# Warm and Hot dark matter density profiles

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For cold dark matter, density profiles are well known and easy to find information about - eg. NFW, Burkert, Einasto, and others.

But for some reason I couldn't find explicit expressions for the density profiles for Hot and Warm dark matter.

I need to know what are $ho_{_{HDM}}(r)$,$ho_{_{WDM}}(r)$.

I'm interested in the differences between cold/hot/warm dark matter and why do we use Cold dark matter ($Lambda$-CMD model) and not Hot or Cold dark matter. I need to back my claims with formal quantitative analysis and not just a qualitative explanation.

If you can recommend about other aspects which differentiate the models, or a good review paper on the subject, I would welcome it.

I think you're going to have a difficult time finding this. The reason being, nobody has really bothered studying non-CDM density profiles because it was pretty clear from the onset that CDM was the (most promising) answer. Why spend time further analyzing a model that looks wrong? I will say though, that there are issues with CDM models (e.g., where are all the "satellite" halos that CDM predicts), and because of that, some people have turned to WDM or a Cold-Warm dark matter model.

But how do we know these non-CDM models are wrong, you may ask. The answer for that comes from N-body simulations. There have been a number of continually impressive simulations over the decades that model the formation of large structure in our universe (see this paper for example). These simulations have included various forms of dark matter in an attempt to discover how different types of dark matter affect the formation of structure and content in our universe. The resounding answer seems to always be that hot dark matter just produces an incompatible universe from what we actually observe in ours. There's no point in thoroughly modeling a hot dark matter density profile when it is clear that the HDM universe is drastically different from our own.

I would suggest that if you want to mathematically compare the various dark matter models, that you look at the power spectra from them. A good place to start might be this paper.

There are indeed models for halos made of warm dark matter. The profiles will depend on exactly what the dark matter is and what its temperature is. I am no expert, but a starting point could be a paper by Vinas et al. (2012), who claim that the profiles are much flatter in the centre than those of CDM halos.

http://arxiv.org/abs/1202.2860

Hot dark matter is defined as such during the early universe and will be nearly uniformly distributed at the epochs of early structure formation. However at later epochs, hot dark matter with rest mass can cool down. For example, the cosmic neutrino background would have been highly uniform when it decoupled and when most galaxies formed. But because of the non-zero neutrino rest mass and the expansion of the universe, these neutrinos are now non-relativistic and will be affected by cosmic structures and become "clumpy". The same will be true for any dark matter particle with a rest mass greater than about 0.1 eV.

## Dark Matter as Perfect Fluid in Low Surface Brightness Galaxies (Cosmology / Astronomy)

Tang and colleagues carry out the study on the equation of state (EoS) of dark matter.

The dark matter is a unsolved puzzle in cosmology and particle physics, and it probably consists of particles that are weakly interacting. Though many astronomical observations, like Cosmic Microwave Background, approximately dark matter makes up 23% of today’s Universe. Cosmological models based on cold dark matter in reproducing the large-scale structure of the Universe is quite well and get great success. The most popular candidate for cold dark matter is the weakly interacting massive particles (WIMPs), which are particles with negligible self-interactions, they are stable and collisionless. Their particle masses estimated are in the range 10 GeV ∼ 1 TeV.

However, a plenty of serious challenges to cold dark matter model have emerged on the small scale, such as the scale of individual galaxies and their central core. For example, in the cold dark matter model, halos can be characterized by a power-law mass density distribution with a steep power index at the Central core, which is contrary to observation in small scale, such as the observed rotation curves of low surface brightness (LSB) galaxies, which consists of a very small proportion of ordinary baryonic matter so that their stellar populations make only a relative small contribution to the observed rotation curves, so that the central constant-density dark matter core exits. Making use of cold dark matter model, numerical N-body simulations can’t reproduce a central constant-density dark matter core. This phenomenon is called core-cusp problem.

There exits many other famous model to explain this core-cusp problem, such as self-interacting dark matter and warm dark matter model. Two of the most canonical candidates for WDM are the sterile neutrino and the gravitino. The dark matter particles are usually classified by their velocity dispersion given in terms of three broad categories: hot (HDM), warm (WDM) and cold (CDM) dark matter. In principle HDM is relativistic at all cosmological relevant scales. When a particle’s momentum is equal to or less than its mass (the speed of light are set equal to 1), it become non-relativistic. The warm dark matter have bigger velocity than cold dark matter because of their mass. The typical mass of WDM particle is around 1 KeV. On subgalactic and galactic scales, their non-zero thermal velocities have a strong suppression effect on the steep dark matter power spectrum.

