The scale and redshift variation of density and velocity distributions in dark matter flow and two-thirds law for pairwise velocity. (arXiv:2202.06515v2 [astro-ph.CO] UPDATED)

The scale and redshift variation of density and velocity distributions in dark matter flow and two-thirds law for pairwise velocity. (arXiv:2202.06515v2 [astro-ph.CO] UPDATED)
<a href="http://arxiv.org/find/astro-ph/1/au:+Xu_Z/0/1/0/all/0/1">Zhijie Xu</a>

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
$langle(Delta u_L)^{2n}ranglepropto{(-epsilon_ur)}^{2/3}$, while odd order
moments $langle(Delta u_L)^{2n+1}rangle=(2n+1)langle(Delta
u_L)^{2n}ranglelangleDelta u_Lranglepropto{r}$ 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.

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
$langle(Delta u_L)^{2n}ranglepropto{(-epsilon_ur)}^{2/3}$, while odd order
moments $langle(Delta u_L)^{2n+1}rangle=(2n+1)langle(Delta
u_L)^{2n}ranglelangleDelta u_Lranglepropto{r}$ 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.

http://arxiv.org/icons/sfx.gif