Jun’ichi Yokoyama (RESCEU)

2. §６ Observational Determination of Cosmological Paramegers (As of 2002, just before WMAP data came.) Λ Jun’ichi Yokoyama (RESCEU)

3. Radiation Contents Photon density dominated by Cosmic Microwave Background (CMB) Black body radiation with temperature Neutrino Background for 3 species in the standard model (massless)

5. Material Contents Baryon density Density of Visible Matter Luminosity density of galaxies solar luminosity Mass-to-Light ratio (It simply means that our Sun is a typical star.)

6. Baryon density All Baryon density Big bang Nucleosynthesis (BBN) theory and Observations of light elements (D, He4, Li…) constrain Baryon-to-Photon ratio . BBN is one of the most important subjects of the standard cosmology. But I do not discuss it here any further, since it will be covered by lectures on Nuclear Physics III.

7. 前ページと左図は ApJ600(2004)544 右図は astro-ph/0307244 による。

8. Material Contents Total Matter (Baryon + Cold Dark Matter) Rotation curve of a spiral galaxy 渦巻き銀河の回転曲線 Mass within radius r Rotation curve remain constant even beyond the size of the galactic disk, which indicates the existence of dark matter.

9. Total Matter (Baryon + Cold Dark Matter) • Random velocities of galaxies in a group of galaxies • Cluster baryon fraction from X-ray emissivity and baryon density from primordial nucleosynthesis • Shape parameter of the transfer function of CDM scenario of structure formation • Many others Virial Theorem gives an estimate of gravitational potential energy Mass.

10. Current data 2Mpc 2Mpc Cosmic Expansion Hubble`s discovery The Greatest Blunder

11. To measure cosmic expansion, acceleration/deceleration, distance measurement is the most important. Luminosity Distance Absolute Luminosity Cepheid(variable stars), Tully Fisher relation Type Ia Supernovae Angular Diameter Distance Absolute Size Cosmic Microwave Background(CMB) Baryon Acoustic Oscillations(BAO)

12. Before turning into observations, some terminologies… g r i z Apparent magnitude

13. Extinction by dusts etc. = Reddening Light with shorter wavelength is more likely absorbed/scattered. Distance modulus in parsec in Mpc Color, Colours, … e.g. Absolute magnitude Measure of the absolute luminosity Apparent magnitude seen 10pc away from the star. (1pc = 3.26ly = 3.0856×1018cm).

14. K correction When we observe high-redshift objects, we observe at a longer wavelength than the rest-frame counterpart. Hence depending on the spectral shape of the object, we must correct the flux or the apparent magnitude of each band. Color excess e.g. Extinction is proportional to color excess. standard text-book value

15. The Hubble Parameter A suffix 0 denotes the present value. HST Key Project • CepheidsH0=75±10km/s/Mpc • SNIa H0=71±2(stat)±6(syst)km/s/Mpc • Tully-Fisher H0=71±3±7km/s/Mpc • Surface Brightness Fluctuation H0=70±5±6km/s/Mpc • SNII H0=72±9±7km/s/Mpc • Fundamental Plane of Elliptical Galaxies H0=82±6±9km/s/Mpc SummaryH0=72±8km/s/Mpc (Freedman et al ApJ 553(2001)47)

16. Cepheid 動径脈動型変光星 They change their size with a certain constant period P=5-70 days. Their absolute magnitude M is proportional to logP. Hubble space telescope (HST) measured 20 cepheids in M100 galaxy, for example. H0=75±10km/s/Mpc distance to LMC = 51kpc (46kpc previously). This distance is also determined using variable stars (Mira type). NB. Parallax distance can be determined only up to 100pc or so. This method is used to measure the distance to relatively close galaxies and it serves as the second step to the cosmic distance ladder.

17. Tully Fisher relation Rotation velocity of a spiral galaxy is correlated with its absolute luminosity. Line broadening by Doppler effect=Observable

18. Surface Brightness Fluctuations Nearby Mountains =Trees can be resolved. Distant Mountains =Looks homogeneous. Galaxies consist of stars. Distant galaxies looks more homogeneous with smaller pixel-to-pixel fluctuations of surface brightness.

