MOdified MOdified Newtonian DynamicsNewtonian Dynamicsan introductory reviewan introductory review

Riccardo ScarpaRiccardo ScarpaEuropean Southern ObservatoryEuropean Southern Observatory

By

NGC 3198 (NGC 3198 (Begeman Begeman 1987)1987)

Rotational velocitysensibly constant atlarge radii

Implies an halo ofnon-luminous mattersurrounds galaxies

Halo density ∝ 1/r,mass diverges

Everything started in 1933 with the work by Zwicky on theComa cluster of galaxies, but were galaxy rotation curves toconvince everybody there was dark matter in the universe

Justification for ModifyingJustification for Modifying Newtonian Dynamics Newtonian Dynamics

IIt is increasingly difficult to explain observations with non-t is increasingly difficult to explain observations with non-baryonic dark matter.baryonic dark matter.

Effects of non-baryonic dark matter appears Effects of non-baryonic dark matter appears when and onlywhen and onlywhenwhen the acceleration of gravity (computed including only the acceleration of gravity (computed including onlybaryons) falls below a certain value, baptized abaryons) falls below a certain value, baptized a00..

a a00 is smaller th is smaller thaan the smallest acceleration probed in then the smallest acceleration probed in thesolar systemsolar system, e.g., the acceleration of Mercury on Pluto is > a, e.g., the acceleration of Mercury on Pluto is > a00

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

Proposed by M. Proposed by M. Milgrom Milgrom in 1983,in 1983,MOND introduces MOND introduces a new constant ofa new constant of

physics: aphysics: a00

What matters is the strength of the acceleration, not distance/sizeof objects (though for any given object low accelerations are

reached at correspondingly large distances).

Distance doesnDistance doesn’’t matter!t matter!

MOND basic definitionFunctional form derived fromrotation curves, where we knowv = constant ⇒ a ∝1/r at large radii.Square root of Newtonianacceleration ∝ 1/r.Multiplied by an acceleration we getright dimensions.

An interpolation function derivedempirically joins the two regimes

!

aN

= aµa

a0

"

# $

%

& '

!

a >> a0"

a << a0"

#

$ %

& %

!

aN

=GM

r2

!

a =GMa

0

r

⇒

!

µa

a0

"

# $

%

& ' = (a /a0) 1+

a2

a0

2

"

# $

%

& '

(1/ 2

Comparing MOND to real data

MONDDARK MATTER

Galaxies Rotation Curves with MONDGalaxies Rotation Curves with MOND

Velocity in km/sDistance in kpc

Sanders & Verheijen1998.Rotation curvesderived from stellarlight and 21cmhydrogen line

!

a =GMa

0

r

Fits to v(r) for LSB & HSB GalaxiesFits to v(r) for LSB & HSB GalaxiesSanders & McGaugh 02a0=1.2 x10-8 cm s-2

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 the discovery of3 elliptical galaxieswithout dark matter halo.

Dashed line:isothermal dark-matterhalo

Dotted line:constant mass-to-lightratio and NO darkmatter.

No! No! These galaxies are in These galaxies are in NewtonianNewtonian regime regime

Milgrom & Sanders 03

Dotted line:Newtonian predictionfor constant M/L.

Solid line:MOND prediction forthe same M/L.

a>a0

The Tully-FisherThe Tully-FisherRelationRelation

!

v4"L

v ⇐

A relation betweenasymptotic velocity andluminosity of galaxies

GalaxiesGalaxies’’ mean surface mean surfacebrightness brightness Σ

High surface Brightness Low surface brightness

Galaxy luminosity L = πr2Σ

Newtonian dynamics and T-FNewtonian dynamics and T-F

!

v2

r=GM

r2

!

v4

=(GM)

2

r2

!

"

!

v4"M

2#

L2L = $ 2#L

!

L = "r2#

!

{

!

{

!

r2

=L

"# T-F requires τ2Σ = const. But M/L=τ depends on stellar population, basically the same

in all galaxies

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

Therefore Newton implies a link of two very unrelatedquantities and predicts LSB and HSB galaxies to followdifferent T-F relations.

Tully-Fisher relation and MONDTully-Fisher relation and MOND

MOND requires M/L= constant

!

v4 "M

L

L=

M

L

#

$ %

&

' ( L

!

v2

r=

GMa0

r⇒

AND

The T-F is universal

The Tully-Fisher is universal asThe Tully-Fisher is universal asMOND predictedMOND predicted

Sanders & Verheijen

LSB

HSB

Note that data forlow surfacebrightness galaxiesbecame availablesome 10 years laterMilgrom made itsprediction.

Baryonic Tully-Fisher McGaugh et al. 2000 ApJL, 533, 99

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

Right:Including gas therelation is restored.