Now, Tang and colleagues studied the equation of state (EoS) of dark matter which treat as a perfect fluid. Because many halo density profiles, like Navarro-Frenk-White (NFW) profile or pseudo-isothermal profile, can be used to fit the density profile of the galaxies from small sizes to large sizes effectively, they could assume that the equation of state is independent of the scaling transformation.

But, when EoS is independent of the scaling transformation, it doesn’t obviously contained x. Because the rotation velocity is far less than the speed of light (i.e. F is very small), they used the Taylor expansion to represent EOS approximately. Its first order terms got the pressure proportional to density. While, its second order terms naturally yield random motions of dark matter, which are correlated to the particle rotational motions. Finally, they got a simplest EOS, i.e. p = ζρ + 2∊Vrot²ρ.

The term ζρ can lead to a constant-density core. The constant-density central core can exit in the region with|F| ≪ ζ. The second order terms in the Taylor expansion can lead to there exits a transition zone between density core and outer region for power index α when density is characterized by power law relation. So it can obtain a density profile which is similar to the pseudo-isothermal halo model when ∊ is around 0.15. By means of the classical least chi square methodology, researchers showed that this profile can perfectly fit the observed rotation curves of LSB galaxies.

When ζ = 0, the term ∊Vrot²ρ can get a power law density beyond the region which include a black hole and of which mass is √2 times the black hole mass. The power index α is – 1+4∊/4∊. When ζ > 0 and ∊ is big, this power law density with α = – 4∊+1/4∊ also exit in the very outer region. If ζ is proportional to the square of velocity dispersion at galaxy Center, then the LSB galaxies with bigger velocity dispersion at galaxy Center should have bigger the peak rotation speed.

For the equation of state which include the polytropic model, i.e.

they got the density profiles with constant-density core and index α is less than -2 at very large radius, such as the profile which is nearly same with the Burkert profile.

“Based on the nature of warm dark matter, we think dark matter have a nonzero random motions in the density core. But when dark matter is a perfect fluid, our observations showed that the velocity of this random motions is far less than the speed of light. It indicates that dark matter is a dust-like CDM. By taking into account the properties of WIMPs, we can assume that random motions of dark matter are positive correlation to the particle rotational motions.”, said authors of the study.

Figure 1. Observed LSB galaxy rotation curves with the best-fitting dark matter model. The solid line, the dashed line and the dotted line represent the numerical model with ∊ = 0.5, 0.25, 0.15 respectively. © Tang et al. Figure 2.Comparison results between the numerical profile and the pseudo-isothermal profile. The solid line, the dashed line and the dotted line represent the numerical model with ζ = 10^-6 and ∊ = 0.5, 0.25, 0.15 respectively. The dash-dotted lines is for the pseudo-isothermal model with core radius of 1.0 kpc. Filled circles are the observed data of the slope α. © Tang et al.

“In this simple phenomenological model, we saw the dark matter halo profile is in agreement with the observations.”, concluded authors of the study.

Their work is supported by the National Natural Science Foundation (NSF) of China (No. 11973081, 11573062, 11403092, 11390374, 11521303), the YIPACAS Foundation (No. 2012048), the Chinese Academy of Sciences (CAS, KJZD-EW-M06-01), the NSF of Yunnan Province (No. 2019FB006) and the Youth Project of Western Light of CAS. Software they used are: NumPY, SciPy, Matplotlib.

References: Xiaobo Gong, Zhaoyi Xu, Meirong Tang, “Dark Matter as Perfect Fluid in Low Surface Brightness Galaxies”, ArXiv, pp. 1-6, 2020. https://arxiv.org/abs/2007.02583v2

Copyright of this article totally belongs to our author S. Aman. One is allowed to use it only by giving proper credit either him or to us.

## Warm and Hot dark matter density profiles - Astronomy

I have heard of something called HDM which is a theory to explain dark matter that is no longer as popular as it used to be. What is HDM?

Two theories to explain the composition of dark matter are Hot Dark Matter theory (HDM) and Cold Dark Matter theory (CDM). The main difference between the two theories is the speed of the candidate particles. As you may have guessed, HDM particles move quickly (and are thus "hot") while CDM particles move slowly. Neutrinos are the main HDM candidate for dark matter as they are very weakly interacting and exist in such large numbers in the universe.

