MOND (Modified Newtonian dynamics) habitats inside the Solar system
JoJoãão o MagueijoMagueijo
Perimeter Institute,Perimeter Institute,CITA,CITA,
Imperial CollegeImperial College
Based on Bekenstein & Magueijo, astro-ph/0602266
The MOND vs Dark Matter conflict
Everything outside the Solar system refuses Everything outside the Solar system refuses to follow the laws of General Relativity/ to follow the laws of General Relativity/ Newtonian gravityNewtonian gravity
Either gravity is fine, but there is an extra Either gravity is fine, but there is an extra source we can’t see: the dark matter.source we can’t see: the dark matter.
Or the observations are telling us to modify Or the observations are telling us to modify gravity.gravity.
We need a direct detection!
Dark matter searches: the game is over if a Dark matter searches: the game is over if a dark matter particle is detected!dark matter particle is detected!
What is the equivalent “backyard” detection What is the equivalent “backyard” detection of MONDian behavior?of MONDian behavior?
(Spiral) Galaxy rotation curves:
Flattening of rotation curves Flattening of rotation curves
Anomalous behaviour triggered byAnomalous behaviour triggered by
Tully-Fisher relationTully-Fisher relation
rv
r
v
r
GM 12
2
2100 10 msa
MLv 4
vv
Take these facts as “Kepler’s laws” for a new theory of gravity
Milgrom’s insight:Milgrom’s insight:
A better formulation:A better formulation:
(often quoted as a rule of thumb)(often quoted as a rule of thumb)
20
4
20
2
ra
v
r
GM
a
amF
NFF
0aa
0|| aFN
What the Solar system needs from MOND:
A modified Poisson equationA modified Poisson equation
(there are several relativistic, Lagrangian (there are several relativistic, Lagrangian formulations leading to this)formulations leading to this)
Why a direct test? Both approaches have been in turn un/successful
LeVerrier prediction of Neptune from LeVerrier prediction of Neptune from Uranus orbital anomalies (first example of Uranus orbital anomalies (first example of dark matter). dark matter).
Attemps to explain the anomalous Attemps to explain the anomalous precession of the perihelion of Mercury precession of the perihelion of Mercury with “Vulcanus”with “Vulcanus”
Naïve expectation:
MONDian tidal stresses should diverge at MONDian tidal stresses should diverge at the saddle:the saddle:
Newtonian result:Newtonian result:
Take the squareroot:Take the squareroot:
Outside (perturbative) region
Maximal fractional Maximal fractional effect is at the border effect is at the border ellipsoidellipsoid
Its value is Its value is
It then falls off as It then falls off as 1/r^21/r^2
0025.04
k
F
F
The inner region profile
The angular profile is The angular profile is approximately approximately NewtonianNewtonian
The tidal stress The tidal stress divergence is there but divergence is there but it’s much softer due to it’s much softer due to the curl termthe curl term
24.0
04
r
rk
F
F
A target for LPF?
Accelerometers have a sensitivity ofAccelerometers have a sensitivity of
Target region for Sun/Earth saddle has size Target region for Sun/Earth saddle has size
21510
sr
a
Km 3830r
CONCLUSIONS
Don’t accuse us of not providing you with a Don’t accuse us of not providing you with a targettarget
Most of other approaches are too fudged to Most of other approaches are too fudged to make concrete predictions at this level make concrete predictions at this level
If you don’t like the model (I don’t) the If you don’t like the model (I don’t) the solution is simple:solution is simple:
KILL IT!