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.