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MOND Modified Newtonian Dynamics A Humble Introduction Johannes Kepler Isaac Newton Markus Nielbock

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Overview Gravitational Law (Newton/Kepler) Application: Solar System (Theory/Observation) Application: Galaxies (Theory/Observation) Modification of Newton‘s Gravitational Law Consequences of MOND (rotation curves, surface density, isothermal spheres) Difficulties Summary

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Newton‘s Gravity Gravitation: m fixed g assigns a weight to m m free weight of m is zero, accelerated with a / 3. Keplerian Law Centrifugal force:

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Solar System

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Solar System Rotation Curve

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Galaxies The laws of physics concerning (Newtonian) gravitation seem to be transferrable from laboratory scales to the solar system. Rotation curve: We are confident, they are valid even on larger scales like galaxies.

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Rotation Curves of Galaxies measured stars gas Observations contradict theoretical predictions. 1. Orbital velocities are too high. 2. Rotation curves stay flat. „Dark Matter“

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MOND Modified Newtonian Dynamics Might be a coincidence. if New fundamental constant: (empirical) based on Newtonian, non-relativistic gravitational theory Milgrom (1983) modification of inertiamodification of gravity if

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MOND Modified Newtonian Dynamics analytic form of µ unknown, often assumed to be like:

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MOND Modified Newtonian Dynamics if Gravitational forces in bound systems mostly Newtonian. In our solar system, the gravitational acceleration of all planets lies well above a 0. But: a = a 0 for R = 7700 AU Oort Cloud Only at large distances from the central mass (e.g. in galaxies), the acceleration declines below a 0 ( R = 11.8 kpc for M = M ).

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Rotation Curves with MOND What is the rotation velocity with MOND, where ? Gravitational acceleration: Centrifugal force: For a given mass, the rotation velocity converges to a constant value. This is in accord with observations. Tully-Fisher

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Rotation Curves with MOND The fitting procedure: assumption: M/L is constant NIR surface photometry preferred (old stars, extinction) include neutral hydrogen and correct for helium abundance calculate the Newtonian gravitational force for a thin disk and add a bulge, if necessary calculate the MONDian gravitational force with a fixed a 0 and use the M/L ratio as the only free parameter

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Comparison: MOND vs. Dark Matter Begeman et al. (1991) HSB galaxies

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Comparison: MOND vs. Dark Matter Begeman et al. (1991) LSB galaxies MOND fits rotation curves as good as „Dark Matter“ or better substantial improvement for LSB galaxies

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The Critical Surface Density Can we find a diagnostic quantity that indicates the validity of MOND? M h A Galaxy Critical surface density: LSB galaxies: rotation curves rising asymptotically Spiral galaxies:rotation curves Keplerian-like

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Disk Instabilities rotating, gravitating systems unstable in MOND: (Spirals) galactic bar formation NGC 2903 BKs most spiral galaxies should have bars corroborated by observations (NIR)

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Isothermal Pressure-Supported Systems Elliptical galaxies radial velocity dispersion: similar to Faber-Jackson relation Isothermal spheres with have galactic mass. Molecular clouds MOND predicts „dark matter“ problem low-mass extension of Faber-Jackson relation 10 5 M for typical velocity dispersion ~ 5 km/s

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The Equivalence Principle Inertia and weight are not equivalent. Mass of weight and mass of inertia are not the same, but depend on the state of acceleration. Theory of Relativity?

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Difficulties and Problems with MOND claims a 0 may not be universal not confirmed: data quality, poor statistics The case NGC 2841 Sanders (1996) poor fit distance derived from redshift excellent fit distance free fitting parameter Cepheid distance: 14.1 Mpc Cepheid calib. T-F: 23 Mpc Supernova (Ia ?): 24 Mpc

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Difficulties and Problems with MOND MOND is derived from classical Newtonian Gravitational Theory, and therefore is incompatible with General Relativity. Just like Newtons Gravity, MOND cannot give reliable answers to: Cosmology Relativistic Phenomena

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Summary Rotation curves of galaxies are not Keplerian/Newtonian. Apparently contain more matter than is visible (Dark Matter). Alternative Explanation: Modification of Gravity (MOND) MOND describes galactic rotation curves very well. MOND provides predictions verified by observations. Just like Newton‘s Gravity, MOND cannot explain relativististic effects. Dark Matter and MOND should be treated equally.

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