Galactic Matter and Dark Matter

1. Galactic Matter and Dark Matter RamanathCowsik and Benjamin Burch Physics Department McDonnell Center for the Space Sciences Washinton University in St. Louis, USA 63130 WHEPP XII: Mahabaleshwar, India January 4-5 Thanks to Professor SreerupRaychaudhuri & Professor UtpalSarkar

3. Density Distribution Of Dark Matter Friedman-Robertson-Walker Cosmologies  1.9 x 10-29 h2 g cm-3  104h2 eV cm-3 Einstein-de Sitter Model • Preferred On the basis of • Observations • Structure formation • Inflation (temporal Copernicus principle)

4. Spectrum of the thermal microwave background at ~2.73 K.

5. Cowsik, McCleland, Zeldovich Bound(PRL 29, 669, 1972) ; After annihilation of e+ e-,

6. ,

8. Zwicky - Evidence for unseen gravitating mass in clusters (1933)Cowsik & McClelland – ‘Impossible to see’ –”weakly interacting” particles from big bang generally lead to halos of Dark-Matter surrounding galactic systems. (1973). Recently, Nieuwenhuizen has ressurected this idea.

9. Evidence for the presence of dominant mass in invisible “dark matter”

10. M100 - A Galaxy Notice the beautifully formed spiral arms. The speed of stars in their circular path increases from the center and reaches a constant value just beyond the nucleus. We need a halo of invisible dark matter to counteract the centrifugal force

12. Dark Energy in the Universe

14. Insert WMAP picture The microwave sky: The radiation that fills the universe is highly isotropic- almost the same intensity whichever way we look. This necessarily implies that dark matter is needed for the formation of galaxies and other visible structures in the universe.

15. Multipole power spectrum of the CMB temperature fluctuations of WMAP and other CMB anisotropy experiments. Position of the first peak at l≈200 indicates the flatness of the Universe; height of the first peak determines the matter density, and the ratio of the first to second peaks determines the baryon density. Together with SDSS large-scale structure data, the CMB measurements have determined the shape and composition of the Universe: Ωtot=1.003±0.010, ΩM=0.24±0.02, ΩB=0.042±0.002, and ΩΛ=0.76±0.02. The curve is the theoretical prediction of the “concordance cosmology”, with a band that indicates cosmic variance.

18. “Metals” 0.01% Visible H, He 0.5% Tytler astro-ph 0001318 Dark Matter 27% Dark Energy Cosmological Constant  72% A New Order J. Primack

20. Einstein’s equations for a homogeneous and isotropic universe Friedman equations for expanding universe using the cosmological principle: r-r Component : t-t Component :

22. Weakly interacting particles adequately survive annihilation to constitute dark matter in the Universe. (From Kolb and Turner)

23. Early ‘mass-models’ of the Galaxy. The need for a “Corona” (of dark matter) to explain the rotation curve of the Galaxy was well recognized. The Keplarian fall-off vc~r-1/2 of the ‘bulge’ may be noted. This is an adaptation of the model by Schmidt (1985).

24. Sketch of the Galaxy based on radio, infrared and optical observations. (Churchwell et al. 2009)

25. NIR surface brightness of the inner Galaxy from IRAS and COBE/DIRBE observations. (Launhardt, Zylka, and Mezger 2002)

26. Dynamical model for the dark matter halo • density→potential→orbits →velocities→density • potential gets contribution from visible matter and dark matter • Visible matter • Central Bulge: • Thin and Thick disk: (Burch and Cowsik 2011)

27. Dark Matter-satisfies the stationary collisionless Boltzmann equation. Jeans theorem applies:Reduced isothermal phase space distribution Coupled non-linear differential equation, solved iteratively using eigenfunction expansion method

29. Comparison of theory with observed rotation curve Parameters for ΦDM: truncation radius of the dark matter distribution

30. It may be difficult to distinguish between dark matter described by a King distribution (thin lines) and a NFW distribution (thick line). • From the square of the dark matter density, we may be able to estimate the expected gamma-ray and e± flux from dark matter annihilation. • Knowing the dark matter density also allows us to estimate the capture of dark matter by stars.

32. Here we see that the inner rotation curve is easily fit with a Plummer-type density distribution and the outer rotation curve is dominated by the Galactic disk, modeled by a double-exponential. • The difference between the calculated rotation curve from visible matter and the observations allows us to determine the distribution of dark matter in the Galaxy. (Burch and Cowsik 2011)

33. It is clear that in the inner bulge region of the Milky Way (r<1.5 kpc), dark matter contributes negligibly to the rotation speed of the Galaxy.

34. A sample of theoretically calculated rotation curves of the Galaxy based on our self-consistent model, including lower bounds derived from the study of dynamics of dwarf spheroidals. That dark matter is modeled as having a lowered (truncated) isothermal distribution.

35. The density of dark at the Galactic center is less than 25% of the stellar density. (Cowsik, Ratnam, Bhattacharjee, Majumdar, and Burch)

36. Gamma-ray flux from the galactic disk-ascribed to cosmic ray interactions. We may expect 1-100 GeV gamma rays from the annihilations of dark matter particles.

37. Gamma-ray flux from the galactic disk-ascribed to cosmic ray interactions. We may expect 1-100 GeV gamma rays from the annihilations of dark matter particles, which are to be detected against a strong background generated by molecular interactions and inverse Compton scattering of cosmic rays.

40. Dynamical model for the dark matter halo • density→potential→orbits →velocities→density • potential gets contribution from visible matter and dark matter • Visible matter • Central Bulge: • Thin and Thick disk: (Burch and Cowsik 2011)

41. Dark Matter-satisfies the stationary collisionless Boltzmann equation. Jeans theorem applies:Reduced isothermal phase space distribution Coupled non-linear differential equation, solved iteratively using eigenfunction expansion method

42. CDMS II(Cold Dark Matter Survey: Soudan) 10-41cm2 weakly interacting CDMS compares phonon (WIMP) yield to ionization (background) in Ge detectors.(arXiv 0802:3530) CDMS-II XENON10 SUSY 103 GeV signal region After cut to remove surface events massive

43. Summary • NFW profiles may arise as self-consistent solutions to reduced isothermal distributions in the presence of baryonic matter. • Self-consistent solutions yield local dispersion velocities for DM particles. • Accurate astronomical measurements of rotation curves at galactocentric distances > 10 kpc are needed for accurate modeling of galactic dark matter. • Astrophysical considerations for identifying the missing baryons in our galactic neighborhood are called for. • The self-consistent solutions allow a wide range of DM densities at the galactic center: this leads to even wider range of predictions for gamma ray and other astronomical signatures of DM annihilations; the DM density is at most 10% of the stellar density at the galactic center, which would therefore dominate the accretion by the black hole. • The possibility of neutrino as DM is being reconsidered. The standard constraint on neutrino masses from their role in erasing small scale perturbations in the density of cold DM, from laboratory measurements and from their role in generating baryon asymmetry and dark energy condensates etc. should revisited.

45. Thanks to WHEPP XII organizers & participants