Abstract
We have derived exact axisymmetric solutions of the two-dimensional Lane-Emden equations with rotation. These solutions are intrinsically favored by the differential equations regardless of any adopted boundary conditions and the physical solutions of the Cauchy problem are bound to oscillate about and remain close to these intrinsic solutions. The isothermal solutions are described by power-law density profiles in the radial direction, whereas the polytropic solutions are described by radial density profiles that are powers of the zeroth-order Bessel function of the first kind. Both families of solutions decay exponentially in the vertical direction and both result in increasing or nearly flat radial rotation curves. The results are applicable to gaseous spiral-galaxy disks that exhibit flat rotation curves and to the early stages of protoplanetary disk formation before the central star is formed.
Highlights
We use a new method to solve analytically the axisymmetric Lane-Emden equations [1] [2] with rotation in two dimensions
We have derived exact axisymmetric solutions of the two-dimensional Lane-Emden equations with rotation. These solutions are intrinsically favored by the differential equations regardless of any adopted boundary conditions and the physical solutions of the Cauchy problem are bound to oscillate about and remain close to these intrinsic solutions
The isothermal solutions are described by power-law density profiles in the radial direction, whereas the polytropic solutions are described by radial density profiles that are powers of the zeroth-order Bessel function of the first kind
Summary
We use a new method to solve analytically the axisymmetric Lane-Emden equations [1] [2] with rotation in two dimensions. The method is an extension of the one-dimensional algorithm that we applied to ordinary second-order differential equations of mathematical physics [3] [4] [5] and produces separable equations in two dimensions [6]. The two-dimensional analytic solutions show that both the densities and the rotation. We derive the exact solutions of the 2-D Lane-Emden equations with rotation in the isothermal case (Section 2) and in the general polytropic case (Section 3), and we discuss the astrophysical implications of our results (Section 4)
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
