论文标题
精确的分析近似Sérsic概况
A Precise Analytical Approximation for the Deprojection of the Sérsic Profile
论文作者
论文摘要
已知Sérsic模型非常适合椭圆星系和星系凸起的表面亮度（或表面密度）曲线，可能适合矮球星系和球形簇。去底密度和质量谱对于许多天体物理应用很重要，尤其是这些系统的质量轨道建模。但是，SérsicModel的确切depRoction公式采用了大多数计算机语言中无法使用的特殊功能。我们表明，以前对3D密度概况的所有分析近似在低sérsic索引（$ n \ lyssim 1.5 $）处不精确。我们通过将二维10阶多项式与数值deprodotion的对数差异和Lima Neto Neto Neto Neto等人的分析近似差异拟合，从而得出了更精确的分析近似。 （1999，LGM）一方面的密度曲线和另一只手的质量分布。我们的基于LGM的多项式拟合的密度和质量配置文件的典型相对精度优于$ 0.2 \％$，Sérsic指数$ 0.5 \ leq n \ leq N \ leq 10 $和Radii $ 0.001 <r/r/r _ {\ rm e} <1000 $。我们的近似值比LGM，Simonneau＆Prada（1999，2004），Trujillo等人要精确得多。 （2002年）对于该索引的非半数值，以及Emsellem＆van de Ven（2008）的非第十一位值，具有$ n \ lyssim 3 $，但对于较大的Sérsic独立组件，对于密度和质量配置文件而言，对于较大的Sérsic和sérsic的$ 0.2 \％$精确。附录将被删除的sérsic概况与Plummer（1911），Jaffe（1983），Hernquist（1990），Navarro等人的流行简单模型的简单模型进行了比较。 （1996）和Einasto（1965）。
The Sérsic model is known to fit well the surface brightness (or surface density) profiles of elliptical galaxies and galaxy bulges, and possibly for dwarf spheroidal galaxies and globular clusters. The deprojected density and mass profiles are important for many astrophysical applications, in particular for mass-orbit modeling of these systems. However, the exact deprojection formula for the Sérsic model employs special functions not available in most computer languages. We show that all previous analytical approximations to the 3D density profile are imprecise at low Sérsic index ($n \lesssim 1.5$). We have derived a more precise analytical approximation to the deprojected Sérsic density profile by fitting two-dimensional 10th-order polynomials to the differences of the logarithms of the numerical deprojection and of the analytical approximation by Lima Neto et al. (1999, LGM) of the density profile on one hand and of the mass profile on the other. Our LGM-based polynomial fits have typical relative precision better than $0.2\%$ for both density and mass profiles, for Sérsic indices $0.5 \leq n \leq 10$ and radii $0.001 < r/R_{\rm e} < 1000$. Our approximation is much more precise than those of LGM, Simonneau & Prada (1999, 2004), Trujillo et al. (2002) for non-half-integer values of the index, and of Emsellem & van de Ven (2008) for non-one-tenth-integer values with $n \lesssim 3$, and are nevertheless more than $0.2\%$ precise for larger Sérsic indices, for both density and mass profiles. An appendix compares the deprojected Sérsic profiles with those of the popular simple models from Plummer (1911), Jaffe (1983), Hernquist (1990), Navarro et al. (1996), and Einasto (1965).
