المؤلفون: Xu, Zhijie (Jay)

المصدر: Astronomy & Astrophysics 675 A92

مصطلحات موضوعية: cosmology, dark matter, turbulence, simulation, astronomy, astrophysics, dark matter halo, correlation, statistical analysis, self-gravitating, collisionless, N body, maximum entropy, velocity distribution, energy distribution, speed distribution

الوصف: Maximum entropy distributions of dark matter in ΛCDM cosmology Small-scale challenges to ΛCDM cosmology require a deeper understanding of dark matter physics. This paper aims to develop the maximum entropy distributions for dark matter particle velocity (denoted by X), speed (denoted by Z), and energy (denoted by E) that are especially relevant on small scales where system approaches full virialization. For systems involving long-range interactions, a spectrum of halos of different sizes is required to form to maximize system entropy. While the velocity in halos can be Gaussian, the velocity distribution throughout the entire system, involving all halos of different sizes, is non-Gaussian. With the virial theorem for mechanical equilibrium, we applied the maximum entropy principle to the statistical equilibrium of entire system, such that the maximum entropy distribution of velocity (the X distribution) could be analytically derived. The halo mass function was not required in this formulation, but it did indeed result from the maximum entropy. The predicted X distribution involves a shape parameter \(\alpha\) and a velocity scale, \(v_0\). The shape parameter \(\alpha\) reflects the nature of force (\(\alpha\rightarrow0\) for long-range force or \(\alpha\rightarrow\infty\) for short-range force). Therefore, the distribution approaches Laplacian with \(\alpha\rightarrow0\) and Gaussian with \(\alpha\rightarrow\infty\). For an intermediate value of \(\alpha\), the distribution naturally exhibits a Gaussian core for \(v\ll v_0\) and exponential wings for \(v\gg v_0\), as confirmed by N-body simulations. From this distribution, the mean particle energy of all dark matter particles with a given speed, v, follows a parabolic scaling for low speeds (\(\propto v^2\) for \(v\ll v_0\) in halo core region, i.e., "Newtonian") and a linear scaling for high speeds (\(\propto v\) for \(v\gg v_0\) in halo outskirt, i.e., exhibiting "non-Newtonian" behavior in MOND due to long-range gravity). We compared our results against ...

العلاقة: https://zenodo.org/record/6640373Test; https://doi.org/10.48550/arXiv.2110.03126Test; oai:zenodo.org:6640373

الإتاحة: https://doi.org/10.48550/arXiv.2110.03126Test
https://doi.org/10.5281/zenodo.6569901Test
https://doi.org/10.5281/zenodo.6569898Test
https://doi.org/10.5281/zenodo.6541230Test
https://doi.org/10.5281/zenodo.6586212Test
https://doi.org/10.48550/arXiv.2109.12244Test
https://doi.org/10.48550/arXiv.2109.09985Test
https://doi.org/10.48550/arXiv.2110.05784Test
https://doi.org/10.48550/arXiv.2110.09676Test
https://doi.org/10.48550/arXiv.2110.13885Test

المؤلفون: Xu. Zhijie (Jay)

المصدر: Physics of Fluids 35 077105

مصطلحات موضوعية: cosmology, dark matter, turbulence, simulation, astronomy, astrophysics, dark matter halo, correlation function, structure function, statistical analysis, self-gravitating, collisionless, N body, velocity correlation, density correlation, potential correlation

الوصف: On the statistical theory of self-gravitating collisionless dark matter flow Dark matter, if exists, accounts for five times as much as the ordinary baryonic matter. Compared to hydrodynamic turbulence, the flow of dark matter might possess the widest presence in our universe. This paper presents a statistical theory for the flow of dark matter that is compared with N-body simulations. By contrast to hydrodynamics of normal fluids, dark matter flow is self-gravitating, long-range, and collisionless with a scale dependent flow behavior. The peculiar velocity field is of constant divergence nature on small scale and irrotational on large scale. The statistical measures, i.e. correlation, structure, dispersion, and spectrum functions are modeled on both small and large scales, respectively. Kinematic relations between statistical measures are fully developed for incompressible, constant divergence, and irrotational flow. Incompressible and constant divergence flow share same kinematic relations for even order correlations. The limiting correlation of velocity \(\rho_L=1/2\) on the smallest scale (r=0) is a unique feature of collisionless flow (\(\rho_L=1\) for incompressible flow). On large scale, transverse velocity correlation has an exponential form \(T_2\propto e^{-r/r_2}\) with a constant comoving scale \(r_2=21.3Mpc/h\) that maybe related to the horizon size at matter-radiation equality. All other correlation, structure, dispersion, and spectrum functions for velocity, density, and potential fields are derived analytically from kinematic relations for irrotational flow. On small scale, longitudinal structure function follows one-fourth law of \(S^l_2\propto r^{1/4}\). All other statistical measures can be obtained from kinematic relations for constant divergence flow. Vorticity is negatively correlated for scale \(r\) between \(1\) and \(7Mpc/h\). Divergence is negatively correlated for \(r>30Mpc/h\) that leads to a negative density correlation. Applications of cascade and statistical theory for dark ...

