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Figure 3. The predicted number of dark matter clumps of varying mass for different dark matter models. The x-axis is mass, and the y-axis is number of clumps with mass greater than M.
The heaviest dark matter models red predict many more dark matter clumps, especially at the lowest masses. In this paper they compared heavy 1 GeV dark matter red to light 3.
Source: Figure 1 in the paper. The authors use this information to predict the number of collisions with dark matter clumps of various masses over the lifetime of a stellar stream.
They find that for the lowest mass dark matter particles a typical stream has only a couple collisions.
However, for the heaviest particles the stream would collide with more like 50 clumps. They then simulate this process with the expected number of collisions to see the final density of stars along the stream.
Figure 4 shows the expected density resulting from these simulations. They find that heavy cold dark matter does indeed produce more small gaps.
Interestingly, they also see that a larger number of collisions does not just lead to more gaps, but pushes the stars toward the center of the stream to the right of these plots.
This means that instead of simply looking for individual gaps caused by single collisions, perhaps the best way to study the effect of dark matter clumps is by looking at the variations in density along the entire stream.
Figure 4. Density variations along stellar streams caused by collisions with dark matter clumps. The x-axis shows the length along the stream, and the y-axis shows the ratio between the density of a stream that has collided with dark matter clumps and one that has not.
This means that if there were zero dark matter clumps, the density would be equal to 1. The left panel shows the expected variations for light warm dark matter.
The right panel shows heavy cold dark matter. As with galaxy rotation curves, the obvious way to resolve the discrepancy is to postulate the existence of non-luminous matter.
Galaxy clusters are particularly important for dark matter studies since their masses can be estimated in three independent ways:.
Generally, these three methods are in reasonable agreement that dark matter outweighs visible matter by approximately 5 to 1.
One of the consequences of general relativity is massive objects such as a cluster of galaxies lying between a more distant source such as a quasar and an observer should act as a lens to bend the light from this source.
The more massive an object, the more lensing is observed. Strong lensing is the observed distortion of background galaxies into arcs when their light passes through such a gravitational lens.
It has been observed around many distant clusters including Abell In the dozens of cases where this has been done, the mass-to-light ratios obtained correspond to the dynamical dark matter measurements of clusters.
By analyzing the distribution of multiple image copies, scientists have been able to deduce and map the distribution of dark matter around the MACS J Weak gravitational lensing investigates minute distortions of galaxies, using statistical analyses from vast galaxy surveys.
By examining the apparent shear deformation of the adjacent background galaxies, the mean distribution of dark matter can be characterized.
The mass-to-light ratios correspond to dark matter densities predicted by other large-scale structure measurements. Light follows the curvature of spacetime, resulting in the lensing effect.
Although both dark matter and ordinary matter are matter, they do not behave in the same way. In particular, in the early universe, ordinary matter was ionized and interacted strongly with radiation via Thomson scattering.
Dark matter does not interact directly with radiation, but it does affect the CMB by its gravitational potential mainly on large scales , and by its effects on the density and velocity of ordinary matter.
Ordinary and dark matter perturbations, therefore, evolve differently with time and leave different imprints on the cosmic microwave background CMB.
The cosmic microwave background is very close to a perfect blackbody but contains very small temperature anisotropies of a few parts in , A sky map of anisotropies can be decomposed into an angular power spectrum, which is observed to contain a series of acoustic peaks at near-equal spacing but different heights.
The series of peaks can be predicted for any assumed set of cosmological parameters by modern computer codes such as CMBFast and CAMB, and matching theory to data, therefore, constrains cosmological parameters.
After the discovery of the first acoustic peak by the balloon-borne BOOMERanG experiment in , the power spectrum was precisely observed by WMAP in —, and even more precisely by the Planck spacecraft in — The results support the Lambda-CDM model.
The observed CMB angular power spectrum provides powerful evidence in support of dark matter, as its precise structure is well fitted by the Lambda-CDM model ,  but difficult to reproduce with any competing model such as modified Newtonian dynamics MOND.
