Modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies

作     者：James Q.Feng C.F.Gallo 

作者机构：Superconix Inc2440 Lisbon AvenueLake ElmoMN 55042USA 

出 版 物：《Research in Astronomy and Astrophysics》 (天文和天体物理学研究（英文版）)

年 卷 期：2011年第11卷第12期

页      面：1429-1448页

核心收录：

学科分类：07[理学] 070401[理学-天体物理] 0704[理学-天文学] 

基　　金：Noteworthy here is that the(removable)singularities in the kernels of the integral equation when properly treated lead to a diagonally dominant Jacobian matrix with a bounded condition number in the Newton-Raphson formulation(Pressetal.1988) This fact makes the matrix equation robust for any straightforward matrix solver 

主　　题：galaxy: disk    galaxies: general    galaxies: kinematics and dynamics    galaxies: structure    methods: numerical and analytical 

摘      要：We present an efficient, robust computational method for modeling the Newtonian dynamics for rotation curve analysis of thin-disk galaxies. With appropriate mathematical treatments, the apparent numerical difficulties associated with singularities in computing elliptic integrals are completely removed. Using a boundary element discretization procedure, the governing equations are transformed into a linear algebra matrix equation that can be solved by straightforward Gauss elimination in one step without further iterations. The numerical code implemented according to our algorithm can accurately determine the surface mass density distribution in a disk galaxy from a measured rotation curve （or vice versa）. For a disk galaxy with a typical flat rotation curve, our modeling results show that the surface mass density monotonically decreases from the galactic center toward the periphery, according to Newtonian dynamics. In a large portion of the galaxy, the surface mass density follows an approximately exponential law of decay with respect to the galactic radial coordinate. Yet the radial scale length for the surface mass density seems to be generally larger than that of the measured brightness distribution, suggesting an increasing mass-tolight ratio with the radial distance in a disk galaxy. In a nondimensionalized form, our mathematical system contains a dimensionless parameter which we call the ＂galactic rotation number＂ that represents the gross ratio of centrifugal force and gravitational force. The value of this galactic rotation number is determined as part of the numerial solution. Through a systematic computational analysis, we have illustrated that the galactic rotation number remains within 4-10% of 1.70 for a wide variety of rotation curves. This implies that the total mass in a disk galaxy is proportional to V02 Rg, with V0 denoting the characteristic rotation velocity （such as the ＂flat＂ value in a typical ro- tation curve） and Rg the radius of the galacti