Transcript MOND
MOND Modified Newtonian Dynamics A Humble Introduction Markus Nielbock Johannes Kepler 1571 - 1630 Isaac Newton 1643 - 1727 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 Newton‘s Gravity GMm Gravitation: Fg g m 2 R m free weight of m is zero, accelerated with a m fixed g assigns a weight to m / Centrifugal force: 3. Keplerian Law Solar System GM 2 R 2 P 4π 3 Solar System Rotation Curve GM v R Galaxies The laws of physics concerning (Newtonian) gravitation seem to be transferrable from laboratory scales to the solar system. We are confident, they are valid even on larger scales like galaxies. Rotation curve: GM ( R) v R Rotation Curves of Galaxies Observations contradict theoretical predictions. 1. Orbital velocities are too high. measured 2. Rotation curves stay flat. GM ( R) v R gas „Dark Matter“ MOND Modified Newtonian Dynamics Milgrom (1983) based on Newtonian, non-relativistic gravitational theory modification of inertia modification of gravity if if New fundamental constant: (empirical) Might be a coincidence. MOND Modified Newtonian Dynamics analytic form of µ unknown, often assumed to be like: μx x 1 x2 MOND Modified Newtonian Dynamics if Gravitational forces in bound systems mostly Newtonian. Only at large distances from the central mass (e.g. in galaxies), the acceleration declines below a0 (R = 11.8 kpc for M = 1011 M). In our solar system, the gravitational acceleration of all planets lies well above a0. But: a = a0 for R = 7700 AU Oort Cloud Rotation Curves with MOND What is the rotation velocity with MOND, where ? Gravitational acceleration: GMa0 a R Centrifugal force: v2 a R GMa0 v 2 R R v (GMa0 ) 1 4 For a given mass, the rotation velocity converges to a constant value. This is in accord with observations. v ~ L 4 Tully-Fisher 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 a0 and use the M/L ratio as the only free parameter Comparison: MOND vs. Dark Matter HSB galaxies Begeman et al. (1991) Comparison: MOND vs. Dark Matter LSB galaxies Begeman et al. (1991) • MOND fits rotation curves as good as „Dark Matter“ or better • substantial improvement for LSB galaxies The Critical Surface Density Can we find a diagnostic quantity that indicates the validity of MOND? M M 2 A πR GM a a 2 R πG A M Galaxy a0 M Critical surface density: m 228 2 πG pc M Spiral galaxies: 1000 2 rotation curves Keplerian-like pc LSB galaxies: rotation curves rising asymptotically h NGC 2903 Disk Instabilities • rotating, gravitating systems unstable • galactic bar formation • in MOND: m (Spirals) B • most spiral galaxies should have bars • corroborated by observations (NIR) Ks Isothermal Pressure-Supported Systems r M radial velocity dispersion: 11 10 M 100 km s 4 • Elliptical galaxies similar to Faber-Jackson relation Isothermal spheres with r 100 300 km s have galactic mass. • Molecular clouds MOND predicts „dark matter“ problem low-mass extension of Faber-Jackson relation 105 M for typical velocity dispersion ~5 km/s 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? Difficulties and Problems with MOND • claims a0 may not be universal not confirmed: data quality, poor statistics • The case NGC 2841 poor fit distance derived from redshift distance free fitting parameter excellent fit Cepheid distance: 14.1 Mpc Cepheid calib. T-F: 23 Mpc Supernova (Ia ?): 24 Mpc Sanders (1996) 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 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.