Structure formation refers to the period after the Big Bang when density perturbations collapsed to form stars, galaxies, and clusters.
Prior to structure formation, the Friedmann solutions to general relativity describe a homogeneous universe. Later, small anisotropies gradually grew and condensed the homogeneous universe into stars, galaxies and larger structures.
Ordinary matter is affected by radiation, which is the dominant element of the universe at very early times. As a result, its density perturbations are washed out and unable to condense into structure.
Dark matter provides a solution to this problem because it is unaffected by radiation. Therefore, its density perturbations can grow first.
The resulting gravitational potential acts as an attractive potential well for ordinary matter collapsing later, speeding up the structure formation process.
If dark matter does not exist, then the next most likely explanation must be general relativity — the prevailing theory of gravity — is incorrect and should be modified.
The Bullet Cluster, the result of a recent collision of two galaxy clusters, provides a challenge for modified gravity theories because its apparent center of mass is far displaced from the baryonic center of mass.
Type Ia supernovae can be used as standard candles to measure extragalactic distances, which can in turn be used to measure how fast the universe has expanded in the past.
Data indicates the universe is expanding at an accelerating rate, the cause of which is usually ascribed to dark energy.
Baryon acoustic oscillations BAO are fluctuations in the density of the visible baryonic matter normal matter of the universe on large scales.
These are predicted to arise in the Lambda-CDM model due to acoustic oscillations in the photon—baryon fluid of the early universe, and can be observed in the cosmic microwave background angular power spectrum.
BAOs set up a preferred length scale for baryons. This feature was predicted theoretically in the s and then discovered in , in two large galaxy redshift surveys, the Sloan Digital Sky Survey and the 2dF Galaxy Redshift Survey.
Large galaxy redshift surveys may be used to make a three-dimensional map of the galaxy distribution. These maps are slightly distorted because distances are estimated from observed redshifts ; the redshift contains a contribution from the galaxy's so-called peculiar velocity in addition to the dominant Hubble expansion term.
On average, superclusters are expanding more slowly than the cosmic mean due to their gravity, while voids are expanding faster than average.
In a redshift map, galaxies in front of a supercluster have excess radial velocities towards it and have redshifts slightly higher than their distance would imply, while galaxies behind the supercluster have redshifts slightly low for their distance.
This effect causes superclusters to appear squashed in the radial direction, and likewise voids are stretched. Their angular positions are unaffected.
This effect is not detectable for any one structure since the true shape is not known, but can be measured by averaging over many structures.
It was predicted quantitatively by Nick Kaiser in , and first decisively measured in by the 2dF Galaxy Redshift Survey.
In astronomical spectroscopy , the Lyman-alpha forest is the sum of the absorption lines arising from the Lyman-alpha transition of neutral hydrogen in the spectra of distant galaxies and quasars.
Lyman-alpha forest observations can also constrain cosmological models. There are various hypotheses about what dark matter could consist of, as set out in the table below.
Dark matter can refer to any substance which interacts predominantly via gravity with visible matter e. Hence in principle it need not be composed of a new type of fundamental particle but could, at least in part, be made up of standard baryonic matter, such as protons or neutrons.
Baryons protons and neutrons make up ordinary stars and planets. However, baryonic matter also encompasses less common non-primordial black holes , neutron stars , faint old white dwarfs and brown dwarfs , collectively known as massive compact halo objects MACHOs , which can be hard to detect.
Candidates for non-baryonic dark matter are hypothetical particles such as axions , sterile neutrinos , weakly interacting massive particles WIMPs , gravitationally-interacting massive particles GIMPs , supersymmetric particles, or primordial black holes.
Unlike baryonic matter, nonbaryonic matter did not contribute to the formation of the elements in the early universe Big Bang nucleosynthesis  and so its presence is revealed only via its gravitational effects, or weak lensing.
In addition, if the particles of which it is composed are supersymmetric, they can undergo annihilation interactions with themselves, possibly resulting in observable by-products such as gamma rays and neutrinos indirect detection.