19. The Hubble Parameter A suffix 0 denotes the present value. HST Key Project • CepheidsH0=75±10km/s/Mpc • SNIa H0=71±2(stat)±6(syst)km/s/Mpc • Tully-Fisher H0=71±3±7km/s/Mpc • Surface Brightness Fluctuation H0=70±5±6km/s/Mpc • SNII H0=72±9±7km/s/Mpc • Fundamental Plane of Elliptical Galaxies H0=82±6±9km/s/Mpc SummaryH0=72±8km/s/Mpc (Freedman et al ApJ 553(2001)47)

20. Supernovae: as bright as a galaxy Type I : No H lines, Type II : H lines Gravitational Collapse and Bounce

21. Type Ia Supernovae Accretion to a C+O white dwarf in a binary system It approaches Chandrasekhar mass (1.38 M), the maximum mass that can be supported by degenerate electron pressure. Radius of the white dwarf drops rapidly with increased central temperature, leading to the ignition of Carbon Deflagration and Detonation

22. Type Ia Supernovae Large luminosity ～ whole galaxy Measurable at cosmological distances Theoretical studies including numerical simulations have been in difficult situations to realize explosion… Observations of nearby SNIa indicate that they can be used as a standard candle whose absolute luminosity can be found from the light curve shape and color.. SN1994D in NGC4526

23. Scatter in the maximum absolute magnitudes are quite large: ±0.79mag in B, ±0.59mag in V, ±0.46mag in V They cannot be used as a standard candle as they are. But a strong correlation was found between the maximum magnitudes and decline rate of the light curve. , drop in the B magnitude during the first 15 days after the maximum is strongly correlated to the maximum absolute magnitude. Absolute Magnitude of Ia Supernovae: First Step Phillips (1993) Astrophys J 413, L105 Measured B, V, I absolute magnitudes of 9 SNIa using host-galaxy distances estimated by the surface-brightness fluctuations or Tully-Fisher relation. Light curve observed for > 20 days after the maximum.

24. MB 0 15 days Peak luminosity-decline rate relation

25. The light curve of SNIa is powered by the radiative decay of 56Ni  56Co  56Fe, so its luminosity depends on the amount of 56Ni synthesized in the explosion. More 56Ni →larger luminosity → higher temperature → higher opacity → broader light curve

26. Absolute Magnitude of Ia Supernovae: Another Approach Perlmutter et al (1997) Astrophys J 483, 565 (Supernova Cosmology Project) Light curve width – Luminosity relation The stretch factor linearly broadens or narrows the rest-frame time scale of an average template light curve. Related to as . Corrected magnitude From 6 distant supernovae with z=0.35-0.46 they found no evidence for the dark energy.

28. Discovery of the Dark Energy by SCP Perlmutter et al (1999) Astrophys J 517, 565 (Supernova Cosmology Project) 42 SNIa at z=0.18-0.83 and are nuisance parameters to be integrated out. 42 60

29. Distant SN and closer SN have the same property.

30. log(dL) z Cosmological Parameters • Type Ia Supernovae m-z relation

31. various tests

32. The angular scale subtending the sound horizon at decoupling depends on spatial geometry. What makes up the rest of the Universe? Cosmological Parameters • Location of 1st peak in the angular power spectrum of CMB anisotropy in accordance with (standard) Inflation

33. Cosmological Parameters SNIa

34. Cosmological Parameters SNIa+CMB

35. Cosmological Parameters SNIa+CMB +Matter density

36. H0=72±8km/s/Mpc, centered around Observation: from globular cluster from cosmological nuclear chronology Concordance Model of the Universe as predicted by Inflation Cosmic age

37. Expected accuracy of MAP satellite Forthcoming CMB data Present status will make it possible to determine cosmological parameters much more accurately. Perturbation spectrum as well.

38. The Universe observational astronomers believed. Actual Universe as of today: The Concordance bad news as predicted by Inflation good news The Universe theorists expected decades ago.