Modified Newtonian Dynamics a phenomenological review Benoit Famaey

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 M 31 (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? ar. Xiv: astro-ph/0608376 No 200 0 ESO 79 -G 14 (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 baryons at all radii and wiggles of rotation curves even follow wiggles of baryons (TF at all radii) • Tidal Dwarf Galaxies with DM? (Bournaud et al. 2007 Science) et al. 2007 Science

Tidal dwarf galaxies Numerical 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 system Bournaud et al. (2007) show HI VLA observations of the NGC 5291 system Several tidal dwarf galaxies are found blue: HI white: optical red: UV Only 3 are large enough for mass modelling (N 5291 N, N 5291 SW) Bournaud et al. (2007)

The NGC 5291 system Bournaud 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 H 2 molecules? CDM expectation

The conspiracy in other galaxies can be summarized by MOND • Correlation summarized by this formula in galaxies (Milgrom 1983): (g/a 0) g = g. N bar where a 0 ~ c. H 0 ~ c 1/2 (V 2/ra 0) V 2/r = g. N bar ~ (x) = x/(1+x) 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, Mc. Gaugh 2008) No cusp problem + explains the RC wiggles following the baryons Tully-Fisher relation (observed with small scatter): V∞ 4 = GMbara 0 Predicts that the discrepancy always appear at V 2/r ~ a 0 => in LSB where << a 0/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

Famaey et al. 2007 Phys. Rev. D 75 (2007) 063002 ar. Xiv: astro-ph/0611132

M*/L ratios

The NGC 5291 system In Gentile et al. (2007, A&A, 472, L 25) we see how MOND does (first assuming an inclination of 45 o): 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

8 12 Conspiracy 10 -> 10 baryonic M (Gentile et al. A&A 472 L 25) Gentile et al. i=45° Newton i=45° for TDGs of NGC 5291 Why does the formula work in CDM and CDM-free galaxies? ? ? sun

• 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 gravity d) all of the above . [ ( /a 0) ] = 4 π G bar • Modifying GR to obtain MOND in static weak-field limit: dynamical 4 -vector field U U = – 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 ar. Xiv: 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