If dark matter is composed of weakly-interacting particles, an obvious question is whether it can form objects equivalent to planets , stars , or black holes.
Historically, the answer has been it cannot,   because of two factors:. In — the idea dense dark matter was composed of primordial black holes , made a comeback  following results of gravitational wave measurements which detected the merger of intermediate mass black holes.
It was proposed the intermediate mass black holes causing the detected merger formed in the hot dense early phase of the universe due to denser regions collapsing.
A later survey of about a thousand supernova detected no gravitational lensing events, when about eight would be expected if intermediate mass primordial black holes above a certain mass range accounted for the majority of dark matter.
Tiny black holes are theorized to emit Hawking radiation. However the detected fluxes were too low and did not have the expected energy spectrum suggesting tiny primordial black holes are not widespread enough to account for dark matter.
In , the lack of microlensing effects in the observation of Andromeda suggests tiny black holes do not exist. However, there still exists a largely unconstrained mass range smaller than that can be limited by optical microlensing observations, where primordial black holes may account for all dark matter.
Dark matter can be divided into cold , warm , and hot categories. Primordial density fluctuations smaller than this length get washed out as particles spread from overdense to underdense regions, while larger fluctuations are unaffected; therefore this length sets a minimum scale for later structure formation.
The categories are set with respect to the size of a protogalaxy an object that later evolves into a dwarf galaxy : Dark matter particles are classified as cold, warm, or hot according to their FSL; much smaller cold , similar to warm , or much larger hot than a protogalaxy.
Cold dark matter leads to a bottom-up formation of structure with galaxies forming first and galaxy clusters at a latter stage, while hot dark matter would result in a top-down formation scenario with large matter aggregations forming early, later fragmenting into separate galaxies; [ clarification needed ] the latter is excluded by high-redshift galaxy observations.
These categories also correspond to fluctuation spectrum effects and the interval following the Big Bang at which each type became non-relativistic.
Davis et al. Candidate particles can be grouped into three categories on the basis of their effect on the fluctuation spectrum Bond et al.
If the dark matter is composed of abundant light particles which remain relativistic until shortly before recombination, then it may be termed "hot".
The best candidate for hot dark matter is a neutrino Such particles are termed "warm dark matter", because they have lower thermal velocities than massive neutrinos Any particles which became nonrelativistic very early, and so were able to diffuse a negligible distance, are termed "cold" dark matter CDM.
There are many candidates for CDM including supersymmetric particles. The 2. Conversely, much lighter particles, such as neutrinos with masses of only a few eV, have FSLs much larger than a protogalaxy, thus qualifying them as hot.
Cold dark matter offers the simplest explanation for most cosmological observations. It is dark matter composed of constituents with an FSL much smaller than a protogalaxy.
This is the focus for dark matter research, as hot dark matter does not seem capable of supporting galaxy or galaxy cluster formation, and most particle candidates slowed early.
The constituents of cold dark matter are unknown. Studies of Big Bang nucleosynthesis and gravitational lensing convinced most cosmologists       that MACHOs   cannot make up more than a small fraction of dark matter.
Peter: " Warm dark matter comprises particles with an FSL comparable to the size of a protogalaxy. Predictions based on warm dark matter are similar to those for cold dark matter on large scales, but with less small-scale density perturbations.
This reduces the predicted abundance of dwarf galaxies and may lead to lower density of dark matter in the central parts of large galaxies.
Some researchers consider this a better fit to observations. No known particles can be categorized as warm dark matter.
A postulated candidate is the sterile neutrino : A heavier, slower form of neutrino that does not interact through the weak force , unlike other neutrinos.
Some modified gravity theories, such as scalar—tensor—vector gravity , require "warm" dark matter to make their equations work.
Hot dark matter consists of particles whose FSL is much larger than the size of a protogalaxy. The neutrino qualifies as such particle.
