Hydrodynamic Stability of Newtonian and Non-Newtonian fluids
MOND Modified Newtonian Dynamics
description
Transcript of MOND Modified Newtonian Dynamics
![Page 1: MOND Modified Newtonian Dynamics](https://reader035.fdocuments.in/reader035/viewer/2022062423/56814655550346895db36e6c/html5/thumbnails/1.jpg)
MONDModified Newtonian
DynamicsA Humble Introduction
Johannes Kepler1571 - 1630
Isaac Newton1643 - 1727
Markus Nielbock
![Page 2: MOND Modified Newtonian Dynamics](https://reader035.fdocuments.in/reader035/viewer/2022062423/56814655550346895db36e6c/html5/thumbnails/2.jpg)
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
![Page 3: MOND Modified Newtonian Dynamics](https://reader035.fdocuments.in/reader035/viewer/2022062423/56814655550346895db36e6c/html5/thumbnails/3.jpg)
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:
![Page 4: MOND Modified Newtonian Dynamics](https://reader035.fdocuments.in/reader035/viewer/2022062423/56814655550346895db36e6c/html5/thumbnails/4.jpg)
Solar System
22
3
4P
π
GMR
![Page 5: MOND Modified Newtonian Dynamics](https://reader035.fdocuments.in/reader035/viewer/2022062423/56814655550346895db36e6c/html5/thumbnails/5.jpg)
Solar System Rotation Curve
R
GMv
![Page 6: MOND Modified Newtonian Dynamics](https://reader035.fdocuments.in/reader035/viewer/2022062423/56814655550346895db36e6c/html5/thumbnails/6.jpg)
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.
![Page 7: MOND Modified Newtonian Dynamics](https://reader035.fdocuments.in/reader035/viewer/2022062423/56814655550346895db36e6c/html5/thumbnails/7.jpg)
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“
![Page 8: MOND Modified Newtonian Dynamics](https://reader035.fdocuments.in/reader035/viewer/2022062423/56814655550346895db36e6c/html5/thumbnails/8.jpg)
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
![Page 9: MOND Modified Newtonian Dynamics](https://reader035.fdocuments.in/reader035/viewer/2022062423/56814655550346895db36e6c/html5/thumbnails/9.jpg)
MONDModified Newtonian Dynamics
analytic form of µ unknown, often assumed to be like:
21 x
xxμ
![Page 10: MOND Modified Newtonian Dynamics](https://reader035.fdocuments.in/reader035/viewer/2022062423/56814655550346895db36e6c/html5/thumbnails/10.jpg)
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).
![Page 11: MOND Modified Newtonian Dynamics](https://reader035.fdocuments.in/reader035/viewer/2022062423/56814655550346895db36e6c/html5/thumbnails/11.jpg)
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
![Page 12: MOND Modified Newtonian Dynamics](https://reader035.fdocuments.in/reader035/viewer/2022062423/56814655550346895db36e6c/html5/thumbnails/12.jpg)
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
![Page 13: MOND Modified Newtonian Dynamics](https://reader035.fdocuments.in/reader035/viewer/2022062423/56814655550346895db36e6c/html5/thumbnails/13.jpg)
Comparison: MOND vs. Dark Matter Begeman et al. (1991)HSB
galaxies
![Page 14: MOND Modified Newtonian Dynamics](https://reader035.fdocuments.in/reader035/viewer/2022062423/56814655550346895db36e6c/html5/thumbnails/14.jpg)
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
![Page 15: MOND Modified Newtonian Dynamics](https://reader035.fdocuments.in/reader035/viewer/2022062423/56814655550346895db36e6c/html5/thumbnails/15.jpg)
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
![Page 16: MOND Modified Newtonian Dynamics](https://reader035.fdocuments.in/reader035/viewer/2022062423/56814655550346895db36e6c/html5/thumbnails/16.jpg)
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)
![Page 17: MOND Modified Newtonian Dynamics](https://reader035.fdocuments.in/reader035/viewer/2022062423/56814655550346895db36e6c/html5/thumbnails/17.jpg)
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
![Page 18: MOND Modified Newtonian Dynamics](https://reader035.fdocuments.in/reader035/viewer/2022062423/56814655550346895db36e6c/html5/thumbnails/18.jpg)
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?
![Page 19: MOND Modified Newtonian Dynamics](https://reader035.fdocuments.in/reader035/viewer/2022062423/56814655550346895db36e6c/html5/thumbnails/19.jpg)
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
![Page 20: MOND Modified Newtonian Dynamics](https://reader035.fdocuments.in/reader035/viewer/2022062423/56814655550346895db36e6c/html5/thumbnails/20.jpg)
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
![Page 21: MOND Modified Newtonian Dynamics](https://reader035.fdocuments.in/reader035/viewer/2022062423/56814655550346895db36e6c/html5/thumbnails/21.jpg)
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.