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)

ku

4

0

4

u

Gu

hFu N )(

ua0||

20 |||| ua

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”

A backyard detection of MOND?

Lagrange points?Lagrange points? Saddle points.Saddle points.

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:

Earth/Moon 140Km

unJupiter /S Km109.6

Earth/Sun Km 383

16

5

20

2

0

Ak

ar

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

LISA Pathfinder mission

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!