the case for modified gravity
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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
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