العلاقة: https://zenodo.org/record/6640705Test; https://doi.org/10.48550/arXiv.2202.00910Test; oai:zenodo.org:6640705

الإتاحة: https://doi.org/10.48550/arXiv.2202.00910Test
https://doi.org/10.5281/zenodo.6569901Test
https://doi.org/10.5281/zenodo.6569898Test
https://doi.org/10.5281/zenodo.6541230Test
https://doi.org/10.5281/zenodo.6586212Test
https://doi.org/10.48550/arXiv.2109.12244Test
https://doi.org/10.48550/arXiv.2110.03126Test
https://doi.org/10.48550/arXiv.2110.05784Test
https://doi.org/10.48550/arXiv.2110.09676Test
https://doi.org/10.48550/arXiv.2110.13885Test

المؤلفون: Xu, Zhijie (Jay)

مصطلحات موضوعية: Cosmology, dark matter, turbulence, simulation, astronomy, astrophysics, dark matter halo, correlation, statistical analysis, self-gravitating, collisionless, N Body

الوصف: Dark matter, if exists, accounts for five times as much as ordinary baryonic matter. Therefore, dark matter flow might possess the widest presence in our universe. The other form of flow, hydrodynamic turbulence in air and water, is without doubt the most familiar flow in our daily life. During the pandemic, we have found time to think about and put together a systematic comparison for the similarities and differences between two types of flow, both of which are typical non-equilibrium systems. The goal of this presentation is to leverage this comparison for a better understanding of the nature and properties of dark matter and its flow behavior on all scales. Applications of cascade and statistical theory for dark matter and bulge-SMBH evolution: Dark matter particle mass ,size, and properties from energy cascade in dark matter flow: 1) arxiv 2) zenodo slides Origin of MOND acceleration & deep-MOND from acceleration fluctuation & energy cascade: 1) arxiv 2) zenodo slides The baryonic-to-halo mass relation from mass and energy cascade in dark matter flow: 1) arxiv 2) zenodo slides Universal scaling laws and density slope for dark matter haloes: 1) arxiv 2) zenodo slides 3) paper Dark matter halo mass functions and density profiles from mass/energy cascade: 1) arxiv 2) zenodo slides 3) paper Energy cascade for distribution and evolution of supermassive black holes (SMBHs): 2) zenodo slides Condensed slides for all applications "Cascade Theory for Turbulence, Dark Matter, and bulge-SMBH evolution " The two relevant datasets and accompanying presentation can be found at: Dark matter flow dataset Part I: Halo-based statistics from cosmological N-body simulation Dark matter flow dataset Part II: Correlation-based statistics from cosmological N-body simulation. A comparative study of Dark matter flow & hydrodynamic turbulence and its applications The same dataset also available on Github at: Github: dark_matter_flow_dataset and zenodo at: Dark matter flow dataset from cosmological N-body simulation. ...

