Development of general functional form of the gravitational potential: Addressing the Flatness Problem in Galactic Rotation Curves

Document Type : Letter


1 Department of Physics, Government Degree College, Tangmarg, Kashmir, 193402 India

2 Department of Physics, Government Degree College Tangmarg, Jammu and Kashmir


This letter presents a mathematical model that may help address the long-standing problem of galaxy rotation curves. The strategy involves exploring the variation of circular velocity `ν' with respect to radial distance `r' as a result of which a Bessel differential equation is developed, yielding a general functional form of the potential as a Bessel function. Employing this potential in the case of galaxies, we find the velocity profile in terms of Bessel functions. This approach establishes Bessel functions as a powerful choice for investigating galactic rotation and deepening our understanding of the universe.


Main Subjects


Article PDF

 [1] V. C. Rubin, Jr. W. K. Ford, N. Thonnard, Rotational properties of 21 SC galaxies with a large range of luminosities and radii, from NGC 4605 (R= 4kpc) to UGC 2885 (R= 122 kpc), Astrophysical Journal 238, 471-487 (1980). DOI: 10.1086/158003
[2] J. Binney, S. Tremaine, Galactic dynamics, Princeton university press; 2011 Oct 30.
[3] Y. Sofue, V. Rubin, Rotation curves of spiral galaxies, Annual Review of Astronomy and Astrophysics 39 (1) 137-174 (2001). DOI: 10.1146/annurev.astro.39.1.137
[4] F. Bowman, Introduction to Bessel functions, Courier Corporation; 2012 Apr 27.
[5] A. Gray. G. B. Mathews, A treatise on Bessel functions and their applications to physics, Macmillan; 1895.
[6] Y. L. Luke, Integrals of Bessel functions, Courier Corporation; 2014 Dec 17.
[7] P. Bhattacharjee, S. Chaudhury, S. Kundu, Rotation Curve of the Milky Way out to 200 kpc, The Astrophysical Journal 785 (1), 63 (2014). DOI: 10.1088/0004-637X/785/1/63 
Volume 3, Issue 4
November 2023
Pages 1-4
  • Receive Date: 22 September 2023
  • Revise Date: 01 October 2023
  • Accept Date: 06 October 2023