MOND and the Galaxies Françoise Combes Observatoire de Paris With Olivier Tiret Angus, Famaey, Gentile, Wu, Zhao Wednesday 1st July 2009
MOND =MOdified Newtonian Dynamics Modification at weak acceleration a = (a 0 a N ) 1/2 a N ~ 1/r 2 a ~ 1/r V 2 = cste a 2 ~V 4 /R 2 ~ GM/R 2 (Tully-Fisher) (Milgrom 1983) Reviews by Sanders & Mc Gaugh 2002 Milgrom 2008 a N = a µ (x) x = a/a 0 a 0 = 1.2 10-10 m/s 2 or 1 Angstroms/s 2 x << 1 Mondian regime µ(x) x x>>1 Newtonian µ(x) 1 2
Dynamic Mass / Visible Mass The ratio remarquably depends on acceleration, The only variable controling the gravity regime universally Mdyn/Mvis 10 1 Radius Velocity Acceleration/a0 3
Motivation: solve the problems of CDM at galaxy scales? -- Over concentration of CDM in galaxies -- Simulated cusps instead of observed cores --Angular momentum problem -- missing satellites problem Feedback from SF? AGN? 4
Constraints on MOND from galaxy dynamics and observations Are the stability, evolution & formation of galaxies stringent tests of the theory? Can we determine the form of the interpolation function µ? 5
MOND in the Milky Way Vrot TVC: Terminal Velocity Curve Vs longitude No-DM Radius Contrary to CDM predictions MW is dominated by baryons 6
Choice of the function µ(x) standard simple Difficulties with the TEVES function (Bekenstein 2004) Famaey & Binney (2005) Standard simple 7
Escape velocity Potential in the MONDian regime Φ( r ) = (GMa 0 ) 1/2 ln r ½ V esc 2 = Φ ( ) Φ( r ) no escape possible! But a galaxy is never totally isolated External field effect (EFE) 8
EFE: External Field Effect If external field g e, is in the X direction At large radii, it is equivalent to a dilatation Δ Define an internal potential Φ int Where g << g e << a 0 Keplerian dependence, with renormalization G Ga 0 /g e 9
Milky Way: effect from Andromeda Observations RAVE (Smith et al 2007) 498 < v esc < 608kms -1 544 km/s g e = a 0 /100 RAVE Wu et al 2007 Simulations with the Besançon model of MW 10
Dwarf Irregular NGC 1560 Escape from a dwarf galaxy? 0. 0.3a 0 Rotation curve 2a 0 11
EFE disk precession Newton: no effect MOND: non-linear effect, gravitationnal torque and precession Violation of the strong equivalence principle Origine of Warps? (also Brada & Milgrom 2000, LMC/MW) 12
Stability of galaxy disks spirals and bars are the motor of evolution CDM: Spheroidal haloes stabilise the disks MOND; disks are entirely self-gravitating However, the gravity law is not linear but in M 1/2 in the MOND regime Bars grow when angular momentum is transfered accepted by spheroidal haloes 13
Disk dynamics in MOND Multi-grid algorithm Finite Differences + adaptative grid 14
Influence of DM halo With DM halo Without DM (MOND) Tiret & Combes 2007 15
Bar strength and pattern speed with and w/o DM DM With DM, the bar appears later, and can reform after the peanut weakening through halo AM exchange, But Ωb falls off Ωb Tiret & Combes 2007 16
Peanut formation/evolution Angular momentum exchange with the DM halo DM MOND Simulations with stars only (no gas) The peanut moves in radius due to the slowing down of the bar 17
Almost 80% of spiral galaxies are barred today Statistics of bar strength Complex problem: the presence of gas destroys the bar, and gas accretion can form another bar DM Sa Sb MOND MOND no gas MOND+gas Sc DM no gas DM+gas MOND compatible with observations 18
Resonant rings with MOND Now with gas Observations MOND Tiret & Combes 07 19
Crucial test of MOND: interactions of galaxies, dynamical friction The Antennae Prototype of major merger 20
Interactions of galaxies: the Antennae: MOND versus CDM Dynamical friction is much lower with MOND: mergers last much longer CDM MOND Also much longer time-scale for merging of dissipationless galaxies (Nipoti et al 2007) 21
Adaptive mesh Tiret 2008 22
Adaptive grid for galaxy interactions 23
Simulations of the Antennae 24
MOND Observations 25
O. Tiret 26
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Dynamical Friction 28