العلاقة: https://zenodo.org/record/6643911Test; https://doi.org/10.5281/zenodo.6643911Test; oai:zenodo.org:6643911

الإتاحة: https://doi.org/10.5281/zenodo.6643911Test
https://doi.org/10.5281/zenodo.6569901Test
https://doi.org/10.5281/zenodo.6569898Test
https://doi.org/10.5281/zenodo.6541230Test
https://doi.org/10.5281/zenodo.6586212Test
https://doi.org/10.48550/arXiv.2109.09985Test
https://doi.org/10.48550/arXiv.2109.12244Test
https://doi.org/10.48550/arXiv.2110.03126Test
https://doi.org/10.48550/arXiv.2110.05784Test
https://doi.org/10.48550/arXiv.2110.09676Test

المؤلفون: Xu, Zhijie (Jay)

مصطلحات موضوعية: cosmology, dark matter, turbulence, simulation, astronomy, astrophysics, dark matter halo, correlation, statistical analysis, self-gravitating, collisionless, N body, halo energy, halo momentum, integral constant of motion, halo spin parameter

الوصف: Evolution of energy, momentum, and spin parameter in dark matter flow and integral constants of motion N-body equations of motion in comoving system and expanding background are reformulated in a transformed system with static background and fixed damping. The energy and momentum evolution in dark matter flow are rigorously formulated for both systems. The energy evolution in transformed system has a simple form that is identical to the damped harmonic oscillator. The cosmic energy equation can be easily derived in both systems. For entire N-body system, 1) combined with the two-body collapse model (TBCM), kinetic and potential energy increase linearly with time $t$ such that \(K_p=\varepsilon_ut\) and \(P_y=-7\varepsilon_ut/5\), where \(\varepsilon_u\) is a constant rate of energy cascade; 2) an effective gravitational potential exponent \(n_e=-10/7\ne-1\) (\(n_e=-1.38\) from simulation) can be identified due to surface energy of fast growing halos; 3) the radial momentum \(G\propto a^{3/2}\) and angular momentum \(H\propto a^{5/2}\), where \(a\) is the scale factor. On halo scale, 1) halo kinetic and potential energy can be modelled by two dimensionless constants \(\alpha_s^*\) and \(\beta_s^*\). Both constants are independent of time and halo mass; 2) both halo radial and angular momentum \(\propto a^{3/2}\) and can be modeled by two mass-dependent coefficients \(\tau_s^*\) and \(\eta_s^*\); 3) halo spin parameter is determined by \(\alpha_s^*\) and \(\eta_s^*\) and decreases with halo mass with derived values of 0.09 and 0.031 for small and large halos. Finally, the radial and angular momentum are closely related to the integral constants of motion \(I_m\), i.e. the integral of velocity correlation or the \(m\)th derivative of energy spectrum at long wavelength limit. On large scale, angular momentum is negligible, \(I_2\)=0 reflects the conservation of linear momentum, while \(I_4\) reflects the fluctuation of radial momentum \(G\). On halo scale, \(I_4\) is determined by both momentum that are comparable ...

العلاقة: https://zenodo.org/record/6640322Test; https://doi.org/10.48550/arXiv.2202.04054Test; oai:zenodo.org:6640322

الإتاحة: https://doi.org/10.48550/arXiv.2202.04054Test
https://doi.org/10.5281/zenodo.6569898Test
https://doi.org/10.5281/zenodo.6541230Test
https://doi.org/10.5281/zenodo.6586212Test
https://doi.org/10.5281/zenodo.6569901Test
https://doi.org/10.48550/arXiv.2109.12244Test
https://doi.org/10.48550/arXiv.2110.03126Test
https://doi.org/10.48550/arXiv.2110.05784Test
https://doi.org/10.48550/arXiv.2110.09676Test
https://doi.org/10.48550/arXiv.2110.13885Test

المؤلفون: Xu, Zhijie (Jay)

مصطلحات موضوعية: cosmology, dark matter, turbulence, simulation, astronomy, astrophysics, dark matter halo, correlation, statistical analysis, self-gravitating, collisionless, N body, two-thrids law, mass cascade, energy cascade, dark matter particle mass, dark matter particle size, dark matter particle property

