# 10.11. Anisotropy profiles $$\beta_{\rm ani}(r)$$¶

Possible keyword choices for the anisotropy profile to be set in the file gLIST_HALOES_JEANS (no named variable):

 Keyword Anisotropy $$\beta_{\rm anis}(r)$$ $$f(r)$$ to solve Eq. (6.12) $$=\nu(r)\bar{v_r^2}(r)$$ Kernel $${\cal K}(u,u_a)$$ to solve Eq. (6.14) $$=I(R)\sigma_p^2(R)$$ Refs (for profile and/or solution) kCONSTANT $$\beta_0$$ $$r^{2\beta_0}$$ $$\frac{\sqrt{1-u^{-2}}}{1-2\beta_0}+\frac{\sqrt{\pi}}{2}\frac{\Gamma(\beta_0-1/2)}{\Gamma(\beta_0)}u^{2\beta_0-1}$$ $$\left(\frac{3}{2}-\beta_0\right)\left[1-I\left(\frac{1}{u^2},\beta_0+\frac{1}{2},\frac{1}{2}\right)\right]$$ with $$I(x,a,b)=$$ incomplete Beta function Mamon and Lokas (2005,2006) kBAES $$\frac{\beta_0 + \beta_\infty (r/r_a)^\eta}{1+(r/r_a)^\eta}$$ $$r^{2\beta_0}\left[1+\left(\frac{r}{r_a}\right)^\eta\right]^{2(\beta_\infty-\beta_0)/\eta}$$ No analytical Kernel Baes & van Hese (2007) kOSIPKOV $$\frac{r^2}{r^2+r_a^2}$$ (special case of kBAES) $$\frac{r_a^2+r^2}{r_a^2}$$ $$\displaystyle\frac{(u^2+u_a^2)(u_a+1/2)}{u(u_a^2+1)^{3/2}}\tan^{-1}\sqrt{\frac{u^2-1}{u_a^2+1}}$$ $$-\displaystyle\frac{\sqrt{1-u^{-2}}}{2(u_a^2+1)}$$ Osipkov (1979), Merritt (1985), Mamon and Lokas (2005, 2006)