1. Review MOND: an alternative to DM?
H.S. Zhao
Univ. of St. Andrews

2. 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

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

4. 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.

5. a0 everywhere: everyone has a weak spot
The location of an object above or below the a0 line tells of the internal dynamics and how far they are from Newtonian.
It is not claiming a velocity-dispersion size correlation.
It is not clear how Newtonian theory with dark matter might account for the fact that these different objects, with a large range in size and environments, all have comparable internal accelerations.
Spirals
Ga0 ~ Rotation V4 /[Luminosity *(M/L)]
GlobularCluster, MolecularCloud, dwarf, Ellip, X-Cluster
a0 ~ Velocity2 /Length scale ~ cH0/6 ~ 100Msun/pc2

6. 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 weak
g = 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
Crude: g not curl-free unlike
gn= -Grad (G M_i/R_i)

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

8. Orbits in disk MOND potential mimic in mild oblate CDM
Read & Moore (high a0)

9. 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 = 0.125116 Simulate LSB disksMWHSB ellipticals
Strong-g
Weak-g

10. Nature's accelerators: Galaxies V2/R=g
Surprisingly V2
~ R2 (Dwarf Irregular)
~ cst (in Spirals)
~ 1/R (Ellipticals)

11. Explained: Rise/fall/wiggles in Ellip & Spiral & Dwarves
Milgrom & Sanders, Sanders & McGaugh

12. Dark Matter/Baryon Exchange Rate Fluctuates
D/B =?
Fornax (10-100)
Milky Way (10)
Globulars (0-1)
Any ratio is possible

13. Fitting RCs by varying DM density cusp α?

14. 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?
IF MOND works, we can fold all our dark matter experiments, save millions

15. Reviewed by Sanders & McGaugh ARAA
Good & bad of non-linear MOND as a Full theory.
Ugly: fudged lensing

16. Relativity Bekenstein version: TeVeS fields astro-ph/0403694
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
e.g. k~0.04, a0~1.2e-8 put in by hand

17. 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

18. 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

19. MOND is Fair Gravity= baryon content 105 Msun gas cloud
= 105 Msun black hole
= 105 suns globular
= 105 suns dwarf gal
… any density profile
Blunt tool

20. 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.)

21. Skordis et al. on CMB Pointecouteau & Silk Famaey & Binney
Possible consistency
Pointecouteau & Silk
need for DM in cluster
Famaey & Binney
High a0 for Milky Way

22. N Draco © SDSS

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

24. MOND: Many Open Questions
Galaxy Clusters
Cosmology
Lensing
Dwarf galaxies and Globular clusters
! watch this space!
! Your input welcome!