الوصف: Predicting dark matter particle mass and properties from two-thirds law and energy cascade in dark matter flow Dark matter can be characterized by the mass and size of its smallest constituents, which are challenging to be directly probed and detected. After years of null results in the search for thermal WIMPs, a different prospective might be required beyond the standard WIMP paradigm. We present a new approach to estimate the dark matter particle mass, size, density, and many other relevant properties based on the nature of flow of dark matter. A comparison with hydrodynamic turbulence is presented to reveal the unique features of self-gravitating collisionless dark matter flow, i.e. an inverse mass and energy cascade from small to large scales with a scale-independent rate of energy cascade \(\varepsilon_u\approx -4.6\times 10^{-7}m^2/s^3\). For the simplest case with only gravitational interaction involved and in the absence of viscosity in flow, the energy cascade leads to a two-thirds law for pairwise velocity that can be extended down to the smallest scale, where quantum effects become important. Combining the rate of energy cascade \(\varepsilon_u\), the Planck constant \(\hbar\), and the gravitational constant \(G\) on the smallest scale, the mass of dark matter particles is found to be around \(0.9\times10^{12}GeV\) with a size around \(3\times10^{-13}m\). Since the mass scale \(m_X\) is only weakly dependent on \(\varepsilon_u\) as \(m_X \propto (-\varepsilon_u\hbar^5/G^4)^{1/9}\), the estimation of \(m_X\) should be pretty robust for a wide range of possible values of \(\varepsilon_u\). If gravity is the only interaction and dark matter is fully collisionless, mass of around \(10^{12}GeV\) is required to produce the given rate of energy cascade \(\varepsilon_u\). In other words, if mass has a different value, there must be some new interaction beyond gravity. This work strongly suggests a heavy dark matter scenario produced in the early universe (\(\sim 10^{-14}s\)) with a mass much greater than ...

العلاقة: https://zenodo.org/record/6640353Test; https://doi.org/10.48550/arXiv.2202.07240Test; oai:zenodo.org:6640353

الإتاحة: https://doi.org/10.48550/arXiv.2202.07240Test
https://doi.org/10.5281/zenodo.6569901Test
https://doi.org/10.5281/zenodo.6569898Test
https://doi.org/10.5281/zenodo.6541230Test
https://doi.org/10.5281/zenodo.6586212Test
https://doi.org/10.48550/arXiv.2109.12244Test
https://doi.org/10.48550/arXiv.2110.03126Test
https://doi.org/10.48550/arXiv.2110.05784Test
https://doi.org/10.48550/arXiv.2110.09676Test
https://doi.org/10.48550/arXiv.2110.13885Test

المؤلفون: Xu, Zhijie (Jay)

مصطلحات موضوعية: cosmology, dark matter, turbulence, simulation, astronomy, astrophysics, dark matter halo, correlation, statistical analysis, self-gravitating, collisionless, N body, MOND, critical acceleration, modified Newtonian dynamics, deep MOND, mass and energy cascade, acceleration fluctuation, dark energy

الوصف: The origin of MOND acceleration and deep-MOND from acceleration fluctuation and energy cascade in dark matter flow MOND is an empirically motivated theory using modified gravity to reproduce many astronomical observations without invoking the dark matter hypothesis. Instead of falsifying the existence of dark matter, we propose that MOND is an effective theory naturally emerging from the long-range interaction and collisionless nature of dark matter flow. It describes the dynamics of baryonic mass suspended in fluctuating dark matter fluid. To maximize system entropy, the long-range interaction requires a broad size of halos to be formed. These halos facilitate an inverse mass and energy cascade from small to large mass scales with a constant rate of energy cascade \(\varepsilon _{u} \approx -4.6\times 10^{-7} {m^{2} /s^{3}}\). In addition to velocity fluctuation with a typical scale \(u\), the long-range interaction leads to a fluctuation in acceleration with a typical scale \(a_{0}\). The velocity and acceleration fluctuations in dark matter flow satisfy \(\varepsilon _{u} =-{a_{0}u/(3\pi) ^{2}}\) that determines \(a_0\), where factor \(3\pi\) is from the angle of incidence. With \(u_{0} \equiv u(z=0)\approx 354.61{km/s}\) from N-body simulation, the value of \(a_{0} \left(z=0\right)\approx 1.2\times 10^{-10} {m/s^{2}}\) can be easily obtained and \(a_0 \propto t^{-1/2}\). While Planck constant \(\hbar\), gravitational constant \(G\), and \(\varepsilon_{u}\) are proposed to find the dark matter particle properties on the smallest scale, the velocity scale \(u\), \(G\), and \(\varepsilon_{u}\) determine the halo properties on the largest scale. For a given particle velocity \(v_{p}\), maximum entropy distributions developed for dark matter flow lead to a particle kinetic energy \(\varepsilon _{k} \propto v_{p}\) at small acceleration \(a a_{0}\). Combining this with the constant rate of energy cascade \(\varepsilon _{u}\), both Newtonian dynamics and "deep-MOND" behavior can be fully recovered. A notable ...

