arXiv subjects

Zhijie

Publications and source records attributed to Zhijie.

5 recordsLinked to original sources

arXiv2022

Dark matter halo mass functions and density profiles from mass and energy cascade

Without relying on a spherical or ellipsoidal collapse model, we analytically derive the halo mass function and cuspy halo density (inner slope of -4/3) based on the mass and energy cascade theory in dark matter flow. The hierarchical halo structure formation leads to halo or particle random walk with a position-dependent waiting time $\tau_g$. The inverse mass cascade from small to large scales leads to the halo random walk in mass space with $\tau_g\propto m_h^{-\lambda}$, where $m_h$ is the halo mass and $\lambda$ is a halo geometry parameter with predicted value of 2/3. The corresponding Fokker-Planck solution for halo random walk in mass space gives rise to the halo mass function with a power-law behavior on small scale and exponential decay on large scale. This can be further improved by considering two different $\lambda$ for haloes below and above a critical mass scale $m_h^*$, i.e. a double-$\lambda$ halo mass function. A double-$\gamma$ density profile can be derived based on the particle random walk in 3D space with a position-dependent waiting time $\tau_g \propto \Phi(r)^{-1} \propto r^{-\gamma}$, where $\Phi$ is the gravitational potential and $r$ is the particle distance to halo center. Theory predicts $\gamma=2/3$ that leads to a cuspy density profile with an inner slope of -4/3, consistent with the predicted scaling laws from energy cascade. The Press-Schechter mass function and Einasto density profile are special cases of proposed models. The small scale permanence can be identified due to the scale-independent rates of mass and energy cascade, where density profiles of different halo masses and redshifts converge to the $-4/3$ scaling law ($\rho_h \propto r^{-4/3}$) on small scales. Theory predicts halo number density scales with mass as $\propto m_h^{-1.9}$, while halo mass density scales as $\propto m_h^{4/9}$. Results were compared against the Illustris simulations.

astro-ph.CO↗

arXiv2022

On a critical acceleration scale of dark matter in Lambda-CDM and dynamical dark energy

Universal acceleration $a_0$ emerges in various empirical laws, yet its fundamental nature remains unclear. Using Illustris and Virgo N-body simulations, we propose $a_0$ is the scale of acceleration fluctuations in collisionless dark matter involving long-range gravity. In contrast, in the kinetic theory of gases, molecules undergo random elastic collisions involving short-range interactions, where only velocity fluctuations are relevant. We identify the redshift evolution $a_0\propto (1+z)^{3/4}$ that is in good agreement with Magneticum and EAGLE simulations and in reasonable agreement with limited observations. This suggests a larger $a_0$ at a higher redshift such that galaxies of fixed baryonic mass rotate faster at a higher redshift. The velocity fluctuations involve a critical velocity $u_c\propto (1+z)^{-3/4}$. The acceleration fluctuations involve a critical acceleration $a_c\propto (1+z)^{3/4}$. Two critical quantities are related by the rate of energy cascade $\varepsilon_{u}\approx -{a_c u_c/[2(3\pi)^2]}$, where factor $3\pi$ is from the angle of incidence and $\varepsilon_u\approx -10^{-7}$m$^2$/s$^3$. With critical velocity $u_c$ on the order of 300 km/s at $z=0$, the critical acceleration is determined to be $a_{c0}\equiv a_c(z=0) \approx 10^{-10}$m/s$^2$, suggesting $a_c$ might explain the universal acceleration $a_0\approx 10^{-10}$m/s$^2$ in the empirical Tully-Fisher relation or modified Newtonian dynamics (MOND). Note that dark energy (DE) density $\rho_{DE0}\approx {a_{c0}^{2}/G}=10^{-10}$J/m$^3$, we postulate an entropic origin of the dark energy from acceleration fluctuations of dark matter, in analogy to the gas pressure from velocity fluctuations. This leads to a dynamical dark energy coupled to the structure evolution involving a relatively constant DE density followed by a slow weakening phase, suggesting possible deviations from the standard $\Lambda$CDM.

