From dark matter to MOND

1. From dark matter to MOND or Problems for dark matter on galaxy scales R.H. Sanders, Blois, 2008

2. MOND: French: the world German: the moon Dutch: mouth Astronomers: Modified Newtonian Dynamics. (Milgrom 1983– alternative to dm.)

3. What is MOND? (a minimalist definition) MOND is an algorithm that permits calculation of the radial distribution of force in an object from the observable distribution of baryonic matter with only one additional fixed parameter having units of acceleration. It works! (at least for galaxies) And this is problematic for dark matter.

4. Moreover, explains systematic aspects of galaxy photometry and kinematics, and…..makes predictions! (cdm gets it wrong) The Algorithm: (acceleration based) (Milgrom 1983) -- true gravitational acceleration -- Newtonian acceleration -- fixed acceleration parameter

5. or Asymptotically, Low accelerations: For point mass: , mass rotation vel. relationship Flat rotation curves as Predates most data.

6. An acceleration scale: Newtonian M/L ( ) for UMa spirals (Sanders & Verheijen 1998) Discrepancy is larger not for larger galaxies but for galaxies with lower centripetal acceleration! There exist an acceleration scale: (cdm halos do not contain an acceleration scale.)

7. Asymptotically flat rotation curves: (Begeman 1990) But also reproduces structure in inner regions.

8. Tully-Fisher relation for UMa galaxies (Sanders & Verheijen 1998) Mass-velocity relation Tully-Fisher Relation: (MOND sets slope and intercept.)

9. Baryonic TF relation (McGaugh): Mass of stellar disk Stellar disk including gas The asymptotic rotation velocity ( dm determined by halo) is tightly correlated with mass of baryons (including gas).

10. Prediction for cdm halos (Steinmetz & Navarro 1999): All halos at a given time have similar densities: with large scatter Baryon fraction must systematically decrease with halo mass— (baryonic blowout?) and maintain tight correlation.

11. When then large discrepancy (LSB galaxies) gm/cm General trends: (embodied by MOND) 1. There exists a critical surface density With M/L = 1-2 implies critical surface brightness. When then small discrepancy (HSB galaxies) (Globular clusters, luminous ellipticals) (dwarf spheroidals, LSB spirals)

12. 2. Newtonian discs are unstable. This implies an upper limit to the mean surface density of discs Freeman’s Law: 3. Rotation curve shapes Low surface brightness Rotation curve rises to asymptotic value High surface brightness Rotation curve falls to asymptotic value

13. LSB: (Broeils) HSB: (Begeman)

14. 4. Isothermal spheres 4. 4. Isothermal spheres: where is given by the MOND formula \ is Isothermalsphereshave finite mass; MOND regime: or Thus… with Faber-Jackson relationship:

15. -- galaxy mass. Any object with -- cluster of galaxies -- globular cluster All pressure supported systems will lie on the same FJ relation Also– sphere is truncated beyond This means that all isothermal pressure-supported objects have about the same internal acceleration:

16. Velocity dispersion vs. size for pressure supported systems Points: molecular clouds Stars: globular clusters Triangles: dwarf Sph. Crosses: E. galaxies Dashes: compact dwarfs Squares: clusters of galaxies Solid line corresponds to Within a factor of 5, all systems have same internal acceleration

17. Rotation curve analysis • Assume– light traces mass (M/L = constant in a given galaxy) • But which band? Near IR is best. • Include HI with correction for He. • Calculate from Poisson eq. (stars and gas in thin disc). • Calculate from MOND formula ( fixed). • Compute rotation curve and adjust M/L until fit is optimal. • M/L is the single free parameter. Warning: Not all rotation curves are perfect tracers of radial force distribution (bars, warps, asymmetries)

18. Examples Dotted: New. stellar disk Dashed: New. Gas disc Long dashed: bulge Solid: MOND M/L is single parameter

19. Are the fitted values of M/L reasonable? Points are fitted M/L values for UMa spirals (Sanders & Verheijen 1998) Curves are population synthesis models (Bell & de Jong 2001)

20. Can measure light and gas distribution, color, take M/L from pop. synthesis, and… Predict rotation curves! (no free parameters). Dark matter does not do this (can’t). Fit rotation curves by adjusting parameters.

21. UGC 7524: Dwarf, LSB galaxy. Concentration of light and gas 1.5<R<2 … Corresponding feature In Newtonian and TOTAL rotation curves. (largely from stars) D = 2.5 Mpc, M/L = 1.6 (Swaters 1999)

22. UGC 6406: LSB with cusp in light distribution…. sharply rising rotation curve Gas becomes dominant in outer regions…. asymptotically rising rotation curve D = 26.4 Mpc, M/L = 2.5 (Zwaan, Bosma & van der Hulst)

23. Renzo’s law: For every feature in the surface brightness distribution (or gas surface density distribution) there is a corresponding feature in the observed rotation curve (and vice versa). Dark Matter? Distribution of baryons determines the distribution of dark matter-- Halo with structure. Seems un-natural But with MOND (or modification of gravity) this is expected. What you see is all there is!

24. With MOND clusters still require undetected (dark) matter! (The & White 1984, Gerbal et al. 1992, Sanders 1999, 2003) Bullet cluster : Clowe et al. 2006 No new problem for MOND– but DM is dissipationless!

25. Non-baryonic dark matter exists! Neutrinos Only question is how much. When MeV neutrinos in thermal equilibrium with photons. Number density of neutrinos comparable to that of photons. per type, at present. Three types of active neutrinos:

26. Oscillation experiments measure difference in squares of masses. eV for most massive type. Absolute masses not known, but experimentally eV (tritium beta decay) If eV then eV for all types and Possible that and Phase space constraints– will collect in clusters, not in galaxies.

27. Successes of MOND • Predicts observed form of galaxy rotation curves from observable mass distribution. Reasonable M/L. • Presence of preferred surface density in spirals (Freeman law). LSB– large discrepancy, HSB– small discrepancy. • Preferred internal acceleration in near-isothermal pressure supported systems (molecular clouds to clusters of galaxies). • Existence of TF for spirals, FJ relation for pressure-supported in general. • All with • But underpinned by new physics?

28. Or, is MOND a summary of how DM behaves? Ubiquitous appearance of -- acceleration at which discrepancy appears in galaxies. -- normalization of TF -- normalization of FJ -- internal acceleration of spheroidal systems (sub-gal.) -- critical surface brightness would seem difficult to understand in the context of DM. Correlation of DM with baryons implied by MOND is curious -- behave differently (dissipative vs. non-dissipative). 90% of baryons are missing from galaxies (weak lensing). Baryonic blowout, halo collisions… haphazard processes. Why is TF relation so good? How do leftover baryons determine properties of DM halo?

29. Solar system tests The holy grail of modified gravity theories. Just as direct particle detection for dark matter theories. (Sanders astro-ph/0602161, Bekenstein & Magueijo astro-ph/0602266) Pioneer effect, MOND regions between earth and sun.

30. An alternative: TeVeS as written: q is non dynamical scalar playing role of An obvious extension is to make q dynamical. then, . Biscalar tensor vector theory For reasonable V(q), oscillations develop early (pre-recombination)

31. Scalar field oscillations develop as q settles to bottom of V(q). May have long de Broglie wavelength NO CLUSTERING ON SCALE OF GALAXIES but on scale of clusters and third-peak! 2 scalars: matter coupling field yields MOND coupling strength field– oscillations provide cosmic CDM