Dark Matter: What is it? Where is it? Do we need it? How much?

1. Dark Matter:What is it? Where is it?Do we need it? How much? History: 1937: like many things in astronomy, dark matter was first postulated by Fritz Zwicky. Apply virial theorem to indiv. galaxies in the Virgo cluster  Mgalaxy Apply virial theorem to cluster as a whole  Mcluster Zwicky found M/Lcluster ~200 ?? M/Lgalaxy~8 ~1970:Vera Rubin, Ken Freeman and others explore rotation curves and (re-)find the need for dark matter (formerly called missing). Actual diagnosis: gravity acts stronger than expected on the basis of the identified mass (=sources of gravity) Reading: J Peacock, Cosmological Physics, Cambridge Press p367-386 Vatican 2003 Lecture 26 HWR

2. Dark Matter on Different Scales • Basic hypotheses to test: • there is universal “dark matter”, which • was initially distributed like all known matter • interacts with the observed matter (and itself) mostly through gravity • OR, • there is a universal modification to the laws of gravity (Newton AND Einstein) that acts at large scales and/or weak accelerations. • Dark Matter appears to be needed in: • Dwarf spheroidal galaxies: 500 pc • Large galaxies: 20 kpc • Galaxy halos: 50-500 kpc • Galaxy Clusters: 1 Mpc • Large-Scale Structure: 20 Mpc • Cosmic Microwave Background Vatican 2003 Lecture 26 HWR

3. Stellar density contours of Draco from SDSS Odenkirchen et al 2001  Draco is a bound system in equilibrium Dark Matter Evidence Nearby:the Draco dwarf galaxy Sky image of Draco Dsun 70 kpc Vatican 2003 Lecture 26 HWR

4. Stellar density profile of Draco Giant stars with velocities measured • Estimate *(r) from stellar distribution • Giant stars as kinematic tracers • - need velocity precision of  3 km/s Radial Profile and Kinematics of Draco • Modelling options • Stars only tot(r) = *(r) • Stars + DM: tot(r) = *(r) + DM(r) Vatican 2003 Lecture 26 HWR

5. Velocity dispersion profile Jeans equation model Anisotropy Enclosed mass Try models with different DM profiles  M (<10‘) well constrained Mass Modelling of Draco Expected (M/L)* ~ 2  Draco is dark matter dominated Vatican 2003 Lecture 26 HWR

6. Rotation Curves of Spiral Galaxies • Rotation curves show that DM is needed • Total (stars,gas,DM) rotation curve is v~const. for 2-8 Rexp • A so-called non-singular isothermal (s=const.) DM distribution often fits well: • But, is this dark matter profile • Physically motivated? • Physically plausible? • Expectation from cosmological simulations: NFW profile • r~r-1 at small radii and • r~r-3 at large radii Vatican 2003 Lecture 26 HWR

7. Van Albada et al 1985, ApJ, 295, 305 Navarro 1997 Degeneracies in Fitting Rotation Curves Rotation curves do not contain enough information to: Determine the ratio of star to DM mass Distinguish the radial profile of DM Dark matter at small radii is poorly understood! Vatican 2003 Lecture 26 HWR

8. Satellites to the Milky Way  tracers of the mass in the halo SDSS sample: isolated MW-like galaxies 0.5 satellites per galaxy x 1000 galaxies  Synthetic galaxy with 500 satellites unbound systems Dark Matter in Galaxy HalosPrada et al 2003 • MW-like galaxies are at the center of dark matter halos that extend to >200 kpc • DM density profile in the outer parts r~r-3 • identify satellite candidates • make a conservative rejection of unbound systems • calculate resulting velocity dispersion of satellites • compare to cosmological halo formation models  good match Vatican 2003 Lecture 26 HWR

9. T = 106 K  X-ray emission Dark Matter in Galaxy Clusters • In galaxy clusters the masses can be measured three ways • Galaxy clusters contain hot gas ( bound by dark matter?) • Galaxy velocity dispersion • Gravitational lensing Vatican 2003 Lecture 26 HWR

10. X-Ray Gas in Hydrostatic Exquilibrium Mstars~Mgas~3x1013MSun Mtot,cluster(Rvirial)~1015MSun Vatican 2003 Lecture 26 HWR

11. Other Lines of Evidence For Dark Matter • Gravitational lensing (Hans-Walter, next week)  dark matter clumping on largest scales • The Cosmic Microwave Background and the curvature of space (Rachel, Friday)  WM~0.27 • The growth of small fluctuations to strong fluctuations (Rachel, next week) Vatican 2003 Lecture 26 HWR

