Types Of Dark Matter - Their Function in the Formation of Large-Scale Structures

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Though we dont know the precise nature of the dark matter, according to its various gravitational evidence and our cosmological knowledge, we can assort it based on its possible formation (thermal or non-thermal) or based on their constituents' particles nature or according to the mass of the particles constituting the dark matter .

From Thermal History

We can categorize the dark matter depending on the way it got created (either thermally or non-thermally) in the early Universe. When it comes to the thermal production, cosmic plasma generates dark matter via colliding during a epoch that is dominated by radiation. When it comes to the non-thermal production, other processes like the decaying of some heavy particles or specific symmetry contexts that exclude thermal formation may produce the non-thermal dark matter particles.

Thermal Dark Matter

If the early Universe consisted of the dark matter candidates in equilibrium - both thermal and chemical - , they would have separated from universal plasma when the course of interactions became slower than the rate at which the Universe was expanding and the charged-up density of these particles would have stabilized.

It was proved that the inferred pair obliteration cross-section from the empirical results of dark matter copiousness (vestige density) is within the acceptable range of the weak interaction cross-section. So with this in mind, the case of weakly interacting massive particles or WIMPs as the probable dark matter candidates is causing interestingness in this context. The clashing together of the particles in thermal cosmic plasma can generate the WIMPs thermally , which were hanging around in equilibrium - both chemical and thermal - at an enormously high temperature of the Universe prior to their separation or "freeze-out." . This phenomena occurred in the early Universe when they were generated in pairs of particles and antiparticles. The pairs of particles and antiparticles which were manufactured in this way could annihilate each other via the reverse reaction to create the Standard Model particles. These two processes were going on in equilibrium in the beginning. If we indicate the dark matter particle in the current context as ✗ and its number density \( n_{✗} \) ( \( \bar{n_{✗}} \) for antiparticles) , then in this situation \( n_{✗} - \bar{n_{✗}} = 0 \). For temperature \( T < m_{✗}\) ( \(m_{✗}\) being the mass of ✗ ), we can express the number density of such particles using the Boltzmann distribution function (assuming that the WIMP has no chemical potential) as $$ n_{✗} = { n_{✗} - \bar{n_{✗}} ∼ \left( \cfrac{m_{✗}T}{2π} \right)^\cfrac{3}{2} e^{-m_{✗}/T} } $$ In this situation, the number density declines off as \( e^{-m_{✗}/T} \) . This is because only the tail part of the Boltzmann distribution can give out the required kinetic energy for particle-antiparticle clashing together to manufacture WIMP pairs. When the obliteration rate ( or the rate at which the pairs are produced) decreases below the expansion rate, the number of such particles in a charged up volume becomes invariant (constant). Physicists call this as "freeze out" of the varieties from when they hang over as a relic and the temperature at which this freeze-out happened is called as the "freeze-out temperature" for those particle varities.

An illustration of the development of such a WIMP is given in the below figure. The evolution of \( n_{✗} \) (comoving density) is plotted against temperature 1/T (m/T in fact) in arbitrary units. In the begining, when the temperature is too high, \( n_{✗} \) follows its equilibrium value \( (n_{✗}) \). At this epoch \( (T >m_{✗}), n_{✗} ∼ T^3 \).


Comoving number density variation in the early Universe with x = m/T. A relic's freeze-out happens at various T values based on a species' annihilation cross-section. The parallel lines illustrate the abundance of relics and the abundance following the freeze-out. For various annihilation cross-sections, the relic densities and freeze-out temperatures will vary.

When the temperature decreases \( (m_{✗} > T ) \) , \( n_{✗} \) decreases exponentially as the Boltzmann factor; \( n_{✗} ∼ exp(-m_{✗} / T ) \), since the kinetic energy at the tail of Boltzmann distribution can provide the necessary energy to produce WIMP pairs from particle antiparticle collision. The number density \( n_{✗} \) and the ensuing pace of WIMP formation and annihilation decreased as a result of the Universe's expansion by this point. The generation of WIMP stops when the expansion rate surpasses the annihilation (production) rate, resulting in a constant covolume number density. It occurs at the temperature known as the freeze-out. Following the freeze-out, the relic density or density will rely on the annihilation cross-section. In fact, the relic density \( ω_{✗} ∼ \cfrac{1}{σν}\) , where \( ω_{✗} \) is the density of dark matter normalized to the critical density of the Universe, σ and ν are the annihilation cross-section and relative velocity, respectively. The relic density is in fact the solution of the Boltzmann equation given by $$ \cfrac{dn_{✗}}{dt} = { -3Hn_{✗} - (\langle{σν}\rangle) (n_{✗}^2 - (n_{✗})_{eq}^2 ) } $$ The dilution of dark matter ✗ brought on by the Universe's expansion is denoted by the first term on the RHS of Equation (2). Pair annihilation and pair formation of ✗ are described by the second and third terms on the RHS of Equation (2), respectively.