The main problem with HDM theory is that the high speeds of the particles (i.e. neutrinos) in the early universe could not have allowed small density fluctuations to clump together in order to create the large fluctuations we see now. We believe matter (or in other words galaxies) is distributed throughout the universe as it is now due to the growth of small initial fluctuations. Since neutrinos would have been moving so fast that these tiny initial fluctuations would have been smoothed out, HDM theory cannot account for the distribution of galaxies in the universe. The small scale of this initial clumping that is impossible for neutrinos to maintain is supported by COBE observations.

Now when HDM is discussed, it is usually in combination with CDM (the combination is called MDM or "mixed dark matter"). HDM is thought to be limited to at most a few percent of dark matter if the amount is even measurable.

#### Sabrina Stierwalt

Sabrina was a graduate student at Cornell until 2009 when she moved to Los Angeles to become a researcher at Caltech. She now studies galaxy mergers at the University of Virginia and the National Radio Astronomy Observatory in Charlottesville. You can also find her answering science questions in her weekly podcast as Everyday Einstein.

In the NFW profile, the density of dark matter as a function of radius is given by:

where ρ0 and the "scale radius", Rs, are parameters which vary from halo to halo.

The integrated mass within some radius Rmax is

The total mass is divergent, but it is often useful to take the edge of the halo to be the virial radius, Rvir, which is related to the "concentration parameter", c, and scale radius via

The total mass in the halo within R v i r >> is

The specific value of c is roughly 10 or 15 for the Milky Way, and may range from 4 to 40 for halos of various sizes.

This can then be used to define a dark matter halo in terms of its mean density, solving the above equation for ρ 0 > and substituting it into the original equation. This gives

• ρ h a l o ≡ M / ( 4 3 π R v i r 3 ) >equiv M<iggr />left(<3>>pi R_< m >^<3> ight)> is the mean density of the halo,
• A N F W = [ ln ⁡ ( 1 + c ) − c 1 + c ] >=left[ln(1+c)-<1+c>> ight]> is from the mass calculation, and
• x = r / R v i r >> is the fractional distance to the virial radius.

### Higher order moments Edit

The integral of the squared density is

so that the mean squared density inside of Rmax is

which for the virial radius simplifies to

and the mean squared density inside the scale radius is simply

### Gravitational potential Edit

Solving Poisson's equation gives the gravitational potential

The acceleration due to the NFW potential is:

### Radius of the maximum circular velocity Edit

The radius of the maximum circular velocity (confusingly sometimes also referred to as R max > ) can be found from the maximum of M ( r ) / r as

Maximum circular velocity is also related to the characteristic density and length scale of NFW profile:

Over a broad range of halo mass and redshift, the NFW profile approximates the equilibrium configuration of dark matter halos produced in simulations of collisionless dark matter particles by numerous groups of scientists. [4] Before the dark matter virializes, the distribution of dark matter deviates from an NFW profile, and significant substructure is observed in simulations both during and after the collapse of the halos.

Alternative models, in particular the Einasto profile, have been shown to represent the dark matter profiles of simulated halos as well as or better than the NFW profile by including an additional third parameter. [5] [6] The Einasto profile has a finite (zero) central slope, unlike the NFW profile which has a divergent (infinite) central density. Because of the limited resolution of N-body simulations, it is not yet known which model provides the best description of the central densities of simulated dark-matter halos.

Simulations assuming different cosmological initial conditions produce halo populations in which the two parameters of the NFW profile follow different mass-concentration relations, depending on cosmological properties such as the density of the universe and the nature of the very early process which created all structure. Observational measurements of this relation thus offer a route to constraining these properties. [7]

The dark matter density profiles of massive galaxy clusters can be measured directly by gravitational lensing and agree well with the NFW profiles predicted for cosmologies with the parameters inferred from other data. [8] For lower mass halos, gravitational lensing is too noisy to give useful results for individual objects, but accurate measurements can still be made by averaging the profiles of many similar systems. For the main body of the halos, the agreement with the predictions remains good down to halo masses as small as those of the halos surrounding isolated galaxies like our own. [9] The inner regions of halos are beyond the reach of lensing measurements, however, and other techniques give results which disagree with NFW predictions for the dark matter distribution inside the visible galaxies which lie at halo centers.