The solid line hasslope 4

The T-F is a relation between MASS and Velocity, asindeed predicted by MOND

Fundamental plane of Fundamental plane of ellipticalsellipticals

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

HSBLSB

MOND explanation of the tiltMOND explanation of the tiltTilt due to thedifferent trend ingravitational filedstrength

In HSB theaccelerationdecreases with size

In LSB theaccelerationincreases with size

This is demonstrated by their average surface brightness

MOND defines specific trendsMOND defines specific trends

Log L/Lsun

Acceleration from velocity and luminosityAcceleration from velocity and luminosity

MOND agrees with real data over 7 orders of magnitudes

Ultra Compact Dwarf GalaxiesUltra Compact Dwarf Galaxies

Dwarf galaxies are usually FULLof dark matter with M/L~100, thusplenty of dark matter expected.

Drinkwateret al. 2003

DARK MATTER vs. MONDUCD luminosity and size implyinternal acceleration > a0everywhere, hence no darkmatter should be found.

No Dark Matter Found in No Dark Matter Found in UCDsUCDs

Accepted explanation:The dark matter wasthere but was losttogether with the halo.Possible but NOTpredicted and ad hoc

MOND explanation:simple, elegant, fullylogic and exactly aspredicted!

Clusters of GalaxiesClusters of Galaxies(Sanders 1998)

This may be the only place where MOND fails (by afactor 2.

MOND predicts some baryonic matter still to bediscovered

Gravitational Gravitational lensinglensing

Difficult to address because MOND lack a relativisticExtension

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

Compute field with MOND Double the effect⇒

Warning: Gravitational lensing NEVER occur in MOND regime.

Strong Strong LensingLensing

The critical surface density required for strong lensing is

!

"c

=1

4#

cH0

GF

where F~10 is a dimensionless function of the lens and source redshifts[35]

,

MOND applies at surface densities below Σ ~ a0/G ~ Σc/5

Strong lensing NEVER occurs in MOND regime

We are left with weak We are left with weak lensinglensing

Mortlock & Turner 2001

!

AM

=2"

c2

GMa0

AM= 2” for M=1012 Msun

For a point sourcewe get an asymptoticdeviation:

The deflection isindependent from theimpact parameter asmuch as rotation velocityis independent from r.

Real data agree with MONDReal data agree with MOND

Bulge Bulge vs vs Black Hole massesBlack Hole masses

In presence of darkmatter these tworelations are difficult toexplain because fromthe tilt of thefundamental plane weget M/L∝L0.25.

Piece of cake for MONDbecause M∝L∝σ4

Ferrarese & MerrittAstro-ph 0206222

MBH∝σ4

AND MBH∝L

MOND and WMAPMOND and WMAP

McGaugh 2004 ApJ 611, 26

The ratio of the second to first peakdepends on the baryon density

Power spectrum of temperature fluctuations in CMB

Baryon density from PrimordialBaryon density from PrimordialNucleosynthesisNucleosynthesis

ΛCDM fit to WMAP data (Spergel et al. 2003)implies ωb=0.024 ± 0.001

McGaugh 2004ApJ 611, 26

Modern Cosmology is based on:Modern Cosmology is based on: Cosmological principleCosmological principle

FRW equations based on FRW equations based on eextrapolatixtrapolatingng General relativity to General relativity tolow accelerations (Newtonian limit).low accelerations (Newtonian limit).

If any of these two hypothesis is wrong - MOND suggests thesecond - FRW equations are inappropriate to describe the universe.

Progress in cosmology seems not to depend on one’s ability todescribe observations within one particular FRW based model,rather on re-writing these equations within the contest of a newtheory of gravity.

Thus:

Probing Gravity in the LowProbing Gravity in the LowAcceleration RegimeAcceleration Regime

withwithGlobular ClustersGlobular Clusters

By

Riccardo Scarpa, Gianni Marconi & Roberto Gilmozzi

European Southern Observatory

Membership determination difficultMembership determination difficult

35'x35'

Target selectionbased on:

HR diagram

Proper motion (whenpossible)

Radial velocity

2.1×10-8 cm s-2

ωω Centauri:Centauri: velocity dispersionvelocity dispersionconstantconstant at large radii.at large radii.

M 15 confirms what found for M 15 confirms what found for ωω CenCen

1.7×10-8 cm s-2

1.4×10-8 cm s-2

Also in NGC 6171 the velocity dispersionAlso in NGC 6171 the velocity dispersionprofile flattens out at large radiiprofile flattens out at large radii

All data together206 stars

Conclusions for MONDConclusions for MOND AAmazing ability to mazing ability to describe describe many properties of astronomical objects.many properties of astronomical objects.

Explains many data taken after it was Explains many data taken after it was proposedproposed..

Keep focus on demonstratingKeep focus on demonstrating whether Newtonwhether Newtonian dynamicsian dynamics fails at fails atlow accelerations.low accelerations.

At presentAt present, , I would compare MOND to I would compare MOND to BorBorhh’’s s atom, which wasatom, which wasbased on un-justified assumptions and worked only for Hydrogenbased on un-justified assumptions and worked only for Hydrogen..This model eventuallyThis model eventually became the basis for quantum mechanics.became the basis for quantum mechanics.

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