Non-Thermal Dark Matter

The thermal creation of dark matter that occurred after the thermal microscopic history of the Universe presupposes that
In the case of cold dark matter, ( \( m_{✗} > T \) during the freeze-out or earlier), it is also supposed that there does not exist any other source of such dark matter like the late decays. Considering the maximum annihilation cross-section and the relic density of the thermal relic, the thermal WIMP would have a maximum mass of ∼ a few hundred TeV. As we dont know confidently about the cosmic history before the Big Bang Nucleosynthesis, probably the dark matter particles never reached thermal or chemical equilibrium. Dark matter particles can be created via the process of gravitaional particle creation in which the particles are manufactured because of the expansion of the Universe and they can have a greater mass ( ∼ 10¹³ GeV or higher) than the WIMPs. Superheavy dark matter particles as such are known as WIMPZILLAs. The WIMPZILLAs may be manufactured at the pre-heating stage or during the reheating stage after the inflation. They might also be produced as the universe shifts from an inflationary to a radiation-dominated state. The abundance of such superheavy dark matter particles can be inhibited as a power of the temperature to mass ratio rather than as the Boltzmann factor, as is the case for thermal dark matter.

We can also understand that the non-thermal production of dark matter can occur through the late decays of a scalar field. Standard Model particles will quickly emerge if such decays are caused by renormalizable interactions, unless the coupling is extremely weak. Wino, a supersummetric particle, is a dark matter candidate that can also be produced non-thermally by the decay of long-lived particles. A neutral wino must have a mass of between 2 and 3 TeV in order to be a viable candidate for dark matter, also known as the lightest supersymmetric particle or LSP. However, a non-thermal candidate for dark matter with a lesser wino mass is also feasible for a non-thermal production of wino like these.

Axion is another type of non-thermal dark matter. If there were ever enough thermal axions created, they would have degraded by now because their lifespan is too short. They can also be made without the use of heat. Its foundation is a symmetry known as Peccei Quinn symmetry, which was created to address the challenging CP issue in quantum chromodynamics (QCD). When this symmetry is introduced, a parameter \( \bar{θ} \) that exists in a QCD Lagrangian term becomes zero. This was necessary in order for the neutron dipole moment value to match the experimental bound. The axions had no mass at high temperatures, but at the QCD scale, the axion gains mass when the axion field oscillates around the axion potential minimum. Because of the undamped nature of the oscillation, its energy density is still there today. Typically, the axions have less mass (∼eV).

Based On The Particle Types

Dark matter particles can be classified as either baryonic (in this context, the term "baryonic" refers to all known particles, not just baryons) or non-baryonic.

Baryonic Dark Matter

Dark matter might not be composed of known particles, even though its particle composition has not yet been determined. However, the baryon density in the Universe as determined by the Planck data cannot be explained by the observable Universe. Therefore, in order to explain the Planck results for baryon density, at least some dark matter must be baryonic.

The Big Bang nucleosynthesis which accounts for the priomordial nuclie successfully (for example, ⁴He,¹D,³He and ⁷Li) sets a limit on the baryonic density ω_b of the Universe. However, the latest findings from Planck specified the upper limit for ω_bh²= 002205±000028 where h is the Hubble parameter in the units of 100 Km sec^-1 Mpc^-1. Both measurements are more or less identical in the order. Planck estimations are in the calculated approximation of the density of the luminous matter, ω_v, which comprises dusts, luminous stars, x-ray producing gas in galaxy clusters, and other known astrophysical objects combined together. Thus, even if baryonic dark matter does not have much scope for existence, it's possible that there is invisible baryonic stuff that belongs to this category of baryonic dark matter. The gas in the intergalactic medium (Lyman alpha), drifting stars inside a galaxy cluster, and other objects can contain this type of baryonic dark matter. These stars may have become unnoticeable because they were torn apart from the host galaxy when two galaxies collided. The so-called MACHOs, or gigantic astrophysical halo objects, which have the ability to cause microlensing of a background star may contain baryonic dark matter. Small, compact, dense clouds with masses comparable to that of Jupiter's (about 10^-3 solar masses) may also be potential candidates for baryonic dark matter. They are not even noisy (radio loud) and they don't have any stars to make them bright. Black holes, neutron stars, and white dwarf stars have all been proposed as potential candidates for baryonic dark matter. Primordial black holes and brown dwarfs are other possibilities for baryonic dark matter.

