Review MOND: an alternative to DM?

H.S. Zhao

Univ. of St. Andrews

MOND vs. DM 20-year theory by 2-3 people

Cheap parameter

a0=1mm/hr2

Good for rotation curves &Tully-Fisher correlation

60-year hypothesis + industry of simulators + particle detectors

$Million$ ~100 exotic

candidates

Good lensing & Large scale

“ Let’s kill MOND” Flavours of DM in/out fashion as Rotation Curves wiggle MOND consistently fits RCs, rarely needs fine-

tuning.

In weak-g regime … anything is possible Weak g<a0=1.2x 10-8 cm s-2

~ Self-Grav. sheet of paper! ~ Earth-Grav. at Saturn

10AU still unconstrained by

Ground/space labs (Pioneer) planet motions.

Consequence universe-wise a0 ~ {G P}1/2

P: present mean baryon energy density.

a0 everywhere: everyone has a weak spot

Spirals Ga0 ~ Rotation V4 /[Luminosity *(M/L)]

GlobularCluster, MolecularCloud, dwarf, Ellip, X-Cluster

a0 ~ Velocity2 /Length scale ~ cH0/6 ~ 100Msun/pc2

Baryonic Radical View MOND (Milgrom 1983)

g ~ R-1 far from a point mass g ~ R-2 near a point mass

Strengthened where Newton is weakg = Max[ gn, (a0 gn)1/2 ] > gn =GM/R2

V2/R~ g ~ (gn a0 )1/2 ~ (GMa0)1/2 R-1

flat rotation curve if weak gn<g<a0

Kuzmin MW disk: MOND ~ isothermal halo (20kpc core)

Orbits in disk MOND potential mimic in mild oblate CDM

Read & Moore (high a0)

MOND disks/spheres of increasing core density ?Vrot(R) = (GM/R)1/2 if strong = (GM(R) a0)1/4 if weak

gcore = Newtonian gravity at Core

~ central surface density.

Plummer spheres /Kuzmin disks

gcore /a0 = 0.125116Simulate LSB disksMWHSB

ellipticals

Strong-g

Weak-g

Nature's accelerators: Galaxies V2/R=g

Surprisingly V2

~ R2 (Dwarf Irregular)

~ cst (in Spirals)~ 1/R (Ellipticals)

Explained: Rise/fall/wiggles in Ellip & Spiral & Dwarves

Milgrom & Sanders, Sanders & McGaugh

Dark Matter/Baryon Exchange Rate Fluctuates

D/B =? Fornax (10-

100) Milky Way (10) Globulars (0-1)

Any ratio is possible

Fitting RCs by varying DM density cusp α?

00

0

( )(1 )

/

(Hernquist 1990, Zhao 1996, NFW 1997)

nn r R

R R

R r r

Good questions

MOND precisely describes galaxies, but is MOND

just handy empirical formula Or a decent physical theory?

separable from Dark Matter Or fully degenerate?

Reviewed by Sanders & McGaugh ARAA

Good & bad of non-linear MOND as a Full theory.

Ugly: fudged lensing

Relativity Bekenstein version: TeVeS fields astro-ph/0403694

2

0 ;

,

22, ,

2 4 /

[ ( / ) ] 4

Modified Poisson's eq.

[ ]

[ ]

[ (1 ) ]

N

N

c

a G

where

g u u k

g u u k

c g e u u T

e.g. k~0.04, a0~1.2e-8 put in by hand

Einstein tensor gαβ +

gravitational potential Φ

Scaler field: σ or μ(σ/a0 )

As Dielectric medium to make strong-than-Newtonian force

Time-like vector uβ

Forbid superluminal propagation of signal

MR TeVeS pass

Standard cosmology tests Non-linear MOND effects insignificant Universe mildly weak-g: cH0 ~ 6a0.

Standard strong-g tests in solar system a0 = Earth’s Gravity at Saturn distance

Standard pulsar tests

MOND-like theories

E.g., Geff(g)/G = (a0/g)K

K=1 for BM’s MOND K=0 Newtonian

Gauss theorem well outside the masses GMtot/ (4 Pi R2) = (g/a0)K g= gn

MOND is Fair

Gravity= baryon content 105 Msun gas cloud= 105 Msun black hole = 105 suns globular= 105 suns dwarf gal… any density profile

Post-Bekenstein developments Baumgardt, Grebel, Kroupa (MNRAS):

Inflated dispersion of faint globulars Ciotti & Binney (MNRAS):

Amplified Dynamical Friction. Read & Moore (MNRAS):

Little Procession of satellite orbits Zhao

Roche Lobe of globulars (with L. Tian) Distances in FRW universe (with X. Chen) Lensing in MOND (with Bacon, Taylor et al.)

Skordis et al. on CMB Possible consistency

Pointecouteau & Silk need for DM in cluster

Famaey & Binney High a0 for Milky Way

N2419 105.5

Draco 105 ©

SDSS

Different gravity

Same self-gravity (105 old stars) as Draco dwarf,Why stripped??

MOND: Many Open Questions

Galaxy Clusters Cosmology Lensing Dwarf galaxies and Globular

clusters

! watch this space! ! Your input welcome!