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)