Observations of the inner regions of bright galaxies like the Milky Way and M31 may be compatible with the NFW profile, [10] but this is open to debate. The NFW dark matter profile is not consistent with observations of the inner regions of low surface brightness galaxies, [11] [12] which have less central mass than predicted. This is known as the cusp-core or cuspy halo problem. It is currently debated whether this discrepancy is a consequence of the nature of the dark matter, of the influence of dynamical processes during galaxy formation, or of shortcomings in dynamical modelling of the observational data. [13]

## How Dense Is Dark Matter?

Components of the galaxy cluster Abell 2744, also known as the Pandora Cluster: galaxies (white), . [+] hot gas (red) and dark matter (blue). The image measures about half a degree across. The image is sprinkled with foreground stars belonging to our Galaxy, the Milky Way, which are visible as the roundish objects with diffraction spikes. Image credit: ESA/XMM-Newton (X-rays) ESO/WFI (optical) NASA/ESA & CFHT (dark matter)

It very much depends on where you are! Dark matter as we understand it must be some kind of particle, or at least act like some kind of particle. We’re not exactly clear on what the exact nature of that particle would be, or what its individual mass is, or what kind of interactions it ought to have either with itself or with the matter that makes up our planet and all the stars.

But it certainly does seem that dark matter isn’t spread evenly throughout the entire universe. It’s clustered in lumps, and those lumps become the homes to galaxies. Small gatherings of dark matter are generally assumed to be roundish, since that’s the easiest shape for a three dimensional object to form under the influence of gravity.

For galaxy clusters, we can actually map out the shape of the dark matter surrounding these thousands of galaxies by looking at the way that light bends around that part of the Universe. Not all clusters have particularly spherical dark matter surroundings, and we can see the irregularities because the light from galaxies behind the cluster is not bent in the same way along all of the cluster’s edges.

At first glance, this cosmic kaleidoscope of purple, blue and pink offers a strikingly beautiful — . [+] and serene — snapshot of the cosmos. However, this multi-coloured haze actually marks the site of two colliding galaxy clusters, forming a single object known as MACS J0416.1-2403 (or MACS J0416 for short). Image credit: NASA, ESA, CXC, NRAO/AUI/NSF, STScI, and G. Ogrean (Stanford University)

Within any of these collections of dark matter (technically called halos) surrounding a galaxy or a collection of galaxies, the dark matter is densest at the center, and becomes gradually more diffuse the further out you go. For our own Milky Way, that means that the dark matter density is the highest towards the very center of the galaxy, and out near our solar system, the dark matter density is significantly lower.

Most galaxies contain significantly more mass in dark matter than in luminous matter, but this isn’t because it’s more dense -- the dark matter halo is simply much larger. In the case of the dark matter surrounding our Milky Way, it’s also spherical and not effectively flat, like the bright part of the galaxy is. You can pack a lot more material in a sphere than you can in a circle, so the combination of the dark matter halo being physically larger and a sphere means you wind up with a lot more mass.

This is a mass map of galaxy cluster Cl0024+1654 derived from an extensive Hubble Space Telescope . [+] campaign. The colour image is made from two images: a dark-matter map (the blue part of the image) and a 'luminous-matter' map determined from the galaxies in the cluster (the red part of the image). Image credit: European Space Agency, NASA and Jean-Paul Kneib (Observatoire Midi-Pyrénées, France/Caltech, USA)

The dark matter density near the solar system, from what I could find, sits at around 0.006 solar masses per cubic parsec, which is a set of units that’s not going to make much sense unless you’re a professional astrophysicist. This is extremely low density. Six-thousandths of a solar mass is approximately the same as six Jupiter mass planets, and a parsec is a 75% of the distance from the Sun to the nearest star. So this means if you wanted to reproduce the dark matter density with the luminous matter that planets are made of, you’d have to clear out a cube of space that’s three light years to a side of absolutely everything. No dust, no gas, no stars, no planets. You get six Jupiters in that box, and you’ll have to spread those Jupiters around, since we don’t have any indication that dark matter comes in chunks.

We can scale this metaphor down a bit if you wanted to get the same kind of density but in a cubic kilometer, you’d have to evacuate that square kilometer of absolutely every single atom of material. A single grain of birch pollen floating in that cubic kilometer would contain 20 times more mass than there would be in dark matter in that same volume.

At the center of the galaxy, the dark matter should be more than 150 times more concentrated, but this is very difficult to measure within our own galaxy. So far, our observations seem to line up with the models we’ve developed, but there’s definitely room to improve. In any case, 150 times the density of the solar neighborhood is still not very dense! That gets us all of about eight grains of pollen.

