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Conformal Gravity in the X-ray Cluster Abell 2029

Conformal Gravity in the X-ray Cluster Abell 2029. galaxies. Keith Horne SUPA St Andrews. monster galaxy. 10 8 K gas. Mannheim-Kazanas metric. Source-free field equations:. Static, spherical symmetry:. Analogous results including rotation and charge. Solar System Dynamics.

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Conformal Gravity in the X-ray Cluster Abell 2029

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  1. Conformal Gravity in the X-ray Cluster Abell 2029 galaxies Keith Horne SUPA St Andrews monster galaxy 108K gas

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

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

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

  8. 200 Kpc Probes gravity on 10x larger scales 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.

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

  10. Lewis, Stocke, Buote 2002. X-ray Gas 3-300 kpc r(r) T(r) cs(r) sgals P(r) v* sin(i)

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

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

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

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

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

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

  18. Field Equations

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

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

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

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

  23. Thanks for Listening !

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