They were discovered independently, long before the hunt for dark matter: they were postulated in , and detected in Neutrinos interact with normal matter only via gravity and the weak force , making them difficult to detect the weak force only works over a small distance, thus a neutrino triggers a weak force event only if it hits a nucleus head-on.
The three known flavours of neutrinos are the electron , muon , and tau. Their masses are slightly different. Neutrinos oscillate among the flavours as they move.
It is hard to determine an exact upper bound on the collective average mass of the three neutrinos or for any of the three individually.
CMB data and other methods indicate that their average mass probably does not exceed 0. Thus, observed neutrinos cannot explain dark matter.
Because galaxy-size density fluctuations get washed out by free-streaming, hot dark matter implies the first objects that can form are huge supercluster -size pancakes, which then fragment into galaxies.
Deep-field observations show instead that galaxies formed first, followed by clusters and superclusters as galaxies clump together.
If dark matter is made up of sub-atomic particles, then millions, possibly billions, of such particles must pass through every square centimeter of the Earth each second.
Another candidate is heavy hidden sector particles which only interact with ordinary matter via gravity. These experiments can be divided into two classes: direct detection experiments, which search for the scattering of dark matter particles off atomic nuclei within a detector; and indirect detection, which look for the products of dark matter particle annihilations or decays.
Direct detection experiments aim to observe low-energy recoils typically a few keVs of nuclei induced by interactions with particles of dark matter, which in theory are passing through the Earth.
After such a recoil the nucleus will emit energy in the form of scintillation light or phonons , as they pass through sensitive detection apparatus.
To do this effectively, it is crucial to maintain a low background, and so such experiments operate deep underground to reduce the interference from cosmic rays.
These experiments mostly use either cryogenic or noble liquid detector technologies. Noble liquid detectors detect scintillation produced by a particle collision in liquid xenon or argon.
Both of these techniques focus strongly on their ability to distinguish background particles which predominantly scatter off electrons from dark matter particles that scatter off nuclei.
Currently there has been no well-established claim of dark matter detection from a direct detection experiment, leading instead to strong upper limits on the mass and interaction cross section with nucleons of such dark matter particles.
This results from the expectation that as the Earth orbits the Sun, the velocity of the detector relative to the dark matter halo will vary by a small amount.
A special case of direct detection experiments covers those with directional sensitivity. This is a search strategy based on the motion of the Solar System around the Galactic Center.
WIMPs coming from the direction in which the Sun travels approximately towards Cygnus may then be separated from background, which should be isotropic.
Indirect detection experiments search for the products of the self-annihilation or decay of dark matter particles in outer space. For example, in regions of high dark matter density e.
These processes could be detected indirectly through an excess of gamma rays, antiprotons or positrons emanating from high density regions in our galaxy or others.
A few of the dark matter particles passing through the Sun or Earth may scatter off atoms and lose energy.
This could produce a distinctive signal in the form of high-energy neutrinos. Many experimental searches have been undertaken to look for such emission from dark matter annihilation or decay, examples of which follow.
The Energetic Gamma Ray Experiment Telescope observed more gamma rays in than expected from the Milky Way , but scientists concluded this was most likely due to incorrect estimation of the telescope's sensitivity.
The Fermi Gamma-ray Space Telescope is searching for similar gamma rays. At higher energies, ground-based gamma-ray telescopes have set limits on the annihilation of dark matter in dwarf spheroidal galaxies  and in clusters of galaxies.
They could be from dark matter annihilation or from pulsars. No excess antiprotons were observed. In results from the Alpha Magnetic Spectrometer on the International Space Station indicated excess high-energy cosmic rays which could be due to dark matter annihilation.
An alternative approach to the detection of dark matter particles in nature is to produce them in a laboratory. Because a dark matter particle should have negligible interactions with normal visible matter, it may be detected indirectly as large amounts of missing energy and momentum that escape the detectors, provided other non-negligible collision products are detected.
Because dark matter has not yet been conclusively identified, many other hypotheses have emerged aiming to explain the observational phenomena that dark matter was conceived to explain.
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