## Contents

The presence of dark matter (DM) in the halo is inferred from its gravitational effect on a spiral galaxy's rotation curve. Without large amounts of mass throughout the (roughly spherical) halo, the rotational velocity of the galaxy would decrease at large distances from the galactic center, just as the orbital speeds of the outer planets decrease with distance from the Sun. However, observations of spiral galaxies, particularly radio observations of line emission from neutral atomic hydrogen (known, in astronomical parlance, as 21 cm Hydrogen line, H one, and H I line), show that the rotation curve of most spiral galaxies flattens out, meaning that rotational velocities do not decrease with distance from the galactic center. [11] The absence of any visible matter to account for these observations implies either that unobserved (dark) matter, first proposed by Ken Freeman in 1970, exist, or that the theory of motion under gravity (general relativity) is incomplete. Freeman noticed that the expected decline in velocity was not present in NGC 300 nor M33, and considered an undetected mass to explain it. The DM Hypothesis has been reinforced by several studies. [12] [13] [14] [15]

The formation of dark matter halos is believed to have played a major role in the early formation of galaxies. During initial galactic formation, the temperature of the baryonic matter should have still been much too high for it to form gravitationally self-bound objects, thus requiring the prior formation of dark matter structure to add additional gravitational interactions. The current hypothesis for this is based on cold dark matter (CDM) and its formation into structure early in the universe.

The hypothesis for CDM structure formation begins with density perturbations in the Universe that grow linearly until they reach a critical density, after which they would stop expanding and collapse to form gravitationally bound dark matter halos. These halos would continue to grow in mass (and size), either through accretion of material from their immediate neighborhood, or by merging with other halos. Numerical simulations of CDM structure formation have been found to proceed as follows: A small volume with small perturbations initially expands with the expansion of the Universe. As time proceeds, small-scale perturbations grow and collapse to form small halos. At a later stage, these small halos merge to form a single virialized dark matter halo with an ellipsoidal shape, which reveals some substructure in the form of dark matter sub-halos. [2]

The use of CDM overcomes issues associated with the normal baryonic matter because it removes most of the thermal and radiative pressures that were preventing the collapse of the baryonic matter. The fact that the dark matter is cold compared to the baryonic matter allows the DM to form these initial, gravitationally bound clumps. Once these subhalos formed, their gravitational interaction with baryonic matter is enough to overcome the thermal energy, and allow it to collapse into the first stars and galaxies. Simulations of this early galaxy formation matches the structure observed by galactic surveys as well as observation of the Cosmic Microwave Background. [16]

### Density profiles Edit

A commonly used model for galactic dark matter halos is the pseudo-isothermal halo: [17]

Numerical simulations of structure formation in an expanding universe lead to the empirical NFW (Navarro-Frenk-White) profile: [19]

Higher resolution computer simulations are better described by the Einasto profile: [21]

### Shape Edit

The collapse of overdensities in the cosmic density field is generally aspherical. So, there is no reason to expect the resulting halos to be spherical. Even the earliest simulations of structure formation in a CDM universe emphasized that the halos are substantially flattened. [23] Subsequent work has shown that halo equidensity surfaces can be described by ellipsoids characterized by the lengths of their axes. [24]

Because of uncertainties in both the data and the model predictions, it is still unclear whether the halo shapes inferred from observations are consistent with the predictions of ΛCDM cosmology.

### Halo substructure Edit

Up until the end of the 1990s, numerical simulations of halo formation revealed little substructure. With increasing computing power and better algorithms, it became possible to use greater numbers of particles and obtain better resolution. Substantial amounts of substructure are now expected. [25] [26] [27] When a small halo merges with a significantly larger halo it becomes a subhalo orbiting within the potential well of its host. As it orbits, it is subjected to strong tidal forces from the host, which cause it to lose mass. In addition the orbit itself evolves as the subhalo is subjected to dynamical friction which causes it to lose energy and angular momentum to the dark matter particles of its host. Whether a subhalo survives as a self-bound entity depends on its mass, density profile, and its orbit. [18]

### Angular momentum Edit

As originally pointed out by Hoyle [28] and first demonstrated using numerical simulations by Efstathiou & Jones, [29] asymmetric collapse in an expanding universe produces objects with significant angular momentum.

