THE CASE FOR MODIFIED
GRAVITY
James Binney
Oxford University
Outline
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MOND as a replacement for DM
(Sanders & McGaugh 02)
Absence of DM interior to the Sun
(Bissantz et al 03, 04)
TeVeS Lorentz-covariant MOND
(Bekenstein 2004)
NGC 3198
Begeman (1987)
Modifying gravity
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Modify Newtonian theory
at large distances?
or at low accelerations?
Adding a0
Bekenstein—Milgrom Eq.
Tully-Fisher
• Deep MOND regime – when µ(x)~x
Sanders
& Verheijen
• At large r always enter deep
MOND
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 Maj
Sanders & Verheijen
Recover predicted M/L values
Data: Sanders & Verheijen
Models: Bell & de Jong 01
Giant E
galaxies
Data:
Romanowsky et al 03
Models:
Milgrom & Sanders 03
Solid: isotropic
Clusters of Galaxies
dSph
galaxies
η = Fi/Ft
DM in the MW?
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Bissantz & Gerhard (02)
Determine near-IR luminosity density from COBE
K & L photometry
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
Fit M/L, ωbar, ωspiral
M/L for stars set by dynamics of nonaxisymmetric structure
DM halo makes up balance for tangent-velocity
curve
Bissantz Englmaier & Gerhard
CO observed
simulated
m=2 x 1.5
Bissantz Englmaier & Gerhard (03)
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Find ωbar in good agreement solar nhd
kinematics
With 4 arms get good pattern of ridge
lines
Vc near sun ~35 km/s below true value
unless DM halo with a=10.7 kpc added
With (x)=x/(1+x)
KhN/KhM=0.95§0.15 (Famaey & B 04)
Microlensing
Optical depths
Bissantz &
Gerhard (02)
Bissantz Debattista & Gerhard (04)
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Use novel N-body technique to find
dynamical model that reproduces Bissantz
& Gerhard photometry
Adopt M/L, ω normalization from BEG
No free parameters in Φ
Reproduce proper motions of bulge stars
in Baade’s window etc
For plausible mass function of stars,
reproduce MACHO microlensing event
duration distribution
(ML<,ML>)=(.04,10) or (.075,10)
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Conclusion: stars-only MW gives good fits
to both optical depth & duration
distribution
Klypin et al (02)
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ΛCDM models of MW
Adiabatic compression & optional L exchange
No L exchange
L exchange
TeVeS
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Bekenstein (04) presents Lorentzcovariant theory (TeVeS) that reduces to
MOND in appropriate limit
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Standard cosmologies
Grav. Lensing as if DM present
No superluminal modes
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TeVeS important development
Link to effective field theory?
Can now extend MOND to CMB and largescale structure
If not worse than CDM in these fields,
must be favoured theory
Then question: significance of Uµ and Φ
fields in TeVeS
Conclusions
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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
Compelling evidence that negligible DM
interior to Sun
Now limiting form of Lorentz covariant
theory
MOND really might be the next great step
in physics