Modified Newtonian Dynamics: a phenomenological review

Benoit Famaey (ULB, Brussels)

The old missing mass problem

• 1781: William and Caroline Herschel discover Uranus

• 1792: Delambre publishes orbit of Uranus, non-Newtonian even after taking the perturbations of other planets into account

• 1834: Hussey proposes new planet, Airy believes in new gravitational law

• 1846: Le Verrier calculates the position of the new planet

Galle discovers Neptune

• 1859: perihelion precession of Mercury of 43 arcsec per century, Leverrier postulates the existence of the small planet Vulcan

But correct answer for Mercury found by Einstein in 1915

The modern-day missing mass

• 1933: Zwicky observes velocity dispersion of individual galaxies in the Coma cluster, and finds M/Mvis ≈ 20

• 1973: Rubin & Ford measure the asymptotically FLAT rotation curve of M31 (Andromeda) instead of a Keplerian 1/√r falloff

Doppler Shift: (-0)/0 = Vr / c

CDM and the cusp problem

• Simulations of clustering CDM halos (e.g.Diemand et al.) predict a central cusp r- , with > 1

• Feedback from the baryons makes the problem worse

• Angular momentum transfer from the bar

• WDM?• Other solutions?• Hiding cusps by triaxiality of

the halo? arXiv:astro-ph/0608376 No

0

200

ESO79-G14 (Gentile et al. 2004)

CDM and the « conspiracy » problem

• Each time one sees a feature in the light, there is a feature in the rotation curve (Sancisi’s rule)

• Baryonic Tully-Fisher relation

V∞4 Mbar (tight->triaxiality of halo?)

• Amount of DM determined by the distribution of baryonsat all radii and wiggles of rotation curves even follow wiggles of baryons (TF at all radii)

• Tidal Dwarf Galaxies with DM?Tidal Dwarf Galaxies with DM?(Bournaud et al. 2007 Science(Bournaud et al. 2007 Science)

Tidal dwarf galaxiesNumerical simulations of tidal dwarf galaxies formation:

Barnes & Hernquist (1992)

Tidal dwarf galaxies are formed out of material

that was in a rotating disk.

They have virtually

no collisionless dark matter !

The NGC 5291 systemBournaud et al. (2007) show HI VLA observations

of the NGC 5291 system

Several tidal dwarf galaxies

are found

Only 3 are large enough

for mass modelling

(N5291N, N5291S,

N5291SW)

blue: HI

white: optical

red: UV

Bournaud et al. (2007)

The NGC 5291 systemBournaud et al. derive the rotation curves of these 3 tidal dwarf galaxies:

visible

These galaxies show a mass discrepancy

According to CDM there should be almost no dark matter (5-10% at most).

Bournaud et al.: baryonic dark matter e.g. in the form of cold H2 molecules?

CDM

expectation

The conspiracy in other galaxies can be summarized by MOND

• Correlation summarized by this formula in galaxies (Milgrom 1983):

(g/a(g/a00) g) g = g= gN barN bar where a0 ~ cH0 ~ c1/2

(V(V22/ra/ra00) V) V22/r/r = g= gN barN bar

with (x) = x for x « 1

(x) = 1 for x »1

• Until we reproduce a relation like this from simulations, we cannot yet claim to fully undertstand DM

• OK for the Milky Way TVC (Famaey & Binney 2005, Wu et al. 2008, McGaugh 2008)

• No cusp problem + explains the RC wiggles following the baryons

• Tully-Fisher relation (observed with small scatter): V∞4 = GMbara0

• Predicts that the discrepancy always appear at V2/r ~ a0 => in LSB where << a0/G

• Mbar(r)/Mtot(r) = (halo-by-halo missing baryons problem: ≠ cosmic ratio at large radii)

• Predicts the correct order of magnitude for the local galactic escape speed

~ (x) = x/(1+x)

Famaey et al. 2007

Phys.Rev. D75 (2007) 063002

arXiv:astro-ph/0611132

M*/L ratios

The NGC 5291 system

In Gentile et al. (2007, A&A, 472, L25) we see how MOND does

(first assuming an inclination of 45o):

MOND

Red curve: baryonic contribution

Black curve: MOND curve (*not* at fit, zero free parameters!)

We also took into account the external field effect from NGC 5291

Conspiracy 108 -> 1012 baryonic Msun

i=45° for TDGs of NGC5291

i=45° Newton

((Gentile et al. Gentile et al. A&A 472 L25)

Why does the formula work in CDM and CDM-free galaxies???

• At least, the MOND formula might tell us something we are not yet understanding in galaxy formation (« gastrophysical » feedbacks). Surprising regularity!

• Non-standard: a) fundamental property of DM (see Blanchet)b) modification of « inertia »

(Milgrom 1994, not clear what to do at relatvistic level, non-metric theory?)

c) modification of gravityd) all of the above

. [ (/a0) ] = 4 π G bar

• Modifying GR to obtain MOND in static weak-field limit: dynamical 4-vector field UU = –1, with free function in the action playing the role of (Bekenstein 2004; Zlosnik et al. 2007; Bruneton & Esposito-Farese 2007; Halle, Zhao & Li 2008)

• Double-imaged strong lenses well fitted, except a few outliers in groups and clusters (Shan et al. 2008 arXiv:0804.2668)

Conclusions

• « DM » is distributed in galaxies in a regular and predictive manner (not as messy as expected)

• One formula fits >2000 galaxy rotation curves data points

• RCs of TDGs of NGC 5291 are difficult to understand in the CDM framework but MOND fits them very well