SBP Profiles of Galaxies

The Sersic Function

 * Explanations on Wikipedia can be found here
 * $$I={I_0}\exp(-\frac{1}{k}r^{1/n})$$
 * $$I(r)={I_e}\exp[-{b_n}((\frac{r}{r_e})^{1/n}-1)]$$
 * For $$n>0.36$$, $${b_n}=2n-\frac{1}{3}+\frac{4}{405n}+\frac{46}{25525n^2}+\frac{131}{1148175n^3}-\frac{2194697}{30690717750n^4}$$.

Important References

 * Original definition is Sersic 1963, BAAA 
 * Stellar systems following the R exp 1/m luminosity law
 * Ciotti 1991, A&A
 * On the Shape of the Light Profiles of Early Type Galaxies
 * Caon, Capaccioli, D'Onofrio 1993, MNRAS
 * The application of Sersic profile on galaxy SBP fitting.
 * Structure of Disk-dominated Galaxies. I. Bulge/Disk Parameters, Simulations, and Secular Evolution
 * MacArthur, Courteau, Holtzman 2003, ApJ
 * Derived a accurate function for the Sersic b(n) parameter (for n<0.36)
 * A Concise Reference to (Projected) Sérsic R^1/n Quantities, Including Concentration, Profile Slopes, Petrosian Indices, and Kron Magnitudes
 * Graham & Driver 2005, PASA

Useful Tools

 * The Sersic Constant webpage by Mohammad Akhlaghi
 * For n<0.35, he derived accurate enough value of the b(n), and here is the table.
 * The Python code to derive them is also provided here


 * Example of how to simulate 2-D Sersic component using IDL by GEMS group


 * '''get_sersicb.pro by John Moustakas
 * Compute the Sersic bn parameter using Eq.1 and 4 in Graham & Driver (2005)

Multi-Gaussian Expansion

 * Replacing standard galaxy profiles with mixtures of Gaussians
 * Hogg & Lang 2012, submitted to PASP

MGE by Cappellari

 * MGE_FIT_SECTORS package
 * A set of IDL routines to perform Multi-Gaussian Expansion (MGE) fits to galaxy images
 * This software efficiently obtains an accurate Multi-Gaussian Expansion (MGE) parameterizations (Emsellem et al. 1994) for a galaxy surface brightness, with the fitting method of Cappellari (2002, MNRAS, 333, 400).

Analytical Function by Spergel

 * Analytical Galaxy Profiles for Photometric and Lensing Analysis
 * Spergel 2010, ApJS
 * $${\Sigma}_{\nu} (k)= \frac{L_0}{2\pi{\sqrt{1+({k_x}^2+{k_y}^2)(\frac{r_0}{c_{\nu}})^2}}^{1+{\nu}}}$$