astro-ph.CO↗

arXiv2022

Cold freeze out of superheavy dark matter and Hubble tension

We propose a unified dark matter framework, the "X miracle", in which dark matter consists of superheavy, nonthermal X particles whose relic abundance is set by annihilation or decay inside the earliest self-gravitating bound objects, rather than by conventional weak-scale freeze-out of semi-relativistic WIMPs. X particles are produced nonthermally with an initial overabundance $\rho_{ini}\gg\rho_{\infty}$, become nonrelativistic extremely early, and redshift to ultra-cold velocities. This permits collapse into compact bound states characterized by a quantum-gravitational radius $r_X=4\hbar^2/Gm_X^3=10^{-13}$m, much larger than the Compton wavelength. The framework favors a mass $m_X=10^{12}$GeV and an enhanced effective cross section $10^{-21}$m$^3$/s. Overlapping wavefunctions in these compact states drive efficient annihilation or decay, producing a "cold" freeze-out that converts most $\rho_{ini}$ into radiation and leaves a small relic density $\rho_{\infty}$. Solving Boltzmann equations shows that a level of depletion of one surviving particle per $10^9$ can generate $\Delta N_{eff}\approx$0.4, potentially easing Hubble tension. For $m_X=10^{12}$GeV we obtain a dark coupling $\alpha_X=0.09$, compatible with UHECR limits. Early collapse at $t\sim 10^{-6}$s can release binding energy in high-frequency (~100 kHz) gravitational waves or in ultralight GUT-scale axions with mass ~$10^{-9}$eV. Superheavy sterile neutrinos offer a natural particle realization, linking dark matter to neutrino mass generation and baryogenesis; gravitational production of X then points to high-scale inflation with efficient reheating. The X-miracle scenario demonstrates that dark matter need not be weak-scale: its abundance and observable signatures can instead be governed by small-scale gravitational dynamics, with correlated predictions for UHECRs, axions, gravitational waves, and small-scale structures.

astro-ph.CO↗

arXiv2021

Inverse energy cascade in self-gravitating collisionless dark matter flow and effects of halo shape

Halo-mediated mass and energy cascades are key to understand dark matter flow. Both cascades origin from the mass exchange between halo and out-of-halo sub-systems. Kinetic energy can be from the motion of halos and particle motion in halos. Similarly, potential energy can be due to the inter- and intra-halo interactions. Intra-halo virial equilibrium is established much faster than inter-halo. Change of energy of entire system comes from virilization in halos. At statistically steady state, continuous mass exchange is required to sustain growth of total halo mass $M_h\propto a^{1/2}$ and energy $E\propto a^{3/2}$, where $a$ is scale factor. Inverse cascade is identified for kinetic energy that is transferred from the smallest scale to large mass scales. This is sustained by the direct cascade of potential energy from large to small scale. Both energies have a scale- and time-independent flux in propagation range that is proportional to mass flux. Energy cascade is mostly facilitated by mass cascade, which can be quantitatively described by mass accretion of typical halos. Halo radial, angular momentum, and angular velocity are modelled and inverse cascade is identified for the coherent radial and rotational motion in halos. In turbulence, vortex stretching (shape changing) along its axis of spin enables energy cascade from large to small length scales. However, change in halo shape is not the dominant mechanism for energy cascade as the moment of inertial gained from shape changing is less than 2 times. Large halos exhibit preference for prolateness over oblateness and most halos have spin axis perpendicular to major axis. Since mass cascade is local in mass space, halo shape evolves continuously in mass space with halos formed by incrementally inheriting structure from progenitor halos. A unique evolution path of halos is found that gradually approaches sphere with increasing size.

astro-ph.GA↗

arXiv2021

Inverse mass cascade in dark matter flow and effects on halo deformation, energy, size, and density profiles

Inverse mass cascade is a key feature of the intermediate statistically steady state for self-gravitating collisionless dark matter flow (SG-CFD). This paper focus on effects of mass cascade on halo energy, momentum, dispersion, size, and density. Halo with fast mass accretion has an expanding core. Mass cascade forms a new layer of mass that deforms the original halo and induces nonzero radial flow (outwards in core and inwards in outer regions). The inward/outward flow leads to an extra length scale (scale radius) that is not present in isothermal profile. Halo concentration c=3.5 can be derived for fast growing halos. For cusp-core controversy, a double-power-law density is proposed as a result of nonzero radial flow. The inner/outer density are controlled by halo deformation rate and halo growth, respectively. The slower deformation at center, the steeper density. For fast growing halos, radial flow at center is simply Hubble flow that leads to the existence of central core. Mass cascade leads to nonzero halo surface energy/tension and radial flow that enhances dispersion in outer region. An effective exponent of gravity $n_e$=-1.3 (not -1) is obtained due to halo surface energy. Halo size follows a geometric Brownian motion and lognormal distribution. Brownian motion of particles in evolving halos leads to Fokker-Planck equations for particle distribution that is dependent on the radial and osmotic flow. Complete solutions of particle distribution are presented based on a simple model of osmotic flow. The proposed model agrees with N-body simulation for various halo group sizes. With reference pressure/density defined at center, equation of state can be established for relative pressure/density. Pressure, density, and dispersion at halo center are presented. The core size $x_c$ is obtained where Hubble flow is dominant. Simple closures are proposed for self-consistent halo density.

astro-ph.CO↗