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The Galactic Halo Rotation by Weyl Incorporated Gravity

Asghar Qadir, Ashmal Shahid, Noraiz Tahir

Abstract

A modification of the Einstein-Hilbert Lagrangian by introducing a coupling between the Weyl tensor and the stress-energy tensor was proposed to explain flat galactic rotation curves without the exotic (non-baryonic) dark matter (DM) [1]. The proposed coupling constant was previously determined by fitting the rotational velocities of the Milky Way and M31 modeled with constant density, yielding the same coupling constant for both [2,3]. In this work, we have modified the formalism for a variable density by modeling the galactic systems with realistic, spherically symmetric and radially varying density profiles for the baryonic matter and this analysis is applied to seven edge-on spiral galaxies of the local cluster [4-10] and the Milky Way.

The Galactic Halo Rotation by Weyl Incorporated Gravity

Abstract

A modification of the Einstein-Hilbert Lagrangian by introducing a coupling between the Weyl tensor and the stress-energy tensor was proposed to explain flat galactic rotation curves without the exotic (non-baryonic) dark matter (DM) [1]. The proposed coupling constant was previously determined by fitting the rotational velocities of the Milky Way and M31 modeled with constant density, yielding the same coupling constant for both [2,3]. In this work, we have modified the formalism for a variable density by modeling the galactic systems with realistic, spherically symmetric and radially varying density profiles for the baryonic matter and this analysis is applied to seven edge-on spiral galaxies of the local cluster [4-10] and the Milky Way.

Paper Structure

This paper contains 6 sections, 13 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Review of MORD and its Application to the Milky Way Halo
  3. Brief Review of MORD
  4. The Milky Way Halo Rotational Velocity
  5. Halo Rotational Velocity of other Edge-on Spiral Galaxies
  6. Results and Discussion

Figures (2)

  • Figure 1: The comparison of the three density profiles: the NFW (Blue Curve); Moore (Orange curve); and Burkert (Green Curve) profiles of the Milky Way halo up to $100$ kpc tahir2023galactic, for $r_c= 4.5$ kpc, and $\rho_c=6.99 \times 10^{-23}~{\rm g/cm^3}$shin2007.
  • Figure 2: The total mass of the Milky Way halo within $100$ kpc obtained by using eq. (\ref{['massequation']}). The blue curve represents the mass profile from the NFW model, the orange curve represents the mass profile from the Moore model, and the green curve represents the mass profile obtained from the Burkert model, respectively.