العلاقة: handle:110.48550/arXiv.2202.00910; https://zenodo.org/record/6640386Test; https://doi.org/10.48550/arXiv.2203.05606Test; oai:zenodo.org:6640386

الإتاحة: https://doi.org/10.48550/arXiv.2203.05606Test
https://doi.org/10.5281/zenodo.6569901Test
https://doi.org/10.5281/zenodo.6569898Test
https://doi.org/10.5281/zenodo.6541230Test
https://doi.org/10.5281/zenodo.6586212Test
https://doi.org/10.48550/arXiv.2109.12244Test
https://doi.org/10.48550/arXiv.2110.03126Test
https://doi.org/10.48550/arXiv.2110.05784Test
https://doi.org/10.48550/arXiv.2110.09676Test
https://doi.org/10.48550/arXiv.2110.13885Test

المؤلفون: Xu, Zhijie (Jay)

مصطلحات موضوعية: cosmology, dark matter, turbulence, simulation, astronomy, astrophysics, dark matter halo, correlation, statistical analysis, self-gravitating, collisionless, N body, mass cascade, energy cascade, baryonic-to-halo mass ratio, stellar-to-halo mass ratio

الوصف: The baryonic-to-halo mass relation from mass and energy cascade in dark matter flow The relation between properties of galaxies and dark matter (DM) halos they reside in can be valuable to understand the structure formation and evolution. In particular, the baryonic-to-halo mass ratio (BHMR) and its evolution may provide many important insights. We first review unique properties of self-gravitating collisionless dark matter flow (SG-CFD), followed by their applications in deriving BHMR. To maximize system entropy, the long-range interaction requires a broad size of halos to be formed. These halos facilitate an inverse mass and energy cascade from small to large scales that involves a constant rate of energy cascade \(\varepsilon_u \approx -4.6\times 10^{-7} m^2/s^3\). The mass and energy cascade represent an intermediate statistically steady state of dark matter flow. In addition, dark matter flow exhibits scale-dependent flow behaviors that is incompressible on small scale and irrotational on large scale. Considering a given halo with a total baryonic mass \(m_b\), halo mass \(m_h\), halo virial size \(r_h\), and flat rotation speed \(v_f\), the baryonic-to-halo mass relation can be analytically derived by combining the baryonic Tully-Fisher relation and the rate of energy cascade \(\varepsilon_u\) in small and large halos. We found a maximum BHMR ratio ~0.076 for halos with a critical mass \(m_{hc}\sim 10^{12}M_{sun}\) at z=0. That ratio is much lower for both smaller and larger halos such that two regimes can be identified: i) for incompressible small halos with mass \(m_hm_{hc}\), we have \(\varepsilon_u \propto {v_f^3/r_h}\), \(v_f\propto r_h^{1/3}\), and \(m_b\propto(m_h)^{4/9}\). Combined with double-\(\lambda\) halo mass function, the average BHMR ratio in all halos (~0.024 at z=0) can be analytically derived, along with its redshift ...

العلاقة: https://zenodo.org/record/6640355Test; https://doi.org/10.48550/arXiv.2203.06899Test; oai:zenodo.org:6640355

الإتاحة: https://doi.org/10.48550/arXiv.2203.06899Test
https://doi.org/10.5281/zenodo.6569901Test
https://doi.org/10.5281/zenodo.6569898Test
https://doi.org/10.5281/zenodo.6541230Test
https://doi.org/10.5281/zenodo.6586212Test
https://doi.org/10.48550/arXiv.2109.12244Test
https://doi.org/10.48550/arXiv.2110.03126Test
https://doi.org/10.48550/arXiv.2110.05784Test
https://doi.org/10.48550/arXiv.2110.09676Test
https://doi.org/10.48550/arXiv.2110.13885Test

المؤلفون: Xu, Zhijie (Jay)

مصطلحات موضوعية: cosmology, dark matter, turbulence, simulation, astronomy, astrophysics, dark matter halo, correlation, statistical analysis, self-gravitating, collisionless, N body, Mean flow, Velocity dispersion, rotating halos, growing halos, energy transfer

