1. Conformal Gravity in the X-ray Cluster Abell 2029 Keith Horne SUPA St Andrews 10 8 K gas galaxies monster galaxy

2. Mannheim-Kazanas metric Source-free field equations: Static, spherical symmetry: Analogous results including rotation and charge.

3. Solar System Dynamics Schwarzschild metric: Fixes one parameter

4. Galaxy Rotation Curves Linear potential gives a distance- independent inward acceleration.

5. Galaxy Rotation Curves Mannheim 1993, 1997. Universal inward acceleration. ( fits two more parameters)

6. Exterior mass matters ! Mannheim Newton No net force from external shells Hook’s law force toward centre of external shell

7. Rotation Curve Fits stars gas linear potentia l NGC 1560 poorest fit. Data wiggles follow the gas. Fits adjust [M/L] * All mass in edge-on disk plane.

8. Abell 2029 Chandra X-ray Image of Abell 2029 The galaxy cluster Abell 2029 is composed of thousands of galaxies enveloped in a gigantic cloud of hot gas, and an amount of dark matter equivalent to more than a hundred trillion Suns. At the center of this cluster is an enormous, elliptically shaped galaxy that is thought to have been formed from the mergers of many smaller galaxies. 200 Kpc Probes gravity on 10x larger scales

9. X-ray Gas Spherical symmetry + Hydrostatic Equilibrium: Gravity and Total Mass profile:

10. X-ray Gas 3-300 kpc T(r) P(r)  (r) c s (r) v * sin(i)  gals Lewis, Stocke, Buote 2002.

11. Newtonian Analysis 90% Dark Matter Required ! Gravity and Total Mass profiles: g(r) M(<r) gas star s gas star s g(r) M(<r) gas star s gas star s

12. g(r) M(<r) gas star s gas star s g(r) M(<r) gas star s gas star s Conformal Gravity Dark Matter NOT required ! Gravity and Total Mass profiles: Too Much Conformal Gravity!

13. Newton vs Conformal Gravity g(r) M(<r) gas star s gas star s g(r) M(<r) gas star s gas star s

14. Discussion Points : ) Dark Matter is not needed to bind the X-ray Gas. : ( Too much Conformal Gravity ! Conformal Gravity ruled out? (Not yet.) External material -- external Void ? Mannheim-Kazanas metric incomplete? Not in Higgs gauge --> vacuum polarisation. Quadratic potential terms important? External shells of distant galaxies should generate a universal quadratic potential. Gas not in hydrostatic equilibrium? Rotation/infall/outflow V > 1000 km/s? Doppler shift detectable in future X-ray spectroscopy. Stars generate the gravity -- not the hot gas? Same problem as in the colliding clusters 1E0657-56 ?

15. Conformal Symmetry Invariants: angles, velocities, light cones, causality. Weyl action: Clock ticks and rulers stretch by a factor that can vary in time and space.

16. Conformal Matter Action Fermion mass: Higgs mass: Equations of motion:

17. Ricci scalar: (negative spatial curvature). (negative vacuum energy) Dynamical Mass Generation Higgs mass: Fermion mass: Symmetry Breaking Higgs potential: Higgs potential:

18. Field Equations

19. Higgs Guage = matter + geometry + vacuum matter fields => perfect fluid Fermion mass:

20. Conformal trajectories Conformal trajectories are the geodessic trajectories in the Higgs gauge. Mannheim 1993. Fermion mass: Trajectory for which action is stationary. Test particle action.

21. Trace Condition 0 = matter + geometry + vacuum Ricci scalar in the vacuum

22. MK metric -> Higgs guage Mannheim-Kazanas metric is not in Higgs guage. Test particles will not follow MK geodessics. Ricci scalar:

23. Thanks for Listening !