THE CASE FOR MODIFIED GRAVITY

THE CASE FOR MODIFIED THE CASE FOR MODIFIED GRAVITYGRAVITY

James BinneyJames Binney

Oxford UniversityOxford University

OutlineOutline

MOND as a replacement for DM MOND as a replacement for DM (Sanders & McGaugh 02)(Sanders & McGaugh 02)

Absence of DM interior to the Sun Absence of DM interior to the Sun (Bissantz et al 03, 04) (Bissantz et al 03, 04)

TeVeS Lorentz-covariant MOND TeVeS Lorentz-covariant MOND (Bekenstein 2004)(Bekenstein 2004)

NGC 3198NGC 3198

Begeman (1987)

Modifying gravityModifying gravity Modify Newtonian theory Modify Newtonian theory

at large distances? at large distances? or at low accelerations? or at low accelerations?

Adding a0

Bekenstein—Milgrom Eq.

Tully-Fisher

• Deep MOND regime – when µ(x)~x

• At large r always enter deep MOND

Sanders & Verheijen

Fits to vc(r) for both LSB & HSB Galaxies

(Sanders & McGaugh 02)a0=1.2 10-8 cm s-2 a0~H0c/2π; Λ~3(a0/c)2

U MajSanders & Verheijen

Recover predicted M/L values

Data: Sanders & VerheijenModels: Bell & de Jong 01

dSph dSph galaxiesgalaxies

η = Fi/Ft

Clusters of GalaxiesClusters of Galaxies

DM in the MW?DM in the MW? Bissantz & Gerhard (02) Bissantz & Gerhard (02)

Determine near-IR luminosity density from Determine near-IR luminosity density from COBE K & L photometryCOBE K & L photometry

Advances previous work by including spiral Advances previous work by including spiral structure in diskstructure in disk

Bissantz Englmaier & Gerhard (03) study Bissantz Englmaier & Gerhard (03) study gas flow in gas flow in ΦΦ obtained with spatially const obtained with spatially const M/L + quasi-isothermal DM haloM/L + quasi-isothermal DM halo

Fit M/L, Fit M/L, ωωbarbar, , ωωspiralspiral M/L for stars set by dynamics of non-M/L for stars set by dynamics of non-

axisymmetric structureaxisymmetric structure DM halo makes up balance for terminal-DM halo makes up balance for terminal-

velocity curve velocity curve

Bissantz Englmaier & GerhardBissantz Englmaier & Gerhard

CO observed

simulated

Bissantz Englmaier & Gerhard Bissantz Englmaier & Gerhard (03)(03)

Find Find ωωbarbar in good agreement solar in good agreement solar nhd kinematicsnhd kinematics

With 4 arms get good pattern of With 4 arms get good pattern of ridge linesridge lines

VVcc near sun only ~185km/s unless near sun only ~185km/s unless add DM halo with a=10.7 kpcadd DM halo with a=10.7 kpc

Famaey & Binney 05Famaey & Binney 05 Replace BEG halo with MOND?Replace BEG halo with MOND? Predict vPredict vcc(R) for 2 choices(R) for 2 choices (x)=x/(1+x(x)=x/(1+x22))1/21/2 or or ((x)=x/(1+x)x)=x/(1+x)

Cannot get vCannot get vcc(R(R00)=220 km/s)=220 km/s But vBut vcc(R(R00) not well determined) not well determined Can fit terminal velocities for range Can fit terminal velocities for range

of modelsof models Bottom lines: Bottom lines:

(a) v(a) vcc(R(R00)<210 km/s )<210 km/s (b) v(b) v11=170=170§§5 km/s5 km/s

MicrolensingMicrolensing Microlensing optical depth measures Microlensing optical depth measures

only stellar densityonly stellar density

Optical depthsOptical depths

Bissantz & Gerhard (02)

Bissantz Debattista & Gerhard Bissantz Debattista & Gerhard (04)(04)

Use novel N-body technique to find Use novel N-body technique to find dynamical model that reproduces dynamical model that reproduces Bissantz & Gerhard photometry Bissantz & Gerhard photometry

Adopt M/L, Adopt M/L, ωω normalization from BEG normalization from BEG No free parameters in No free parameters in ΦΦ Reproduce proper motions of bulge Reproduce proper motions of bulge

stars in Baade’s window etcstars in Baade’s window etc For plausible mass function of stars, For plausible mass function of stars,

reproduce MACHO microlensing reproduce MACHO microlensing event duration distributionevent duration distribution

Conclusion: stars-only MW gives Conclusion: stars-only MW gives good fits to both optical depth & good fits to both optical depth & duration distributionduration distribution

(ML<,ML

>)=(.04,10) or (.075,10)

Klypin et al (02)Klypin et al (02)

ΛΛCDM models of MWCDM models of MW Adiabatic compression & optional L exchangeAdiabatic compression & optional L exchange

No L exchange L exchange

TeVeSTeVeS Bekenstein (04) presents Lorentz-Bekenstein (04) presents Lorentz-

covariant theory (TeVeS) that reduces covariant theory (TeVeS) that reduces to MOND in appropriate limitto MOND in appropriate limit

Standard cosmologiesStandard cosmologies Grav. Lensing as if DM presentGrav. Lensing as if DM present No superluminal modesNo superluminal modes

TeVeS important development TeVeS important development Link to effective field theory? Link to effective field theory?

Can now extend MOND to CMB and Can now extend MOND to CMB and large-scale structurelarge-scale structure

If not worse than CDM in these fields, If not worse than CDM in these fields, must be favoured theorymust be favoured theory

Then question: significance of UThen question: significance of Uµµ and and ΦΦ fields in TeVeS fields in TeVeS

ConclusionsConclusions MOND has amazing ability to model MOND has amazing ability to model

data taken after it was inventeddata taken after it was invented Excellent fits to galaxy rotation curves Excellent fits to galaxy rotation curves

require M/L(colour) as from SS theory require M/L(colour) as from SS theory Compelling evidence that negligible Compelling evidence that negligible

DM interior to SunDM interior to Sun Now limiting form of Lorentz covariant Now limiting form of Lorentz covariant

theorytheory MOND really might be the next great MOND really might be the next great

step in physicsstep in physics

m=2 x 1.5

Giant E Giant E galaxiesgalaxies

Data:Romanowsky et al 03Models:Milgrom & Sanders 03Solid: isotropic