论文标题
星系的三点相关函数的分析方程：至密度扰动的三阶
Analytical Equation of Three-point Correlation Function of Galaxies: to Third Order of Density Perturbation
论文作者
论文摘要
通过牛顿重力将功能分化应用于密度场，我们获得了星系$的三点相关函数的静态非线性方程，到达三阶密度扰动。我们使方程关闭并执行质量和牛仔裤波数的重新归一化。 Using the boundary condition inferred from observations, we obtain the third order solution $ζ(r, u, θ)$ at fixed $u=2$, which is positive, exhibits a $U$-shape along the angle $θ$, and decreases monotonously along the radial $r$ up to the range $r \leq 30\, h^{-1}$Mpc in our computation.相应的减少$ Q（r，u，θ）$偏离了高斯案例的1个，沿$θ$具有更深的$ u $ $ $ shape，并且沿$ r $ a $ a $ a $ u $θ$。第三阶解决方案与星系的SDSS数据一致，非常接近上一阶解决方案，尤其是在大尺度上。这表明相关函数的方程与密度扰动的增加顺序提供了对非线性星系系统的稳定描述。
Applying functional differentiation to the density field with Newtonian gravity, we obtain the static, nonlinear equation of the three-point correlation function $ζ$ of galaxies, to the third order density perturbations. We make the equation closed and perform renormalization of the mass and the Jeans wavenumber. Using the boundary condition inferred from observations, we obtain the third order solution $ζ(r, u, θ)$ at fixed $u=2$, which is positive, exhibits a $U$-shape along the angle $θ$, and decreases monotonously along the radial $r$ up to the range $r \leq 30\, h^{-1}$Mpc in our computation. The corresponding reduced $Q(r, u, θ)$ deviates from 1 of the Gaussian case, has a deeper $U$-shape along $θ$, and varies non-monotonously along $r$. The third order solution agrees with the SDSS data of galaxies, quite close to the previous second order solution, especially at large scales. This indicates that the equations of correlation functions with increasing orders of density perturbation provide a stable description of the nonlinear galaxy system.