Debate on dynamical friction Ciotti & Binney 2004 (CB04), Nipoti et al 2008 Analytically, the dynamical friction is predicted stronger with MOND than in the ENS (Equivalent Newtonian System) with dark matter However, depends on geometry, plane-parallel, or spherical Slowing down of bars: CB04 predicts a stronger slowing in MOND But their bars is only 5% of the baryonic mass, not realistic N-body simulations show that CDM bars are much more slowed down (Tiret & Combes 2007a) Nipoti et al 2007, Tiret & Combes 2007b reveal that DF is less efficient in galaxy interactions In CDM, a lot of particles acquire E and AM, and DF concept applicable In MOND, a small number of particles in the outer parts acquire big quantities (no analytical treatment) 29
Merger induced starbursts degeneracy CDM: dynamical friction on DM particles very efficient mergers in one passage MOND: with the same angular momentum, the merger will require many passages Starburst at each passage when minimal approach Number of "merger/sb" can be explained both ways Di Matteo et al 2007 30
Tidal dwarfs HI 21cm Formation of Tidal Dwarfs 31
Formation of Tidal Dwarf Galaxies (TDG) Exchange of AM is within the disk: much easier with MOND to form TDG In DM, requires very extended DM distribution (Bournaud et al 03) 32
TDG in N5291 HI ring Head-on collision simulation Bournaud et al 2007 33
Dynamics of the TDGs With MOND, Gentile et al 2007 All inclinations= 45, from simulations (Bournaud et al 07) dark H 2 34
MOND and the dark baryons Is MOND compatible with the existence of dark gas in galaxies? What fraction provides the best fit to the rotation curves? Fit of ~50 rotation curves, c=m(dark)/mhi Tiret & Combes 08, Milgrom 07 35
Combination with MOND NGC 1560: fits with variation of a 0 ~ 1/(gas/HI) V 4 = a 0 GM Tiret & Combes 2008 36
Dark Matter in Ellipticals Tracers: X-ray gas, GC, Planetary Nebulae: Romanowsky et al 2003 Dearth of dark matter??.. Visible matter (isotropic) - - - isothermal (isotropic) 37
Anisotropy of velocities β= 1 σ 2 θ/σ 2 r, -, 0, 1 β circular, isotropic and radial orbits β When galaxy form by mergers, orbits in the outer parts are strongly radial, which could explain the low projected dispersion (Dekel et al 2005) Radius The observation of the velocity profile is somewhat degenerate and cannot lead to the dark matter content univocally 38
DM profile from satellites in SDSS Klypin & Prada 2009 Statistical satellites Only 1 or 0 for each galaxy 39
Test of the SDSS satellites If the anisotropy parameter is taken into account, MOND gives a good fit Angus et al 2007 NGC 3379 Tiret et al 2007 40
Tiret et al 2007 Velocity dispersion around E-gal in MOND 2 types of CDM CDM1: NFW cusp CDM2: as required by rotation curves DV Km/s PN satellites β Radius (kpc) 41
Large scale structure In comoving coordinates: r = a x, v = da/dt x + a u ΔΦ = 4π G δρ µ (g M /γ) g M = g N + C C = rot (h) γ critical acceleration (=a0) Previous approximations h=0 (Nusser 2002, Knebe & Gibson 2004) Newton and MOND accelerations are then parallel Start from a cosmological Newton+ CDM then find MOND produces as much clustering (γ = cste) δ ~ a 2, instead of δ ~a for Newton+ CDM New code AMIGA, taking into account the curl (Llinares et al 2009) Initial conditions from CMBFAST, displacements ( Zeldovich approx) 128 3 grid, 32h -1 Mpc, assuming Newtonian initial state For that critical acceleration γ varies with time γ = a γ0 42
MOND cosmological simulations Starting z=50, dissipationless matter, 2 low Ω models + ΛCDM Llinares et al 2009 z=2 ΛCDM MOND1 MOND2 z=5 ΛCDM MOND1 MOND2 43
Conclusion MOND solves the problems of CDM at galaxy scales But has to solve its own problem at group and cluster scales (neutrinos, baryons..) Observational tests could constrain the various MOND models Bar formation and angular momentum exchange: Bar frequency compatible with observations EFE, companions, groups Dynamical friction much weaker Number of mergers and starbursts: degenerate situation Spherical systems, and satellites, velocity anisotropy 44