MOdified Newtonian DynamicsMOdified Newtonian Dynamicsan introductory reviewan introductory review

Riccardo ScarpaRiccardo Scarpa

IACIAC

By

     

Justification for ModifyingJustification for Modifying Newtonian Dynamics Newtonian Dynamics

Increasing fine tuning required to explain observations Increasing fine tuning required to explain observations with non-baryonic dark matter.with non-baryonic dark matter.

Effects of non-baryonic dark matter appears Effects of non-baryonic dark matter appears when and when and only whenonly when the acceleration of gravity falls below a the acceleration of gravity falls below a certain value, baptized acertain value, baptized a00..

This acceleration, aThis acceleration, a00, is orders of magnitudes smaller , is orders of magnitudes smaller then the smallest probed in the solar system.then the smallest probed in the solar system.

Thus the idea is simple: Newtonian dynamics breaks down below a0

   

Proposed by M. Milgrom in 1983Proposed by M. Milgrom in 1983AA new constant of physics  new constant of physics introduced: aintroduced: a

00~10~10­8­8 cm s cm s­2­2

Functional form derived fromrotation curves, where we know v = constant  ⇒ a ∝1/r  at large radii.Square root of Newtonian acceleration ∝ 1/r. Multiplied by an acceleration we get right dimensions.

An interpolation function derived empirically joins the two regimes

⇒

a≫a0a=GMr²

a≪a0 a=GMa0

r

f aa0=1

a0

a 2

a N=a f aa0

High Surface Brightness galaxies have in general flat rotation curves: Acceleration proportional to 1/r.Acceleration proportional to 1/r.  

NGC 6503 –  from Begeman, Broeils, and Sanders 1991

Comparing MOND to real dataComparing MOND to real data

                DM

STARS

         GAS MOND

   

Galaxies Rotation Curves with MONDGalaxies Rotation Curves with MOND

Velocity in km/sDistance in kpc

Sanders & Verheijen 1998. Rotation curves derived from stellar light  and 21cm hydrogen line 

a =GMa0

r

   

Fits to v(r) for LSB & HSB GalaxiesFits to v(r) for LSB & HSB GalaxiesSanders & McGaugh 02a0=1.2 x10­8 cm s­2 

   

Does MOND fit any rotation curve?

MOND DARK MATTER

This is a fake galaxy!Photometry from one object and velocity from another!

In this case, a failure is a good thing!

MOND fails to fit this one.

     

Counterexamples?!Counterexamples?!

Romanowsky et al 2003Claimed 3 elliptical galaxieswithout dark matter halo were discovered.

Dashed line:     isothermal halo

Dotted line:    constant mass­to­light     ratio galaxy. 

     

No! No! These galaxies are in Newtonian These galaxies are in Newtonian regimeregime

Milgrom & Sanders 03

Dotted line: Newtonian prediction for constant M/L. Solid line: MOND prediction for the same M/L.

   

The Tully­Fisher The Tully­Fisher RelationRelation

 v ⇐

A relation between asymptotic velocity and luminosity of galaxies

L∝v4

   

Galaxies’ mean surface Galaxies’ mean surface brightnessbrightness s s = L/ = L/ππrr22

High surface Brightness Low surface brightness

Pega

sus

   

Newtonian dynamics and T­FNewtonian dynamics and T­F

The T­F requires  

τ2S= const.

M/L=τ   depends on stellar population, basically the same in all galaxies

 Surface brightness S varies significantly going from HSB to LSB galaxies and has nothing to do with M/L.

Link between two otherwise unrelated quantities implied.

v2=

GMr

L=S r2v4∝

M 2

LS= M2

L2 SL

   

Tully­Fisher relation and MONDTully­Fisher relation and MOND

MOND requires   M/L= constant

 AND

The T­F is universal

v2

r=GMa0

r v4

∝ML

L

   

The Tully­Fisher is universal as The Tully­Fisher is universal as MOND predictedMOND predicted

Sanders & Verheijen

LSB

HSB

Note that data for low surface brightness galaxies became available some 10 years after Milgrom made its prediction.

   

Baryonic Tully­Fisher McGaugh et al. 2000 ApJL, 533, 99

Left: “Luminous mass” vs. rotational  Velocity. Galaxies with v<90 km/s fall below the relation.

Right: Including gas the relation is restored.

The solid line has slope 4

The T­F  is a relation between MASS and Velocity, as indeed predicted by MOND

     

Fundamental plane of Fundamental plane of ellipticals ellipticals

Edge on view of the fundamental planeHSB define a a relation M/L ∝ L 0.25

LSB define an opposite trend M/L ∝ L ­0.40

LSBHSB

k1=log(2re)/√2∝ log(M)

     

MOND explanation of the tiltMOND explanation of the tiltTilt due to different trends of the strength of the  gravitational field:

In HSB the acceleration decreases with size

In LSB the acceleration increases with size 

This is demonstrated by their average surface brightness 

     

MOND defines specific trendsMOND defines specific trends

The slopes predicted by MOND for LSB and HSB do agree with the known trends,­0.4 and 0.25, respectively

     

Newtonian acceleration from velocity Newtonian acceleration from velocity and luminosityand luminosity

MOND agrees with real data over 6 orders of magnitude!