Baryonic Dark Matter

According to the Planck measurements, the universe's dark matter concentration is approximately 26.8%. There isn't a significant baryonic contribution to the dark matter. Therefore, it must be overpoweringly non-baryonic. Since the non-baryonic dark matter particles interact with regular matter extremely little or not at all, it is difficult to find them. Furthermore, the nature of these particles is unknown, therefore no one knows their masses. The Big Bang left behind these non-baryonic dark matter remnants. The density of dark matter relics in the universe may be explained by some of the potential non-baryonic dark matter candidates being bulky and heavy enough.

From Mass And Speed

When the interaction rate of the dark matter particles drops below the universe's expansion rate, the remnant particles known as dark matter candidates detach from the cosmic plasma and their comoving density becomes fixed, or frozen out. When the dark matter separated, its velocity was either relativistic or non-relativistic, depending on the mass of the dark matter particle and the universe's temperature at that time. This has an impact on how dark matter contributes to the development of large-scale structures and galaxy clusters.

Hot Dark Matter

Hot dark matter is what happens when the dark matter travels at relativistic speeds. Its mass is lower than the universe's temperature at a certain point in time. This kind of dark matter was very relativistic during the detaching or freeze-out period because its masses were smaller than its kinetic energy. For hot dark matter, the factor x_f ≲ 3, where x_f = m/T_f (The dark matter particle's mass is represented by m, and its freeze-out temperature is T_f) In general, the hot dark matter candidates have lower masses.

Cold Dark Matter

Conversely, cool dark matter (CDM) is the term used for dark matter types where the dark matter mass m is greater than T which is the universe's temperature at freeze-out. These dark matter particles were non-relativistic at the freeze-out. the factor x_f ≳ 3 for such cold dark matter particles that are non-relativistic. This kind of dark matter is typically composed of heavier particles than the hot variety.

Warm dark matter is another name for dark matter that lies in the middle of the cold and hot dark matter categories. One potential warm dark matter candidate is the sterile neutrino.

Function in the Formation of Structures

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The distribution of galaxies, clusters of galaxies, and other matter in the Universe creates a structure. There are two different methods that are applicable to the structure formation process: the top-down approach and the bottom-up approach. Large structures, like a vast sheet of galaxies, are created by the top-down method, and upon fragmentation, these eventually bring about galaxy clusters, galaxies, dwarf galaxies, etc. This sequence of structure development is influenced by hot dark matter. Because of its extremely fast (relativistic) speed, the hot dark matter eliminated the small-scale differences in matter density. Thus, warm dark matter evens them out. Only scale variations greater than the product of the age and velocity of the universe remain. Galaxies and other objects are created by first creating the large-scale structure and then breaking it apart.

The microscopic mass that makes up the small-scale structure in the bottom-up sequence begins to settle down in the zones of high gravity and modest density fluctuations. Such high gravity zones are produced by the cold dark matter clustering together. Small-scale clustering of cold dark matter becomes possible due to its slower (non-relativistic) velocity and heavier mass. Due to its slower velocity than hot dark matter, cold dark matter does not dilute density fluctuations unlike hot dark matter. The seed for matter clumping is provided by this. As a result, cold dark matter and density fluctuations cause tiny clumps of matter to form, which eventually expand to create small galaxies. Small galaxies gradually develop into larger ones, followed by galaxy clusters, etc., to build large-scale structures.

The galaxy survey of the Universe reveals that galaxies are dispersed throughout the cosmos, creating massive formations that include filaments, voids, and galaxy clusters. Smooth filaments and voids would have been the result of a universe dominated by hot dark matter alone. The intersection of the filaments is where the galaxy clusters are located. However, the structure dominated by cold dark matter would prefer to create sharp clumpy features (galaxy clusters), voids, and weakly connected filaments. However, a scan of the galaxies shows that the large-scale structure of the universe contains both hot and cold dark matter.