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MONDModified Newtonian
DynamicsA Humble Introduction
Johannes Kepler1571 - 1630
Isaac Newton1643 - 1727
Markus Nielbock
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 GravityGravitation: mg
R
GMmFg
2
m fixed g assigns a weight to m
m free weight of m is zero, accelerated with a /
3. Keplerian Law
Centrifugal force:
Solar System
22
3
4P
π
GMR
Solar System Rotation Curve
R
GMv
GalaxiesThe laws of physics concerning (Newtonian) gravitation seem to be transferrable from laboratory scales to the solar system.
Rotation curve:
R
RGMv
)(
We are confident, they are valid even on larger scales like galaxies.
Rotation Curves of Galaxies
measured
stars
gas
Observations contradict theoretical predictions.
1. Orbital velocities are too high.
2. Rotation curves stay flat.
R
RGMv
)(
„Dark Matter“
MONDModified Newtonian Dynamics
Might be a coincidence.
if
New fundamental constant: (empirical)
based on Newtonian, non-relativistic gravitational theory
Milgrom (1983)
modification of inertia modification of gravity
if
MONDModified Newtonian Dynamics
analytic form of µ unknown, often assumed to be like:
21 x
xxμ
MONDModified Newtonian Dynamics
if
Gravitational forces in bound systems mostly Newtonian.
In our solar system, the gravitational acceleration of all planets lies wellabove a0.
But: a = a0 for R = 7700 AU Oort Cloud
Only at large distances from the central mass (e.g. in galaxies), theacceleration declines below a0 (R = 11.8 kpc for M = 1011 M).
Rotation Curves with MONDWhat is the rotation velocity with MOND, where ?
Gravitational acceleration:R
GMaa 0
Centrifugal force:R
va
2
R
v
R
GMa 20
For a given mass, the rotation velocity converges to a constant value.This is in accord with observations.
41
)( 0GMav
Lv ~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 Begeman et al. (1991)HSB
galaxies
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
The Critical Surface Density
Can we find a diagnostic quantity that indicates the validity of MOND?
Mh
A
Galaxy
2πR
M
A
M
2R
GMa
πG
a
Critical surface density: 20
pc228 M
πG
am
LSB galaxies: rotation curves rising asymptotically
Spiral galaxies:
2pc1000 M
rotation curves Keplerian-like
Disk Instabilities
• rotating, gravitating systems unstable
• in MOND: (Spirals)m
• galactic bar formation
NGC 2903
B
Ks
• most spiral galaxies should have bars
• corroborated by observations (NIR)
Isothermal Pressure-Supported Systems
• Elliptical galaxies
radial velocity dispersion:4
11 skm10010
r
M
M
similar to Faber-Jackson relation
skm300100 rIsothermal spheres with 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 inertiaare 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
Sanders (1996)
poor fitdistance derived from
redshift
excellent fit
distance free fitting parameter
Cepheid distance: 14.1 MpcCepheid calib. T-F: 23 MpcSupernova (Ia ?): 24 Mpc
Difficulties and Problems with MONDMOND is derived from classical Newtonian Gravitational Theory, andtherefore is incompatible with General Relativity.
Just like Newtons Gravity, MOND cannot give reliable answers to:
• Cosmology
• Relativistic Phenomena
SummaryRotation 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.