الوصف: The mean flow, velocity dispersion, energy transfer and evolution of rotating and growing dark matter halos By decomposing velocity dispersion into non-spin and spin-induced, mean flow and dispersion are analytically solved for axisymmetric rotating and growing halos. The polar flow can be neglected and azimuthal flow is directly related to dispersion. The fictitious ("Reynolds") stress acts on mean flow to enable energy transfer from mean flow to random motion and maximize system entropy. For large halos (high peak height \(\nu\) at early stage of halo life) with constant concentration, there exists a self-similar radial flow (outward in core and inward in outer region). Halo mass, size and specific angular momentum increase linearly with time via fast mass accretion. Halo core spins faster than outer region. Large halos rotate with an angular velocity proportional to Hubble parameter and spin-induced dispersion is dominant. All specific energies (radial/rotational/kinetic/potential) are time-invariant. Both halo spin (~0.031) and anisotropic parameters can be analytically derived. For "small" halos with stable core and slow mass accretion (low peak height $\nu$ at late stage of halo life), radial flow vanishes. Small halos rotate with constant angular velocity and non-spin axial dispersion is dominant. Small halos are more spherical in shape, incompressible, and isotropic. Radial and azimuthal dispersion are comparable and greater than polar dispersion. Due to finite spin, kinetic energy is not equipartitioned with the greatest energy along azimuthal direction. Different from normal matter, small halos are hotter with faster spin. Halo relaxation (evolution) from early to late stage involves continuous variation of shape, density, mean flow, momentum, and energy. During relaxation, halo isotopically "stretches" with conserved specific rotational kinetic energy, increasing concentration and momentum of inertial. Halo "stretching" leads to decreasing angular velocity, increasing angular momentum and spin ...

العلاقة: https://zenodo.org/record/6640380Test; https://doi.org/10.48550/arXiv.2201.12665Test; oai:zenodo.org:6640380

الإتاحة: https://doi.org/10.48550/arXiv.2201.12665Test
https://doi.org/10.5281/zenodo.6569898Test
https://doi.org/10.5281/zenodo.6541230Test
https://doi.org/10.5281/zenodo.6586212Test
https://doi.org/10.5281/zenodo.6569901Test
https://doi.org/10.48550/arXiv.2109.12244Test
https://doi.org/10.48550/arXiv.2110.03126Test
https://doi.org/10.48550/arXiv.2110.05784Test
https://doi.org/10.48550/arXiv.2110.09676Test
https://doi.org/10.48550/arXiv.2110.13885Test

المؤلفون: Xu, Zhijie (Jay)

مصطلحات موضوعية: cosmology, dark matter, turbulence, probability distribution, simulation, astronomy, astrophysics, dark matter halo, correlation, statistical analysis, self-gravitating, collisionless, N body, density distribution, velocity distribution, two-thirds law, pairwise velocity, dark matter flow

الوصف: The scale and redshift variation of density and velocity distributions in dark matter flow and two-thirds law for pairwise velocity A halo-based non-projection approach is proposed to study the scale and redshift dependence of density and velocity distributions (PDF) in dark matter flow. All particles are divided into halo and out-of-halo particles such that PDF can be studied separately. Without projecting particle fields onto grid, scale dependence is analyzed by counting all pairs on different scales $r$. Redshift dependence is studied via generalized kurtosis. From this analysis, we can demonstrate: i) Delaunay tessellation can be used to reconstruct density field. Density correlations/spectrum are obtained, modeled and compared with theory; ii) $m$th moment of pairwise velocity can be analytically modelled. On small scale, even order moments can be modelled by a two-thirds law \(\langle(\Delta u_L)^{2n}\rangle\propto{(-\epsilon_ur)}^{2/3}\), while odd order moments \(\langle(\Delta u_L)^{2n+1}\rangle=(2n+1)\langle(\Delta u_L)^{2n}\rangle\langle\Delta u_L\rangle\propto{r}\) and satisfy a generalized stable clustering hypothesis (GSCH); iii) Scale dependence is studied for longitudinal velocity \(u_L\) or \(u_L^{'}\), pairwise velocity (velocity difference) \(\Delta u_L=u_L^{'}-u_L\) and velocity sum \(\Sigma u_L=u^{'}_L+u_L\). Fully developed velocity fields are never Gaussian on any scale; iv) On small scale, both \(u_L\) and \(\Sigma u_L\) can be modelled by a \(X\) distribution to maximize system entropy. Distributions of \(\Delta u_L\) is different with its moments analytically derived; v) On large scale, both \(\Delta u_L\) and \(\Sigma u_L\) can be modelled by a logistic function; vi) Redshift evolution of velocity distributions follows prediction of X distribution with a decreasing shape parameter \(\alpha(z)\) to continuously maximize system entropy. Applications of cascade and statistical theory for dark matter and bulge-SMBH evolution: Dark matter particle mass ,size, and properties from energy ...

