Everything in baryons? Benoit Famaey (ULB) Rencontres de Blois 2007 General Relativity -> Dark Matter R αβ - 1/2 R g αβ + Λg αβ = (8πG/c 4 ) T αβ very precisely tested on solar system scales (but Pioneer) Weak-field limit: g 00 = -1-2Φ/c 2 with 2 Φ = 4πGρ Observe ρ bar in galaxies derive Φ bar (R Φ bar / R ) 1/2 = V c bar too low in the galactic plane compared to observed V c => DARK MATTER HALO 1
Concordance model: Assumes GR, DM and Λ DM non-baryonic (Ω b 0.05, Ω m 0.3) and cold (CDM) i.e. massive particles (e.g., neutralino ~ 1TeV) in order to grow hierarchical structure It cannot be ordinary neutrinos, too light (< 2.2 ev) to form hierarchical structure, too light fermions to have a density comparable to DM densities in galaxies (colder than galaxy clusters) However, CDM (necessary in a GR Universe) is not without problems CDM and the missing satellites Simulations predict 10-100 times more satellites (with V c <30km/s) at z=0 than observed Low surface brightness and extinction => not observed? Not that many Cannot form stars? Maybe, thanks to reionization at 6 < z <11 But same problem at galaxy cluster scales (Lake et al.) WDM? Less small-scale power dsph of tidal origin? (Metz & Kroupa 2007) 2
CDM and the cusp problem Simulations of clustering CDM halos (e.g.diemand et al.) predict a central cusp ρ r -γ, with γ > 1 Feedback from the baryons makes the problem worse Angular momentum transfer from the bar WDM, but structure formation and small scale power Other solutions? Hiding cusps by triaxiality of the halo? No Klypin, Zhao & Somerville 2002 The Milky Way HI 21-cm (or CO) (l,v) diagrams Circular orbit at radius R: V r = [V c (R)/R - V c (R 0 )/R 0 ] R 0 sin l Enveloppe: terminal velocity curve V r = sign(l) V c (R 0 sin l) - V c (R 0 ) sin l 3
Bissantz et al. (2003) : baryonic potential from COBE near-ir luminosity density including bar and spiral structure in disk with spatially constant M/L Fit M/L and Ω in potentials of bar and of spiral to gas dynamics Fit to microlensing optical depth No DM Milky Way provides good fits to gas dynamics and microlensing within 5 kpc But V c (R 0 ) = 185 km/s instead of 220 km/s DM halo Φ = 1/2 V 2 ln(r 2 + r c2 ) Negligible contribution inside 5 kpc NOT cuspy if mass inside 5 kpc shifted from baryons to DM, non-circular motions in (l,v) vanish (even shallow halo smoothes bumps and dips in the TVC) CDM: the «correlation» 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 4
If no DM, then GR is wrong -> MOND Correlation summarized by the MOND formula in galaxies (Milgrom 1983) : µ ( g /a 0 ) g = g N baryons where a 0 ~ ch 0 with µ(x) = x for x «1 (MONDian regime) => V 2 /r ~ 1/r => V~cst µ(x) = 1 for x»1 (Newtonian regime) OK for the Milky Way TVC (Famaey & Binney 2005) 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 Predicts stability of disks with Σ <~ a 0 /G Rotation curves of LSB (Σ «a 0 /G => g N «a 0 ), with high-discrepancy Rotation curves of HSB including early-type disks (see e.g. Sanders & McGaugh 2002; Famaey, Gentile, Bruneton, Zhao 2007; Sanders & Noordermeer 2007) Fitted M/L ratios follow predictions of population synthesis models No discrepancy in centre of giant ellipticals + Pne (Milgrom & Sanders 2003) + solution to time-delay problem No discrepancy in nearby globular clusters (Milgrom 1983) (external field effect, breaks the strong equivalence principle) Statistical bar frequency in spirals closer to observations than in DM (Tiret & Combes 2007) Local galactic escape speed (Famaey, Bruneton & Zhao 2007) 5
At the very least, MOND tells us something fundamental we are not understanding in galaxy formation («gastrophysical» feedbacks?), not even close to understanding it! Non-standard: a) fundamental property of DM b) modification of inertia (Milgrom 1994) c) modification of gravity. [ µ ( Φ /a 0 ) Φ] = 4 π G ρ Modifying GR to obtain MOND in static weak-field limit: dynamical 4-vector field U α U α = 1, with free function in the action playing the role of µ (Bekenstein 2004; Zlosnik, Ferreira & Starkman 2007) g αβ = (-1-2Φ/c 2 ) 0 0 0 0 (1-2Φ/c 2 ) 0 0 0 0 (1-2Φ/c 2 ) 0 0 0 0 (1-2Φ/c 2 ) where Φ obeys a MOND-like equation (dynamics and lensing are governed by the same physical metric g αβ as in GR, strong lenses well fitted by point lenses, except a few outliers in clusters, Zhao et al. 2005) 6
MOND and Cosmology Can we form structure without dark matter in relativistic MOND? YES (Dodelson & Liguori 2006) Perturbations in the vector field U ν = (1+α 0, α) where α 0 =-Φ/c 2 through U ν U ν =-1 In Poisson equation: term depending on the spatial part α of the vector field (zero in static systems) Behaves like dark matter on right-hand side of equation This α-term grows in the perturbation and plays the role of DM Matter power spectrum ok without DM (Dodelson & Liguori 2006), but apparently needs DM in the form of 2eV neutrinos to fit the angular power spectrum of the CMB, in order not to change the angular-distance relation by having too much acceleration (Skordis et al. 2006) MOND and galaxy Clusters Rich X-ray emitting clusters of galaxies still need dark matter in MOND, typically in the central ~100 kpc, typically 1 to 3 times more than the total visible mass Bullet cluster (Clowe et al. 2006, Angus et al. 2007)-> must be collisionless Integrated baryonic mass from clusters of galaxies only represent a few percents of BBN, so if the necessary missing baryons are present in clusters, they still represent much less than 1/2 of BBN Other possibility: ordinary neutrinos of 2eV (Sanders 2003), also invoked to fit the CMB (Skordis et al. 2006), not clustering in galaxies Interestingly m ν 6eV (Ω ν 0.12) excluded in standard cosmology 7
Mass of electron neutrino β-decay of tritium ( 3 H) into Helium 3 ion + electron + neutrino: Conclusions CDM has its most outstanding problems (missing satellite, cusp, correlation, time delay, missing baryons) on galactic scales, where MOND does much better and naturally explains the galactic Kepler laws It is not yet clear if a purely baryonic Universe can provide a fully consistent cosmology, more work has to be done along these lines, one must also wait for the basic principle and fundamental theory underlying the MOND paradigm MOND has a missing baryons problem in galaxy clusters, and these baryons must be in collisionless form (clumps of cold gas?) These missing baryons would still represent much less than half of the BBN An interesting alternative possibility would be that neutrinos have a 2eV mass: this is possible in a MOND Universe (and does help the cause of the CMB), but ruled out in standard cosmology 8