Numerical simulations have shown that the spin parameter distribution for halos formed by dissipation-less hierarchical clustering is well fit by a log-normal distribution, the median and width of which depend only weakly on halo mass, redshift, and cosmology: [30]

The visible disk of the Milky Way Galaxy is thought to be embedded in a much larger, roughly spherical halo of dark matter. The dark matter density drops off with distance from the galactic center. It is now believed that about 95% of the galaxy is composed of dark matter, a type of matter that does not seem to interact with the rest of the galaxy's matter and energy in any way except through gravity. The luminous matter makes up approximately 9 × 10 10 solar masses. The dark matter halo is likely to include around 6 × 10 11 to 3 × 10 12 solar masses of dark matter. [32] [33]

## Looking for warm dark matter

Two simulations of galaxy formation at the epoch when the universe was only about one billion years old. The top ("CDM") shows clumps and filaments of young galaxies using a conventional treatment of non-interacting dark matter, while the bottom ("sDAO") shows the slightly different - but measurable - differences that occur if dark matter instead could interact with some particles. Astronomers show that future precise measurements of large-scale galaxy structures could help constrain the nature of the mysterious dark matter in the universe. Credit: Bose et al. 2019

In the last century, astronomers studying the motions of galaxies and the character of the cosmic microwave background radiation came to realize that most of the matter in the universe was not visible. About 84% of the matter in the cosmos is dark, emitting neither light nor any other known kind of radiation. Hence it is called dark matter. One of its other primary qualities is that it only interacts with other matter via gravity: it carries no electromagnetic charge, for example. Dark matter is also "dark" because it is mysterious: it is not composed of atoms or their usual constituents like electrons and protons. Particle physicists have imagined new kinds of matter, consistent with the known laws of the universe, but so far none has been detected or its existence confirmed. The Large Hadron Collider's discovery of the Higgs boson in 2012 prompted a burst of optimism that dark matter particles would soon be discovered, but so far none has been seen and previously promising classes of particles now seem to be long-shots.

Astronomers realize that dark matter is the dominant component of matter in the universe. Whatever its nature, it profoundly influenced the evolution of galactic structures and the distribution of the cosmic microwave background radiation (CMBR). The remarkable agreement between the values of key cosmic parameters (like the rate of expansion) derived from observations of two completely different kinds of large-scale cosmic structures, galaxies and the CMBR. lend credence to inflationary big bang models that include the role dark matter.

Current models of dark matter presume it is "cold," that is, that it does not interact with any other kinds of matter or radiation—or even with itself—beyond the influences of gravity. This version of cosmology is therefore called the cold dark matter scenario. But cosmologists wonder whether more precise observations might be able to exclude even small levels of interactions. CfA astronomer Sownak Bose led a team of colleagues in a study of one very popular (if speculative) "dark matter" particle, one that has some ability to interact with very light particles that move close to the speed of light. This version forms one of several possible warm dark matter (perhaps more accurately called interacting dark matter) scenarios. In particular, the hypothetical particles are allowed to interact with neutrinos (neutrinos are expected to be extremely abundant in the hot early universe).

The scientists used state-of-the-art cosmological simulations of galaxy formation to a model universe with this kind of warm dark matter. They find that for many observations the effects are too small to be noticeable. However, the signature of this warm dark matter is present in some distinct ways, and in particular in the way distant galaxies are distributed in space, something that can be tested by mapping galaxies by looking at their hydrogen gas. The authors conclude that future, highly sensitive observations should be able to make these tests. Detailed new maps of the distribution of hydrogen gas absorption could be used to support—or exclude—this warm dark matter possibility (see the figure), and shed light on this mysterious cosmic component.

## Warm and Hot dark matter density profiles - Astronomy

Context. Inferences about dark matter, dark energy, and the missing baryons all depend on the accuracy of our model of large-scale structure evolution. In particular, with cosmological simulations in our model of the Universe, we trace the growth of structure, and visualize the build-up of bigger structures from smaller ones and of gaseous filaments connecting galaxy clusters.
Aims: Here we aim to reveal the complexity of the large-scale structure assembly process in great detail and on scales from tens of kiloparsecs up to more than 10 Mpc with new sensitive large-scale observations from the latest generation of instruments. We also aim to compare our findings with expectations from our cosmological model.
Methods: We used dedicated SRG/eROSITA performance verification (PV) X-ray, ASKAP/EMU Early Science radio, and DECam optical observations of a