12. Alternatives to Dark Matter • MOND: Modified Newtonian Dynamics (Milgrom 1980s-) • Ansatz: • for accelerations a less than a0, gravity behaves as a(a/a0) = GM/r2 • as a(r) ~ 1/r of a < a0: flat rotation curves Note: • a < a0 untested in the lab • single value of a0 works for all rotation curves • But: • No relativistic version of MOND • MOND has trouble explaining DM in cluster and far out in halos Vatican 2003 Lecture 26 HWR

13. Summary: Dark Matter Evidence • A wide range of dynamical phenomena cannot be explained through the known (baryonic) mass content of the universe alone. • All (well, almost all) these problems can be solved if we make one radical assumption: 85% of all matter with rest mass (M  0.25) is in a form (dark matter) that was • initially distributed as ordinary matter • interacts with the rest (almost) only through gravity • acts like a collisionless “fluid” • is cold, i.e. consists of non-relativistic particles • Stars,gas are now more concentrated/clumped than DM • galaxies sit at the center of much larger DM halos • Note: rbaryon ~8 x rstars • We also need a “cosmological” constant (vacuum energy), i.e. a long-distance ‘repulsive’ force Vatican 2003 Lecture 26 HWR

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15. Nature of the Dark Matter • Non-baryonic, to reconcile M ~0.27 with primordial nucleosynthesis Wb~0.018 and large-scale structure growth • Cold: must not escape from potential wells • (Cold) Dark Matter Candidates: • Black holes • Low-mass objects (“MACHO”s, free-floating planets) • Elementary particles Massive Black Holes as Dark Matter Candidates • (one) plausible mass range: ~106 Msun (Lacey and Ostriker, 1985) • But, such massive black holes cannot be the dark matter in dwarf galaxies (Rix and Lake, 1985). • E.g. c.a. 80 BH’s in Draco, they would disrupt the galaxies! Vatican 2003 Lecture 26 HWR

16. MACHO’s: Massive Compact Halo Objects • Potential mass range: 0.08 MSun (stellar limit) to MEarth Observational test: gravitational microlensing • (MACHO and OGLE) experiments. Idea: • if all the dark matter in the Milky Way’s halo was MACHOS • there is a 10-6 chance that a star (e.g. in the Magellanic Cloud) has a MACHO exactly along the line of sight • focussing  brightening of the stars’ image • as stars move  dime dependent light curve. Implementation: monitor 106 stars Vatican 2003 Lecture 26 HWR

17. Lensing Lightcurve Large Magellanic Cloud Micro-Lensing Cartoon Microlensing Searches Vatican 2003 Lecture 26 HWR

18. MACHO Mass Halo Mass Fraction in MACHOs Are MACHOs the Dark Matter? • MACHO’s make up (at most) 15% of the Milky Ways halo mass • Inferred mass range: 0.4MSun Why would they be invisible? • MACHOs are an enigma, but certainly not the solution to the dark matter problem Alternative: lensing by ordinary stars in the LMC or MW Vatican 2003 Lecture 26 HWR

19. WIMPS as Dark Matter Candidates • “cold” Dark Matter: must become non-relativistic already at T >> 104K  clumping • supersymmetric theories (SUSY) can naturally create particle (pairs with their SUSY partner) - lightest SUSY particle stable: neutralino, gravitino, higgsino, etc. • axions: hypothesized, very light particle; may arise in quantum chromodynamics  WIMPS are a plausible, but not firm, consequence of several theories in particle physics Vatican 2003 Lecture 26 HWR

20. Towards detecting WIMPS • WIMPS: may have exceedingly rare elastic scattering events with crystals and one may measure the recoil. • However: many other particles/processes interact with crystals  high false detection rate. • Reduce background  deep tunnels (e.g. Gran Sasso) • Search for seasonal signature Vatican 2003 Lecture 26 HWR

21. Other experiments seem to rule out DAMA A first detection? … Or not The DAMA experiment in the Gran Sasso claimed to have found a seasonal variation ? 50 GeV particles PROBLEM: cross-section could be 1000 times smaller than current limits Vatican 2003 Lecture 26 HWR

22. Dark Matter Up-Shot • Cold, collisionless ‚Dark Matter‘ with DM  0.25 explains a wide range of phenomena (not only rotation curves) • „universal dark matter“ works • Stars/cold gas are concentrated/clumped than DM • DM poorly understood inside galaxies • Nature of Dark Matter unknown • We only know what it is NOT! Vatican 2003 Lecture 26 HWR