THE CASE FOR MODIFIED GRAVITY James Binney Oxford University

Outline MOND as a replacement for DM (Sanders & McGaugh 02) MOND as a replacement for DM (Sanders & McGaugh 02) Absence of DM interior to the Sun (Bissantz et al 03, 04) Absence of DM interior to the Sun (Bissantz et al 03, 04) TeVeS Lorentz-covariant MOND (Bekenstein 2004) TeVeS Lorentz-covariant MOND (Bekenstein 2004)

NGC 3198 Begeman (1987)

Modifying gravity Modify Newtonian theory at large distances? or at low accelerations? Modify Newtonian theory at large distances? or at low accelerations?

Adding a 0

Bekenstein—Milgrom Eq.

Tully-Fisher Deep MOND regime – when µ(x)~x At large r always enter deep MOND Sanders & Verheijen

Fits to v c (r) for both LSB & HSB Galaxies (Sanders & McGaugh 02) a 0 = cm s -2 a 0 ~H 0 c/2π; Λ~3(a 0 /c) 2

U Maj Sanders & Verheijen

Recover predicted M/L values Data: Sanders & Verheijen Models: Bell & de Jong 01

dSph galaxies η = F i /F t

Clusters of Galaxies

DM in the MW? Bissantz & Gerhard (02) Determine near-IR luminosity density from COBE K & L photometry Bissantz & Gerhard (02) Determine near-IR luminosity density from COBE K & L photometry Advances previous work by including spiral structure in disk Advances previous work by including spiral structure in disk Bissantz Englmaier & Gerhard (03) study gas flow in Φ obtained with spatially const M/L + quasi-isothermal DM halo Bissantz Englmaier & Gerhard (03) study gas flow in Φ obtained with spatially const M/L + quasi-isothermal DM halo Fit M/L, ω bar, ω spiral Fit M/L, ω bar, ω spiral M/L for stars set by dynamics of non- axisymmetric structure M/L for stars set by dynamics of non- axisymmetric structure DM halo makes up balance for terminal-velocity curve DM halo makes up balance for terminal-velocity curve

Bissantz Englmaier & Gerhard CO observed simulated

Bissantz Englmaier & Gerhard (03) Find ω bar in good agreement solar nhd kinematics Find ω bar in good agreement solar nhd kinematics With 4 arms get good pattern of ridge lines With 4 arms get good pattern of ridge lines V c near sun only ~185km/s unless add DM halo with a=10.7 kpc V c near sun only ~185km/s unless add DM halo with a=10.7 kpc

Famaey & Binney 05 Replace BEG halo with MOND? Replace BEG halo with MOND? Predict v c (R) for 2 choices Predict v c (R) for 2 choices  (x)=x/(1+x 2 ) 1/2 or  (x)=x/(1+x 2 ) 1/2 or  (x)=x/(1+x)  (x)=x/(1+x)

Cannot get v c (R 0 )=220 km/s Cannot get v c (R 0 )=220 km/s But v c (R 0 ) not well determined But v c (R 0 ) not well determined Can fit terminal velocities for range of models Can fit terminal velocities for range of models Bottom lines: (a) v c (R 0 )<210 km/s (b) v 1 =170 § 5 km/s Bottom lines: (a) v c (R 0 )<210 km/s (b) v 1 =170 § 5 km/s

Microlensing Microlensing optical depth measures only stellar density Microlensing optical depth measures only stellar density

Optical depths Bissantz & Gerhard (02)

Bissantz Debattista & Gerhard (04) Use novel N-body technique to find dynamical model that reproduces Bissantz & Gerhard photometry Use novel N-body technique to find dynamical model that reproduces Bissantz & Gerhard photometry Adopt M/L, ω normalization from BEG Adopt M/L, ω normalization from BEG No free parameters in Φ No free parameters in Φ Reproduce proper motions of bulge stars in Baade’s window etc Reproduce proper motions of bulge stars in Baade’s window etc For plausible mass function of stars, reproduce MACHO microlensing event duration distribution For plausible mass function of stars, reproduce MACHO microlensing event duration distribution

Conclusion: stars-only MW gives good fits to both optical depth & duration distribution Conclusion: stars-only MW gives good fits to both optical depth & duration distribution (M L )=(.04,10) or (.075,10)

Klypin et al (02) ΛCDM models of MW ΛCDM models of MW Adiabatic compression & optional L exchange Adiabatic compression & optional L exchange No L exchange L exchange

TeVeS Bekenstein (04) presents Lorentz- covariant theory (TeVeS) that reduces to MOND in appropriate limit Bekenstein (04) presents Lorentz- covariant theory (TeVeS) that reduces to MOND in appropriate limit

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

TeVeS important development Link to effective field theory? TeVeS important development Link to effective field theory? Can now extend MOND to CMB and large- scale structure Can now extend MOND to CMB and large- scale structure If not worse than CDM in these fields, must be favoured theory If not worse than CDM in these fields, must be favoured theory Then question: significance of U µ and Φ fields in TeVeS Then question: significance of U µ and Φ fields in TeVeS

Conclusions MOND has amazing ability to model data taken after it was invented MOND has amazing ability to model data taken after it was invented Excellent fits to galaxy rotation curves require M/L(colour) as from SS theory Excellent fits to galaxy rotation curves require M/L(colour) as from SS theory Compelling evidence that negligible DM interior to Sun Compelling evidence that negligible DM interior to Sun Now limiting form of Lorentz covariant theory Now limiting form of Lorentz covariant theory MOND really might be the next great step in physics MOND really might be the next great step in physics

m=2 x 1.5

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