MOND prediction

     

Dense Clusters of GalaxiesDense Clusters of Galaxies(Sanders 1998)

This may be the only place where MOND fails (by a factor 2). MOND predicts some baryonic matter still to be discovered

     

Ultra Compact Dwarf Ultra Compact Dwarf GalaxiesGalaxies

Dwarf galaxies are usually FULL of dark matter with M/L~100, thus plenty of dark matter expected.

Drinkwater et al. 2000

DARK MATTER                    vs.                       MONDUCD luminosity and size imply internal acceleration > a0 everywhere, hence no dark matter should be found. 

     

No Dark Matter in UCDsNo Dark Matter in UCDs

Accepted explanation: The dark matter  was there but was lost together with the halo. Possible but NOT predicted and ad hoc

MOND explanation: simple, elegant, fully logic and exactly  as predicted!

2<M/L<4(Drinkwater et al. 2003)

(Scarpa astro­ph 0504051)

2.1×10­8 cm s­2

MOND and Globular clusters:MOND and Globular clusters:velocity dispersion constant at large radii.velocity dispersion constant at large radii.

Our UVES data (black diamonds) for 75 stars

Radial velocities from Meylan et al. 1995 and Meylan & Mayor 1986 (crosses)

Proper motion data from van Leeuwen et al. 2000

Scarpa, Marconi, & Gilmozzi 2003

All GCs behave the same wayAll GCs behave the same way

MOND or 

Tidal Heating?

CarinaCarina

Wilkinson et al. 2006

LSB spheroidal galaxies have flat LSB spheroidal galaxies have flat velocity dispersion profilesvelocity dispersion profiles

Low surface brightness globular clustersLow surface brightness globular clustersNGC 288NGC 288

Internal acceleration below a0  everywhere. This is the equivalent of a LSB galaxy.

What should we expect?

NGC 288 behaves like a LSB galaxyNGC 288 behaves like a LSB galaxy

The velocity dispersion profile is flat!

Cosmological Difficulties with Modified Newtonian Dynamics (or: La Fin du MOND?)  Astro­ph 0104435

In this paper it is argued that MOND had to be wrong because it failed to describe some fetures of modern cosmology.

Cosmology and MONDCosmology and MOND

Wrong approach: a law of physics DOESN'T have to agree with cosmology!!

It is cosmology that HAS TO AGREE with law of physics!!

     

MOND and WMAPMOND and WMAP

Dark matter NO dark matter

McGaugh 2004, ApJ 611, 26

     

Big Bang nuclesyntesisBig Bang nuclesyntesis

Values implied by WMAP fits systematically above prediction

McGaugh 2004, ApJ 611, 26

Virtually all theore­tical predictions below 0.02

No­CDM models agree with BBN

     

Gravitational lensingGravitational lensing

Difficult to address because MOND lack(ed) a relativistic extension

The Usual assumption is that light is bent twice has much as predicted by Newton’s law. That is:

Compute field with MOND Double the effect⇒

Warning: Gravitational lensing NEVER occur in MOND regime.

     

We are left with We are left with MicrolensingMicrolensing

Mortlock & Turner 2001

AM =2p

c 2 GMa0

AM= 2” for M=1012 Msun

For a point sourcewe get an asymptoticdeviation:

The deflection is independent from the impact parameter as much as rotation velocity is independent from r.

     

Real data agree with MONDReal data agree with MOND

     

MOND is gaining consensusMOND is gaining consensus

The seminal paper by Milgrom in 1983 cited 450 times.

     

Conclusions for MONDConclusions for MOND Amazing ability to describe many properties of astronomical Amazing ability to describe many properties of astronomical

objects.objects.

Explains data taken after it was proposed. Agreement Explains data taken after it was proposed. Agreement generally improve as data quality improve.generally improve as data quality improve.

Keep focus on demonstrating whether Newtonian dynamics Keep focus on demonstrating whether Newtonian dynamics fails at low accelerations.fails at low accelerations.

At present, I would compare MOND to Borh’s atom, which At present, I would compare MOND to Borh’s atom, which was based on un-justified assumptions and worked only for was based on un-justified assumptions and worked only for Hydrogen. This model eventually became the basis for Hydrogen. This model eventually became the basis for quantum mechanics.quantum mechanics.

Similarly, MOND might be the way to the next great step in Similarly, MOND might be the way to the next great step in physics.physics.