On the statistical theory of self-gravitating collisionless dark matter flow: Scale and redshift variation of velocity and density distributions
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2022
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| _version_ | 1866915036037906432 |
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| author | Xu, Zhijie |
| author_facet | Xu, Zhijie |
| contents | This paper studies the scale and redshift variation of density and velocity distributions in self-gravitating collisionless dark matter flow by a halo-based non-projection approach. All particles are divided into halo and out-of-halo particles for redshift variation of distributions. Without projecting particle fields onto a structured grid, the scale variation is analyzed by identifying all particle pairs on different scales $r$. We demonstrate that: i) Delaunay tessellation can be used to reconstruct the density field. The density correlation, spectrum, and dispersion functions were obtained, modeled, and compared with the N-body simulation; ii) the velocity distributions are symmetric on both small and large scales and are non-symmetric with a negative skewness on intermediate scales due to the inverse energy cascade at a constant rate $\varepsilon_u$; iii) On small scales, the even order moments of pairwise velocity $Δu_L$ follow a two-thirds law $\propto{(-\varepsilon_ur)}^{2/3}$, while the odd order moments follow a linear scaling $\langle(Δu_L)^{2n+1}\rangle=(2n+1)\langle(Δu_L)^{2n}\rangle\langleΔu_L\rangle\propto{r}$; iv) The scale variation of the velocity distributions was studied for longitudinal velocities $u_L$ or $u_L^{'}$, pairwise velocity (velocity difference) $Δu_L$=$u_L^{'}$-$u_L$ and velocity sum $Σu_L$=$u^{'}_L$+$u_L$. Fully developed velocity fields are never Gaussian on any scale, despite that they can initially be Gaussian; v) On small scales, $u_L$ and $Σu_L$ can be modeled by a $X$ distribution to maximize the system entropy; vi) On large scales, $Δu_L$ and $Σu_L$ can be modeled by a logistic or a $X$ distribution; vii) the redshift variation of the velocity distributions follows the evolution of the $X$ distribution involving a shape parameter $α(z)$ decreasing with time. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2202_06515 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On the statistical theory of self-gravitating collisionless dark matter flow: Scale and redshift variation of velocity and density distributions Xu, Zhijie Cosmology and Nongalactic Astrophysics Astrophysics of Galaxies Fluid Dynamics This paper studies the scale and redshift variation of density and velocity distributions in self-gravitating collisionless dark matter flow by a halo-based non-projection approach. All particles are divided into halo and out-of-halo particles for redshift variation of distributions. Without projecting particle fields onto a structured grid, the scale variation is analyzed by identifying all particle pairs on different scales $r$. We demonstrate that: i) Delaunay tessellation can be used to reconstruct the density field. The density correlation, spectrum, and dispersion functions were obtained, modeled, and compared with the N-body simulation; ii) the velocity distributions are symmetric on both small and large scales and are non-symmetric with a negative skewness on intermediate scales due to the inverse energy cascade at a constant rate $\varepsilon_u$; iii) On small scales, the even order moments of pairwise velocity $Δu_L$ follow a two-thirds law $\propto{(-\varepsilon_ur)}^{2/3}$, while the odd order moments follow a linear scaling $\langle(Δu_L)^{2n+1}\rangle=(2n+1)\langle(Δu_L)^{2n}\rangle\langleΔu_L\rangle\propto{r}$; iv) The scale variation of the velocity distributions was studied for longitudinal velocities $u_L$ or $u_L^{'}$, pairwise velocity (velocity difference) $Δu_L$=$u_L^{'}$-$u_L$ and velocity sum $Σu_L$=$u^{'}_L$+$u_L$. Fully developed velocity fields are never Gaussian on any scale, despite that they can initially be Gaussian; v) On small scales, $u_L$ and $Σu_L$ can be modeled by a $X$ distribution to maximize the system entropy; vi) On large scales, $Δu_L$ and $Σu_L$ can be modeled by a logistic or a $X$ distribution; vii) the redshift variation of the velocity distributions follows the evolution of the $X$ distribution involving a shape parameter $α(z)$ decreasing with time. |
| title | On the statistical theory of self-gravitating collisionless dark matter flow: Scale and redshift variation of velocity and density distributions |
| topic | Cosmology and Nongalactic Astrophysics Astrophysics of Galaxies Fluid Dynamics |
| url | https://arxiv.org/abs/2202.06515 |