15 deg 2 region around the nearby interacting galaxy cluster system A3391/95 to study the warm-hot gas in cluster outskirts and filaments, the surrounding large-scale structure and its formation process, the morphological complexity in the inner parts of the clusters, and the (re-)acceleration of plasma. We also used complementary Sunyaev-Zeldovich (SZ) effect data from the Planck survey and custom-made Galactic total (neutral plus molecular) hydrogen column density maps based on the HI4PI and IRAS surveys. We relate the observations to expectations from cosmological hydrodynamic simulations from the Magneticum suite.
Results: We trace the irregular morphology of warm and hot gas of the main clusters from their centers out to well beyond their characteristic radii, r 200 . Between the two main cluster systems, we observe an emission bridge on large scale and with good spatial resolution. This bridge includes a known galaxy group but this can only partially explain the emission. Most gas in the bridge appears hot, but thanks to eROSITA's unique soft response and large field of view, we discover some tantalizing hints for warm, truly primordial filamentary gas connecting the clusters. Several matter clumps physically surrounding the system are detected. For the "Northern Clump," we provide evidence that it is falling towards A3391 from the X-ray hot gas morphology and radio lobe structure of its central AGN. Moreover, the shapes of these X-ray and radio structures appear to be formed by gas well beyond the virial radius, r 100 , of A3391, thereby providing an indirect way of probing the gas in this elusive environment. Many of the extended sources in the field detected by eROSITA are also known clusters or new clusters in the background, including a known SZ cluster at redshift z = 1. We find roughly an order of magnitude more cluster candidates than the SPT and ACT surveys together in the same area. We discover an emission filament north of the virial radius of A3391 connecting to the Northern Clump. Furthermore, the absorption-corrected eROSITA surface brightness map shows that this emission filament extends south of A3395 and beyond an extended X-ray-emitting object (the "Little Southern Clump") towards another galaxy cluster, all at the same redshift. The total projected length of this continuous warm-hot emission filament is 15 Mpc, running almost 4 degrees across the entire eROSITA PV observation field. The Northern and Southern Filament are each detected at >4σ. The Planck SZ map additionally appears to support the presence of both new filaments. Furthermore, the DECam galaxy density map shows galaxy overdensities in the same regions. Overall, the new datasets provide impressive confirmation of the theoretically expected structure formation processes on the individual system level, including the surrounding warm-hot intergalactic medium distribution the similarities of features found in a similar system in the Magneticum simulation are striking. Our spatially resolved findings show that baryons indeed reside in large-scale warm-hot gas filaments with a clumpy structure.

## What is the difference between hot dark matter and cold dark matter? What difference does it make to cosmology?

Hot Dark Matter : Dark Matter moving at relativistic speeds.
Cold Dark Matter: Dark Matter moving at non-relativistic speeds.
They affect the way structures form in the Universe.

#### Explanation:

Depending on how a particle's kinetic energy compares with its rest mass energy, particles are classified into:

Non-relativistic: #E_k ltlt E_0# ,
Relativistic : #E_k approx E_0# ,
Super-relativistic: #E_k gtgt E_0#

HDM & CDM : If the dark-matter particles are relativistic or super-relativistic they are called Hot Dark Matter (HDM), otherwise they are called Cold Dark Matter (CDM).

Since Dark Matter has not been detected yet, Cosmologists can only speculate about the nature of Dark Matter - Is it hot or cold? The current consensus view is that it is cold for most part. Because if it were hot, then the structure formation theories predict that all structures smaller than massive galaxies would have been destroyed by a process called Free Streaming. Since we have structures smaller than galaxies we conclude that the Dark Matter cannot be predominantly hot. Though there could be little bit of hot dark matter mixed among predominantly cold matter.

## Controversy over detection of dark matter

Several attempts has been made by proponents of Big Bang cosmology paradigm to establish the existence of dark matter as fact and demolish the criticisms of ‘dark matter sceptics’. [26] [27] The latest claim published in journal Nature (4 July 2012) is that "A ‘finger’ of the Universe’s dark-matter skeleton, which ultimately dictates where galaxies form, has been observed for the first time." Despite the bold statement that "Researchers have directly detected a slim bridge of dark matter joining two clusters of galaxies", the declaration seems self-contradictory as at the same time it has been admitted that the results were obtained by usage of computer simulations and astrophysicists are still faced with necessity to identify what the dark matter is made of. It has been proposed that this mysterious invisible substance that should dominate the space all around us in concentrations six or seven times more than normal matter could be either: