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 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

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)

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 = 0.125116 Simulate LSB disksMWHSB 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?

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

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 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

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 Blunt tool

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 Pointecouteau & Silk Famaey & Binney 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!