cosmology team has started collaboration with the high-energy physics team lead by Martti Raidal. I met Martti during my visit to Fermilab at 2000, and asked him whether he is interested in coming back to Estonia. He worked many years in leading high-energy physics centers, most notably at CERN. Now he is back and has created a very strong team of young physicists in Tallinn in the National Institute of Chemical Physics and Biophysics. Presently we have a joint Center of Excellence “Dark Matter, Astroparticle Physics and Cosmology” together with the Raidal team, who has access to CERN experiments, and represents the particle physics aspect of the problem. Our team adds knowledge in cosmology. We have published a number of joint studies, among them by Hütsi et al. (2009, 2010,2011), Tempel et al. (2012b), Tempel et al. (2012a), and Hektor et al. (2013).
The story of the birth of the last papers is interesting.
One of the recently analysed datasets of interest to investigate possible effects of dark matter comes from the Fermi Gamma-ray Space Telescope, launched on June 11, 2008. Its Large Area Telescope (LAT) can detect gamma rays in an energy interval from about 20 MeV to 300 GeV. Such gamma rays are emitted only in the most extreme conditions, by particles moving at a speed close to the speed of light. If the existing cosmological dark matter is a thermal relic consisting of weakly interacting massive particles, DM annihilations into standard model (SM) particles or gamma-rays should provide evidence of DM particle annilihilations. In this scenario the first emerging signal of DM annihilations is expected to appear either from Galactic centre or from other nearby DM- dominated objects.
Indeed, recently Weniger (2012) claimed that there is 4.5σ evidence of a monochromatic gamma-ray line from the Galaxy centre with an energy E = 130 GeV present in the Fermi Large Area Telescope data. Christoph Weniger is a postdoc at the Max-Planck-Institut für Physik in Munich, a previously unknown young scientist. He published in arXiv his first papers on this subject on March 6 and April 12, 2012. An overview of Fermi LAT’s search for signatures from dark matter annihilations was given by Bringmann et al. (2012), received by the publisher on March 26, 2012, and was sent immediately to arXiv. However, the physics community noticed the work only after Weniger gave a seminar talk at CERN on April 25. Martti Raidal and his collaborator Andi Hektor participated in the seminar. Next day they contacted Elmo Tempel via Skype and discussed if we can add something to the solution of the problem. Martti and Andi had no previous experience in cosmology, and Elmo in particle physics. Within about a week they found a way how to reduce Fermi data in a better way, and sent their analysis to arXiv on May 4 (Tempel et al., 2012b).
Initially the astroparticle community was rather sceptical about these results. Folks did not take the announcements seriously until Su & Finkbeiner (2012b) confirmed the detection; their paper was published on arXiv on June 7. One of the authors of the last paper is Douglas Finkbeiner, a recognised authority on the subject, working in the Harvard Center for Astrophysics. From now on the problem was taken seriously. Soon Su & Finkbeiner (2012a) detected that actually there is a double line spectrum with peaks at energies at 111 and 129 GeV in the Galactic center. This detected gamma ray signal can be explained by dark matter direct two-body annihilation into photons. Figure 6.4 shows the observed 110 and 130 GeV excess in Fermi LAT data.
Fig. 6.4 Gamma-ray spectra for 6° regions around the 18 galaxy clusters as functions of photon energy (bold solid curve). The bold dashed line shows a fit to the background together with its 95% error band. The light dashed curve shows the reduced signal from the Galactic center for comparison (Hektor et al., 2013).
The 110 GeV and 130 GeV peak features are being searched for from other nearby dark matter dominated objects. Both peaks are visible from the stacked signal of 18 nearby galaxy clusters (Hektor et al., 2013). This paper was initially sent to “Nature”, but was rejected since one referee suggested that before we can claim this result, confirmation from other experiments is needed. So the paper was sent to “ApJ Letters”, where it was accepted immediately.
The double peak-like excess can be interpreted as a signal of DM annihilations into two channels with monochromatic final-state photons. The signal from galaxy clusters is boosted due to galaxy cluster subhalos. Since the signals from
the Galaxy centre and from nearby galaxy clusters show exactly the same double peak structure, the signal must come from the same physics (Tempel et al., 2012a), showing very strong indication of a particle physics origin (Su & Finkbeiner, 2012b). Tempel et al. (2012a) concluded: “The presence of double peak is a generic prediction of Dark Matter annihilation pattern in gauge theories, corresponding to γγ and γZ final states. Thus the two seemingly unrelated gamma-ray spectra, from the Galactic centre and from the galaxy clusters, favour the particle physics origin of the excess over any astrophysics origin”.
This discovery has created an avalanche of studies. Almost all possible dark matter models were tested. Elmo had a talk on this topic in our astronomy seminar on January 16, 2013. Up to now 129 papers have been written on the subject, while the total number of authors and coauthors is 132. The papers by Tempel et al. (2012a,b) and Hektor et al. (2013) have over 100 citations combined. If these claims are true, this could be a strong evidence that DM is of particle physics origin, representing a breakthrough both in cosmology and in particle physics.
6.3 Alternatives to dark matter
The presence of large amounts of matter of unknown origin has given rise to speculations on the validity of the Newton’s law of gravity at large distances. One such attempt is Modified Newtonian Dynamics (MOND), suggested by Milgrom & Bekenstein (1987). Indeed, MOND is able to explain a number of observational data without assuming the presence of some hidden matter. There exist also a large number of attempts to generalise MOND dynamics, one of them is the Tensor-vector-scalar gravity (TeVeS) model developed by Jacob Bekenstein (2004).
It is fair to say that in comparison to the dark matter paradigm the consequences of various modifications to Newtonian gravity have not been worked out in detail. Thus it still needs to be seen if any of those modified pictures could provide a viable alternative to the dark matter. However, one has to keep in mind that despite us having a good idea of what might make up dark matter, the dark matter paradigm is remarkably simple: one just needs an additional cold collisionless component that interacts only through gravity. Once this component is accepted, a host of apparent problems, starting from galaxy and galaxy cluster scales and extending to the largest scales as probed by the large scale structure and CMB, get solved. So in that respect one might say that there is certainly some degree of elegance in the dark matter picture. On the other hand, taking into account the simplicity of the dark matter paradigm, it is quite hard to believe that any alternatives described above could achieve a similar level of agreement with observational data over such a large range of spatial and temporal scales. Indeed, it seems that for different scales one might need “a different MOND”.