العلاقة: handle:110.48550/arXiv.2110.03126; https://zenodo.org/record/6640676Test; https://doi.org/10.48550/arXiv.2202.06515Test; oai:zenodo.org:6640676

الإتاحة: https://doi.org/10.48550/arXiv.2202.06515Test
https://doi.org/10.5281/zenodo.6569898Test
https://doi.org/10.5281/zenodo.6541230Test
https://doi.org/10.5281/zenodo.6586212Test
https://doi.org/10.5281/zenodo.6569901Test
https://doi.org/10.48550/arXiv.2109.12244Test
https://doi.org/10.48550/arXiv.2110.05784Test
https://doi.org/10.48550/arXiv.2110.09676Test
https://doi.org/10.48550/arXiv.2110.13885Test
https://doi.org/10.48550/arXiv.2201.12665Test

المؤلفون: Xu, Zhijie (Jay)

مصطلحات موضوعية: cosmology, dark matter, turbulence, simulation, astronomy, astrophysics, dark matter halo, correlation function, structure function, statistical analysis, self-gravitating, collisionless, N body, Kinematic relation, Dynamic relation, velocity correlation

الوصف: The statistical theory of dark matter flow and high order kinematic and dynamic relations for velocity correlation functions Statistical theory for self-gravitating collisionless dark matter flow is not fully developed because of 1) intrinsic complexity involving constant divergence flow on small scale and irrotational flow on large scale; 2) lack of self-closed description for peculiar velocity; and 3) mathematically challenging. To better understand dark matter flow, kinematic and dynamic relations among different statistical measures of velocity must be developed for different types of flow. In this paper, a compact derivation is presented to formulate general kinematic relations of any order for incompressible, constant divergence, and irrotational flow. Results are validated by N-body simulation. Dynamic relations can only be determined from self-closed description of velocity evolution. On large scale, we found i) third order velocity correlation can be related to density correlation or pairwise velocity; ii) effective viscosity in adhesion model originates from velocity fluctuations; iii) negative viscosity is due to inverse energy cascade; iv) \(q\)th order velocity correlations follow \(\propto a^{(q+2)/2}\) for odd q and \(\propto a^{q/2}\) for even q; v) overdensity is proportional to density correlation on the same scale, \(\langle\delta\rangle\propto\langle\delta\delta'\rangle\); vi) (reduced) velocity dispersion is proportional to density correlation on the same scale. On small scale, self-closed description for velocity evolution is developed by decomposing velocity into motion in halo and motion of halos. Vorticity, enstrophy, and energy evolution can all be derived from self-closed equation for velocity. Dynamic relation is derived to relate second and third order correlations. Third moment of pairwise velocity is determined by energy cascade rate \(\epsilon_u\) or \(\langle(\Delta u_L)^3\rangle\propto\epsilon_uar\). Finally, combined kinematic and dynamic relations determines the exponential ...

العلاقة: https://zenodo.org/record/6640684Test; https://doi.org/10.48550/arXiv.2202.02991Test; oai:zenodo.org:6640684

الإتاحة: https://doi.org/10.48550/arXiv.2202.02991Test
https://doi.org/10.5281/zenodo.6569898Test
https://doi.org/10.5281/zenodo.6541230Test
https://doi.org/10.5281/zenodo.6586212Test
https://doi.org/10.5281/zenodo.6569901Test
https://doi.org/10.48550/arXiv.2109.12244Test
https://doi.org/10.48550/arXiv.2110.03126Test
https://doi.org/10.48550/arXiv.2110.05784Test
https://doi.org/10.48550/arXiv.2110.09676Test
https://doi.org/10.48550/arXiv.2110.13885Test