# 10.12. Light profiles¶

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

 Keyword Surface brightness $$\Sigma(R)\equiv I(R)$$ Density profile $$\rho(r) \equiv\nu(r)$$ # free param. References kEXP2D $$\mathbf{\Sigma_0 \times \exp\left(-\frac{R}{r_c}\right)}$$ $$\rightarrow$$ $$\frac{\Sigma_0}{\pi r_c}\times K_0\left(\frac{r}{r_c}\right)$$ 2 Evans, An, and Walker (2009) kEXP3D $$2\rho_0 \,R\times K_1\left(\frac{R}{r_c}\right)$$ $$\leftarrow$$ $$\mathbf{\rho_0 \times \exp\left(-\frac{r}{r_c}\right)}$$ 2 Evans, An, and Walker (2009) kKING2D $$\mathbf{\Sigma_0\times\bigg[\left(1+\frac{R^2}{r_c^2}\right)^{-1/2}}$$ $$\mathbf{-\left(1+\frac{r_{\rm lim}^2}{r_c^2}\right)^{-1/2}\bigg]^2}$$ $$\rightarrow$$ $$\frac{\Sigma_0}{\pi r_c}\times\frac{\cos^{-1}(z)/z-\sqrt{1-z^2}}{z^2(1+r_{\rm lim}^2/r_c^2)^{3/2}}$$ with $$z^2 = \frac{1+r^2/r_c^2}{1+r_{\rm lim}^2/r_c^2}$$ 3 King (1962), Strigari et al. (2008) kPLUMMER2D $$\mathbf{\frac{\Sigma_0}{\pi r_c^2}\times \left(1+\frac{R^2}{r_c^2}\right)^{-2}}$$ $$\rightarrow$$ $$\frac{3\Sigma_0}{4\pi r_c^3}\times \left(1+\frac{r^2}{r_c^2}\right)^{-5/2}$$ 2 Plummer (1911), Evans et al. (2009) kSERSIC2D $$\mathbf{\Sigma_0\!\times\!\exp\left\{\!-b_n\!\left[\left(\frac{R}{r_c}\right)^{\frac{1}{n}}\!-\!\!1\right]\right\}}$$ with $$b_n=2n-1/3+0.009876/n$$ $$\rightarrow$$ $$-\frac{1}{\pi} \int_r^\infty \frac{{\rm d}\Sigma(R)}{{\rm d}R}\times \frac{{\rm d}R}{\sqrt{R^2-r^2}}$$ 3 Sérsic (1968), Prugniel & Simien (1997), Graham and Driver (2005), Merritt et al. (2006) kZHAO3D $$2 \int_R^\infty \rho(r)\,r\times\frac{{\rm d}r}{\sqrt{r^2-R^2}}$$ $$\leftarrow$$ $$\mathbf{\rho_0\times\frac{(r/r_s)^{-\gamma}}{\left[1+\left(\frac{r}{r_s}\right)^\alpha\right]^{(\beta-\gamma)/\alpha}}}$$ 5 Hernquist (1990), Zhao (1996)

See also