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/M vis ≈ : Rubin & Ford measure the asymptotically FLAT rotation curve of M31 (Andromeda) instead of a Keplerian 1/√r falloff Doppler Shift: ( - 0 )/ 0 = V r / 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/ No arXiv:astro-ph/ 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  M bar (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?Tidal Dwarf Galaxies with DM? (Bournaud et al Science (Bournaud et al 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 Only 3 are large enough for mass modelling (N5291N, N5291S, N5291SW) blue: HI white: optical red: UV 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  (g/a 0 ) g = g N bar where a 0 ~ cH 0 ~ c  1/2  (V 2 /ra 0 ) V 2 /r = g N 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 = GM bar a 0 Predicts that the discrepancy always appear at V 2 /r ~ a 0 => in LSB where  << a 0 /G M bar (r)/M tot (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 Phys.Rev. D75 (2007) arXiv:astro-ph/

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 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

The NGC 5291 system But geometry of the NGC 5291 system is poorly known: we also considered inclination as a free parameter Best-fit inclinations not far from 45 o (our initial assumption)

Conspiracy > baryonic M sun i=45° for TDGs of NGC529 1 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 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 arXiv: )

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